Permalink
Cannot retrieve contributors at this time
Fetching contributors…
Cannot retrieve contributors at this time
| <?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.1d1 20130915//EN" "JATS-archivearticle1.dtd"><article article-type="research-article" dtd-version="1.1d1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><front><journal-meta><journal-id journal-id-type="nlm-ta">elife</journal-id><journal-id journal-id-type="hwp">eLife</journal-id><journal-id journal-id-type="publisher-id">eLife</journal-id><journal-title-group><journal-title>eLife</journal-title></journal-title-group><issn publication-format="electronic">2050-084X</issn><publisher><publisher-name>eLife Sciences Publications, Ltd</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">02078</article-id><article-id pub-id-type="doi">10.7554/eLife.02078</article-id><article-categories><subj-group subj-group-type="display-channel"><subject>Research article</subject></subj-group><subj-group subj-group-type="heading"><subject>Neuroscience</subject></subj-group></article-categories><title-group><article-title>Cell-intrinsic mechanisms of temperature compensation in a grasshopper sensory receptor neuron</article-title></title-group><contrib-group><contrib contrib-type="author" id="author-10084"><name><surname>Roemschied</surname><given-names>Frederic A</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/><xref ref-type="other" rid="par-1"/><xref ref-type="other" rid="par-5"/><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-10085"><name><surname>Eberhard</surname><given-names>Monika JB</given-names></name><xref ref-type="aff" rid="aff3"/><xref ref-type="other" rid="par-2"/><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-10086"><name><surname>Schleimer</surname><given-names>Jan-Hendrik</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/><xref ref-type="other" rid="par-3"/><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-10087"><name><surname>Ronacher</surname><given-names>Bernhard</given-names></name><xref ref-type="aff" rid="aff2"/><xref ref-type="aff" rid="aff3"/><xref ref-type="other" rid="par-2"/><xref ref-type="other" rid="par-4"/><xref ref-type="other" rid="par-5"/><xref ref-type="fn" rid="con4"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes" id="author-9759"><name><surname>Schreiber</surname><given-names>Susanne</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/><xref ref-type="corresp" rid="cor1">*</xref><xref ref-type="other" rid="par-1"/><xref ref-type="other" rid="par-2"/><xref ref-type="other" rid="par-3"/><xref ref-type="other" rid="par-4"/><xref ref-type="other" rid="par-5"/><xref ref-type="fn" rid="con5"/><xref ref-type="fn" rid="conf1"/></contrib><aff id="aff1"><institution content-type="dept">Institute of Theoretical Biology, Department of Biology</institution>, <institution>Humboldt-Universität zu Berlin</institution>, <addr-line><named-content content-type="city">Berlin</named-content></addr-line>, <country>Germany</country></aff><aff id="aff2"><institution>Bernstein Center for Computational Neuroscience Berlin</institution>, <addr-line><named-content content-type="city">Berlin</named-content></addr-line>, <country>Germany</country></aff><aff id="aff3"><institution content-type="dept">Behavioral Physiology Group, Department of Biology</institution>, <institution>Humboldt-Universität zu Berlin</institution>, <addr-line><named-content content-type="city">Berlin</named-content></addr-line>, <country>Germany</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Calabrese</surname><given-names>Ronald L</given-names></name><role>Reviewing editor</role><aff><institution>Emory University</institution>, <country>United States</country></aff></contrib></contrib-group><author-notes><corresp id="cor1"><label>*</label>For correspondence: <email>s.schreiber@hu-berlin.de</email></corresp></author-notes><pub-date date-type="pub" publication-format="electronic"><day>08</day><month>05</month><year>2014</year></pub-date><pub-date pub-type="collection"><year>2014</year></pub-date><volume>3</volume><elocation-id>e02078</elocation-id><history><date date-type="received"><day>16</day><month>12</month><year>2013</year></date><date date-type="accepted"><day>03</day><month>04</month><year>2014</year></date></history><permissions><copyright-statement>© 2014, Roemschied et al</copyright-statement><copyright-year>2014</copyright-year><copyright-holder>Roemschied et al</copyright-holder><license xlink:href="http://creativecommons.org/licenses/by/3.0/"><license-p>This article is distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">Creative Commons Attribution License</ext-link>, which permits unrestricted use and redistribution provided that the original author and source are credited.</license-p></license></permissions><self-uri content-type="pdf" xlink:href="elife02078.pdf"/><abstract><object-id pub-id-type="doi">10.7554/eLife.02078.001</object-id><p>Changes in temperature affect biochemical reaction rates and, consequently, neural processing. The nervous systems of poikilothermic animals must have evolved mechanisms enabling them to retain their functionality under varying temperatures. Auditory receptor neurons of grasshoppers respond to sound in a surprisingly temperature-compensated manner: firing rates depend moderately on temperature, with average Q<sub>10</sub> values around 1.5. Analysis of conductance-based neuron models reveals that temperature compensation of spike generation can be achieved solely relying on cell-intrinsic processes and despite a strong dependence of ion conductances on temperature. Remarkably, this type of temperature compensation need not come at an additional metabolic cost of spike generation. Firing rate-based information transfer is likely to increase with temperature and we derive predictions for an optimal temperature dependence of the tympanal transduction process fostering temperature compensation. The example of auditory receptor neurons demonstrates how neurons may exploit single-cell mechanisms to cope with multiple constraints in parallel.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.001">http://dx.doi.org/10.7554/eLife.02078.001</ext-link></p></abstract><abstract abstract-type="executive-summary"><object-id pub-id-type="doi">10.7554/eLife.02078.002</object-id><title>eLife digest</title><p>Warm-blooded animals—including mammals and birds—expend large amounts of energy in keeping their body temperature constant regardless of how hot or cold their environment is. By contrast, the body temperature of cold-blooded animals—including amphibians, reptiles, and insects—follows that of their surroundings. Cold-blooded animals must therefore have evolved a means to cope with the effects of changes in temperature, but exactly how they do this is not clear.</p><p>Now, Roemschied et al. have obtained new insights into this process by studying the nerve cells in grasshoppers that allow them to hear sounds. The auditory system of the grasshopper comprises sensory receptor neurons that are located on the abdomen of the insect. Sound waves move the tympanal membrane, which causes ion channels within the cell membranes to open. This enables the neurons to produce an electrical signal known as a spike.</p><p>Recordings from grasshoppers revealed that changing the outside temperature by up to 10°C affected the rate at which the neurons produced spikes by only about half the amount expected. Given that these neurons do not receive inputs from any other cells, this ability to withstand changes in temperature must be intrinsic to the neurons themselves. Consistent with this, computational modeling showed that while the activity of individual ion channels did indeed vary with changes in temperature, these changes in ion channel activity had little overall effect on the rate at which a neuron produced spikes.</p><p>Whereas it has previously been assumed that compensation for changes in temperature occurs at the level of networks of neurons, the work of Roemschied et al. reveals that such compensation can occur in individual cells, and that it need not require a lot of energy to be expended.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.002">http://dx.doi.org/10.7554/eLife.02078.002</ext-link></p></abstract><kwd-group kwd-group-type="author-keywords"><title>Author keywords</title><kwd>grasshopper</kwd><kwd>insect auditory periphery</kwd><kwd>mathematical neuron models</kwd><kwd>energy efficiency</kwd><kwd>sensitivity analysis</kwd><kwd>temperature compensation</kwd></kwd-group><kwd-group kwd-group-type="research-organism"><title>Research organism</title><kwd>other</kwd></kwd-group><funding-group><award-group id="par-1"><funding-source><institution-wrap><institution>Federal Ministry of Education and Research (BMBF)</institution></institution-wrap></funding-source><award-id>01GQ0901</award-id><principal-award-recipient><name><surname>Roemschied</surname><given-names>Frederic A</given-names></name><name><surname>Schreiber</surname><given-names>Susanne</given-names></name></principal-award-recipient></award-group><award-group id="par-2"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/501100001659</institution-id><institution>Deutsche Forschungsgemeinschaft (DFG)</institution></institution-wrap></funding-source><award-id>SFB 618</award-id><principal-award-recipient><name><surname>Eberhard</surname><given-names>Monika JB</given-names></name><name><surname>Ronacher</surname><given-names>Bernhard</given-names></name><name><surname>Schreiber</surname><given-names>Susanne</given-names></name></principal-award-recipient></award-group><award-group id="par-3"><funding-source><institution-wrap><institution>Federal Ministry of Education and Research (BMBF)</institution></institution-wrap></funding-source><award-id>01GQ0972</award-id><principal-award-recipient><name><surname>Schleimer</surname><given-names>Jan-Hendrik</given-names></name><name><surname>Schreiber</surname><given-names>Susanne</given-names></name></principal-award-recipient></award-group><award-group id="par-4"><funding-source><institution-wrap><institution>Federal Ministry of Education and Research (BMBF)</institution></institution-wrap></funding-source><award-id>01GQ1001A</award-id><principal-award-recipient><name><surname>Ronacher</surname><given-names>Bernhard</given-names></name><name><surname>Schreiber</surname><given-names>Susanne</given-names></name></principal-award-recipient></award-group><award-group id="par-5"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/501100001659</institution-id><institution>Deutsche Forschungsgemeinschaft (DFG)</institution></institution-wrap></funding-source><award-id>GRK 1589/1</award-id><principal-award-recipient><name><surname>Roemschied</surname><given-names>Frederic A</given-names></name><name><surname>Ronacher</surname><given-names>Bernhard</given-names></name><name><surname>Schreiber</surname><given-names>Susanne</given-names></name></principal-award-recipient></award-group><funding-statement>The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.</funding-statement></funding-group><custom-meta-group><custom-meta><meta-name>elife-xml-version</meta-name><meta-value>2</meta-value></custom-meta><custom-meta specific-use="meta-only"><meta-name>Author impact statement</meta-name><meta-value>The firing rates of neurons in the grasshopper auditory system are surprisingly robust to changes in temperature, and cell-intrinsic mechanisms are sufficient to explain this temperature insensitivity.</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>Changes in temperature considerably modulate physico-chemical processes and, consequently, also affect neural processing (<xref ref-type="bibr" rid="bib47">Schmidt–Nielsen, 1997</xref>; <xref ref-type="bibr" rid="bib45">Robertson and Money, 2012</xref>). The dependence of neural activity on temperature poses a particular challenge for animals without central heat regulation, like insects, who are permanently exposed to temperature fluctuations. These animals must have evolved intrinsic mechanisms at the behavioral, systems, or cellular level that help to circumvent temperature-induced behavioral modulations. Such compensatory mechanisms, however, may also come into play for homeothermic animals under pathological conditions, like fever or hypothermia in mammals.</p><p>Nevertheless, our understanding of generic design principles that enhance robustness to temperature fluctuations remains limited. The goal of this study is to identify mechanisms and limitations of cellular temperature compensation at the level of firing rates. We start from a characterization of the temperature dependence of neural responses in an insect auditory system, which we find to be surprisingly robust to temperature changes. The absence of network inputs to these receptor neurons (<xref ref-type="bibr" rid="bib59">Vogel and Ronacher, 2007</xref>; <xref ref-type="bibr" rid="bib10">Clemens et al., 2011</xref>) suggests that a cellular mechanism underlies the observed temperature compensation and hence raises the more general question to what extent temperature compensation can be achieved at the level of individual cells. Based on generic conductance-based models of spike generation, we then show that the experimentally observed degree of temperature compensation can be explained by physiological properties intrinsic to single cells despite a substantial dependence of ion channels on temperature.</p><p>Temperature dependence is usually quantified by the so-called <inline-formula><mml:math id="inf1"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> value, which characterizes the relative change of a variable when temperature rises by 10°C. Several invertebrate species were found to have firing-rate <inline-formula><mml:math id="inf2"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values above 2 (i.e., to double their neurons' firing rate), which is in line with the fact that many underlying biochemical processes also exhibit <inline-formula><mml:math id="inf3"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values of two or more (<xref ref-type="bibr" rid="bib21">French and Kuster, 1982</xref>; <xref ref-type="bibr" rid="bib42">Pfau et al., 1989</xref>; <xref ref-type="bibr" rid="bib60">Warzecha et al., 1999</xref>; <xref ref-type="bibr" rid="bib26">Hille, 2001</xref>; <xref ref-type="bibr" rid="bib52">Spavieri et al., 2010</xref>). In contrast, we found that grasshopper auditory receptor neurons on average increased their firing rate by only ∼40–50% (corresponding to a <inline-formula><mml:math id="inf4"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> value of 1.4–1.5). Receptor responses are shaped by a cascade of two major steps (<xref ref-type="bibr" rid="bib23">Gollisch and Herz, 2005</xref>)—(1) auditory transduction, which translates the vibrations of the tympanal membrane into receptor currents and (2) spike generation. Temperature compensation of the response must be achieved by compensatory mechanisms in these individual components or their combined output.</p><p>Based on a computational analysis, we first investigate how the second component, that is cellular spike generation in terms of the translation from input current to firing rate, can be temperature compensated in generic model neurons and identify conductances whose temperature dependence favors robustness. As energy efficiency of signaling is an important constraint (<xref ref-type="bibr" rid="bib3">Attwell and Laughlin, 2001</xref>; <xref ref-type="bibr" rid="bib40">Niven and Laughlin, 2008</xref>), we also resolve whether the identified mechanisms for temperature compensation come at an additional metabolic cost and identify the key parameters of temperature dependence that increase energy efficiency of action-potential generation as well as of the maintenance of the resting potential. Moreover, we show that information transfer (via spike rates) is fostered by temperature increments.</p><p>Second, we combine spike generation with a phenomenological model of mechanotransduction and predict properties of the temperature dependence of this nonlinear transformation that would allow for an efficient compensation in firing rates to the degree observed in our experimental data. As our model-based approach generalizes beyond the grasshopper system, our findings can be expected to reflect principles that could be implemented in many invertebrate and vertebrate species.</p></sec><sec id="s2" sec-type="results"><title>Results</title><sec id="s2-1"><title>Temperature dependence of locust auditory receptor neuron responses to acoustic stimuli</title><p>Based on recordings of auditory receptor neurons in the metathoracic ganglion of the grasshopper <italic>Locusta migratoria,</italic> we quantified the dependence of the firing rate on temperature. <xref ref-type="fig" rid="fig1">Figure 1A</xref> shows voltage responses to stimulation at three different sound intensities and two different temperatures, as well as spike shapes. Interestingly, spike rates at a given sound intensity did not differ much between the low and high temperatures and mildly increased from low to high temperature, while spike width decreased. In general, firing rates of grasshopper receptor neurons are relatively high, saturating only at several hundreds of Hz. At a given temperature, the transfer function, that is the firing rate as a function of sound intensity, has a sigmoidal shape (<xref ref-type="fig" rid="fig1">Figure 1B</xref>). Three parameters (saturation rate, half-max sound level, and dynamic-range width) are sufficient to capture the experimental transfer functions (<italic>R</italic><sup>2</sup> >0.95 for all response curves). Comparing transfer functions at the two different temperatures revealed that their temperature dependence was surprisingly low (<xref ref-type="fig" rid="fig1">Figure 1C</xref>): all corresponding median <inline-formula><mml:math id="inf5"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values were below 1.5; the sound intensity at half-maximal response (half-max sound level) remained almost unchanged, as did the median of the slope at half-max sound level. The width of action potentials, in contrast, was lower at the higher temperature.<fig-group><fig id="fig1" position="float"><object-id pub-id-type="doi">10.7554/eLife.02078.003</object-id><label>Figure 1.</label><caption><title>Cooling mildly affected electrophysiologically recorded firing rates generated by auditory receptor neurons in response to sound.</title><p>(<bold>A</bold>) Voltage traces at 29 and 21°C for one neuron (red and blue lines, respectively). Black horizontal lines mark time intervals of stimulus presentation; stimulus intensity as indicated. (<bold>B</bold>) Firing-rate as a function of sound intensity was well described by sigmoidal functions at both temperatures (same neuron as in <bold>A</bold>). The three sigmoidal parameters (saturation rate, sound level at half-maximum, and dynamic-range width) were extracted from fits to the experimental data. (<bold>C</bold>) Statistics of the measured temperature dependence, <inline-formula><mml:math id="inf6"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>10</mml:mn><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, were computed for several quantities <italic>x</italic>. For a population of nine receptor neurons all three parameters of the sigmoidal function, as well as the spike rate and slope at the cold half-maximum were temperature compensated (median <inline-formula><mml:math id="inf7"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mo>∈</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1.5</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, see also <xref ref-type="fig" rid="fig1s2">Figure 1—figure supplement 2</xref> and <xref ref-type="fig" rid="fig1s3">Figure 1—figure supplement 3</xref>).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.003">http://dx.doi.org/10.7554/eLife.02078.003</ext-link></p></caption><graphic xlink:href="elife02078f001"/></fig><fig id="fig1s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02078.004</object-id><label>Figure 1—figure supplement 1.</label><caption><title>Temperature calibration curve.</title><p>Time course of temperature changes during the cooling-down procedure at the Peltier element (blue) and the tissue close to the tympanal membrane, where auditory receptor neurons attach (red); recordings from four animals. These curves were used as reference to estimate the temperature change during electrophysiological recordings.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.004">http://dx.doi.org/10.7554/eLife.02078.004</ext-link></p></caption><graphic xlink:href="elife02078fs001"/></fig><fig id="fig1s2" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02078.005</object-id><label>Figure 1—figure supplement 2.</label><caption><title>Sound-intensity resolved p-values of statistical differences between firing rates at the two temperatures.</title><p>Stimuli at each sound intensity were presented five times (before and after the temperature change). It was tested whether the corresponding firing rates at the two temperatures belong to an identical distribution with equal medians (ranksum test; p-values < 0.05 indicate a significant effect of temperature on firing rate). The figure illustrates the distribution of the test's p-values across all neurons at different levels of sound intensity (the symbol + indicates an outlier). The effect of temperature on firing rate was most significant for high sound intensities. Presumably, a higher relative variability in firing rate obscured the effect of temperature at lower firing rates (i.e., at lower sound intensities).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.005">http://dx.doi.org/10.7554/eLife.02078.005</ext-link></p></caption><graphic xlink:href="elife02078fs002"/></fig><fig id="fig1s3" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02078.006</object-id><label>Figure 1—figure supplement 3.</label><caption><title>Statistical analysis of Q10 values.</title><p>Statistical significance of observables shown in <xref ref-type="fig" rid="fig1">Figure 1C</xref>. Based on a Wilcoxon signed rank test the null hypotheses that the median of a distribution was 1, 1.5, or 2 were tested. For values of <inline-formula><mml:math id="inf8"><mml:mrow><mml:mi>p</mml:mi><mml:mo><</mml:mo><mml:mn>0.05</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="inf9"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> medians were statistically different (from 1, 1.5, or 2.0, respectively). Spike rates both at half-max and at saturation were significantly affected by temperature changes (<inline-formula><mml:math id="inf10"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0.001</mml:mn></mml:mrow></mml:math></inline-formula>), but not significantly different from 1.5 (<inline-formula><mml:math id="inf11"><mml:mrow><mml:mi>p</mml:mi><mml:mo>≥</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></inline-formula>), indicating temperature compensation. <inline-formula><mml:math id="inf12"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values of saturation spike rates, in particular, were also significantly lower than 2.0. The median temperature dependencies of half-max sound level and slope at half-max were not significantly different from 1, indicating temperature invariance. Dynamic-range width and action-potential width significantly increased with cooling (<inline-formula><mml:math id="inf13"><mml:mrow><mml:mrow><mml:mtext>median</mml:mtext></mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mo><</mml:mo><mml:mn>0.01</mml:mn></mml:mrow></mml:math></inline-formula>).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.006">http://dx.doi.org/10.7554/eLife.02078.006</ext-link></p></caption><graphic xlink:href="elife02078fs003"/></fig></fig-group></p><p>Compared to the temperature dependencies previously observed in other species like moth auditory receptor neurons, locust stretch receptors, and fly H1 neurons and photoreceptors (<inline-formula><mml:math id="inf14"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>(spike rate) ∼2, <xref ref-type="bibr" rid="bib42">Pfau et al., 1989</xref>; <xref ref-type="bibr" rid="bib13">Coro and Perez, 1990</xref>; <xref ref-type="bibr" rid="bib60">Warzecha et al., 1999</xref>; <xref ref-type="bibr" rid="bib54">Tatler et al., 2000</xref>), the grasshopper responses were temperature compensated; the dependence was similar to what has been referred to as <italic>warm-insensitive</italic> in hypothalamic neurons of the rat (<inline-formula><mml:math id="inf15"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>(spike rate) ∼1.3, <xref ref-type="bibr" rid="bib15">Curras and Boulant, 1989</xref>). To understand this low dependence of receptor neuron firing rate on temperature, we next turned to mathematical modeling.