elife02758.xml

<?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">02758</article-id><article-id pub-id-type="doi">10.7554/eLife.02758</article-id><article-categories><subj-group subj-group-type="display-channel"><subject>Research article</subject></subj-group><subj-group subj-group-type="heading"><subject>Cell biology</subject></subj-group><subj-group subj-group-type="heading"><subject>Microbiology and infectious disease</subject></subj-group></article-categories><title-group><article-title>Evidence for a DNA-relay mechanism in ParABS-mediated chromosome segregation</article-title></title-group><contrib-group><contrib contrib-type="author" id="author-12186"><name><surname>Lim</surname><given-names>Hoong Chuin</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/><xref ref-type="other" rid="par-4"/><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf2"/></contrib><contrib contrib-type="author" id="author-12187"><name><surname>Surovtsev</surname><given-names>Ivan Vladimirovich</given-names></name><xref ref-type="aff" rid="aff2"/><xref ref-type="aff" rid="aff3"/><xref ref-type="aff" rid="aff5"/><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf2"/></contrib><contrib contrib-type="author" id="author-12189"><name><surname>Beltran</surname><given-names>Bruno Gabriel</given-names></name><xref ref-type="aff" rid="aff4"/><xref ref-type="aff" rid="aff5"/><xref ref-type="other" rid="par-6"/><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf2"/></contrib><contrib contrib-type="author" id="author-12190"><name><surname>Huang</surname><given-names>Fang</given-names></name><xref ref-type="aff" rid="aff6"/><xref ref-type="other" rid="par-5"/><xref ref-type="fn" rid="con4"/><xref ref-type="fn" rid="conf2"/></contrib><contrib contrib-type="author" id="author-2353"><name><surname>Bewersdorf</surname><given-names>Jörg</given-names></name><xref ref-type="aff" rid="aff6"/><xref ref-type="aff" rid="aff7"/><xref ref-type="other" rid="par-3"/><xref ref-type="fn" rid="con5"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes" id="author-4254"><name><surname>Jacobs-Wagner</surname><given-names>Christine</given-names></name><xref ref-type="aff" rid="aff2"/><xref ref-type="aff" rid="aff3"/><xref ref-type="aff" rid="aff5"/><xref ref-type="aff" rid="aff8"/><xref ref-type="corresp" rid="cor1">*</xref><xref ref-type="other" rid="par-1"/><xref ref-type="other" rid="par-2"/><xref ref-type="fn" rid="con6"/><xref ref-type="fn" rid="conf2"/></contrib><aff id="aff1"><institution content-type="dept">Department of Molecular Biophysics and Biochemistry</institution>, <institution>Yale University</institution>, <addr-line><named-content content-type="city">New Haven</named-content></addr-line>, <country>United States</country></aff><aff id="aff2"><institution>Microbial Diversity Institute, Yale University</institution>, <addr-line><named-content content-type="city">West Haven</named-content></addr-line>, <country>United States</country></aff><aff id="aff3"><institution content-type="dept">Department of Molecular, Cellular and Developmental Biology</institution>, <institution>Yale University</institution>, <addr-line><named-content content-type="city">New Haven</named-content></addr-line>, <country>United States</country></aff><aff id="aff4"><institution content-type="dept">Department of Mathematics</institution>, <institution>Louisiana State University</institution>, <addr-line><named-content content-type="city">Baton Rouge</named-content></addr-line>, <country>United States</country></aff><aff id="aff5"><institution>Howard Hughes Medical Institute, Yale University</institution>, <addr-line><named-content content-type="city">New Haven</named-content></addr-line>, <country>United States</country></aff><aff id="aff6"><institution content-type="dept">Department of Cell Biology</institution>, <institution>Yale School of Medicine</institution>, <addr-line><named-content content-type="city">New Haven</named-content></addr-line>, <country>United States</country></aff><aff id="aff7"><institution content-type="dept">Department of Biomedical Engineering</institution>, <institution>Yale University</institution>, <addr-line><named-content content-type="city">New Haven</named-content></addr-line>, <country>United States</country></aff><aff