</p></sec><sec id="s2-2"><title>Influence of temperature on spike generation in single-neuron models</title><p>The grasshopper auditory periphery consists of a relatively simple feed-forward network, in which the receptor neurons constitute the first layer. Receptor neurons are known to respond to vibrations of the tympanal membrane, but they do not receive input from the neuronal network. Mechanisms of temperature compensation must hence be cell-intrinsic. To resolve which intrinsic processes can be sufficient to account for the observed degree of temperature compensation, we first focussed on spike generation, leaving mechanotransduction aside. We analyzed in generic model neurons, how the temperature dependence of ionic conductances mediating spike generation can reduce the dependence of firing rate on temperature.</p><p>We used the Connor–Stevens model (<xref ref-type="bibr" rid="bib12">Connor et al., 1977</xref>; <xref ref-type="bibr" rid="bib16">Dayan and Abbott, 2005</xref>) to simulate a type I spike generation process (<xref ref-type="bibr" rid="bib29">Izhikevich, 2007</xref>) as it is assumed for grasshopper receptor neurons (<xref ref-type="bibr" rid="bib4">Benda, 2002</xref>). Besides a sodium and a leak conductance (<inline-formula><mml:math id="inf16"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf17"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), this model comprises a delayed-rectifier and an A-type potassium conductance (<inline-formula><mml:math id="inf18"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>K</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf19"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), which are both known to be present in the grasshopper nervous system (<xref ref-type="bibr" rid="bib44">Ramirez et al., 1999</xref>). Temperature dependence was assumed to affect the opening and closing rates of all gates of the three ion channel types (i.e., the <italic>m</italic> and <italic>h</italic> gates for <inline-formula><mml:math id="inf195"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <italic>n</italic> gates for <inline-formula><mml:math id="inf196"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>K</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <italic>a</italic> and <italic>b</italic> gates for <inline-formula><mml:math id="inf197"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), as well as their peak conductances (<inline-formula><mml:math id="inf20"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf21"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>K</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf22"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and that of the leak conductance, <inline-formula><mml:math id="inf23"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. For a systematic analysis (refers to (<xref ref-type="bibr" rid="bib43">Prinz et al., 2003</xref>)), we independently varied the temperature dependence of these parameters (comprising a total of nine) within physiologically realistic ranges: <inline-formula><mml:math id="inf24"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>∈</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mn>2.0</mml:mn><mml:mo>,</mml:mo><mml:mn>4.0</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> for transition rates and <inline-formula><mml:math id="inf25"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>∈</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mn>1.2</mml:mn><mml:mo>,</mml:mo><mml:mn>2.0</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> for peak conductances (<xref ref-type="bibr" rid="bib41">Partridge and Connor, 1978</xref>; <xref ref-type="bibr" rid="bib26">Hille, 2001</xref>). For each combination of parameters, the transfer function (input current to firing rate; i.e., the f-I curve) was computed at two temperatures: 18 and 28°C (<xref ref-type="fig" rid="fig2">Figure 2A,B</xref>).<fig-group><fig id="fig2" position="float"><object-id pub-id-type="doi">10.7554/eLife.02078.007</object-id><label>Figure 2.</label><caption><title>Temperature dependence of spike generation in a conductance-based neuron model.</title><p>(<bold>A</bold>) Voltage responses to step current stimuli of different amplitudes; blue: 18°C (the reference temperature), red: 28°C. Top trace corresponds to a model with strongly temperature-dependent firing rate, middle trace to a temperature-compensated model. (<bold>B</bold>) f-I curves at both temperatures, corresponding to the examples shown in <bold>A</bold>. (<bold>C</bold>) Results of the sensitivity analysis for the RMSD. The largest impact is exerted by temperature dependencies of the potassium conductances (<inline-formula><mml:math id="inf26"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf27"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>A</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf28"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>K</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>). Signs +/− indicate the qualitative impact (see main text for details). (<bold>D</bold>) Distribution of the RMSD, across all models. Note that a <inline-formula><mml:math id="inf29"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> of 1.5 corresponds to an RMSD of ∼0.5 (50% relative change). (<bold>E</bold>) Parameter impacts on RMSD were robust against ±20% perturbation of the model's peak conductances at 18°C (black symbols: perturbations of individual peak conductances; grey symbols: all combinations of ±20% changes to the four peak conductances). (<bold>F</bold>) Results of the sensitivity analysis for the temperature dependence of the slope of f-I curves. (<bold>G</bold>) Distribution of <inline-formula><mml:math id="inf30"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values of the slope across all models. (<bold>H</bold> and <bold>I</bold>) as panels (<bold>F</bold>) and (<bold>G</bold>), but for the threshold of the f-I curves. (<bold>J</bold> and <bold>K</bold>) Sensitivity analysis of information transfer. For two basic noise models (Poissonian and input-independent Gaussian), the temperature dependence of firing rate-based information transfer <italic>J</italic> is related to that of the slope of the f-I curve: <inline-formula><mml:math id="inf31"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>〈</mml:mo><mml:mi>J</mml:mi><mml:mo>〉</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>slope</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>4</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. The conductance parameters with highest impact were very similar to those of the changes in slope (compare to panel <bold>F</bold>). Information transfer increased with temperature for all models. (<bold>L</bold>) Visualization of the RMSD for the parameter space spanned by the temperature dependencies of the Connor-Stevens model based on dimensional stacking. Axes order was chosen according to the impact ranking as presented in (<bold>C</bold>); color code as in (<bold>D</bold>).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.007">http://dx.doi.org/10.7554/eLife.02078.007</ext-link></p></caption><graphic xlink:href="elife02078f002"/></fig><fig id="fig2s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02078.008</object-id><label>Figure 2—figure supplement 1.</label><caption><title>Temperature compensation in the Traub-Miles model.</title><p>Temperature compensation of spike generation is also possible in a structurally different Traub-Miles model despite a realistic temperature dependence of its conductances (<inline-formula><mml:math id="inf186"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). Shown are the model at reference temperature (32°C for this model, black curve), and the model heated up by 10°C (red curve) or cooled down by 10°C (blue curve), with temperature parameters that minimize the RMSD of the corresponding f-I curves within the physiologically realistic range (identical to that explored for the Connor-Stevens model with peak conductances (<inline-formula><mml:math id="inf187"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>∈</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mn>1.2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>) and transition rates of the (in-) activation variables <inline-formula><mml:math id="inf188"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>β</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>∈</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>4</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>). Optimal parameters minimizing the RMSD were identified by a genetic algorithm. Relative changes in firing rate were on the order of those observed experimentally (<inline-formula><mml:math id="inf189"><mml:mrow><mml:mtext>RMSD</mml:mtext><mml:mo>=</mml:mo><mml:mn>0.34</mml:mn></mml:mrow></mml:math></inline-formula> for the red curve and <inline-formula><mml:math id="inf190"><mml:mrow><mml:mtext>RMSD</mml:mtext><mml:mo>=</mml:mo><mml:mn>0.55</mml:mn></mml:mrow></mml:math></inline-formula> for the blue curve).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.008">http://dx.doi.org/10.7554/eLife.02078.008</ext-link></p></caption><graphic xlink:href="elife02078fs004"/></fig></fig-group></p><p>To estimate the temperature dependence of a whole f-I curve, <inline-formula><mml:math id="inf32"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values are not ideal, as they are defined as the ratio of firing rates at two different temperatures, which will be infinitely large for inputs that only elicit spikes at the higher, but not the lower temperature. To circumvent this bias, we assessed the temperature dependence of a model neuron as the root-mean-squared difference between the firing rates at the two temperatures (mean taken across input currents), normalized by the mean rate elicited at the colder temperature. We refer to this quantity as RMSD. It reflects the average relative change in firing rate with temperature. Note that a <inline-formula><mml:math id="inf33"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> value of 1.5 is hence comparable to an RMSD of 0.5 (50% relative change). Across all model combinations, the relative change, RMSD, was distributed between 0.22 and 2.14, with a median of 0.68 (<xref ref-type="fig" rid="fig2">Figure 2D</xref>). This means that, intuitively, the median of the average change in firing rate of an f-I curve was 68%. The analysis showed that the effect of temperature on spike generation depended strongly on the specific temperature dependence of the ionic conductances. A fraction of models (18%) exhibited temperature compensation with relative changes in firing rate comparable to those found experimentally (RMSD <0.5). This result shows that a low dependence of firing rate on temperature is feasible despite a substantial (and hence realistic) dependence of the individual conductances on temperature.</p><p>Next, we asked which of the nine parameters (i.e., the temperature dependence of peak conductances and transition rates) most affected the dependence of firing rate on temperature. To this end, we performed a systematic sensitivity analysis in the nine-dimensional space of all possible parameter combinations. We created—for each parameter—a distribution of local changes in RMSD induced by changes in that parameter. Specifically, this distribution captured changes in RMSD between all neighboring points along a specific parameter's dimension. Each distribution sampled the whole parameter space (i.e., all possible combinations of the other parameters), also see ‘Materials and methods’. The <italic>impact</italic> of a given parameter on the temperature dependence of the f-I curve was then defined as the median of its specific distribution, directly relating the impact of a parameter to its quantitative effect on RMSD. <xref ref-type="fig" rid="fig2">Figure 2C</xref> depicts the impact values of all <inline-formula><mml:math id="inf34"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> parameters on the RMSD. The sum of all absolute values of impacts is normalized to unity. The impact sign, that is whether an increase in a parameter on average led to an increase or decrease in the observable, is indicated by + and −, respectively. The analysis revealed that the largest impact on the RMSD was exerted by three parameters of potassium channels: temperature dependence of the delayed-rectifier potassium kinetics, <inline-formula><mml:math id="inf35"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, and the A-type and delayed-rectifier potassium peak conductances, <inline-formula><mml:math id="inf36"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>A</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf37"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>K</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, respectively. The impacts of both potassium channel peak conductances were negative (i.e., increases in their <inline-formula><mml:math id="inf38"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values decreased the <inline-formula><mml:math id="inf39"><mml:mrow><mml:mtext>RMSD</mml:mtext></mml:mrow></mml:math></inline-formula>), while the potassium activation <inline-formula><mml:math id="inf40"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> had a positive impact (i.e., increases in its temperature dependence increased the RMSD).</p><p>To confirm that the results do not strongly depend on the specific choice of peak conductances in the Connor–Stevens model, we tested 24 alternative models with changes of ± 20% in the peak conductances of sodium, both potassium, and leak channels. The impact ranking across those models was highly similar to the ranking in the original Connor–Stevens model (<xref ref-type="fig" rid="fig2">Figure 2E</xref>) and we conclude that our results are robust. Moreover, we note that our results are not unique to the Connor–Stevens model. An analysis of a structurally different Traub–Miles model (<xref ref-type="bibr" rid="bib57">Traub et al., 1991</xref>; <xref ref-type="bibr" rid="bib4">Benda, 2002</xref>) showed that an equally low temperature dependence is possible (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>).</p><p>On a side note, a visualization of the RMSD across the complete nine-dimensional parameter space based on dimensional stacking is shown in <xref ref-type="fig" rid="fig2">Figure 2L</xref>, see ‘Materials and methods’ for details (<xref ref-type="bibr" rid="bib34">LeBlanc et al., 1990</xref>; <xref ref-type="bibr" rid="bib55">Taylor et al., 2006</xref>). Dimensional stacking maps the nine-dimensional space onto a two-dimensional representation with nine axes. Ordering of the axes is arbitrary and hence requires optimization to maximize visual information (<xref ref-type="bibr" rid="bib55">Taylor et al., 2006</xref>). Here, we introduce a new way to determine optimal axes order, defined directly by the ranking of impact scores. Parameters with highest impact on the RMSD are depicted on large-scale axes and parameters with low impact on small-scale axes. The success of the ordering is reflected in the visually structured areas of equal RMSD. As only a subset of all parameters had relevant influence on the RMSD, optimal axes ordering led to a clear visual structure. In contrast, for arbitrary axes ordering visual structure would be hard to recognize.</p></sec><sec id="s2-3"><title>Temperature effects on f-I threshold and slope</title><p>As we saw, the temperature dependence of potassium channels plays a crucial role for temperature compensation. For a more detailed and intuitive understanding of the underlying mechanism, we next analyzed the transformation of the shape of f-I curves with temperature. Type I f-I curves, as they are found in the grasshopper, can be described by a square root function (<xref ref-type="bibr" rid="bib29">Izhikevich, 2007</xref>). Temperature affects an f-I curve by shifting the curve horizontally (i.e., changing its threshold) and by changing its slope (which can also be termed gain). We used fits of the f-I curves by a square root model <inline-formula><mml:math id="inf41"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mo>·</mml:mo><mml:msqrt><mml:mrow><mml:mi>I</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula>, based on the parameters <italic>A</italic> (slope) and <inline-formula><mml:math id="inf42"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (threshold). With heating, the slope always increased (<xref ref-type="fig" rid="fig2">Figure 2G</xref>), while we found changes in both directions for the threshold (<xref ref-type="fig" rid="fig2">Figure 2I</xref>).</p><p>Temperature dependencies of the A-type potassium and leak peak conductances had the strongest influence on the threshold (<xref ref-type="fig" rid="fig2">Figure 2H</xref>). In contrast, the slope was most sensitive to the temperature dependence of the delayed-rectifier potassium channel, <inline-formula><mml:math id="inf43"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf44"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>K</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, and the sodium channel inactivation, <inline-formula><mml:math id="inf45"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig2">Figure 2F</xref>). Beyond clarifying the specific effect of the aforementioned parameters on changes to the f-I curve, the analysis shows that temperature compensation (i.e., lower RMSD values) was usually achieved by modest increases in threshold balancing the effects of an increase in slope (<xref ref-type="fig" rid="fig2">Figure 2B</xref>).</p><p>Changes in slope also have direct implications for the ability to infer information about the sound intensity from the firing-rate output of receptor neurons. We hence quantified how the capacity to transmit information from input <italic>I</italic> to firing rate <italic>f</italic> changes with temperature. To this end we use Fisher information. Considering the average information transferred for a given interval of firing rates [<italic>f</italic><sub>min</sub>, <italic>f</italic><sub>max</sub>], information transfer scales with the slope of the f-I curve and its temperature dependence hence with <inline-formula><mml:math id="inf46"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>4</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (‘Materials and methods’). Consequently, the same parameters that had the largest impact on the slope–potassium channel rate (<inline-formula><mml:math id="inf47"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>) and peak conductances (<inline-formula><mml:math id="inf48"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>K</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf49"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>A</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>) and sodium channel inactivation (<inline-formula><mml:math id="inf50"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>)—also influenced information transfer most (<xref ref-type="fig" rid="fig2">Figure 2J</xref>). Overall, heating was advantageous for information transfer (<xref ref-type="fig" rid="fig2">Figure 2K</xref>).</p></sec><sec id="s2-4"><title>Influence of temperature on the energy efficiency of spike generation</title><p>Metabolic cost is increasingly recognized as an important constraint for neural function (<xref ref-type="bibr" rid="bib3">Attwell and Laughlin, 2001</xref>; <xref ref-type="bibr" rid="bib40">Niven and Laughlin, 2008</xref>) and is likely to have shaped the design of neural systems—the more so if firing rates are large. In the grasshopper auditory periphery firing rates often exceed several hundreds of Hz, suggesting that metabolic cost may have played a role in the design of these cells. It is hence interesting to explore whether robustness to temperature changes compromises energy efficiency. To this end, we computed the energetic cost of spike generation and maintenance of the resting potential (<xref ref-type="fig" rid="fig3">Figure 3A</xref>). Cost was quantified in terms of the total sodium current (per action potential or per time, respectively). To assess the changes of energy consumption with temperature, energy use was characterized by its <inline-formula><mml:math id="inf51"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> value (i.e., the ratio of energetic cost at 28° and 18°) and averaged across input currents.<fig-group><fig id="fig3" position="float"><object-id pub-id-type="doi">10.7554/eLife.02078.009</object-id><label>Figure 3.</label><caption><title>Temperature dependence of the metabolic cost (spiking and maintenance of the resting potential).</title><p>(<bold>A</bold>) Illustration of the periods during which spiking cost and resting-potential cost were estimated in terms of the Na<sup>+</sup> current (two corresponding examples at the higher and lower temperature; red and blue curves, respectively). Energy consumption during spiking was averaged per spike and across the suprathreshold parts of the f-I curve. (<bold>B</bold>) Distribution of the temperature dependence of the spiking cost <inline-formula><mml:math id="inf52"><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>spiking</mml:mtext><mml:mo> </mml:mo><mml:mtext>cost</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>. Top: all models; middle and bottom: distribution across the 25% of models with lowest and highest temperature dependence of firing rate (RMSD), respectively. Spiking cost decreased at higher temperature for the majority of models. In particular, values of minimal energy consumption at the higher temperature were similar for the subgroups of models with lowest and highest temperature dependence. (<bold>C</bold>) Distribution of the temperature dependence of the resting cost <inline-formula><mml:math id="inf53"><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>resting</mml:mtext><mml:mo> </mml:mo><mml:mtext>cost</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, analog to (<bold>B</bold>). Resting-potential cost decreased for the majority of models; top, middle and bottom panels comprising subgroups of models as in (<bold>B</bold>). (<bold>D</bold>) Temperature dependence of firing rate and spiking energy consumption are determined by different sets of conductance parameters. While potassium-channel temperature dependencies have the largest impact on firing rate (<xref ref-type="fig" rid="fig2">Figure 2C</xref>), the energy consumption per spike was predominantly determined by sodium-channel temperature dependence. Faster sodium inactivation (<inline-formula><mml:math id="inf54"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>) and lower peak sodium conductance <inline-formula><mml:math id="inf55"><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mtext>Na</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> fostered energy efficiency at higher temperature. (<bold>E</bold>) Parameters that reduce resting energy at high temperature also reduce RMSD (same sign of the impact values as in <xref ref-type="fig" rid="fig2">Figure 2C</xref>). (<bold>F</bold> and <bold>G</bold>) Impacts on energy consumption were robust against ±20% perturbations of the model's peak conductances at 18°C (<xref ref-type="fig" rid="fig2">Figure 2E</xref>, ‘Materials and methods’).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.009">http://dx.doi.org/10.7554/eLife.02078.009</ext-link></p></caption><graphic xlink:href="elife02078f003"/></fig><fig id="fig3s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02078.010</object-id><label>Figure 3—figure supplement 1.</label><caption><title>Alternative measures of metabolic cost and energy efficiency of spiking.</title><p>(<bold>A</bold>) Schematic illustration of the measures used (sodium-current-based and potassium-current-based cost, as well as energy efficiency estimated by the separability of sodium and potassium currents either in relation to the sodium current or the potassium current). (<bold>B</bold>) Impact of the model parameters' <inline-formula><mml:math id="inf191"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values for all four measures. In all cases, temperature dependence of sodium inactivation, <inline-formula><mml:math id="inf192"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> had the largest impact on metabolic cost or energy efficiency. In contrast, the temperature dependence of delayed-rectifier potassium activation, <inline-formula><mml:math id="inf193"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> (which proved most influential for the temperature dependence of firing rate) exerted a smaller impact on both potassium- and sodium-based energy consumption. (<bold>C</bold>) The distribution of energy measures across all spike generation models as well as models with particularly high and low RMSD (subgroup of models within the bottom and top 25 percentile of RMSDs).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.010">http://dx.doi.org/10.7554/eLife.02078.010</ext-link></p></caption><graphic xlink:href="elife02078fs005"/></fig><fig id="fig3s2" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02078.011</object-id><label>Figure 3—figure supplement 2.</label><caption><title>Potassium-current based resting cost.</title><p>(<bold>A</bold>) The distribution of the temperature dependence (<inline-formula><mml:math id="inf194"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values) of the resting cost based on potassium-current across all spike generation models as well as models with particularly high and low RMSD (subgroup of models within the bottom and top 25 percentile of RMSDs). Overall, this type of resting cost increased with larger temperatures because A-type potassium currents were larger. (<bold>B</bold>) The temperature dependence of the leak conductance influenced this type of resting cost most.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.011">http://dx.doi.org/10.7554/eLife.02078.011</ext-link></p></caption><graphic xlink:href="elife02078fs006"/></fig></fig-group></p><p>For the majority of models, the energetic cost of an action potential decreased with heating (93% of models, <xref ref-type="fig" rid="fig3">Figure 3B</xref>). On average, temperature-compensated spike generation models (25% of models with lowest RMSD) were slightly more costly than the most temperature-dependent models (25% of models with highest RMSD), see <xref ref-type="fig" rid="fig3">Figure 3B</xref>. Nevertheless, the minimum energy consumption was comparable in both groups. Resting cost was substantially lower than spiking cost, this trend increasing with larger firing rates. Sodium-current based resting cost tended to decrease with heating (77% of models). It was slightly lower for temperature-compensated models compared to strongly temperature-dependent models (<xref ref-type="fig" rid="fig3">Figure 3C</xref>).</p><p>The sensitivity analysis (performed in analogy to the analysis of temperature dependence of firing rate) revealed that the temperature-dependence of the sodium conductance (<inline-formula><mml:math id="inf56"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf57"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>) influenced energy consumption of spike generation the most (<xref ref-type="fig" rid="fig3">Figure 3D</xref>).</p><p>The impacts of conductance parameters on f-I curve temperature dependence and energy consumption were not significantly correlated in this case (<italic>ρ</italic> = −0.23, <italic>p</italic>=0.56). In particular, the key parameters of largest influence on these features belonged to different channel groups: potassium channels in case of temperature compensation and sodium channels in case of energy efficiency of spike generation. We verified that the large influence of sodium channels was not biased by our sodium-current-based definition of metabolic cost. Three alternative measures—two quantifying energy efficiency based on the separability of sodium and potassium currents (<xref ref-type="bibr" rid="bib2">Alle et al., 2009</xref>), the other defined by the total potassium current—all confirmed the temperature dependence of sodium channel inactivation <inline-formula><mml:math id="inf58"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> as the most influential parameter for spiking cost (<xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1</xref>).</p><p>The sodium-current based resting cost was qualitatively influenced in a similar way as temperature dependence of firing rate (<xref ref-type="fig" rid="fig3">Figure 3E</xref>): for all four relevant <inline-formula><mml:math id="inf59"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> parameters a reduction of resting cost co-occurred with a reduction in temperature dependence of firing rate (same sign of corresponding impacts, <xref ref-type="fig" rid="fig2">Figure 2C</xref>). For a potassium-current based resting cost the temperature dependence of leak channels had the dominant impact (<xref ref-type="fig" rid="fig3s2">Figure 3—figure supplement 2</xref>). In contrast to the sodium-current based resting cost, the potassium-current-based cost was larger at higher temperatures. For the majority of models, inactivation of A-type potassium channels was lower at the higher temperature (due to a more negative resting potential) and hence increased the A-type current.</p><p>In summary, striving for temperature compensation does not have to compromise a neuron's energy efficiency. Both results (for spiking and resting cost) generalize beyond the specific choice of peak conductances in the Connor–Stevens model (<xref ref-type="fig" rid="fig3">Figure 3F,G</xref>).</p></sec><sec id="s2-5"><title>Model-based inference of the auditory transduction function</title><p>In the previous paragraphs, we have shown that spike generation by itself can achieve a remarkably high invariance to temperature changes. The receptor neurons, however, have an additional processing stage involved in transferring the external input signal to a firing-rate response: the so-called transduction mediated by the mechanosensitive channels in the vicinity of the tympanal membrane. Transduction precedes spike generation and translates vibrations of the tympanal membrane caused by the sound pressure wave into receptor currents through these channels, which in turn drive spike generation (<xref ref-type="bibr" rid="bib23">Gollisch and Herz, 2005</xref>). This mechanism may also contribute to temperature compensation. We therefore explored how temperature compensation can benefit from linking spike generation with the transduction process.</p><p>Little is known about the temperature dependence of transduction in the grasshopper. Here, we combined the computational analysis of spike generation with the experimental findings for the sound-intensity to firing-rate relation in order to predict on a phenomenological level which features of the auditory transduction and its temperature dependence would improve temperature compensation. The experimentally measured receptor neuron responses to sound stimuli <inline-formula><mml:math id="inf60"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ρ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> can be expressed as a cascade of mechanosensory transduction (<inline-formula><mml:math id="inf61"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>θ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, with current <inline-formula><mml:math id="inf62"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and sound intensity <inline-formula><mml:math id="inf63"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and spike generation <inline-formula><mml:math id="inf64"><mml:mrow><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>:</mml:mo><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>θ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>.</p><p>Let us think of the Connor–Stevens spike generation model at the colder temperature (illustrated in <xref ref-type="fig" rid="fig4">Figure 4A</xref>, blue curve). When combined with an (upstream) nonlinear translation of sound intensity to current (<xref ref-type="fig" rid="fig4">Figure 4B</xref>, blue curve), it yields the full sound-intensity to firing-rate relation (<xref ref-type="fig" rid="fig4">Figure 4C</xref>, blue curve), which corresponds to the quantity measured experimentally. Hence, if the receptor neuron response as a function of sound intensity is known from experimental data and we assume a specific spike generation model (i.e., a specific f-I curve), we can mathematically infer the transduction nonlinearity that gives the best match to the experimentally recorded sound-intensity to firing-rate relation by nonlinear regression (<xref ref-type="fig" rid="fig4">Figure 4C</xref>, blue curves). We use the term reverse-engineering for this approach. It can be used at the higher temperature as well and enables us to derive for each of the more than 260.000 spike generation models <italic>the corresponding ideal</italic> transduction curve that best matches the experimentally recorded sound-intensity to firing-rate relation at this higher temperature (<xref ref-type="fig" rid="fig4">Figure 4B,C</xref>, red curves). Comparing the reverse-engineered transduction curve at the colder temperature to the reverse-engineered curve at the higher temperature (for each spike generation model), allows us to identify trends in the temperature dependence of mechanotransduction, which would foster a temperature robustness of the firing rate.<fig id="fig4" position="float"><object-id pub-id-type="doi">10.7554/eLife.02078.012</object-id><label>Figure 4.</label><caption><title>Reverse engineering mechanosensory transduction functions that favor temperature compensation of firing rate.</title><p>(<bold>A</bold>) Example of a model-based f-I curve, denoted <inline-formula><mml:math id="inf65"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, at two temperatures. (<bold>B</bold>) Example of a sigmoidal transduction function converting sound intensity to current, <inline-formula><mml:math id="inf66"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>θ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>. (<bold>C</bold>) Representative receptor neuron responses, <inline-formula><mml:math id="inf67"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ρ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, at two temperatures (dotted lines), as well as a receptor neuron response, <inline-formula><mml:math id="inf68"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>θ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, ‘constructed’ from the f-I curve in <bold>A</bold> and the transduction function in <bold>B</bold>. For each model of spike generation, the optimal transduction function, <inline-formula><mml:math id="inf69"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>θ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, minimizing the error between the corresponding ‘constructed’ receptor neuron response and the representative receptor neuron response (dotted line in <bold>C</bold>) was derived. (<bold>D</bold>) The statistics of temperature dependence of the optimal transduction functions, <inline-formula><mml:math id="inf70"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, across all models. The width of the dynamic range depended most on temperature and increased with heating for nearly all optimized transduction functions. But the temperature dependence of the saturation current and the half-maximum sound intensity (mainly when decreasing with temperature) were also found to contribute to temperature compensation. Note that the ranges marked by the whiskers cover all data (including outliers) in this plot.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02078.012">http://dx.doi.org/10.7554/eLife.02078.012</ext-link></p></caption><graphic xlink:href="elife02078f004"/></fig></p><p>Specifically, we exploited the fact that experimental response curves (firing rate to sound intensity) were well fitted by a sigmoidal function (<xref ref-type="fig" rid="fig1">Figure 1C</xref>) and also assumed a sigmoidal shape for the transduction curves (<xref ref-type="bibr" rid="bib28">Hudspeth et al., 2000</xref>; <xref ref-type="bibr" rid="bib18">Fisch et al., 2012</xref>). Accordingly, we reverse-engineered the ideal transduction sigmoid at the warmer temperature for each spike generation model (e.g., those contributing to <xref ref-type="fig" rid="fig2">Figure 2C</xref>), so that the resulting sound-intensity to firing-rate relation best matched a representative receptor neuron response (<xref ref-type="fig" rid="fig4">Figure 4C</xref>, for details on representative receptor neuron response, ‘Materials and methods’). The model response curves <inline-formula><mml:math id="inf71"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>θ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> matched the experimental representative response curve very well (<italic>R</italic><sup>2</sup> >0.98 for 99.5% of all models). Temperature dependence of the reverse-engineered transduction was then quantified based on the <inline-formula><mml:math id="inf72"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values (i.e., the relative changes with temperature) of the three parameters that define each transduction sigmoid: saturation current, half-maximum sound intensity, and dynamic-range width (<xref ref-type="fig" rid="fig4">Figure 4D</xref>).</p><p>Evaluating the distribution of changes of the ideal transduction curves with temperature across all spike generation models, we found that the largest temperature dependence of these ‘matching’ transduction curves was to be expected for their dynamic-range width (median <inline-formula><mml:math id="inf73"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></inline-formula>). In addition, changes in saturation current and half-maximum sound level also contributed to fostering temperature compensation of firing rate (<xref ref-type="fig" rid="fig4">Figure 4D</xref>). These results show in particular that a suitable temperature dependence of the transduction process can support temperature compensation, even in cases where spike generation is less temperature robust.</p></sec></sec><sec id="s3" sec-type="discussion"><title>Discussion</title><p>We studied the temperature sensitivity of the firing rate in individual neurons of the grasshopper auditory periphery and found responses to auditory stimulation to be surprisingly temperature compensated. Based on biophysically-motivated neuron models, we identified mechanisms that account for the experimentally observed <italic>cell-intrinsic</italic> temperature compensation. Our theoretical analysis suggests that spike generation itself can be relatively temperature insensitive, even though the conductances involved are affected by temperature changes. Importantly, mechanisms increasing the robustness to temperature changes need not compromise the energy efficiency of action-potential generation nor the resting cost. In general, the capacity to transmit rate-based information of sound intensity moderately increased with temperature due to the increase in steepness of the f-I curve. We also predict optimal temperature dependencies of the tympanum-mediated transduction process from sound to receptor current that contribute to temperature compensation. On a side note, we introduced a computationally efficient way to optimize visualization of model-derived observables in a high-dimensional parameter space in the context of dimensional stacking (<xref ref-type="bibr" rid="bib34">LeBlanc et al., 1990</xref>; <xref ref-type="bibr" rid="bib55">Taylor et al., 2006</xref>).</p><sec id="s3-1"><title>Temperature dependence of firing rate in single neurons</title><p>Neuronal processing is significantly challenged by variation in temperature due to the changes in chemical and physical processes. In many neurons across invertebrates and vertebrates, firing rate has been observed to at least double with increases of temperature, corresponding to <inline-formula><mml:math id="inf74"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values of two or above (<xref ref-type="bibr" rid="bib21">French and Kuster, 1982</xref>; <xref ref-type="bibr" rid="bib13">Coro and Perez, 1990</xref>; <xref ref-type="bibr" rid="bib60">Warzecha et al., 1999</xref>). It was hence surprising to observe that neurons in the auditory periphery of grasshoppers show <inline-formula><mml:math id="inf75"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values on the order of 1.5 and consequently are remarkably temperature compensated (<xref ref-type="bibr" rid="bib25">Hazel and Prosser, 1974</xref>; <xref ref-type="bibr" rid="bib6">Boulant and Dean, 1986</xref>). The temperature robustness of these neurons is hence comparable to that of ‘warm-insensitive’ neurons in the mammalian brain (<xref ref-type="bibr" rid="bib15">Curras and Boulant, 1989</xref>).</p><p>Temperature compensation has been studied in the context of neurons embedded in a network in a variety of systems (see, e.g., <xref ref-type="bibr" rid="bib61">Wechselberger et al., 2006</xref>; <xref ref-type="bibr" rid="bib53">Tang et al., 2010</xref>; <xref ref-type="bibr" rid="bib45">Robertson and Money, 2012</xref>). Temperature compensation in grasshopper receptor neurons, by comparison, must be based on cell-intrinsic processes. A similar temperature compensation that must be based on a single-cell mechanism has so far—to our knowledge—only been described experimentally for tarsal hairs in the locust (<xref ref-type="bibr" rid="bib36">Miles, 1985</xref>).</p><p>The cell-intrinsic mechanisms identified in our computational study attribute the observed robustness to a balancing of opposing processes. Phenomenologically, a rise in slope (consistent across the whole parameter range explored) is compensated for by an increase in the threshold of the f-I curve, minimizing the effect of temperature across a broader range of inputs. While alterations in threshold can be produced by changes in peak conductances of ion channels, they have also been described experimentally by heating in invertebrate systems (<xref ref-type="bibr" rid="bib7">Burkhardt, 1959</xref>; <xref ref-type="bibr" rid="bib1">Abrams and Pearson, 1982</xref>; <xref ref-type="bibr" rid="bib32">Kispersky et al., 2012</xref>) in agreement with our observations. Biophysically, a heating-induced increase in the speed of repolarizing gating kinetics is opposed by an increase in peak potassium conductances which promote a more negative resting potential (as can be derived from <xref ref-type="disp-formula" rid="equ35">Equation 2</xref>). Although the balancing is not perfect, average deviations on the order of not more than 50% can be easily achieved with strongly temperature-dependent conductances (in particular, <inline-formula><mml:math id="inf76"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mo>∈</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mn>2</mml:mn><mml:mo>;</mml:mo><mml:mn>4</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> for all activation- and inactivation rates) for ∼18% of the models. The temperature dependence of both delayed-rectifier and A-type potassium channels has a particularly large impact on temperature compensation. This matches experimental observations in neurons of the pancreas of mice (<xref ref-type="bibr" rid="bib63">Xu et al., 2006</xref>) and molluscan neurons as well as previous simulations of an extended Hodgkin–Huxley model (<xref ref-type="bibr" rid="bib46">Rush and Rinzel, 1995</xref>) and is consistent with the effect of peak conductances on firing rate, for example (<xref ref-type="bibr" rid="bib48">Schreiber et al., 2004</xref>). Our results also hold for reference models quantitatively different from the original Connor-Stevens model—both for the total fraction of temperature-compensated models RMSD <0.5) and the strong influence of potassium channel dynamics on the temperature dependence of firing rate (<xref ref-type="fig" rid="fig2">Figure 2E</xref>), ‘Materials and methods’ for details. These findings show that our results generalize beyond the specific quantitative choice of peak conductance parameters of the Connor–Stevens model. This is further supported by the fact that a structurally different Traub–Miles model could also exhibit a temperature dependence of firing rate as low as that described for the Connor–Stevens model.</p></sec><sec id="s3-2"><title>Energy efficiency and information transfer</title><p>For auditory receptor neurons in the grasshopper energy efficiency of spike generation is likely to be a relevant factor, also see <xref ref-type="bibr" rid="bib39">Niven and Farris (2012)</xref>. Firing rates in these cells approach 400 Hz and likely entail a high total cost of electrical signaling. Our results, however, show that temperature compensation need not impair energy efficiency of spike generation nor of maintenance of the resting potential. The rate of sodium channel inactivation (<xref ref-type="fig" rid="fig3">Figure 3D</xref>) proved to be most relevant in setting the energy consumption per spike generated, which is consistent with simulations and dynamic clamp experiments in various model systems (<xref ref-type="bibr" rid="bib2">Alle et al., 2009</xref>; <xref ref-type="bibr" rid="bib24">Hasenstaub et al., 2010</xref>; <xref ref-type="bibr" rid="bib49">Sengupta et al., 2010</xref>). We demonstrated that energy efficiency improved with heating for a wide range of temperature dependencies of ion channels, as was previously described for a model with fixed <inline-formula><mml:math id="inf77"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values (<xref ref-type="bibr" rid="bib64">Yu et al., 2012</xref>). A fast sodium inactivation limits the duration of the spike; this was consistent with the experimental data, as spike width decreased with heating. Most importantly, the key parameters regulating the energy efficiency of spiking were different from those regulating temperature compensation of firing rate (<xref ref-type="fig" rid="fig2">Figure 2C</xref>, <xref ref-type="fig" rid="fig3">Figure 3D</xref>). The results could be confirmed for alternative measures of energy (separability of sodium and potassium currents as well as the total potassium current). Apart from confirming the role of sodium channel inactivation, these analyses substantiated that the delayed-rectifier potassium channel kinetics (which were most influential to the robustness of firing rate) did not substantially contribute to metabolic costs based on potassium currents. Overall, our analysis focusses on a major source of metabolic cost: the flow of Na<sup>+</sup> and K<sup>+</sup> ions which on larger time scales can be compensated by the Na-K-ATPase. For completeness it should be noted, however, that in living cells metabolic costs can also arise from the flow of other ions not included in our study, like Ca<sup>2+</sup>.</p><p>Summarizing the considerations on metabolic cost, we find most noteworthy that from an evolutionary perspective, the relevant features—robustness of firing rate to temperature changes and reduction of metabolic cost—could both be achieved in parallel.</p><p>Nevertheless, temperature compensation and energy efficiency would be of little use if the fundamental function of information transmission was impaired. Our sensitivity analysis revealed that higher temperatures are also advantageous for the transmission of information about sound intensity. This conclusion is based on our finding that the slope of the f-I curve increased with heating. The capacity to transmit information was affected most by the temperature dependence of the delayed-rectifier potassium conductance. These data, however, need to be interpreted with care. We cannot exclude that channel-type specific stochastic dynamics further influence information transfer in ways not captured by our approach. Implementing the specific stochastic dynamics for the whole parameter space of more than 260.000 models, however, goes beyond the scope of this study and merits future investigation.</p></sec><sec id="s3-3"><title>Optimization of the input layer is important</title><p>Auditory receptor neurons in the grasshopper constitute the bottom layer of a feedforward network: approximately 80 receptor neurons converge to ∼15 local neurons, which in turn project to ∼20 ascending neurons (<xref ref-type="bibr" rid="bib59">Vogel and Ronacher, 2007</xref>). All auditory input passes through this peripheral network, which preprocesses information and extracts behaviorally-relevant features (<xref ref-type="bibr" rid="bib10">Clemens et al., 2011</xref>). The large investment into high firing rates and a comparatively high redundancy between neurons in this layer (<xref ref-type="bibr" rid="bib35">Machens et al., 2001</xref>) also increases the need for energy-efficient spike generation. Optimization of receptor neurons in terms of temperature compensation hence seems a reasonable ‘strategy’, as all effects of temperature on receptor neurons will be passed on to downstream neurons, where they may multiply. Although we currently do not know to which extent other parts of the auditory system are compensated, it is likely to ‘pay off’ to constrain the effects of temperature in the initial stages. Downstream neurons, in contrast, may be expected to adopt different strategies, as they can make use of different mechanisms: balancing of inhibition and excitation for robustness to temperature changes (<xref ref-type="bibr" rid="bib45">Robertson and Money, 2012</xref>) as well as an increase in population and temporal sparseness for energy efficiency and information transfer (<xref ref-type="bibr" rid="bib11">Clemens et al., 2012</xref>).