id="aff8"><institution content-type="dept">Department of Microbial Pathogenesis</institution>, <institution>Yale School of Medicine</institution>, <addr-line><named-content content-type="city">New Haven</named-content></addr-line>, <country>United States</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Balasubramanian</surname><given-names>Mohan</given-names></name><role>Reviewing editor</role><aff><institution>University of Warwick</institution>, <country>United Kingdom</country></aff></contrib></contrib-group><author-notes><corresp id="cor1"><label>*</label>For correspondence: <email>christine.jacobs-wagner@yale.edu</email></corresp></author-notes><pub-date date-type="pub" publication-format="electronic"><day>23</day><month>05</month><year>2014</year></pub-date><pub-date pub-type="collection"><year>2014</year></pub-date><volume>3</volume><elocation-id>e02758</elocation-id><history><date date-type="received"><day>11</day><month>03</month><year>2014</year></date><date date-type="accepted"><day>16</day><month>05</month><year>2014</year></date></history><permissions><copyright-statement>© 2014, Lim et al</copyright-statement><copyright-year>2014</copyright-year><copyright-holder>Lim 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="elife02758.pdf"/><related-article ext-link-type="doi" id="ra1" related-article-type="commentary" xlink:href="10.7554/eLife.03435"/><abstract><object-id pub-id-type="doi">10.7554/eLife.02758.001</object-id><p>The widely conserved ParABS system plays a major role in bacterial chromosome segregation. How the components of this system work together to generate translocation force and directional motion remains uncertain. Here, we combine biochemical approaches, quantitative imaging and mathematical modeling to examine the mechanism by which ParA drives the translocation of the ParB/<italic>parS</italic> partition complex in <italic>Caulobacter crescentus</italic>. Our experiments, together with simulations grounded on experimentally-determined biochemical and cellular parameters, suggest a novel 'DNA-relay' mechanism in which the chromosome plays a mechanical function. In this model, DNA-bound ParA-ATP dimers serve as transient tethers that harness the elastic dynamics of the chromosome to relay the partition complex from one DNA region to another across a ParA-ATP dimer gradient. Since ParA-like proteins are implicated in the partitioning of various cytoplasmic cargos, the conservation of their DNA-binding activity suggests that the DNA-relay mechanism may be a general form of intracellular transport in bacteria.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.001">http://dx.doi.org/10.7554/eLife.02758.001</ext-link></p></abstract><abstract abstract-type="executive-summary"><object-id pub-id-type="doi">10.7554/eLife.02758.002</object-id><title>eLife digest</title><p>DNA molecules exist in cells as tightly packed structures called chromosomes. During the cell cycle, chromosomes duplicate, and the two copies separate, ready to end up in two separate daughter cells. The process of chromosome separation in cells of higher organisms such as animals and plants is well understood. A protein-based structure called the spindle apparatus guides the separating chromosomes to different ends of the dividing cell. However, how chromosome separation occurs in bacteria is not well understood despite its importance in bacterial multiplication.</p><p>The nucleoprotein complex ParABS is critical for separating chromosomes in bacteria. The complex is made up of three parts: <italic>parS</italic>, a stretch of DNA located at the point where chromosome duplication begins; and two proteins called ParB and ParA. While the molecular players are known, how they work together to separate chromosomes is under debate. One popular suggestion is that ParA forms a spindle-like structure. Alternatively, a diffusion-based mechanism has been proposed, where a gradient of ParA molecules bound to the chromosome interacts with a <italic>parS</italic>/ParB complex, directing the diffusion of the complex.