</p></sec><sec id="s3-4"><title>Temperature dependence of the transduction process</title><p>While the considerations above refer to spike generation, little is known about the temperature dependence of the preceding transduction process. One hypothesis is that a change in the half-maximum sound intensity of the transduction process could foster temperature compensation in firing rate. Our computational analysis shows that, indeed, a slight shift of transduction to lower sound intensities with higher temperatures may be favorable. Such a shift would occur if the amplitude of the tympanal vibration increased with heating and a stimulus of given intensity hence opened more transduction channels. However, the computationally-derived changes are relatively moderate (<xref ref-type="fig" rid="fig4">Figure 4D</xref>). This is consistent with the observation that the tympanal vibration in cicadas is relatively temperature independent (<xref ref-type="bibr" rid="bib19">Fonseca and Correia, 2007</xref>).</p><p>The other two parameters characterizing transduction (saturation current and dynamic-range width) reflect properties of the transduction channels (i.e., their peak conductance and activation range, respectively). The increase in dynamic-range width with heating can be interpreted as a decrease in gating force in a gating-spring model for the transduction as proposed for mechanosensory transduction in bullfrog saccular hair cells (<xref ref-type="bibr" rid="bib27">Howard and Hudspeth, 1988</xref>). Again, increases in temperature are advantageous, because the gating-force magnitude is inversely related to transduction accuracy (<xref ref-type="bibr" rid="bib58">van Netten et al., 2003</xref>). Depending on the spike-generation process, increases or decreases in the saturation current foster temperature compensation. The former may directly arise from the temperature dependence of the transduction channels' maximal conductance. The latter may require additional heat-sensitive channels with a modulatory influence on the transduction process, such as thermosensitive transient receptor channels (TRPA) (<xref ref-type="bibr" rid="bib31">Kang et al., 2012</xref>), which in principle could down-regulate the saturation level of the transduction function via their increased calcium response (<xref ref-type="bibr" rid="bib9">Chadha and Cook, 2012</xref>).</p><p>Generally, the analysis shows that the transduction process can contribute to temperature compensation. While spike generation alone is sufficient to mediate robustness of the firing rate, a matched temperature dependence of the transduction process may allow for more flexibility in the ‘choice’ of spike generation parameters, including the possibility to meet additional constraints.</p></sec><sec id="s3-5"><title>Conclusions</title><p>Altogether, our data show that auditory receptor neurons in the grasshopper represent an example of remarkable cell-intrinsic temperature compensation in the absence of network effects. Our computational analysis clarifies that spike generation alone can achieve this high degree of invariance of firing rate to temperature changes. The identified mechanisms generalize to spike generation in other cell types. Moreover, additional nonlinear processing by static nonlinearities (here interpreted as the transduction process involving the tympanal membrane, but on a wider scope also reflecting properties of synaptic transmission) may foster temperature compensation, if well matched with the temperature dependence of spike generation. Overall, the dependence of neuronal processing on temperature merits further investigation, in particular as temperature fluctuations are an oftentimes underestimated variable in mammalian systems too.</p></sec></sec><sec id="s4" sec-type="materials|methods"><title>Materials and methods</title><sec id="s4-1"><title>Experimental animals and electrophysiology</title><p>Experiments were performed on adult <italic>L. migratoria</italic>, obtained from a commercial supplier and held at room temperature (22–25°C). Intracellular recordings from auditory neurons within the metathoracic ganglion were conventionally conducted as described elsewhere (<xref ref-type="bibr" rid="bib20">Franz and Ronacher, 2002</xref>; <xref ref-type="bibr" rid="bib62">Wohlgemuth and Ronacher, 2007</xref>), using glass microelectrodes filled with a 3–5% solution of Lucifer yellow in 0.5 M LiCl. Neuronal responses were amplified (BRAMP-01; npi electronic GmbH, Tamm, Germany) and recorded by a data-acquisition board (BNC-2090A; National Instruments, Austin, TX) with 20 kHz sampling rate. To control for temperature, the preparation was placed directly on a Peltier element connected to a 2 V battery and a potentiometer. Temperature was monitored and recorded with a digital thermometer (GMH 3210, Greisinger electronic GmbH, Regenstauf, Germany) connected to a NiCr-Ni-thermoelement (GTF 300, Type K, Greisinger electronic GmbH, Regenstauf, Germany). For each experiment, recordings were conducted first at a fixed higher tissue temperature (in the range of 28–29°C), then the preparation was cooled down to a lower temperature (in the range of 21–23°) and recordings were repeated.</p><p>To control for differences between the temperatures of the Peltier element and the tissue at the inner side of the tympanal membrane at the attachment site of receptor neurons, the dependence between those variables was measured directly and used for calibration (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref>). The calibration shows that at the higher Peltier temperature (30°C) tissue temperature only reached 28°C (in the steady state) due to heat dissipation. After the cooling process the difference between Peltier and tissue temperature in the steady-state was less than 0.5°C. Moreover, cooling down proved to be slower in the tissue than at the Peltier element. In order not to underestimate <inline-formula><mml:math id="inf78"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values, we took a conservative approach: Electrophysiological recordings started 3–5 min after induction of the temperature change. Tissue temperature was derived from the calibration curve at the onset of a recording (lasting 40 s). Although temperature may still have been subject to small changes during the recording, this procedure ensured that temperature changes (i.e., the difference between high and low temperature) were—at most—slightly underestimated, favoring larger <inline-formula><mml:math id="inf79"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values. Consequently, the estimated <inline-formula><mml:math id="inf80"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values constitute an upper bound. In contrast, we cannot exclude that real <inline-formula><mml:math id="inf81"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values may even be slightly smaller, that is even more temperature compensated.</p><p>After completion of the recordings, Lucifer yellow was injected into the recorded cell by applying a hyperpolarizing current. Subsequently, the thoracic ganglia were removed, fixed in 4% paraformaldehyde, dehydrated, and cleared in methylsalicylate. The stained cells were identified under a fluorescent microscope according to their characteristic morphology. Altogether, nine receptor neurons were recorded in eight preparations.</p></sec><sec id="s4-2"><title>Acoustic stimulation</title><p>To obtain spike rate vs intensity curves (response curves), we used acoustic broad band stimuli (100 ms duration, 1–40 kHz bandwidth) repeated five times each at 8 intensities, rising from 32 to 88 dB SPL. Acoustic stimuli were stored digitally and delivered by a custom-made program (LabView 7 Express, National Instruments, Austin, TX). Following a 100 kHz D/A conversion (BNC-2090A; National Instruments, Austin, TX), the stimulus was routed through a computer-controlled attenuator (ATN-01M; npi electronic GmbH, Tamm, Germany) and an audio amplifier (Pioneer stereo amplifier A-207R, Pioneer Electronics Inc., USA). Acoustic stimuli were broadcast unilaterally by speakers (D2905/970000; Scan-Speak, Videbæk, Denmark) located at ± 90° and 30 cm from the preparation. Sound intensity was calibrated with a half inch microphone (type 4133; Brüel & Kjær, Nærum, Denmark) and a measuring amplifier (type 2209; Brüel & Kjær, Nærum, Denmark), positioned at the site of the preparation.</p></sec><sec id="s4-3"><title>Analysis of experimental data</title><p>Experimental spike times were extracted from the digitized recordings by applying a voltage threshold above background noise level. Mean spike rates were calculated for each intensity to obtain response curves (spike rate <italic>r</italic> vs sound intensity <inline-formula><mml:math id="inf82"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) per neuron, stimulation side, and temperature. We fit a three-parameter sigmoid to each response curve, <inline-formula><mml:math id="inf83"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ρ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mtext>sat</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>50</mml:mn><mml:mo>,</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>ρ</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, with saturation spike rate <inline-formula><mml:math id="inf84"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mtext>sat</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, half-maximum sound intensity <inline-formula><mml:math id="inf85"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>50</mml:mn><mml:mo>,</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, and dynamic-range width <inline-formula><mml:math id="inf86"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>ρ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p></sec><sec id="s4-4"><title>Quantification of temperature effects</title><p>Unless noted otherwise, temperature dependence of a given observable <italic>x</italic> was quantified by the temperature coefficient<disp-formula id="equ1"><mml:math id="m1"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>10</mml:mn><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p><inline-formula><mml:math id="inf87"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> is the factor by which <italic>x</italic> changes after a temperature increase of 10°C. <inline-formula><mml:math id="inf88"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf89"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></inline-formula> indicate an increase or decrease, respectively, of <italic>x</italic> with heating, while <inline-formula><mml:math id="inf90"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></inline-formula> indicates perfect temperature invariance. For plots of <inline-formula><mml:math id="inf91"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values data points were presented as outliers when they fell outside the interval <inline-formula><mml:math id="inf92"><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mn>1.5</mml:mn><mml:mo>·</mml:mo><mml:mtext>iqr</mml:mtext><mml:mo>,</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.5</mml:mn><mml:mo>·</mml:mo><mml:mtext>iqr</mml:mtext><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, with the 25<sup>th</sup> and the 75<sup>th</sup> percentile defining <inline-formula><mml:math id="inf93"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf94"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and an interquartile range <inline-formula><mml:math id="inf95"><mml:mrow><mml:mtext>iqr</mml:mtext><mml:mo>=</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.</p></sec><sec id="s4-5"><title>Temperature dependence of action-potential width</title><p>We also quantified the temperature-dependence of action-potential width at half-maximum amplitude, <inline-formula><mml:math id="inf96"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>AP</mml:mtext><mml:mo> </mml:mo><mml:mtext>width</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, for every neuron during the stimulus period, separately at each stimulus. <xref ref-type="fig" rid="fig1">Figure 1C</xref> shows the distribution of <inline-formula><mml:math id="inf97"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>AP</mml:mtext><mml:mo> </mml:mo><mml:mtext>width</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> pooled across all stimulus amplitudes (median 0.66). Our results qualitatively agree with the finding of broader action potentials at lower temperatures reported for various vertebrate and invertebrate neurons (<xref ref-type="bibr" rid="bib56">Thompson et al., 1985</xref>; <xref ref-type="bibr" rid="bib5">Bestmann and Dippold, 1989</xref>; <xref ref-type="bibr" rid="bib30">Janssen, 1992</xref>; <xref ref-type="bibr" rid="bib22">Gabbiani et al., 1999</xref>). Further, our results agree quantitatively with those reported for locust motor neurons and locust L-neurons (<xref ref-type="bibr" rid="bib8">Burrows, 1989</xref>; <xref ref-type="bibr" rid="bib51">Simmons, 1990</xref>).</p></sec><sec id="s4-6"><title>Adaptation</title><p>We checked that our results on the temperature dependence of firing rate were not compromised by the effects of adaptation. To this end, we re-analyzed the experimental data, separately focusing on the early phase of stimulus presentation (10–40 ms post stimulus onset), and the late phase (70–100 ms post stimulus onset). Effects of adaptation were reflected in a ratio of the respective parameter values (early-versus-late phase) that differed from one. While individual characteristics of experimentally measured firing-rate curves were subject to adaptation (e.g., the slope at half-maximum sound level was steeper early on and shallower in the later part), the early-to-late ratios did not significantly change with temperature.</p></sec><sec id="s4-7"><title>Single-neuron models</title><sec id="s4-7-1"><title>Model definition</title><p>We performed simulations of neuronal membrane potential dynamics using a single-compartment Connor–Stevens model (original model described in <xref ref-type="bibr" rid="bib12">Connor et al., 1977</xref>; parameters taken from <xref ref-type="bibr" rid="bib16">Dayan and Abbott 2005</xref>):<disp-formula id="equ2"><mml:math id="m2"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>L</mml:mi></mml:msub><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mo>·</mml:mo><mml:msup><mml:mi>m</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mi>h</mml:mi><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>K</mml:mi></mml:msub><mml:mo>·</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mn>4</mml:mn></mml:msup><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>K</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>A</mml:mi></mml:msub><mml:mo>·</mml:mo><mml:msup><mml:mi>a</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mi>b</mml:mi><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p><p>The original model was defined at a temperature of 18°C, where the parameters take the following values: peak conductances <inline-formula><mml:math id="inf98"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>L</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.003</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf99"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1.2</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf100"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>K</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.2</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf101"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>A</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.477</mml:mn></mml:mrow></mml:math></inline-formula> (mS/mm<sup>2</sup>), and reversal potentials <inline-formula><mml:math id="inf102"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>17</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf103"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>55</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf104"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>72</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf105"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>75</mml:mn></mml:mrow></mml:math></inline-formula> (mV). All gating variables, <inline-formula><mml:math id="inf106"><mml:mrow><mml:mi>x</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>h</mml:mi><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, follow first-order kinetics:<disp-formula id="equ3"><mml:math id="m3"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>V</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>V</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>V</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:msub><mml:mi>τ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>V</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>V</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p><inline-formula><mml:math id="inf107"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> denotes the steady-state (in-)activation function of <italic>x</italic>, <inline-formula><mml:math id="inf108"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the time constant of (in-)activation, and <italic>α</italic> and <inline-formula><mml:math id="inf109"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math></inline-formula> opening and closing rates of <italic>x</italic>, respectively. Specifically,<disp-formula id="equ4"><mml:math id="m4"><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>0.38</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>29.7</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.1</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>29.7</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula><disp-formula id="equ5"><mml:math id="m5"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>15.2</mml:mn><mml:mo>·</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.0556</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>54.7</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula><disp-formula id="equ6"><mml:math id="m6"><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.266</mml:mn><mml:mo>·</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.05</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>48</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula><disp-formula id="equ7"><mml:math id="m7"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>3.8</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.1</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>18</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula><disp-formula id="equ8"><mml:math id="m8"><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>0.02</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>45.7</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.1</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>45.7</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula><disp-formula id="equ9"><mml:math id="m9"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.25</mml:mn><mml:mo>·</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.0125</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>55.7</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula><disp-formula id="equ10"><mml:math id="m10"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.3632</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1.158</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0.0497</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>55.96</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula><disp-formula id="equ11"><mml:math id="m11"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mn>0.0761</mml:mn><mml:mo>·</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0.0314</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>94.22</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0.0346</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>1.17</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula><disp-formula id="equ12"><mml:math id="m12"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1.24</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>2.678</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0.0624</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>50</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula><disp-formula id="equ13"><mml:math id="m13"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0.0688</mml:mn><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>+</mml:mo><mml:mn>53.3</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>4</mml:mn></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>All simulations were performed in Matlab (variable-order solver ode15 s [<xref ref-type="bibr" rid="bib50">Shampine and Reichelt, 1997</xref>] with time step 0.01 ms).</p></sec></sec><sec id="s4-8"><title>Temperature dependence of the model</title><p>The dependence on temperature <italic>T</italic>(°C) was introduced to the model at the level of reversal potentials <inline-formula><mml:math id="inf110"><mml:mrow><mml:mi>E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, peak conductances <inline-formula><mml:math id="inf111"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, and time constants of (in-)activation <inline-formula><mml:math id="inf112"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>. The Nernst equation defined the temperature dependence of reversal potentials:<disp-formula id="equ14"><mml:math id="m14"><mml:mrow><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>R</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>z</mml:mi><mml:mi>F</mml:mi></mml:mrow></mml:mfrac><mml:mtext>ln</mml:mtext><mml:mfrac><mml:mrow><mml:mo>[</mml:mo><mml:mtext>ion</mml:mtext><mml:mo> </mml:mo><mml:mtext>outside</mml:mtext><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mtext>ion</mml:mtext><mml:mo> </mml:mo><mml:mtext>inside</mml:mtext><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>⇒</mml:mo><mml:mi>E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>273.15</mml:mn></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p><italic>R</italic> denotes the universal gas constant, <italic>z</italic> the valence of the considered ion, and <italic>F</italic> the Faraday constant. <italic>T</italic><sub><italic>0</italic></sub> = 18°C sets the reference temperature, <inline-formula><mml:math id="inf113"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula> temperature differences. Temperature dependence of <inline-formula><mml:math id="inf114"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> is determined by the choice of the parameter <inline-formula><mml:math id="inf115"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>:<disp-formula id="equ15"><mml:math id="m15"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub><mml:mo>·</mml:mo><mml:msubsup><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>X</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mi>L</mml:mi><mml:mo>,</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>For <inline-formula><mml:math id="inf116"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></inline-formula> each <inline-formula><mml:math id="inf117"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> takes the value of its original definition at 18°C. For a given gating variable, temperature dependence of its opening and closing rates are identical and read:<disp-formula id="equ16"><mml:math id="m16"><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>·</mml:mo><mml:msubsup><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:msubsup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula><disp-formula id="equ17"><mml:math id="m17"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>·</mml:mo><mml:msubsup><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>x</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>h</mml:mi><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo>}</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>Consequently,<disp-formula id="equ18"><mml:math id="m18"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:msub><mml:mi>τ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>τ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><sec id="s4-8-1"><title>Exploration of the parameter space</title><p>The model totals nine temperature-dependence parameters which span the parameter range explored: <inline-formula><mml:math id="inf118"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, with <inline-formula><mml:math id="inf119"><mml:mrow><mml:mi>X</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>L</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf120"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, with <inline-formula><mml:math id="inf121"><mml:mrow><mml:mi>x</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>h</mml:mi><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>. Each parameter was sampled in four steps within realistic intervals (<xref ref-type="bibr" rid="bib41">Partridge and Connor, 1978</xref>; <xref ref-type="bibr" rid="bib26">Hille, 2001</xref>; <xref ref-type="bibr" rid="bib53">Tang et al., 2010</xref>): <inline-formula><mml:math id="inf122"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>X</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>∈</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mn>1.2</mml:mn><mml:mo>,</mml:mo><mml:mn>2.0</mml:mn><mml:mo>]</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>∈</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mn>2.0</mml:mn><mml:mo>,</mml:mo><mml:mn>4.0</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, resulting in a total number of 4<sup>9</sup> models. Step currents of different amplitudes (<inline-formula><mml:math id="inf123"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>∈</mml:mo></mml:mrow></mml:math></inline-formula> [0.05, 0.6] <italic>µ</italic>A/mm<sup>2</sup>, varied in 0.05 <italic>µ</italic>A/mm<sup>2</sup> steps) and 100 ms duration served as stimulus to the model neurons. Preceding and following a stimulus, periods of 50 ms were simulated without current stimulation. For each model, simulations were performed at 28°C and referenced with model behavior at 18°C to derive the temperature dependence.</p></sec></sec><sec id="s4-9"><title>Quantification of f-I curve temperature dependence</title><p>Spike rates <italic>f</italic> in response to <italic>N</italic> = 12 current amplitudes <inline-formula><mml:math id="inf124"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> defined the f-I curve for a given temperature (spike detection threshold −30 mV). Temperature dependence of the f-I curve was quantified as the root-mean-squared difference between firing rates at the two temperatures across input currents, normalized by the average spike rate elicited at the lower temperature:<disp-formula id="equ19"><mml:math id="m19"><mml:mrow><mml:mtext>RMSD</mml:mtext><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msqrt><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>N</mml:mi></mml:mfrac><mml:munderover><mml:mstyle displaystyle="true"><mml:mo>∑</mml:mo></mml:mstyle><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mtext>cold</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mtext>hot</mml:mtext></mml:msub></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msqrt></mml:mrow><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>N</mml:mi></mml:mfrac><mml:mstyle displaystyle="true"><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mtext>cold</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mstyle></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>with <italic>T</italic><sub>cold</sub> = 18°C and <italic>T</italic><sub>hot</sub> = 28°C. In agreement with the functional shape of type I spiking (<xref ref-type="bibr" rid="bib17">Ermentrout, 1996</xref>), f-I curves for each <inline-formula><mml:math id="inf125"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> parameter combination were fit to a square root model,<disp-formula id="equ20"><mml:math id="m20"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mo>·</mml:mo><mml:msqrt><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:msqrt><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>where <italic>A</italic> denotes slope and <inline-formula><mml:math id="inf126"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> firing threshold of the f-I curve (quality of fit <italic>R</italic><sup>2</sup> >0.97 for 99% of the models).</p></sec><sec id="s4-10"><title>Fisher information</title><p>For a spike generation process <inline-formula><mml:math id="inf129"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, Fisher information <inline-formula><mml:math id="inf130"><mml:mrow><mml:mi>J</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> is a measure of how accurately a particular input current <italic>I</italic> can be decoded from the firing-rate response <inline-formula><mml:math id="inf131"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>. It is formally defined as<disp-formula id="equ21"><mml:math id="m21"><mml:mrow><mml:mi>J</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mstyle displaystyle="true"><mml:mo>∫</mml:mo></mml:mstyle></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>I</mml:mi></mml:mrow></mml:mfrac><mml:mtext>ln</mml:mtext><mml:mi>P</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mo>|</mml:mo><mml:mi>I</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mo>|</mml:mo><mml:mi>I</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mi>d</mml:mi><mml:mi>f</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>with the conditional probability density of the spike rate given an input current, <inline-formula><mml:math id="inf132"><mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mo>|</mml:mo><mml:mi>I</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, characterizing the output noise (i.e., spike-rate variability). We consider two empirical response models for the spike rate density: Poissonian and input-independent Gaussian, reading<disp-formula id="equ22"><mml:math id="m22"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>P</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mover accent="true"><mml:mi>f</mml:mi><mml:mo>∼</mml:mo></mml:mover></mml:mrow><mml:mo>|</mml:mo><mml:mi>I</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>·</mml:mo><mml:mi>b</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mover accent="true"><mml:mi>f</mml:mi><mml:mo>∼</mml:mo></mml:mover></mml:mrow><mml:mo>·</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mover accent="true"><mml:mi>f</mml:mi><mml:mo>∼</mml:mo></mml:mover></mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>!</mml:mo></mml:mrow></mml:mfrac><mml:mo>·</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo> </mml:mo><mml:mtext>and</mml:mtext></mml:mrow></mml:math></disp-formula><disp-formula id="equ23"><mml:math id="m23"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mover accent="true"><mml:mi>f</mml:mi><mml:mo>∼</mml:mo></mml:mover></mml:mrow><mml:mo>|</mml:mo><mml:mi>I</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msqrt><mml:mrow><mml:mn>2</mml:mn><mml:mi>π</mml:mi><mml:msup><mml:mi>σ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msqrt></mml:mrow></mml:mfrac><mml:mo>·</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mover accent="true"><mml:mi>f</mml:mi><mml:mo>∼</mml:mo></mml:mover></mml:mrow><mml:mo>−</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>·</mml:mo><mml:msup><mml:mi>σ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>respectively. For the Poisson case, <italic>b</italic> denotes the time bin during which a certain spike count <inline-formula><mml:math id="inf133"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is observed. It is assumed to be sufficiently large so that <inline-formula><mml:math id="inf134"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mtext>sp</mml:mtext></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:math></inline-formula> is well approximated by the mean firing rate <inline-formula><mml:math id="inf135"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>. σ<sup>2</sup> denotes the variance of the Gaussian probability density. The corresponding Fisher information is given by<disp-formula id="equ24"><mml:math id="m24"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>P</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mo>′</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac><mml:mo> </mml:mo><mml:mtext>and</mml:mtext></mml:mrow></mml:math></disp-formula><disp-formula id="equ25"><mml:math id="m25"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mo>′</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mi>σ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>respectively. To compare Fisher information across different temperatures, it was averaged across a fixed interval of output firing rates [<italic>f</italic><sub>min</sub>, <italic>f</italic><sub>max</sub>]. Accordingly, the input current interval [<italic>I</italic><sub>min</sub>, <italic>I</italic><sub>max</sub>] was computed for each model and temperature. Average Fisher information reads<disp-formula id="equ26"><mml:math id="m26"><mml:mrow><mml:mo>〈</mml:mo><mml:mi>J</mml:mi><mml:mo>〉</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:munderover><mml:mstyle displaystyle="true"><mml:mo>∫</mml:mo></mml:mstyle><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:mi>d</mml:mi><mml:mi>I</mml:mi><mml:mo> </mml:mo><mml:mi>J</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>For low noise, the average Fisher information is a lower bound to the neuron's capacity to transmit information (<xref ref-type="bibr" rid="bib33">Kostal et al., 2013</xref>),<disp-formula id="equ27"><mml:math id="m27"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mtext>low</mml:mtext></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mtext>ln</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mstyle displaystyle="true"><mml:mo>∫</mml:mo></mml:mstyle><mml:mi>d</mml:mi><mml:mi>I</mml:mi><mml:mo> </mml:mo><mml:mi>J</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:msqrt><mml:mrow><mml:mn>2</mml:mn><mml:mi>π</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>Exploiting the square-root shape of firing-rate curves, <inline-formula><mml:math id="inf136"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mo>·</mml:mo><mml:msqrt><mml:mrow><mml:mi>I</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf137"><mml:mrow><mml:mi>f</mml:mi><mml:mo>′</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mo>·</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>I</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, it follows that<disp-formula id="equ28"><label>(1)</label><mml:math id="m28"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:mfrac><mml:mo>≡</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>f</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>−</mml:mo><mml:msubsup><mml:mi>f</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>For the Poisson probability density Fisher information is given by<disp-formula id="equ29"><mml:math id="m29"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mo>〈</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>P</mml:mi></mml:msub><mml:mo>〉</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:mfrac><mml:munderover><mml:mstyle displaystyle="true"><mml:mo>∫</mml:mo></mml:mstyle><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:mi>d</mml:mi><mml:mi>I</mml:mi><mml:mo> </mml:mo><mml:mi>A</mml:mi><mml:mo>/</mml:mo><mml:mn>4</mml:mn><mml:mo>·</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>I</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>3</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:mfrac><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mi>A</mml:mi><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:msubsup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>I</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:mfrac><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:msubsup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:msqrt><mml:mrow><mml:mi>I</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:msqrt></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:msubsup><mml:mo>.</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p><p>With <xref ref-type="disp-formula" rid="equ28">Equation 1</xref> it can be expressed as<disp-formula id="equ30"><mml:math id="m30"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mo>〈</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>P</mml:mi></mml:msub><mml:mo>〉</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:mfrac><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>f</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>−</mml:mo><mml:msubsup><mml:mi>f</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>=</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mn>4</mml:mn></mml:msup><mml:mo>·</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p><p>For a Gaussian probability density we get<disp-formula id="equ31"><mml:math id="m31"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mo>〈</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mo>〉</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:mfrac><mml:munderover><mml:mstyle displaystyle="true"><mml:mo>∫</mml:mo></mml:mstyle><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:mi>d</mml:mi><mml:mi>I</mml:mi><mml:mrow><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:msup><mml:mi>σ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow><mml:mo>·</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi>I</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:msup><mml:mi>σ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:mfrac><mml:mo>·</mml:mo><mml:msubsup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mtext>ln</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>I</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:msup><mml:mi>σ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:mfrac><mml:mo>·</mml:mo><mml:mtext>ln</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>instead. Fisher information in this case reads<disp-formula id="equ32"><mml:math id="m32"><mml:mrow><mml:mo>〈</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mo>〉</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mi>σ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mi>f</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>−</mml:mo><mml:msubsup><mml:mi>f</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mfrac><mml:mo>·</mml:mo><mml:mtext>ln</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>Because only the slope of the firing-rate curve, <italic>A</italic>, is temperature-dependent in <inline-formula><mml:math id="inf138"><mml:mrow><mml:mo>〈</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>P</mml:mi></mml:msub><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf139"><mml:mrow><mml:mo>〈</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula>, the temperature dependence of Fisher information is given by<disp-formula id="equ33"><mml:math id="m33"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>〈</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>P</mml:mi></mml:msub><mml:mo>〉</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>〈</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mo>〉</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>4</mml:mn></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>For the average value across a fixed output interval [<italic>f</italic><sub>min</sub>, <italic>f</italic><sub>max</sub>] Fisher information is invariant to shifts of the threshold. A heating-induced increase in the accuracy of a decoder hence requires an increase in slope of the firing-rate curve, that is <inline-formula><mml:math id="inf140"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></inline-formula>. This is true for all spike-generation models considered.</p></sec><sec id="s4-11"><title>Measures of energy consumption during spiking and rest</title><sec id="s4-11-1"><title>Spiking cost</title><p>Energy consumption per spike was quantified as the total sodium current (also termed sodium load) (<xref ref-type="bibr" rid="bib24">Hasenstaub et al., 2010</xref>; <xref ref-type="bibr" rid="bib49">Sengupta et al., 2010</xref>) between stimulus onset <inline-formula><mml:math id="inf141"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mtext>start</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and 20 ms post stimulus offset <inline-formula><mml:math id="inf142"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mtext>stop</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, divided by the number of spikes elicited during this period, <inline-formula><mml:math id="inf143"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>:<disp-formula id="equ34"><mml:math id="m34"><mml:mrow><mml:msup><mml:mrow><mml:mtext>Na</mml:mtext></mml:mrow><mml:mo>+</mml:mo></mml:msup><mml:mtext>load</mml:mtext><mml:mo>/</mml:mo><mml:mtext>spike</mml:mtext><mml:mo>=</mml:mo><mml:mrow><mml:munderover><mml:mstyle displaystyle="true"><mml:mo>∫</mml:mo></mml:mstyle><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mtext>start</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mtext>stop</mml:mtext></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>20</mml:mn><mml:mtext>ms</mml:mtext></mml:mrow></mml:munderover></mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mi>d</mml:mi><mml:mi>t</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula></p><p>Considering that the <inline-formula><mml:math id="inf144"><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:math></inline-formula>-<italic>K</italic>-ATPase consumes one ATP molecule per 3 Na<sup>+</sup> ions, this quantity is proportional to the number of ATP molecules per spike. The <inline-formula><mml:math id="inf145"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>(Na<sup>+</sup> load/spike) averaged across all input currents was used for further analysis (and referred to as <inline-formula><mml:math id="inf146"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>(spiking cost)).</p><p>In addition, a measure of energy efficiency based on the separation of charges, that is the fraction of the sodium current that was not counterbalanced by a simultaneous potassium current (<xref ref-type="bibr" rid="bib14">Crotty et al., 2006</xref>), was implemented. As for estimation of the sodium-current-based cost, the stimulus period and the following 20 ms were evaluated. Note that the potassium current in the model comprised two components, <inline-formula><mml:math id="inf147"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mtext>total</mml:mtext></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Temperature effects on energy efficiency (estimated by the corresponding <inline-formula><mml:math id="inf148"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values) were highly similar to those on (the inverse of) spiking energy consumption. Finally, both measures—the current-based cost and the charge-separation-based energy efficiency—were also implemented based on the potassium current instead of the sodium current. In other words, spiking cost was additionally quantified by the total potassium current, energy efficiency based on the fraction of the potassium current that was not counterbalanced by the sodium current.</p></sec><sec id="s4-11-2"><title>Resting cost</title><p>The resting potential <inline-formula><mml:math id="inf149"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of the Connor–Stevens model is given by<disp-formula id="equ35"><label>(2)</label><mml:math id="m35"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>·</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>·</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>L</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mo>·</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mo>·</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>L</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>The numerical solution of this expression for <inline-formula><mml:math id="inf150"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was used to evaluate the sodium current at rest,<disp-formula id="equ36"><mml:math id="m36"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>Na</mml:mtext><mml:mo>,</mml:mo><mml:mtext>rest</mml:mtext></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>·</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>which defines the sodium-current-based cost of the resting potential (assuming the current is proportional to the activity of the <italic>Na</italic>-<italic>K</italic>-ATPase at rest). Likewise, the potassium-current-based cost is defined by<disp-formula id="equ37"><mml:math id="m37"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mtext>rest</mml:mtext></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>·</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>As the resting state is steady, the cost quantities do not depend on the gating variables' (in-) activation time constants and, consequently, the corresponding <inline-formula><mml:math id="inf151"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values do not have an impact on <inline-formula><mml:math id="inf152"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>resting</mml:mtext><mml:mo> </mml:mo><mml:mtext>cost</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>.</p></sec></sec><sec id="s4-12"><title>Sensitivity analysis</title><p>Sensitivity analysis was performed in the parameter space spanned by the nine temperature-dependence parameters (each dimension sampled by four values). To quantify global impact of one parameter on a given observable (like RMSD), we evaluated the distribution of point-wise changes in the observable along the dimension of a specific parameter. In total, for each parameter, <inline-formula><mml:math id="inf153"><mml:mrow><mml:mn>3</mml:mn><mml:mo>·</mml:mo><mml:msup><mml:mn>4</mml:mn><mml:mn>8</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> changes between neighboring points along the corresponding dimension need to be considered. These define a distribution of changes, whose median is indicative of the global <italic>impact</italic> of this parameter on the observable. The distribution's 25% and 75% percentiles are indicated as error bars (see, e.g., <xref ref-type="fig" rid="fig2">Figure 2C</xref>). For each observable, impact values were normalized to give unity when summed across all nine parameters. The sign of the impact provides an estimate of the qualitative influence of the parameter on the observable, that is whether an increase in the parameter value leads to an increase or decrease in the observable. We considered an impact reliable if both percentiles (25% and 75%) had the same sign as the impact.</p><p>Note that our impact evaluation constitutes a <italic>global</italic> sensitivity analysis, comparable to the Morris one-at-a-time method (<xref ref-type="bibr" rid="bib38">Morris, 1991</xref>). In contrast to the latter approach, we use a full factorial (grid) set of inputs instead of a random one. Moreover, our measure is based on the median instead of the mean of a distribution of differences in the observable. Yet, the interpretation of a high absolute impact is comparable to that of a high (absolute) mean elementary effect (the sensitivity measure in <xref ref-type="bibr" rid="bib38">Morris 1991</xref>), as is the interpretation of a large interquartile range of the difference distributions to a large standard deviation of the elementary effect.</p></sec><sec id="s4-13"><title>RMSD minimization with a genetic algorithm</title><p>Alternatively to the coarse parameter grid search, we also used optimization by a genetic algorithm (<xref ref-type="bibr" rid="bib37">Mitchell, 1998</xref>) to validate the minimum RMSD. To this end, the turboGA function was used (Matlab file exchange; settings: population size 1000, 150 generations, 8 bit discretization, initial conditions uniformly random). For the <inline-formula><mml:math id="inf154"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> parameter range used in the main article, the minimum RMSD identified by the genetic algorithm was very close to the minimum value on the grid (0.21 for the genetic algorithm, 0.22 on the grid). On average the coordinates of the grid-based minimum deviated 5% from the coordinates of the genetic algorithm-based minimum.</p></sec><sec id="s4-14"><title>Dimensional stacking</title><p>Dimensional stacking is a method to visualize high-dimensional data, that is an observable <italic>f</italic> as a function of <italic>N</italic> parameters, <inline-formula><mml:math id="inf155"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, evaluated at a discrete set of parameter values. The method is described in detail, for categoric observables, in <xref ref-type="bibr" rid="bib34">LeBlanc et al. (1990)</xref> and <xref ref-type="bibr" rid="bib55">Taylor et al. (2006)</xref>. Mainly, the method maps the <italic>N</italic>-dimensional data to a two-dimensional representation by iteratively slicing the data in one dimension and stacking the slices in 2D (<xref ref-type="fig" rid="fig2">Figure 2L</xref>). In this representation, the position of each pixel in the two-dimensional image corresponds to one parameter combination, and its color encodes the value of the observable. The image has <italic>N</italic> axes of different scales, each associated with one parameter. Visual informativeness of a dimensional stacking image crucially depends on the order in which the dimensions are stacked, that is, the axes order. The parameter dimensions associated with larger variability in the observable should be assigned larger-scale axes; those with lowest variability the small-scale axes. Sorting the axes with respect to their impact on the observable prior to dimensional stacking hence leads to a visually informative image, where color changes can be easily related to changes of the observable with individual parameters. For this study, we used the ranking of absolute impact scores (described above) to define the ‘optimal’ stack order, extending the optimization method described in <xref ref-type="bibr" rid="bib34">LeBlanc et al. (1990)</xref> and <xref ref-type="bibr" rid="bib55">Taylor et al. (2006)</xref>.