</p><p>Lim et al. used quantitative microscopy to observe the movement of the <italic>parS</italic>/ParB complex and the spatial distribution of the ParA proteins in a model bacterium. The results were inconsistent with the presence of a spindle-like structure in the cells. A mathematical model describing chromosome movement—based on the number and activity of ParA and ParB found in live cells—also failed to fit with either the spindle or the diffusion theory.</p><p>Instead, Lim et al. propose a new model, based on the discovery that chromosomes are elastic. In this ‘DNA-relay model’, ParA is bound to DNA. When ParB intermittently binds to ParA, it usually catches the ParA-DNA complex when the complex is elastically stretched. The elasticity of the chromosome itself then makes the <italic>parS</italic>/ParB complex move in the direction where the most ParA molecules are still bound to the chromosome. Lim et al. suggest that similar elastic mechanisms could also be behind more general intracellular transport in bacteria.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.002">http://dx.doi.org/10.7554/eLife.02758.002</ext-link></p></abstract><kwd-group kwd-group-type="author-keywords"><title>Author keywords</title><kwd><italic>Caulobacter crescentus</italic></kwd><kwd>Par system</kwd><kwd>DNA partitioning</kwd><kwd>chromosome dynamics</kwd><kwd>intracellular transport</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-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>R01 GM065835</award-id><principal-award-recipient><name><surname>Jacobs-Wagner</surname><given-names>Christine</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/10.13039/100000011</institution-id><institution>Howard Hughes Medical Institute</institution></institution-wrap></funding-source><principal-award-recipient><name><surname>Jacobs-Wagner</surname><given-names>Christine</given-names></name></principal-award-recipient></award-group><award-group id="par-3"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100004440</institution-id><institution>Wellcome Trust</institution></institution-wrap></funding-source><award-id>095927/A/11/Z</award-id><principal-award-recipient><name><surname>Bewersdorf</surname><given-names>Jörg</given-names></name></principal-award-recipient></award-group><award-group id="par-4"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100005326</institution-id><institution>Yale University</institution></institution-wrap></funding-source><award-id>Edward L. Tatum Fellowship</award-id><principal-award-recipient><name><surname>Lim</surname><given-names>Hoong Chuin</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/10.13039/100006698</institution-id><institution>Child Study Center, Yale School of Medicine (Yale Child Study Center)</institution></institution-wrap></funding-source><award-id>James Hudson Brown- Alexander Brown Coxe Postdoctoral Fellowship</award-id><principal-award-recipient><name><surname>Huang</surname><given-names>Fang</given-names></name></principal-award-recipient></award-group><award-group id="par-6"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000011</institution-id><institution>Howard Hughes Medical Institute (HHMI)</institution></institution-wrap></funding-source><award-id>EXROP Scholarship</award-id><principal-award-recipient><name><surname>Beltran</surname><given-names>Bruno Gabriel</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>In vitro, in vivo and in silico evidence suggests that bacteria exploit intrinsic chromosomal fluctuations to achieve intracellular transport.</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>Perpetuation of life depends on the faithful segregation of genetic material upon division, such that each progeny inherits a full complement of the parental genome. In eukaryotic cells, chromosome segregation is driven by the microtubule-based mitotic spindle in a process for which there is considerable mechanistic understanding (<xref ref-type="bibr" rid="bib63">McIntosh et al., 2012</xref>). In contrast, much less is known in bacteria. Yet a robust segregation mechanism must be in place to keep up with the fast-paced proliferation of bacterial cells. Such segregation mechanism is also critical for maintaining the precise organization of the chromosome and the reproducible positioning of gene loci over generations (<xref ref-type="bibr" rid="bib72">Reyes-Lamothe et al., 2012</xref>; <xref ref-type="bibr" rid="bib98">Wang et al., 2013</xref>).</p><p>Recent studies on various bacteria have shown that chromosome segregation is a multi-step process that initiates with the segregation of the duplicated chromosomal origin regions shortly following their replication (<xref ref-type="bibr" rid="bib84">Shebelut et al., 2010</xref>; <xref ref-type="bibr" rid="bib98">Wang et al., 2013</xref>). How the newly replicated chromosomal origin regions segregate remains poorly understood. In recent years, the ParABS systems, which are conserved among most bacterial species (<xref ref-type="bibr" rid="bib59">Livny et al., 2007</xref>), have been recognized as important active transport systems of chromosomal origin regions in diverse bacteria (<xref ref-type="bibr" rid="bib65">Mohl and Gober, 1997</xref>; <xref ref-type="bibr" rid="bib48">Kim et al., 2000</xref>; <xref ref-type="bibr" rid="bib30">Godfrin-Estevenon et al., 2002</xref>; <xref ref-type="bibr" rid="bib55">Lewis et al., 2002</xref>; <xref ref-type="bibr" rid="bib28">Fogel and Waldor, 2006</xref>; <xref ref-type="bibr" rid="bib78">Saint-Dic et al., 2006</xref>; <xref ref-type="bibr" rid="bib51">Lasocki et al., 2007</xref>; <xref ref-type="bibr" rid="bib43">Jakimowicz et al., 2007a</xref>, <xref ref-type="bibr" rid="bib44">2007b</xref>; <xref ref-type="bibr" rid="bib91">Toro et al., 2008</xref>; <xref ref-type="bibr" rid="bib8">Bartosik et al., 2009</xref>; <xref ref-type="bibr" rid="bib19">Donovan et al., 2010</xref>; <xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>; <xref ref-type="bibr" rid="bib84">Shebelut et al., 2010</xref>; <xref ref-type="bibr" rid="bib32">Harms et al., 2013</xref>; <xref ref-type="bibr" rid="bib41">Iniesta, 2014</xref>)<italic>.</italic> ParABS systems, first identified on plasmids for their role in stable plasmid inheritance (<xref ref-type="bibr" rid="bib3">Austin and Abeles, 1983</xref>), consist of three components: the DNA sequence <italic>parS</italic>, the DNA-binding protein ParB, and the deviant Walker A-type ATPase ParA (<xref ref-type="bibr" rid="bib22">Ebersbach and Gerdes, 2005</xref>). ParB specifically recognizes <italic>parS</italic> sequences, which are typically found near the origin of replication of most bacterial chromosomes (<xref ref-type="bibr" rid="bib59">Livny et al., 2007</xref>). Upon binding to <italic>parS</italic>, ParB is thought to spread on flanking sequences to form the so-called ParB/<italic>parS</italic> partition complex (<xref ref-type="bibr" rid="bib76">Rodionov et al., 1999</xref>; <xref ref-type="bibr" rid="bib68">Murray et al., 2006</xref>; <xref ref-type="bibr" rid="bib12">Breier and Grossman, 2007</xref>). ParA dimerizes upon ATP binding, which in turn promotes nonspecific DNA binding (<xref ref-type="bibr" rid="bib54">Leonard et al., 2005</xref>; <xref ref-type="bibr" rid="bib34">Hester and Lutkenhaus, 2007</xref>). Various in vitro studies have also observed that ParA-ATP dimers can further assemble into filaments (<xref ref-type="bibr" rid="bib7">Barilla et al., 2005</xref>; <xref ref-type="bibr" rid="bib23">Ebersbach et al., 2006</xref>; <xref ref-type="bibr" rid="bib6">Barilla et al., 2007</xref>; <xref ref-type="bibr" rid="bib60">Machon et al., 2007</xref>; <xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>). By itself, ParA has a weak ATPase activity but this activity is generally stimulated by an interaction with ParB (<xref ref-type="bibr" rid="bib17">Davis et al., 1992</xref>; <xref ref-type="bibr" rid="bib20">Easter and Gober, 2002</xref>; <xref ref-type="bibr" rid="bib54">Leonard et al., 2005</xref>; <xref ref-type="bibr" rid="bib6">Barilla et al., 2007</xref>; <xref ref-type="bibr" rid="bib1">Ah-Seng et al., 2009</xref>; <xref ref-type="bibr" rid="bib82">Scholefield et al., 2011</xref>). While these biochemical properties have been documented for many ParABS systems, how they give rise to directional transport remains a hot topic of debate (<xref ref-type="bibr" rid="bib36">Howard and Gerdes, 2010</xref>; <xref ref-type="bibr" rid="bib89">Szardenings et al., 2011</xref>; <xref ref-type="bibr" rid="bib94">Vecchiarelli et al., 2012</xref>).