</p></sec><sec id="s4-16"><title>Model robustness</title><p>The sensitivity analysis was performed with the Connor–Stevens model with original parameters for peak conductances <inline-formula><mml:math id="inf157"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mtext>Na</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf158"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mtext>K</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf159"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mtext>A</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf160"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mtext>L</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> at the colder temperature (<xref ref-type="bibr" rid="bib16">Dayan and Abbott, 2005</xref>). To test that our results are robust and do not strongly depend on this specific parameter choice, we additionally performed the whole sensitivity analysis for 24 models with peak conductances of the reference model perturbed by ±20% (8 models with one individual peak conductance lowered or raised by 20%; 16 models with all combinations of the four conductances either lowered or raised by 20%). The impacts for those models are summarized in <xref ref-type="fig" rid="fig2">Figure 2E</xref> and <xref ref-type="fig" rid="fig3">Figure 3F,G</xref> (individual changes in peak conductances represented by black symbols, combined changes by gray ones). Note that for computational efficiency only three values per parameter (instead of four) were taken (for perturbed models as well as the reference model, as presented in <xref ref-type="fig" rid="fig2">Figure 2E</xref>). The fraction of models with <inline-formula><mml:math id="inf161"><mml:mrow><mml:mtext>RMSD</mml:mtext><mml:mo><</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:math></inline-formula> (across the temperature dependence parameter space) was 18% in the original Connor–Stevens model. Variations in peak conductances did not change this finding much: for each perturbed model 15–19% of its temperature dependence combinations gave <inline-formula><mml:math id="inf162"><mml:mrow><mml:mtext>RMSD</mml:mtext><mml:mo><</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:math></inline-formula>.</p><p>For completeness, we also checked that a structurally different vertebrate model with type I dynamics (Traub-Miles, <xref ref-type="bibr" rid="bib57">Traub et al., 1991</xref>), as defined in <xref ref-type="bibr" rid="bib4">Benda 2002</xref>) was able to display temperature compensation despite a substantial temperature dependence of individual conductances (same range of temperature parameters as in the Connor–Stevens models, <xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>). The search for the lowest temperature dependence within the parameter space (sodium and potassium kinetics <inline-formula><mml:math id="inf163"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf164"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf165"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, and the peak conductances of sodium, potassium and leak <inline-formula><mml:math id="inf166"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf167"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>K</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf168"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>g</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>L</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>) was performed based on the genetic algorithm described above. As the model operates at 32°, we checked both heating and cooling the model by 10°.</p></sec><sec id="s4-17"><title>Reverse-engineering the transduction and its temperature dependence</title><p>For a given pair of a receptor neuron response <inline-formula><mml:math id="inf169"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ρ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> and a spike generation model <inline-formula><mml:math id="inf170"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, the transduction function (current <inline-formula><mml:math id="inf171"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> vs sound intensity <inline-formula><mml:math id="inf172"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) can be inferred. We assumed a sigmoidal shape of the transduction function, <inline-formula><mml:math id="inf173"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>θ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mtext>sat</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>50</mml:mn><mml:mo>,</mml:mo><mml:mi>θ</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>θ</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, with transduction saturation current <inline-formula><mml:math id="inf174"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mtext>sat</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, half-maximum sound intensity <inline-formula><mml:math id="inf175"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>50</mml:mn><mml:mo>,</mml:mo><mml:mi>θ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, and dynamic-range width <inline-formula><mml:math id="inf176"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>θ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Further, we chose representative parameters for the receptor neuron response. To this end, the median cold temperature, <inline-formula><mml:math id="inf177"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>T</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the median receptor neuron response parameters at cold temperature, <inline-formula><mml:math id="inf178"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>p</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>ρ</mml:mi></mml:msub><mml:mo>∈</mml:mo><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>r</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mtext>sat</mml:mtext></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>I</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>50</mml:mn><mml:mo>,</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>w</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>ρ</mml:mi></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, and the median temperature dependencies of the three receptor neuron response parameters, <inline-formula><mml:math id="inf179"><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>Q</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi>ρ</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, were determined from the experimental data. Using these, receptor neuron response parameters were inferred for temperatures of 18 and 28° (the temperatures at which spike generation simulations were performed), according to <inline-formula><mml:math id="inf180"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>ρ</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>p</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>ρ</mml:mi></mml:msub><mml:mo>·</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>Q</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi>ρ</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mi>T</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The resulting representative receptor neuron responses were used as objective functions for reverse engineering of the transduction curve. To infer the three parameters characterizing the optimal transduction curve for a given spike generation model <inline-formula><mml:math id="inf181"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, we computed<disp-formula id="equ38"><mml:math id="m38"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>θ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mo>·</mml:mo><mml:msqrt><mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mtext>sat</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>50</mml:mn><mml:mo>,</mml:mo><mml:mi>θ</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi>θ</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:msqrt><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>The transduction parameters were chosen such that they minimized the root mean squared error between <inline-formula><mml:math id="inf182"><mml:mrow><mml:mi>ϕ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>θ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> and the representative receptor neuron response <inline-formula><mml:math id="inf183"><mml:mrow><mml:mi>ρ</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>:<disp-formula id="equ39"><mml:math id="m39"><mml:mrow><mml:mi>θ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mtext>optimal</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mtext>arg</mml:mtext><mml:mo> </mml:mo><mml:msub><mml:mrow><mml:mtext>min</mml:mtext></mml:mrow><mml:mrow><mml:mi>θ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mstyle displaystyle="true"><mml:mo>∫</mml:mo></mml:mstyle><mml:msup><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mi>ρ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>θ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mi>d</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math></disp-formula></p><p>This fitting procedure was repeated for all hot and cold spike generation processes, and the temperature coefficients for the three transduction parameters were computed. The transduction parameters at the reference temperature (18°C) were: <inline-formula><mml:math id="inf184"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mtext>cold</mml:mtext></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mtext>dB</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mn>0.40</mml:mn><mml:mi>μ</mml:mi><mml:mtext>A</mml:mtext><mml:mo>/</mml:mo><mml:msup><mml:mrow><mml:mtext>mm</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>.</p></sec></sec></body><back><ack id="ack"><title>Acknowledgements</title><p>This work was funded by grants from the Federal Ministry of Education and Research, Germany (01GQ1001A, 01GQ0901, 01GQ0972) and the Deutsche Forschungsgemeinschaft (SFB618, GRK1589/1).</p></ack><sec sec-type="additional-information"><title>Additional information</title><fn-group content-type="competing-interest"><title>Competing interests</title><fn fn-type="conflict" id="conf1"><p>The authors declare that no competing interests exist.</p></fn></fn-group><fn-group content-type="author-contribution"><title>Author contributions</title><fn fn-type="con" id="con1"><p>FAR, Implemented the mathematical modeling,Wrote the article, Conception and design, Analysis and interpretation of data</p></fn><fn fn-type="con" id="con2"><p>MJBE, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con3"><p>J-HS, Conception and design, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con4"><p>BR, Conception and design, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con5"><p>SS, Wrote the article, Conception and design, Analysis and interpretation of data</p></fn></fn-group></sec><ref-list><title>References</title><ref id="bib1"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Abrams</surname><given-names>TW</given-names></name><name><surname>Pearson</surname><given-names>KG</given-names></name></person-group><year>1982</year><article-title>Effects of temperature on identified central neurons that control jumping in the grasshopper</article-title><source>The Journal of Neuroscience: the Official Journal of the Society for Neuroscience</source><volume>2</volume><fpage>1538</fpage><lpage>1553</lpage></element-citation></ref><ref id="bib2"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Alle</surname><given-names>H</given-names></name><name><surname>Roth</surname><given-names>A</given-names></name><name><surname>Geiger</surname><given-names>JRP</given-names></name></person-group><year>2009</year><article-title>Energy-efficient action potentials in hippocampal mossy fibers</article-title><source>Science</source><volume>325</volume><fpage>1405</fpage><lpage>1408</lpage><pub-id pub-id-type="doi">10.1126/science.1174331</pub-id></element-citation></ref><ref id="bib3"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Attwell</surname><given-names>D</given-names></name><name><surname>Laughlin</surname><given-names>SB</given-names></name></person-group><year>2001</year><article-title>An energy budget for signaling in the grey matter of the brain</article-title><source>Journal of Cerebral Blood Flow and Metabolism: official Journal of the International Society of Cerebral Blood Flow and Metabolism</source><volume>21</volume><fpage>1133</fpage><lpage>1145</lpage><pub-id pub-id-type="doi">10.1097/00004647-200110000-00001</pub-id></element-citation></ref><ref id="bib4"><element-citation publication-type="web"><person-group person-group-type="author"><name><surname>Benda</surname><given-names>J</given-names></name></person-group><year>2002</year><article-title>Single neuron dynamics. Ph.D. thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I</article-title><comment>URL <ext-link ext-link-type="uri" xlink:href="http://edoc.hu-berlin.de/docviews/abstract.php?id=10393">http://edoc.hu-berlin.de/docviews/abstract.php?id=10393</ext-link></comment></element-citation></ref><ref id="bib5"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bestmann</surname><given-names>H</given-names></name><name><surname>Dippold</surname><given-names>K</given-names></name></person-group><year>1989</year><article-title>Temperature dependence of electrophysiological responses of lepidopteran antennae</article-title><source>Z Naturforsch, C: Biosci</source><volume>44</volume><fpage>333</fpage><lpage>344</lpage></element-citation></ref><ref id="bib6"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Boulant</surname><given-names>JA</given-names></name><name><surname>Dean</surname><given-names>JB</given-names></name></person-group><year>1986</year><article-title>Temperature receptors in the central nervous system</article-title><source>Annual Review of Physiology</source><volume>48</volume><fpage>639</fpage><lpage>654</lpage><pub-id pub-id-type="doi">10.1146/annurev.ph.48.030186.003231</pub-id></element-citation></ref><ref id="bib7"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Burkhardt</surname><given-names>D</given-names></name></person-group><year>1959</year><article-title>Effect of temperature on isolated stretch-receptor organ of the crayfish</article-title><source>Science</source><volume>129</volume><fpage>392</fpage><lpage>393</lpage><pub-id pub-id-type="doi">10.1126/science.129.3346.392</pub-id></element-citation></ref><ref id="bib8"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Burrows</surname><given-names>M</given-names></name></person-group><year>1989</year><article-title>Effects of temperature on a central synapse between identified motor neurons in the locust</article-title><source>Journal of Comparative Physiology A, Sensory, Neural, and Behavioral Physiology</source><volume>165</volume><fpage>687</fpage><lpage>695</lpage><pub-id pub-id-type="doi">10.1007/BF00611000</pub-id></element-citation></ref><ref id="bib9"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Chadha</surname><given-names>A</given-names></name><name><surname>Cook</surname><given-names>B</given-names></name></person-group><year>2012</year><article-title>Dissection of gain control mechanisms in <italic>Drosophila</italic> mechanotransduction</article-title><source>The Journal of Neuroscience: the Official Journal of the Society for Neuroscience</source><volume>32</volume><fpage>13052</fpage><lpage>13061</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.2171-12.2012</pub-id></element-citation></ref><ref id="bib10"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Clemens</surname><given-names>J</given-names></name><name><surname>Kutzki</surname><given-names>O</given-names></name><name><surname>Ronacher</surname><given-names>B</given-names></name><name><surname>Schreiber</surname><given-names>S</given-names></name><name><surname>Wohlgemuth</surname><given-names>S</given-names></name></person-group><year>2011</year><article-title>Efficient transformation of an auditory population code in a small sensory system</article-title><source>Proceedings of the National Academy of Sciences of the United States of America</source><volume>108</volume><fpage>13812</fpage><lpage>13817</lpage><pub-id pub-id-type="doi">10.1073/pnas.1104506108</pub-id></element-citation></ref><ref id="bib11"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Clemens</surname><given-names>J</given-names></name><name><surname>Wohlgemuth</surname><given-names>S</given-names></name><name><surname>Ronacher</surname><given-names>B</given-names></name></person-group><year>2012</year><article-title>Nonlinear computations underlying temporal and population sparseness in the auditory system of the grasshopper</article-title><source>The Journal of Neuroscience: the Official Journal of the Society for Neuroscience</source><volume>32</volume><fpage>10053</fpage><lpage>10062</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.5911-11.2012</pub-id></element-citation></ref><ref id="bib12"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Connor</surname><given-names>JA</given-names></name><name><surname>Walter</surname><given-names>D</given-names></name><name><surname>McKown</surname><given-names>R</given-names></name></person-group><year>1977</year><article-title>Neural repetitive firing: modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons</article-title><source>Biophysical Journal</source><volume>18</volume><fpage>81</fpage><lpage>102</lpage><pub-id pub-id-type="doi">10.1016/S0006-3495(77)85598-7</pub-id></element-citation></ref><ref id="bib13"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Coro</surname><given-names>F</given-names></name><name><surname>Perez</surname><given-names>M</given-names></name></person-group><year>1990</year><article-title>Temperature affects auditory receptor response in an arctiid moth</article-title><source>Die Naturwissenschaften</source><volume>77</volume><fpage>445</fpage><lpage>447</lpage><pub-id pub-id-type="doi">10.1007/BF01135949</pub-id></element-citation></ref><ref id="bib14"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Crotty</surname><given-names>P</given-names></name><name><surname>Sangrey</surname><given-names>T</given-names></name><name><surname>Levy</surname><given-names>WB</given-names></name></person-group><year>2006</year><article-title>Metabolic energy cost of action potential velocity</article-title><source>Journal of Neurophysiology</source><volume>96</volume><fpage>1237</fpage><lpage>1246</lpage><pub-id pub-id-type="doi">10.1152/jn.01204.2005</pub-id></element-citation></ref><ref id="bib15"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Curras</surname><given-names>MC</given-names></name><name><surname>Boulant</surname><given-names>JA</given-names></name></person-group><year>1989</year><article-title>Effects of ouabain on neuronal thermosensitivity in hypothalamic tissue slices</article-title><source>The American Journal of Physiology</source><volume>257</volume><fpage>R21</fpage><lpage>R28</lpage></element-citation></ref><ref id="bib16"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Dayan</surname><given-names>P</given-names></name><name><surname>Abbott</surname><given-names>LF</given-names></name></person-group><year>2005</year><source>Theoretical neuroscience : computational and mathematical modeling of neural systems</source><publisher-loc>Cambridge, MA</publisher-loc><publisher-name>MIT Press</publisher-name></element-citation></ref><ref id="bib17"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ermentrout</surname><given-names>B</given-names></name></person-group><year>1996</year><article-title>Type i membranes, phase resetting curves, and synchrony</article-title><source>Neural Computation</source><volume>8</volume><fpage>979</fpage><lpage>1001</lpage><pub-id pub-id-type="doi">10.1162/neco.1996.8.5.979</pub-id></element-citation></ref><ref id="bib18"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Fisch</surname><given-names>K</given-names></name><name><surname>Schwalger</surname><given-names>T</given-names></name><name><surname>Lindner</surname><given-names>B</given-names></name><name><surname>Herz</surname><given-names>AVM</given-names></name><name><surname>Benda</surname><given-names>J</given-names></name></person-group><year>2012</year><article-title>Channel noise from both slow adaptation currents and fast currents is required to explain spike-response variability in a sensory neuron</article-title><source>The Journal of Neuroscience: the Official Journal of the Society for Neuroscience</source><volume>32</volume><fpage>17332</fpage><lpage>17344</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.6231-11.2012</pub-id></element-citation></ref><ref id="bib19"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Fonseca</surname><given-names>PJ</given-names></name><name><surname>Correia</surname><given-names>T</given-names></name></person-group><year>2007</year><article-title>Effects of temperature on tuning of the auditory pathway in the cicada <italic>Tettigetta josei</italic> (Hemiptera, Tibicinidae)</article-title><source>The Journal of Experimental Biology</source><volume>210</volume><fpage>1834</fpage><lpage>1845</lpage><pub-id pub-id-type="doi">10.1242/jeb.001495</pub-id></element-citation></ref><ref id="bib20"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Franz</surname><given-names>A</given-names></name><name><surname>Ronacher</surname><given-names>B</given-names></name></person-group><year>2002</year><article-title>Temperature dependence of temporal resolution in an insect nervous system</article-title><source>Journal of Comparative Physiology A, Neuroethology, Sensory, Neural, and Behavioral Physiology</source><volume>188</volume><fpage>261</fpage><lpage>271</lpage><pub-id pub-id-type="doi">10.1007/s00359-002-0298-6</pub-id></element-citation></ref><ref id="bib21"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>French</surname><given-names>AS</given-names></name><name><surname>Kuster</surname><given-names>JE</given-names></name></person-group><year>1982</year><article-title>The effects of temperature on mechanotransduction in the cockroach tactile spine</article-title><source>Journal of Comparative Physiology A, Neuroethology, Sensory, Neural, and Behavioral Physiology</source><volume>147</volume><fpage>251</fpage><lpage>258</lpage><pub-id pub-id-type="doi">10.1007/BF00609849</pub-id></element-citation></ref><ref id="bib22"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gabbiani</surname><given-names>F</given-names></name><name><surname>Krapp</surname><given-names>HG</given-names></name><name><surname>Laurent</surname><given-names>G</given-names></name></person-group><year>1999</year><article-title>Computation of object approach by a wide-field, motion-sensitive neuron</article-title><source>The Journal of Neuroscience: the Official Journal of the Society for Neuroscience</source><volume>19</volume><fpage>1122</fpage><lpage>1141</lpage></element-citation></ref><ref id="bib23"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gollisch</surname><given-names>T</given-names></name><name><surname>Herz</surname><given-names>AMV</given-names></name></person-group><year>2005</year><article-title>Disentangling sub-millisecond processes within an auditory transduction chain</article-title><source>PLOS Biology</source><volume>3</volume><fpage>e8</fpage><pub-id pub-id-type="doi">10.1371/journal.pbio.0030008</pub-id></element-citation></ref><ref id="bib24"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hasenstaub</surname><given-names>A</given-names></name><name><surname>Otte</surname><given-names>S</given-names></name><name><surname>Callaway</surname><given-names>E</given-names></name><name><surname>Sejnowski</surname><given-names>TJ</given-names></name></person-group><year>2010</year><article-title>Metabolic cost as a unifying principle governing neuronal biophysics</article-title><source>Proceedings of the National Academy of Sciences of the United States of America</source><volume>107</volume><fpage>12329</fpage><lpage>12334</lpage><pub-id pub-id-type="doi">10.1073/pnas.0914886107</pub-id></element-citation></ref><ref id="bib25"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hazel</surname><given-names>JR</given-names></name><name><surname>Prosser</surname><given-names>CL</given-names></name></person-group><year>1974</year><article-title>Molecular mechanisms of temperature compensation in poikilotherms</article-title><source>Physiological