</p><p>ParABS-mediated chromosomal segregation has probably been most studied in <italic>Caulobacter crescentus</italic> where ParA and ParB are essential for viability (<xref ref-type="bibr" rid="bib65">Mohl and Gober, 1997</xref>). In this bacterium, the single, densely packed circular chromosome spans the entire cell and is spatially arranged such that the ParB/<italic>parS</italic> partition complex and the nearby replication origin are located at the ‘old’ cell pole while the replication terminus is localized at the opposite, ‘new’ pole (<xref ref-type="bibr" rid="bib46">Jensen and Shapiro, 1999</xref>). Epifluorescence microscopy studies in live cells have shown that prior to DNA replication, ParA forms a cloud-like localization pattern that spans from the new pole to about midcell (<xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>; <xref ref-type="bibr" rid="bib84">Shebelut et al., 2010</xref>). Replication of the origin region results in two physically separated copies of the ParB/<italic>parS</italic> complex. The ParB/<italic>parS</italic> complex closer to the old pole remains there while the other one, upon contact with the edge of the ParA cloud, migrates toward the new pole in the wake of the receding ParA cloud, as if retraction of ParA was ‘pulling’ the partition complex (<xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>; <xref ref-type="bibr" rid="bib84">Shebelut et al., 2010</xref>). This correlated spatial dynamics between ParA and ParB/<italic>parS</italic> is a common characteristic of ParABS systems involved in chromosome or plasmid partitioning (<xref ref-type="bibr" rid="bib23">Ebersbach et al., 2006</xref>; <xref ref-type="bibr" rid="bib28">Fogel and Waldor, 2006</xref>; <xref ref-type="bibr" rid="bib33">Hatano et al., 2007</xref>; <xref ref-type="bibr" rid="bib74">Ringgaard et al., 2009</xref>; <xref ref-type="bibr" rid="bib32">Harms et al., 2013</xref>; <xref ref-type="bibr" rid="bib41">Iniesta, 2014</xref>).</p><p>The physical mechanism that underlies this correlated dynamics is generally thought to be analogous to the eukaryotic spindle-based mechanism that segregates chromosomes during mitosis (<xref ref-type="bibr" rid="bib29">Gerdes et al., 2010</xref>). According to this popular spindle-like model, ParA polymerizes into a thin filament bundle upon ATP binding. Depolymerization of ParA filaments through ParB-induced ATP hydrolysis then pulls the ParB/<italic>parS</italic> complex and its associated chromosomal origin region. However, the significance of ParA DNA-binding activity remains unclear, even though this activity is essential for the segregation process based on mutational analysis (<xref ref-type="bibr" rid="bib34">Hester and Lutkenhaus, 2007</xref>; <xref ref-type="bibr" rid="bib15">Castaing et al., 2008</xref>; <xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>). Recent in vitro studies have proposed an alternative ‘Brownian-ratchet’ mechanism for the partitioning of P1 and F plasmids (<xref ref-type="bibr" rid="bib92">Vecchiarelli et al., 2010</xref>; <xref ref-type="bibr" rid="bib94">Vecchiarelli et al., 2012</xref>, <xref ref-type="bibr" rid="bib93">2013</xref>, <xref ref-type="bibr" rid="bib95">2014</xref>; <xref ref-type="bibr" rid="bib40">Hwang et al., 2013</xref>). However, it is unclear whether the proposed mechanism can support plasmid translocation under physiological conditions.</p><p>Apart from chromosome and plasmid segregation, ParA-like proteins have been implicated in the positioning of other cellular components such as metabolic microcompartments and cytosolic chemotaxis clusters (<xref ref-type="bibr" rid="bib79">Savage et al., 2010</xref>; <xref ref-type="bibr" rid="bib73">Ringgaard et al., 2011</xref>; <xref ref-type="bibr" rid="bib75">Roberts et al., 2012</xref>), highlighting the versatility of the ParABS systems. Interestingly, while the chromosomally encoded <italic>Bacillus subtilis</italic> ParA (Soj) and ParB (Spo0J) orthologs have been implicated in chromosome partitioning in sporulating cells (<xref ref-type="bibr" rid="bib42">Ireton et al., 1994</xref>; <xref ref-type="bibr" rid="bib83">Sharpe and Errington, 1996</xref>; <xref ref-type="bibr" rid="bib102">Wu and Errington, 2003</xref>; <xref ref-type="bibr" rid="bib53">Lee and Grossman, 2006</xref>), they are involved in the regulation of DNA replication in vegetative cells (<xref ref-type="bibr" rid="bib67">Murray and Errington, 2008</xref>). <italic>B. subtilis</italic> Spo0J binds to <italic>parS</italic> sites proximal to the origin of replication similar to ParB orthologs involved in chromosome segregation (<xref ref-type="bibr" rid="bib58">Lin et al., 1997</xref>; <xref ref-type="bibr" rid="bib57">Lin and Grossman, 1998</xref>; <xref ref-type="bibr" rid="bib68">Murray et al., 2006</xref>). Like ParA proteins involved in cargo partitioning, Soj forms ATP-dependent dimers that bind DNA in vitro (<xref ref-type="bibr" rid="bib82">Scholefield et al., 2011</xref>) and display nucleoid-associated localization in cells lacking Spo0J (<xref ref-type="bibr" rid="bib67">Murray and Errington, 2008</xref>). However, in wild-type cells, Soj mostly displays a diffuse distribution in the <italic>B. subtilis</italic> cytoplasm (with a weak accumulation at the Spo0J/<italic>parS</italic> location) (<xref ref-type="bibr" rid="bib67">Murray and Errington, 2008</xref>). This pattern is in stark contrast to the cloud-like localization pattern characteristic of ParA orthologs dedicated to cargo transport. Why ParA localization in <italic>B. subtilis</italic> differs remains enigmatic.</p><p>In this study, we combined biochemical and cell biological experiments with computational modeling to investigate how the ParABS system drives chromosomal segregation in <italic>C. crescentus</italic>. Our findings are inconsistent with a spindle-like or Brownian ratchet mechanism. Rather, our experiments and simulations support a novel physical mechanism in which chromosome dynamics and the rate of ATP hydrolysis are critical for efficient and robust ParA-dependent translocation of the ParB/<italic>parS</italic> complex. Our data also suggest that the difference in localization and possibly function between <italic>B. subtilis</italic> Soj and <italic>C. crescentus</italic> ParA can be explained by a biochemical difference in ParB's ability to stimulate ParA ATPase activity.</p></sec><sec id="s2" sec-type="results"><title>Results</title><p>Since the behavior of a biological system is defined by the biochemical properties of its components inside cells, our first aim was to determine the relevant biochemical properties of <italic>C. crescentus</italic> ParA and ParB proteins in vitro and to correlate these properties with the in vivo conditions. Our ultimate goal was to obtain a mechanistic understanding in the form of a mathematical model.</p><sec id="s2-1"><title>ATP-dependent dimerization of ParA</title><p>For the in vitro studies, we purified recombinant <italic>C. crescentus</italic> ParA and ParB proteins from the soluble fraction of <italic>Escherichia coli</italic> lysates (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref>). Obtaining stable preparations of chromosomal ParA proteins is notoriously difficult because of the tendency of these proteins to precipitate (<xref ref-type="bibr" rid="bib36">Howard and Gerdes, 2010</xref>). Through troubleshooting, we found that addition of Mg-ATP to all buffers (including the cell lysis and storage buffers) as well as potassium glutamate (150 mM) after chromatography was crucial to maintain long-term stability of purified <italic>C. crescentus</italic> ParA. Such preparations of ParA were used to investigate the oligomerization state of the protein upon ATP binding by size exclusion chromatography. Prior to chromatography, Mg-ATP was removed from a ParA aliquot via incubation with EDTA followed by buffer exchange ('Materials and methods'). The resulting sample was then split into two samples: one sample remained without ATP, while Mg-ATP was added to the other sample. In the absence of ATP, ParA eluted from the column as a single peak at an elution volume corresponding to the ParA monomer (∼28 kDa) (<xref ref-type="fig" rid="fig1">Figure 1A</xref>). In the presence of Mg-ATP (2.5 mM), ParA eluted earlier, at an elution volume consistent with a dimeric form (∼56 kDa) (<xref ref-type="fig" rid="fig1">Figure 1A</xref>). Thus, <italic>C. crescentus</italic> ParA dimerizes in the presence of ATP concentrations expected to be found inside bacterial cells (<xref ref-type="bibr" rid="bib9">Bennett et al., 2009</xref>).