Reviews</source><volume>54</volume><fpage>620</fpage><lpage>677</lpage></element-citation></ref><ref id="bib26"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Hille</surname><given-names>B</given-names></name></person-group><year>2001</year><article-title>Ion channels of excitable membranes</article-title><publisher-loc>Sunderland, MA</publisher-loc><publisher-name>Sinauer</publisher-name></element-citation></ref><ref id="bib27"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Howard</surname><given-names>J</given-names></name><name><surname>Hudspeth</surname><given-names>A</given-names></name></person-group><year>1988</year><article-title>Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell</article-title><source>Neuron</source><volume>1</volume><fpage>189</fpage><lpage>199</lpage><pub-id pub-id-type="doi">10.1016/0896-6273(88)90139-0</pub-id></element-citation></ref><ref id="bib28"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hudspeth</surname><given-names>AJ</given-names></name><name><surname>Choe</surname><given-names>Y</given-names></name><name><surname>Mehta</surname><given-names>AD</given-names></name><name><surname>Martin</surname><given-names>P</given-names></name></person-group><year>2000</year><article-title>Putting ion channels to work: mechanoelectrical transduction, adaptation, and amplification by hair cells</article-title><source>Proceedings of the National Academy of Sciences of the United States of America</source><volume>97</volume><fpage>11765</fpage><lpage>11772</lpage><pub-id pub-id-type="doi">10.1073/pnas.97.22.11765</pub-id></element-citation></ref><ref id="bib29"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Izhikevich</surname><given-names>EM</given-names></name></person-group><year>2007</year><source>Dynamical systems in neuroscience: the geometry of excitability and bursting</source><publisher-loc>Cambridge, MA</publisher-loc><publisher-name>MIT Press</publisher-name></element-citation></ref><ref id="bib30"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Janssen</surname><given-names>R</given-names></name></person-group><year>1992</year><article-title>Thermal influences on nervous system function</article-title><source>Neuroscience and Biobehavioral Reviews</source><volume>16</volume><fpage>399</fpage><lpage>413</lpage><pub-id pub-id-type="doi">10.1016/S0149-7634(05)80209-X</pub-id></element-citation></ref><ref id="bib31"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kang</surname><given-names>K</given-names></name><name><surname>Panzano</surname><given-names>VC</given-names></name><name><surname>Chang</surname><given-names>EC</given-names></name><name><surname>Ni</surname><given-names>L</given-names></name><name><surname>Dainis</surname><given-names>AM</given-names></name><name><surname>Jenkins</surname><given-names>AM</given-names></name><name><surname>Regna</surname><given-names>K</given-names></name><name><surname>Muskavitch</surname><given-names>MA</given-names></name><name><surname>Garrity</surname><given-names>PA</given-names></name></person-group><year>2012</year><article-title>Modulation of TRPA1 thermal sensitivity enables sensory discrimination in Drosophila</article-title><source>Nature</source><volume>481</volume><fpage>76</fpage><lpage>80</lpage><pub-id pub-id-type="doi">10.1038/nature10715</pub-id></element-citation></ref><ref id="bib32"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kispersky</surname><given-names>TJ</given-names></name><name><surname>Caplan</surname><given-names>JS</given-names></name><name><surname>Marder</surname><given-names>E</given-names></name></person-group><year>2012</year><article-title>Increase in sodium conductance decreases firing rate and gain in model neurons</article-title><source>The Journal of Neuroscience: the Official Journal of the Society for Neuroscience</source><volume>32</volume><fpage>10995</fpage><lpage>11004</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.2045-12.2012</pub-id></element-citation></ref><ref id="bib33"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kostal</surname><given-names>L</given-names></name><name><surname>Lansky</surname><given-names>P</given-names></name><name><surname>McDonnell</surname><given-names>MD</given-names></name></person-group><year>2013</year><article-title>Metabolic cost of neuronal information in an empirical stimulus-response model</article-title><source>Biological Cybernetics</source><volume>107</volume><fpage>355</fpage><lpage>365</lpage><pub-id pub-id-type="doi">10.1007/s00422-013-0554-6</pub-id></element-citation></ref><ref id="bib34"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>LeBlanc</surname><given-names>J</given-names></name><name><surname>Ward</surname><given-names>MO</given-names></name><name><surname>Wittels</surname><given-names>N</given-names></name></person-group><year>1990</year><article-title>Exploring n-dimensional databases</article-title><source>Proceedings of the 1st conference on Visualization’90</source><publisher-loc>Los Alamitos, CA</publisher-loc><publisher-name>IEEE Computer Society Press</publisher-name><fpage>230</fpage><lpage>237</lpage></element-citation></ref><ref id="bib35"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Machens</surname><given-names>CK</given-names></name><name><surname>Stemmler</surname><given-names>MB</given-names></name><name><surname>Prinz</surname><given-names>P</given-names></name><name><surname>Krahe</surname><given-names>R</given-names></name><name><surname>Ronacher</surname><given-names>B</given-names></name><name><surname>Herz</surname><given-names>AV</given-names></name></person-group><year>2001</year><article-title>Representation of acoustic communication signals by insect auditory receptor neurons</article-title><source>The Journal of Neuroscience: the Official Journal of the Society for Neuroscience</source><volume>21</volume><fpage>3215</fpage><lpage>3227</lpage></element-citation></ref><ref id="bib36"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Miles</surname><given-names>CI</given-names></name></person-group><year>1985</year><article-title>The effects of behaviourally relevant temperatures on mechanosensory neurones of the grasshopper, Schistocerca americana</article-title><source>The Journal of Experimental Biology</source><volume>116</volume><fpage>121</fpage><lpage>139</lpage></element-citation></ref><ref id="bib37"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Mitchell</surname><given-names>M</given-names></name></person-group><year>1998</year><source>An introduction to genetic algorithms (complex adaptive systems)</source><publisher-loc>Cambridge, MA</publisher-loc><publisher-name>MIT Press</publisher-name></element-citation></ref><ref id="bib38"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Morris</surname><given-names>MD</given-names></name></person-group><year>1991</year><article-title>Factorial sampling plans for preliminary computational experiments</article-title><source>Technometrics</source><volume>33</volume><fpage>161</fpage><lpage>174</lpage><pub-id pub-id-type="doi">10.2307/1269043</pub-id></element-citation></ref><ref id="bib39"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Niven</surname><given-names>JE</given-names></name><name><surname>Farris</surname><given-names>SM</given-names></name></person-group><year>2012</year><article-title>Miniaturization of nervous systems and neurons</article-title><source>Current Biology</source><volume>22</volume><fpage>R323</fpage><lpage>R329</lpage><pub-id pub-id-type="doi">10.1016/j.cub.2012.04.002</pub-id></element-citation></ref><ref id="bib40"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Niven</surname><given-names>JE</given-names></name><name><surname>Laughlin</surname><given-names>SB</given-names></name></person-group><year>2008</year><article-title>Energy limitation as a selective pressure on the evolution of sensory systems</article-title><source>The Journal of Experimental Biology</source><volume>211</volume><fpage>1792</fpage><lpage>1804</lpage><pub-id pub-id-type="doi">10.1242/jeb.017574</pub-id></element-citation></ref><ref id="bib41"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Partridge</surname><given-names>LD</given-names></name><name><surname>Connor</surname><given-names>JA</given-names></name></person-group><year>1978</year><article-title>A mechanism for minimizing temperature effects on repetitive firing frequency</article-title><source>The American Journal of Physiology</source><volume>234</volume><fpage>C155</fpage><lpage>C161</lpage></element-citation></ref><ref id="bib42"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pfau</surname><given-names>HK</given-names></name><name><surname>Koch</surname><given-names>UT</given-names></name><name><surname>Möhl</surname><given-names>B</given-names></name></person-group><year>1989</year><article-title>Temperature dependence and response characteristics of the isolated wing hinge stretch receptor in the locust</article-title><source>Journal of Comparative Physiology A, Neuroethology, Sensory, Neural, and Behavioral Physiology</source><volume>165</volume><fpage>247</fpage><lpage>252</lpage><pub-id pub-id-type="doi">10.1007/BF00619199</pub-id></element-citation></ref><ref id="bib43"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Prinz</surname><given-names>AA</given-names></name><name><surname>Billimoria</surname><given-names>CP</given-names></name><name><surname>Marder</surname><given-names>E</given-names></name></person-group><year>2003</year><article-title>Alternative to hand-tuning conductance-based models: Construction and analysis of databases of model neurons</article-title><source>Journal of Neurophysiology</source><volume>90</volume><fpage>3998</fpage><lpage>4015</lpage><pub-id pub-id-type="doi">10.1152/jn.00641.2003</pub-id></element-citation></ref><ref id="bib44"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ramirez</surname><given-names>JM</given-names></name><name><surname>Elsen</surname><given-names>FP</given-names></name><name><surname>Robertson</surname><given-names>RM</given-names></name></person-group><year>1999</year><article-title>Long-term effects of prior heat shock on neuronal potassium currents recorded in a novel insect ganglion slice preparation</article-title><source>Journal of Neurophysiology</source><volume>81</volume><fpage>795</fpage><lpage>802</lpage></element-citation></ref><ref id="bib45"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Robertson</surname><given-names>RM</given-names></name><name><surname>Money</surname><given-names>TG</given-names></name></person-group><year>2012</year><article-title>Temperature and neuronal circuit function: compensation, tuning and tolerance</article-title><source>Current Opinion in Neurobiology</source><volume>22</volume><fpage>724</fpage><lpage>734</lpage><pub-id pub-id-type="doi">10.1016/j.conb.2012.01.008</pub-id></element-citation></ref><ref id="bib46"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Rush</surname><given-names>ME</given-names></name><name><surname>Rinzel</surname><given-names>J</given-names></name></person-group><year>1995</year><article-title>The potassium A-current, low firing rates and rebound excitation in Hodgkin-Huxley models</article-title><source>Bulletin of Mathematical Biology</source><volume>57</volume><fpage>899</fpage><lpage>929</lpage><pub-id pub-id-type="doi">10.1007/BF02458299</pub-id></element-citation></ref><ref id="bib47"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Schmidt-Nielsen</surname><given-names>K</given-names></name></person-group><year>1997</year><source>Animal physiology: adaptation and environment</source><publisher-loc>Cambridge, UK</publisher-loc><publisher-name>Cambridge University Press</publisher-name></element-citation></ref><ref id="bib48"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Schreiber</surname><given-names>S</given-names></name><name><surname>Fellous</surname><given-names>JM</given-names></name><name><surname>Tiesinga</surname><given-names>P</given-names></name><name><surname>Sejnowski</surname><given-names>TJ</given-names></name></person-group><year>2004</year><article-title>Influence of ionic conductances on spike timing reliability of cortical neurons for suprathreshold rhythmic inputs</article-title><source>Journal of Neurophysiology</source><volume>91</volume><fpage>194</fpage><lpage>205</lpage><pub-id pub-id-type="doi">10.1152/jn.00556.2003</pub-id></element-citation></ref><ref id="bib49"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sengupta</surname><given-names>B</given-names></name><name><surname>Stemmler</surname><given-names>M</given-names></name><name><surname>Laughlin</surname><given-names>SB</given-names></name><name><surname>Niven</surname><given-names>JE</given-names></name></person-group><year>2010</year><article-title>Action potential energy efficiency varies among neuron types in vertebrates and invertebrates</article-title><source>PLOS Computational Biology</source><volume>6</volume><fpage>e1000840</fpage><pub-id pub-id-type="doi">10.1371/journal.pcbi.1000840</pub-id></element-citation></ref><ref id="bib50"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Shampine</surname><given-names>LF</given-names></name><name><surname>Reichelt</surname><given-names>MW</given-names></name></person-group><year>1997</year><article-title>The MATLAB ODE suite</article-title><source>SIAM Journal of Scientific Computing</source><volume>18</volume><fpage>1</fpage><lpage>22</lpage><pub-id pub-id-type="doi">10.1137/S1064827594276424</pub-id></element-citation></ref><ref id="bib51"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Simmons</surname><given-names>P</given-names></name></person-group><year>1990</year><article-title>The effects of temperature on locust ocellar L-neurones and their interconnections</article-title><source>Journal of Comparative Physiology A, Neuroethology, Sensory, Neural, and Behavioral Physiology</source><volume>166</volume><fpage>575</fpage><lpage>583</lpage><pub-id pub-id-type="doi">10.1007/BF00192028</pub-id></element-citation></ref><ref id="bib52"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Spavieri</surname><given-names>DL</given-names></name><name><surname>Eichner</surname><given-names>H</given-names></name><name><surname>Borst</surname><given-names>A</given-names></name></person-group><year>2010</year><article-title>Coding efficiency of fly motion processing is set by firing rate, not firing precision</article-title><source>PLOS Computational Biology</source><volume>6</volume><fpage>e1000860</fpage><pub-id pub-id-type="doi">10.1371/journal.pcbi.1000860</pub-id></element-citation></ref><ref id="bib53"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tang</surname><given-names>LS</given-names></name><name><surname>Goeritz</surname><given-names>ML</given-names></name><name><surname>Caplan</surname><given-names>JS</given-names></name><name><surname>Taylor</surname><given-names>AL</given-names></name><name><surname>Fisek</surname><given-names>M</given-names></name><name><surname>Marder</surname><given-names>E</given-names></name></person-group><year>2010</year><article-title>Precise temperature compensation of phase in a rhythmic motor pattern</article-title><source>PLOS Biology</source><volume>8</volume><fpage>e1000469</fpage><pub-id pub-id-type="doi">10.1371/journal.pbio.1000469</pub-id></element-citation></ref><ref id="bib54"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tatler</surname><given-names>B</given-names></name><name><surname>O’Carroll</surname><given-names>DC</given-names></name><name><surname>Laughlin</surname><given-names>SB</given-names></name></person-group><year>2000</year><article-title>Temperature and the temporal resolving power of fly photoreceptors</article-title><source>Journal of Comparative Physiology A, Neuroethology, Sensory, Neural, and Behavioral Physiology</source><volume>186</volume><fpage>399</fpage><lpage>407</lpage><pub-id pub-id-type="doi">10.1007/s003590050439</pub-id></element-citation></ref><ref id="bib55"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Taylor</surname><given-names>AL</given-names></name><name><surname>Hickey</surname><given-names>TJ</given-names></name><name><surname>Prinz</surname><given-names>AA</given-names></name><name><surname>Marder</surname><given-names>E</given-names></name></person-group><year>2006</year><article-title>Structure and visualization of high-dimensional conductance spaces</article-title><source>Journal of Neurophysiology</source><volume>96</volume><fpage>891</fpage><lpage>905</lpage><pub-id pub-id-type="doi">10.1152/jn.00367.2006</pub-id></element-citation></ref><ref id="bib56"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Thompson</surname><given-names>S</given-names></name><name><surname>Masukawa</surname><given-names>L</given-names></name><name><surname>Prince</surname><given-names>D</given-names></name></person-group><year>1985</year><article-title>Temperature dependence of intrinsic membrane properties and synaptic potentials in hippocampal CA1 neurons in vitro</article-title><source>The Journal of Neuroscience: the Official Journal of the Society for Neuroscience</source><volume>5</volume><fpage>817</fpage><lpage>824</lpage></element-citation></ref><ref id="bib57"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Traub</surname><given-names>RD</given-names></name><name><surname>Wong</surname><given-names>RK</given-names></name><name><surname>Miles</surname><given-names>R</given-names></name><name><surname>Michelson</surname><given-names>H</given-names></name></person-group><year>1991</year><article-title>A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances</article-title><source>Journal of Neurophysiology</source><volume>66</volume><fpage>635</fpage><lpage>650</lpage></element-citation></ref><ref id="bib58"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>van Netten</surname><given-names>SM</given-names></name><name><surname>Dinklo</surname><given-names>T</given-names></name><name><surname>Marcotti</surname><given-names>W</given-names></name><name><surname>Kros</surname><given-names>CJ</given-names></name></person-group><year>2003</year><article-title>Channel gating forces govern accuracy of mechano-electrical transduction in hair cells</article-title><source>Proceedings of the National Academy of Sciences of the United States of America</source><volume>100</volume><fpage>15510</fpage><lpage>15515</lpage><pub-id pub-id-type="doi">10.1073/pnas.2632626100</pub-id></element-citation></ref><ref id="bib59"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Vogel</surname><given-names>A</given-names></name><name><surname>Ronacher</surname><given-names>B</given-names></name></person-group><year>2007</year><article-title>Neural correlations increase between consecutive processing levels in the auditory system of locusts</article-title><source>Journal of Neurophysiology</source><volume>97</volume><fpage>3376</fpage><lpage>3385</lpage><pub-id pub-id-type="doi">10.1152/jn.00796.2006</pub-id></element-citation></ref><ref id="bib60"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Warzecha</surname><given-names>A</given-names></name><name><surname>Horstmann</surname><given-names>W</given-names></name><name><surname>Egelhaaf</surname><given-names>M</given-names></name></person-group><year>1999</year><article-title>Temperature-dependence of neuronal performance in the motion pathway of the blowfly Calliphora erythrocephala</article-title><source>The Journal of Experimental Biology</source><volume>202</volume><fpage>3161</fpage><lpage>3170</lpage></element-citation></ref><ref id="bib61"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wechselberger</surname><given-names>M</given-names></name><name><surname>Wright</surname><given-names>CL</given-names></name><name><surname>Bishop</surname><given-names>GA</given-names></name><name><surname>Boulant</surname><given-names>JA</given-names></name></person-group><year>2006</year><article-title>Ionic channels and conductance-based models for hypothalamic neuronal thermosensitivity</article-title><source>The American Journal of Physiology</source><volume>291</volume><fpage>R518</fpage><lpage>R529</lpage><pub-id pub-id-type="doi">10.1152/ajpregu.00039.2006</pub-id></element-citation></ref><ref id="bib62"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wohlgemuth</surname><given-names>S</given-names></name><name><surname>Ronacher</surname><given-names>B</given-names></name></person-group><year>2007</year><article-title>Auditory discrimination of amplitude modulations based on metric distances of spike trains</article-title><source>Journal of Neurophysiology</source><volume>97</volume><fpage>3082</fpage><lpage>3092</lpage><pub-id pub-id-type="doi">10.1152/jn.01235.2006</pub-id></element-citation></ref><ref id="bib63"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Xu</surname><given-names>GY</given-names></name><name><surname>Winston</surname><given-names>JH</given-names></name><name><surname>Shenoy</surname><given-names>M</given-names></name><name><surname>Yin</surname><given-names>H</given-names></name><name><surname>Pasricha</surname><given-names>PJ</given-names></name></person-group><year>2006</year><article-title>Enhanced excitability and suppression of A-type K+ current of pancreas-specific afferent neurons in a rat model of chronic pancreatitis</article-title><source>The American Journal of Physiology</source><volume>291</volume><fpage>G424</fpage><lpage>G431</lpage><pub-id pub-id-type="doi">10.1152/ajpgi.00560.2005</pub-id></element-citation></ref><ref id="bib64"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Yu</surname><given-names>Y</given-names></name><name><surname>Hill</surname><given-names>AP</given-names></name><name><surname>McCormick</surname><given-names>DA</given-names></name></person-group><year>2012</year><article-title>Warm body temperature facilitates energy efficient cortical action potentials</article-title><source>PLOS Computational Biology</source><volume>8</volume><fpage>e1002456</fpage><pub-id pub-id-type="doi">10.1371/journal.pcbi.1002456</pub-id></element-citation></ref></ref-list></back><sub-article article-type="article-commentary" id="SA1"><front-stub><article-id pub-id-type="doi">10.7554/eLife.02078.013</article-id><title-group><article-title>Decision letter</article-title></title-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Calabrese</surname><given-names>Ronald L</given-names></name><role>Reviewing editor</role><aff><institution>Emory University</institution>, <country>United States</country></aff></contrib></contrib-group></front-stub><body><boxed-text><p>eLife posts the editorial decision letter and author response on a selection of the published articles (subject to the approval of the authors). An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent (see <ext-link ext-link-type="uri" xlink:href="http://elifesciences.org/review-process">review process</ext-link>). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.</p></boxed-text><p>Thank you for sending your work entitled “Cell-intrinsic mechanisms of temperature compensation in a sensory receptor neuron” for consideration at <italic>eLife</italic>. Your article has been favorably evaluated by a Senior editor and 3 reviewers, one of whom, Ronald L Calabrese, is a member of our Board of Reviewing Editors.</p><p>The Reviewing editor and the other reviewers discussed their comments before we reached this decision, and the Reviewing editor has assembled the following comments to help you prepare a revised submission.</p><p>The authors describe experiments showing temperature insensitivity in locust auditory receptor neurons (Q10< 1.5) and then pursue a modeling approach to explain these results. They concentrate on the spiking mechanisms itself and use an ensemble modeling approach to identify model neurons that will show comparable temperature insensitivity while expressing membrane currents with normal Q10s. These modeling experiments identify key processes (parameters) that give rise to the temperature 'compensation' and show that well-compensated models show a shift in threshold that partially cancels the shift in F-I slope that all models show. They also address the issues of information transfer and metabolic cost as temperature increases and find no restrictions for compensated models. They then use a reverse engineering method to address temperature compensation in the transduction mechanisms (receptor potential). The finding are of general interest because many neurons, including peripheral mammalian neurons, experience temperature changes and these studies show that such changes are easily accommodated/compensated by systems of membrane currents with normal Q10s.</p><p>The three reviewers are from different backgrounds and have different overlapping expertise; their reviews reflect their different backgrounds and expertise, but they all agree that four major revisions are needed.