<fig-group><fig id="fig1" position="float"><object-id pub-id-type="doi">10.7554/eLife.02758.003</object-id><label>Figure 1.</label><caption><title>Biochemical analysis of ParA ATPase cycle.</title><p>(<bold>A</bold>) Gel filtration analysis of purified wild-type ParA (<italic>left</italic>) and DNA-binding deficient mutant ParA<sub>R195E</sub> (<italic>right</italic>) in the presence and absence of ATP. (<bold>B</bold>) Specific activity of ParA (concentration fixed at 6 µM) measured as a function of DNA concentration (0–2.0 mg/ml). Michaelis–Menten equation fit to the data (black) gives <italic>K</italic><sub><italic>DNA</italic></sub> = 0.15 mg/ml. (<bold>C</bold>) Effects of DNA and ParB on ATPase activities of ParA (cyan) and ParA<sub>R195E</sub> (yellow). (<bold>D</bold>) ADP production rate as a function of ParA concentration measured with fixed ATP (2.5 mM) and DNA (1.5 mg/ml) concentrations. Linear fit to the data (black line) gives <italic>k</italic><sub>cat</sub> = 5.8 hr<sup>−1</sup>. (<bold>E</bold>) Dependence of ATPase activity of ParA upon ATP concentration measured with fixed ParA (10 µM) and DNA (1.5 mg/ml) concentrations. Fitting the Michaelis–Menten equation (black line) gives <italic>k</italic><sub>cat</sub> = 5.9 hr<sup>−1</sup> and <italic>K</italic><sub><italic>M</italic></sub> = 150 µM. (<bold>F</bold>) Dependence of ParA (3 µM) ATPase activity on ParB concentrations. Michaelis–Menten equation fit to the data (black line) gives <italic>k</italic><sub>cat</sub> = 120 hr<sup>−1</sup> and <italic>K</italic><sub><italic>M</italic></sub> = 80 µM. (<bold>G</bold>) Model of ParA ATPase cycle. ATP-binding promotes ParA dimerization. Upon binding DNA, ParA-ATP dimers presumably adopt an ATP-hydrolysis competent state. A high concentration of ParB is required to stimulate ATP hydrolysis of DNA-associated ParA-ATP dimers. The cycle reinitiates through nucleotide exchange. SDS-PAGE images showing the purity of the purified protein preparations and the results from experiments comparing the stimulatory effects of wild-type (WT) ParB and mutant ParB<sub>L12A</sub> on ParA ATPase activity are presented in <xref ref-type="fig" rid="fig1s1 fig1s2">Figure 1—figure supplements 1 and 2</xref>. Experiments performed to correlate the biochemical activities measured in vitro with in vivo conditions are presented in <xref ref-type="fig" rid="fig1s3 fig1s4 fig1s5 fig1s6 fig1s7 fig1s8">Figure 1—figure supplements 3–8</xref>.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.003">http://dx.doi.org/10.7554/eLife.02758.003</ext-link></p></caption><graphic xlink:href="elife02758f001"/></fig><fig id="fig1s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.004</object-id><label>Figure 1—figure supplement 1.</label><caption><title>SDS-PAGE analysis of purified protein preparations used in this study.</title><p>(<bold>A</bold>) ParA, (<bold>B</bold>) ParA<sub>R195E</sub>, (<bold>C</bold>) ParB-His6, (<bold>D</bold>) ParB<sub>L12A</sub>-His6, and (<bold>E</bold>) ParA<sub>G16V</sub>-YFP. Approximately 5–15 µg of proteins were loaded in each lane.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.004">http://dx.doi.org/10.7554/eLife.02758.004</ext-link></p></caption><graphic xlink:href="elife02758fs001"/></fig><fig id="fig1s2" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.005</object-id><label>Figure 1—figure supplement 2.</label><caption><title>L12A mutation, which prevents ParA–ParB interaction, severely compromises ParB ability to activate ParA ATPase activity.</title><p>ATPase rates were measured from reactions containing 3 µM ParA and 1.5 mg/ml salmon sperm DNA in the absence or presence of 90 µM of either wild-type ParB or ParB<sub>L12A</sub>. The measured rates were compared to the rate of the reaction lacking ParB. Error bars represent the standard deviations (SD) of results measured in duplicates.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.005">http://dx.doi.org/10.7554/eLife.02758.005</ext-link></p></caption><graphic xlink:href="elife02758fs002"/></fig><fig id="fig1s3" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.006</object-id><label>Figure 1—figure supplement 3.</label><caption><title>Measurement of GFP-ParB distribution at the subcellular level.