</p><p>1) While conciseness is a virtue it should not sacrifice clarity and completeness. We encourage the authors to expand their style in Introduction, Results, and even Methods to add more rationale and fuller explanations of what they did and how the models were constructed and used. In particular the section “Model-based inference of the auditory transduction function” was very difficult to follow. We suggest that the authors expand this section and fully explain what they did, how they did it, and why they did it.</p><p>2) Like prior studies by Laughlin and others on the metabolic cost of neuronal signaling, the authors use Na flux as a proxy for ion pump activity and as their measure of metabolic cost during spiking and at rest. The authors should provide clear rationale for why the cost of other ions were excluded. This seems particularly relevant in light of the authors' finding that the properties of Na channels, more than those of other channels, influence energy efficiency in these model neurons. The model used only includes Na and K currents and so other ions cannot be considered and the cost of K is tied to the cost of Na by the Na/K pump but this and the inherent limitations it imposes on the conclusion should be made explicit.</p><p>3) One reviewer crystallized concerns about the experimental component of the work: “My concerns are with the acquisition of the biological data, particularly with respect to temperature control and measurement…” The authors should make their experimental procedures crystal clear (in both Results and in Methods) and should address each of the questions posed by this reviewer. They should also make arguments about how much error there would have to be to affect their conclusion.</p><p>4) The authors should apply appropriate statistical tests to the biological data in all cases where temperature appears to affect a characteristic, e.g., spike width, so that the reader is confident that the temperature change is large enough to measure valid Q10s.</p><p>Other issues to address:</p><p><italic>Reviewer</italic> <italic>#1:</italic></p><p>The section “Model-based inference of the auditory transduction function” was very difficult to follow. This reviewer is a computational neuroscientist but I am unfamiliar with reverse engineering techniques, and I was not given enough help in reasoning through the experiments and data as would be necessary for the general reader in neuroscience. I suggest that the authors expand this section and fully explain what they did, how they did it, and why they did it. The Methods section helps a bit but only very marginally and is very technically written. Think of the general reader here.</p><p><italic>Reviewer</italic> <italic>#2:</italic></p><p>Like prior studies by Laughlin and others on the metabolic cost of neuronal signaling, the authors use Na flux as a proxy for ion pump activity and as their measure of metabolic cost during spiking and at rest. I have always been puzzled by this choice – why exclude the cost of other ions? I assume there are good reasons for this choice that I am simply not aware of, so I suggest that the authors include a comment on this question. This seems particularly relevant in light of the authors' finding that the properties of Na channels, more than those of other channels, influence energy efficiency in these model neurons. This result makes me wonder if the outcome would have been different (with other ion channels playing a bigger role in energy efficiency) if metabolic cost had been defined in a less Na-centric way.</p><p>Another comment concerns the tests for robustness of their findings to the particular choice of model neuron that the authors describe in the paper. In the Results section we learn that the authors tested for robustness of their results by checking whether a relatively modest (20%) variation of parameters of the Connors-Stevens model used here changes the overall conclusions, and are assured that it does not. While this test for robustness is laudable, I was much more convinced that the findings are robust by a very short comment, hidden in the Methods section, in which the authors state that they also found temperature compensation of firing properties despite temperature dependence of ion channels in a structurally different Traub-Miles model neuron. I recommend that the authors consider giving this latter result a more prominent place in the paper, because it could potentially (since I don't know the details) make the case for generality of the results much stronger.</p><p><italic>Reviewer</italic> <italic>#3:</italic></p><p>The work is novel, interesting and well presented. Though the linkage between the biological neurons and the models is quite tenuous, I have no problems with the computational aspects of the paper. My concerns are with the acquisition of the biological data, particularly with respect to temperature control and measurement. This is important because if the temperature change at the receptor ending is over-estimated then the Q10s will be under-estimated and there may not be an interesting biological phenomenon (the surprisingly low Q10) in need of explanation. The preparation was heated by placing it on a Peltier element i.e. a localized heat source underneath the locust. Heat conduction from that source will vary through the various tissues, cuticle and saline and I would expect that the preparation was not at a uniform temperature throughout. The GTF 300 thermal probe has, according to the manufacturer's website, a diameter of 1mm (assuming that it hadn't been modified) which is relatively large with respect to distances inside the thoracic/abdominal cavity. I wonder if the authors could provide more information in the Methods that might increase confidence that the temperature range reported and used to calculate Q10 was the range that the receptor ending actually experienced. For example, how was the temperature at the attachment site of the receptor neurons measured using the GTF 300 probe? How variable was the temperature at different sites in the preparation (tympanum, saline, ganglion)? What did the calibration curve look like and was a calibration curve generated for every preparation that provided data or from other preparations; how consistent was it between preparations?</p><p>Action potential width was measured at the recording site in the metathoracic ganglion but it is being associated with firing frequency generated at the tympanum. Did these two sites experience the same temperature changes? Given that the density and diversity of conductances can be quite different at different locations of a neuron, do we know whether action potential parameters at these two sites are the same?</p><p>The sample size of 9 neurons in 8 preparations is relatively small. I assume that each preparation provided at least one neuronal recording and one provided two, but this is not explicitly stated. According to <xref ref-type="fig" rid="fig1">Figure 1C</xref>, one or more of the neurons had a Q10 for spike rate at half max greater than 2.5 suggesting that these measures were quite variable. Did the authors perform any statistical comparisons to test significance?</p><p>It is unsurprising to me that metabolic cost was defined as Na load and then the computational analysis revealed that parameters of the Na conductance had the greatest effect on Q10 of metabolic cost. The authors might comment on this.</p></body></sub-article><sub-article article-type="reply" id="SA2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.02078.014</article-id><title-group><article-title>Author response</article-title></title-group></front-stub><body><p><italic>1) While conciseness is a virtue it should not sacrifice clarity and completeness. We encourage the authors to expand their style in Introduction, Results, and even Methods to add more rationale and fuller explanations of what they did and how the models were constructed and used. In particular the section “Model-based inference of the auditory transduction function” was very difficult to follow. We suggest that the authors expand this section and fully explain what they did, how they did it, and why they did it</italic>.</p><p>We have expanded all paragraphs, with a main focus on Results and Methods. In particular the section “Model-based inference of the auditory transduction function” has been rewritten. We have also added a total of six supplemental figures (using the figures supplements in the <italic>eLife</italic> format) for more detailed information on the analyses.</p><p><italic>2) Like prior studies by Laughlin and others on the metabolic cost of neuronal signaling, the authors use Na flux as a proxy for ion pump activity and as their measure of metabolic cost during spiking and at rest. The authors should provide clear rationale for why the cost of other ions were excluded. This seems particularly relevant in light of the authors' finding that the properties of Na channels, more than those of other channels, influence energy efficiency in these model neurons. The model used only includes Na and K currents and so other ions cannot be considered and the cost of K is tied to the cost of Na by the Na/K pump but this and the inherent limitations it imposes on the conclusion should be made explicit</italic>.</p><p>We extended the analysis and included additional measures of energy efficiency/cost). The results for measures of charge separation (for spiking cost) are now shown. Moreover, costs are now also estimated based on the potassium currents (results presented in supplemental figures to <xref ref-type="fig" rid="fig3">Figure 3</xref>). Despite minor quantitative changes, the main findings hold for all measures. As pointed out by the referees, costs arising from the flow of other ions can contribute to the metabolic cost in living cells, but are not included in the model. We assume that the major cost in our study arises from the activity of the Na-K-ATPase.</p><p><italic>3) One reviewer crystallized concerns about the experimental component of the work: “My concerns are with the acquisition of the biological data, particularly with respect to temperature control and measurement…” The authors should make their experimental procedures crystal clear (in both Results and in Methods) and should address each of the questions posed by this reviewer. They should also make arguments about how much error there would have to be to affect their conclusion</italic>.</p><p>Below we are addressing all concerns of the reviewer and provide more detail on the experimental procedures. The calibration curve is now included as a supplement to <xref ref-type="fig" rid="fig1">Figure 1</xref>. The errors in temperature measurement would indeed have to be large in order to substantially affect our results. To moderately change a firing-rate Q10 value from 1.5 to 1.6, the temperature error would have to be on the order of 1 degree Celsius or more. Our error ranges, as can be seen from the calibration curve, are much lower.</p><p><italic>4) The authors should apply appropriate statistical tests to the biological data in all cases where temperature appears to affect a characteristic, e.g., spike width, so that the reader is confident that the temperature change is large enough to measure valid Q10s</italic>.</p><p>As suggested, we have performed additional statistical tests. Tests of differences between warm and cold spike rates are now provided as a function of sound intensity (a corresponding table can be found in a supplement to <xref ref-type="fig" rid="fig1">Figure 1</xref>). Also, a rank sum test was used to test whether the Q10 values of the individual characteristics (spike saturation rate, etc) are significantly different from 1.0, 1.5, and 2.0. These data are also provided.</p><p><italic>Other issues</italic> <italic>to address:</italic></p><p>Reviewer #1:</p><p><italic>The section “Model-based inference of the auditory transduction function” was very difficult to follow. This reviewer is a computational neuroscientist but I am unfamiliar with reverse engineering techniques, and I was not given enough help in reasoning through the experiments and data as would be necessary for the general reader in neuroscience. I suggest that the authors expand this section and fully explain what they did, how they did it, and why they did it. The Methods section helps a bit but only very marginally and is very technically written. Think of the general reader here</italic>.</p><p>The corresponding paragraph was completely rewritten and we hope that it is now better understandable. Where appropriate, also Introduction and Results have been extended. The Methods section now provides more details on additional techniques used (like the charge separation measure and the genetic algorithm).</p><p>Reviewer #2:</p><p><italic>Like prior studies by Laughlin and others on the metabolic cost of neuronal signaling, the authors use Na flux as a proxy for ion pump activity and as their measure of metabolic cost during spiking and at rest. I have always been puzzled by this choice – why exclude the cost of other ions? I assume there are good reasons for this choice that I am simply not aware of, so I suggest that the authors include a comment on this question. This seems particularly relevant in light of the authors' finding that the properties of Na channels, more than those of other channels, influence energy efficiency in these model neurons. This result makes me wonder if the outcome would have been different (with other ion channels playing a bigger role in energy efficiency) if metabolic cost had been defined in a less Na-centric way</italic>.</p><p>We address this criticism and have now also performed the metabolic cost analysis based on potassium current flow. In addition, we use measures of charge separation (for spiking cost), which quantify the degree of overlap between sodium and potassium currents and are hence conceptually different from a cost estimated by pure current flow of one ion type. Nevertheless, also charge separation is biased towards one ion type, as it quantifies the fraction of the Na current that is not counterbalanced by a simultaneous potassium current. This is why we now characterize the “alternative scenario” as well, i.e. the amount of total potassium current that is not counterbalanced by a simultaneous Na current. Despite quantitative differences between the individual measures, temperature dependence of Na channel inactivation remains the main player in all cases and exerts the largest influence on metabolic cost (or energy efficiency). Besides, the main player for firing rate compensation (i.e., the temperature dependence of potassium channel kinetics, Q10(n)) has only little impact on the potassium-current-based metabolic cost.</p><p><italic>Another comment concerns the tests for robustness of their findings to the particular choice of model neuron that the authors describe in the paper. In the Results section we learn that the authors tested for robustness of their results by checking whether a relatively modest (20%) variation of parameters of the Connors-Stevens model used here changes the overall conclusions, and are assured that it does not. While this test for robustness is laudable, I was much more convinced that the findings are robust by a very short comment, hidden in the Methods section, in which the authors state that they also found temperature compensation of firing properties despite temperature dependence of ion channels in a structurally different Traub-Miles model neuron. I recommend that the authors consider giving this latter result a more prominent place in the paper, because it could potentially (since I don't know the details) make the case for generality of the results much stronger</italic>.</p><p>We have taken up this suggestion and now present the results for the Traub- Miles model in a supplemental figure (to <xref ref-type="fig" rid="fig2">Figure 2</xref>). For this model we only performed the (computationally more efficient) search for a minimal RMSD with a genetic algorithm, identifying the most temperature invariant temperature parameter set. The results resolve that also for this model a temperature compensation with RMSD values on the order of 0.35-0.60 can be achieved.</p><p>Reviewer #3:</p><p><italic>The work is novel, interesting and well presented. Though the linkage between the biological neurons and the models is quite tenuous, I have no problems with the computational aspects of the paper. My concerns are with the acquisition of the biological data, particularly with respect to temperature control and measurement. This is important because if the temperature change at the receptor ending is over-estimated then the Q10s will be under-estimated and there may not be an interesting biological phenomenon (the surprisingly low Q10) in need of explanation</italic>.</p><p>We have taken care to avoid an overestimation of the temperature change. Tissue temperature was derived from the calibration curve in such a way, that we explicitly favor an underestimation of the temperature change and hence bias our results towards higher Q10 values. The calibration curve is now included. In particular, temperature changes were estimated based on the temperature at the onset of a recording. During a 40-seconds-long recording, we cannot exclude that temperature further decreased and hence the effective temperature change was larger than assumed by our conservative approach. This way, however, an underestimation of Q10 values is excluded. For more details on the experimental procedures see responses below.</p><p><italic>The preparation was heated by placing it on a Peltier element i.e. a localized heat source underneath the locust. Heat conduction from that source will vary through the various tissues, cuticle and saline and I would expect that the preparation was not at a uniform temperature throughout. The GTF 300 thermal probe has, according to the manufacturer's website, a diameter of 1mm (assuming that it hadn't been modified) which is relatively large with respect to distances inside the thoracic/abdominal cavity. I wonder if the authors could provide more information in the Methods that might increase confidence that the temperature range reported and used to calculate Q10 was the range that the receptor ending actually experienced. For example, how was</italic> <italic>the temperature at the attachment site of the receptor neurons measured using the GTF 300 probe?</italic></p><p>The diameter of the insulated wire of the GTF 300 probe is 1mm but the actual measuring tip consists of two twisted wires (without insulation) with a diameter of 0.2mm each, with the welded tip of the probe having a total diameter of 0.30mm (see <ext-link ext-link-type="uri" xlink:href="https://greisinger.de/files/upload/en/produkte/kat/k13_127_EN_oP.pdf">https://greisinger.de/files/upload/en/produkte/kat/k13_127_EN_oP.pdf</ext-link>).</p><p>The measuring tip of the GTF 300 probe was placed in the saline-filled thoracic cavity, as close as possible to the tympanal membrane (less than 1mm distance between measuring tip and tympanum).</p><p><italic>How variable</italic> <italic>was the temperature at different sites in the preparation (tympanum, saline, ganglion)?</italic></p><p>Temperature at the measuring site next to the tympanum was not significantly different from the temperature at the ganglion (ca. 6-9mm distance between tympanum and ganglion, depending on the size of the locust; Wilcoxon rank sum test: Z= - 0.10, p=0.92); the whole preparation was well filled with ringer’s solution which helped to establish a constant temperature throughout the whole preparation. Within the time window used for the second recording (3-5.5 min after start of cooling), the mean temperature difference between tympanum and ganglion was 0.19°C. Please note that in order to change the Q10 of firing rate by 0.1 (e.g. from 1.5 to 1.6) a temperature deviation of more than 1 degree Celsius would be required for the mean spike rates recorded in the study.</p><p><italic>What did the calibration curve look like and was a calibration curve generated for every preparation that provided data or from other preparations; how consistent was</italic> <italic>it between preparations?</italic></p><p>The calibration curve (supplement to <xref ref-type="fig" rid="fig1">Figure 1</xref>) was generated using four separate preparations, repeating the cooling steps and measurements three times each. The curve was consistent between preparations; different preparations than those used for recording were taken to establish the calibration curve, because a direct measurement was not possible: First, parallel temperature measurements during electrophysiological recordings were not possible due to substantially increased noise and a high risk of tissue damage. Second, temperature measurements after recording would only have been possible in the dissected and hence strongly modified system (after preservation for staining-based cell identification).</p><p><italic>Action potential width was measured at the recording site in the metathoracic ganglion but it is being associated with</italic> <italic>firing frequency generated at the tympanum. Did these two sites experience the same temperature changes?</italic></p><p>Yes. Within the time window used for the second recording (3-5.5 min after start of cooling), the mean temperature difference between tympanum and ganglion was 0.19°C.</p><p><italic>Given that the density and diversity of conductances can be quite different at different locations of a neuron, do we know whether action potential parameters at these two</italic> <italic>sites are the same?</italic></p><p>Action potentials were measured at the same location at both temperatures. We assume that spike initiation happens at the same position at both temperatures and spikes are hence generated by the same set of conductances. Firing rates could in principle be affected by other conductances on the way from the initation site to the ganglion. However, as distances travelled are short (6-9mm), we would not expect a large effect in firing rate, even if conductances of different kinetics were present. In addition, those hypothetical conductances would be subject to the same temperature changes.</p><p><italic>The sample size of 9 neurons in 8 preparations is relatively small. I assume that each preparation provided at least one neuronal recording and one provided two, but this is not explicitly stated</italic>.</p><p>Yes, one of the preparations provided recordings from two neurons.</p><p><italic>According to</italic> <xref ref-type="fig" rid="fig1"><italic>Figure 1C</italic></xref><italic>, one or more of the neurons had a Q10 for spike rate at half max greater than 2.5 suggesting that these measures were quite variable</italic> <italic>. Did the authors perform any statistical comparisons to test significance?</italic></p><p>We now provide statistical tests. First, we test the original firing-rate data. We ask whether mean firing rates at the two temperatures are different, separately analyzed for each sound intensity level (supplement to <xref ref-type="fig" rid="fig1">Figure 1</xref>). These data show that differences only are significant at larger sound intensities. For lower intensities noise is too large to allow for a clear differentiation. This also indicates that the temperature dependence of the saturation-firing rate is more reliable than the rate estimated at half-maximum sound intensity. Second, we tested whether the Q10 values (presented in <xref ref-type="fig" rid="fig1">Figure 1C</xref>) are significantly different from 1.0, 1.5, and 2.0. Again, Q10 values of the half-maximum sound intensity rates are statistically weaker than the saturation-rate based Q10 values. The latter are significantly different from 1.0 as well as 2.0. For the half-maximum intensity values statistical significance is (strictly) only given for difference from 1.0, but not 2.0. These effects arise from two outliers, though, which is now visible in the graphical representation of the data in <xref ref-type="fig" rid="fig1">Figure 1C</xref>.</p><p><italic>It is unsurprising to me that metabolic cost was defined as Na load and then the computational analysis revealed that parameters of the Na conductance had the greatest effect on Q10 of metabolic cost. The authors might comment on this</italic>.</p><p>We kindly refer to our reply to reviewer 2 above, who made a similar comment. In short, we implemented three additional measures (potassium-current based cost and two measures of charge separation). Despite quantitative differences between the individual measures, temperature dependence of Na channel inactivation remained the main player in all cases and exerted the largest influence on metabolic cost (or energy efficiency). Besides, the main player for firing rate compensation (i.e., the temperature dependence of potassium channel kinetics, Q10(n)) had only little impact on the potassium-current-based metabolic cost.</p></body></sub-article></article> |