</title><p>(<bold>A</bold>) Representative fluorescence image showing autofluorescence in wild-type (CB15N) cells and subcellular distribution of GFP-ParB fluorescence in MT174 cells, which produce GFP-ParB from the native <italic>parB</italic> promoter on the chromosome as the only ParB copy. (<bold>B</bold>) Single-cell total fluorescence and cell areas were quantified using MicrobeTracker and a histogram of normalized fluorescence (total fluorescence divided by cell area) is shown. The two-peak distribution was fit by a bimodal Gaussian (black), representing fluorescence detected in two populations of cells: wild-type (magenta) and GFP-ParB-producing cells (cyan). The mean of the magenta curve was designated as the mean normalized autofluorescence (AF<sub>mean</sub>), which was used for background subtraction. (<bold>C</bold>) Histogram showing the fraction of GFP-ParB associated with <italic>parS</italic> in single cells. The experimental distribution (grey) was fitted with a Gaussian function (dashed black curve), giving an average of 80% ParB molecules associated with the partition complex. (<bold>D</bold>) Western blot of a lysate made from an MT174 culture using an anti-GFP monoclonal antibody (JL-8) or an anti-ParB polyclonal antibody (data not shown). GFP-ParB and a degradation fragment were detected. (<bold>E</bold>) The fraction of GFP-ParB fluorescence associated with <italic>parS</italic> stays constant as a function of cell length. Single-cell raw data (grey circles) and average fraction GFP-ParB fluorescence associated with <italic>parS</italic> (black circles) ± SD across 0.25 μm intervals are shown. (<bold>F</bold>) Subcellular volume occupied by a ParB/<italic>parS</italic> complex as determined by PALM microscopy. mEos3.2-ParB synthesis in CJW4978 cells was induced with 0.03% xylose for 1 hr in M2G before imaging using PALM. Fluorescent emitters within six polar partition complexes were analyzed. The histogram was fitted with a Gaussian function with σ = 39 nm (solid line). Radial distribution of mEos3.2-ParB from the foci were then combined and plotted as a histogram (<italic>n</italic> = 440 localizations). This means that 95% of the molecules were localized within 78 nm (2σ) from the center of the spot. We used 78 nm as the radius of the spherical volume occupied by ParB dimers within a partitioning complex. Such a sphere occupied a volume of 2 × 10<sup>−3</sup> fL.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.006">http://dx.doi.org/10.7554/eLife.02758.006</ext-link></p></caption><graphic xlink:href="elife02758fs003"/></fig><fig id="fig1s4" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.007</object-id><label>Figure 1—figure supplement 4.</label><caption><title>Quantification of ParB and ParA abundance in cell lysates by quantitative Western blotting.</title><p>(<bold>A</bold>) <italic>Top</italic>, a Western blot of a wild-type swarmer cell lysate (CB15N producing endogenous ParB) and indicated amounts of purified ParB-His6 using a polyclonal antibody against ParB. <italic>Bottom</italic>, the optical densities (OD) of the bands corresponding to ParB-His6 standards were quantified (black circles) and were fit by a linear function (black line). The amount of ParB in the cell lysate (red circle) was calculated from the calibration. This measurement was repeated twice. The number of ParB per cell was calculated using this formula: <inline-formula><mml:math id="inf3"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>B</mml:mi><mml:mo> </mml:mo><mml:mi>a</mml:mi><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mo> </mml:mo><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mo> </mml:mo><mml:mi>l</mml:mi><mml:mi>y</mml:mi><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mo>×</mml:mo><mml:mi>A</mml:mi><mml:mi>v</mml:mi><mml:mi>o</mml:mi><mml:mi>g</mml:mi><mml:mi>a</mml:mi><mml:mi>d</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mo> </mml:mo><mml:mi>n</mml:mi><mml:mi>u</mml:mi><mml:mi>m</mml:mi><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>B</mml:mi><mml:mo> </mml:mo><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>u</mml:mi><mml:mi>l</mml:mi><mml:mi>r</mml:mi><mml:mo> </mml:mo><mml:mi>w</mml:mi><mml:mi>e</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>h</mml:mi><mml:mi>t</mml:mi><mml:mo>×</mml:mo><mml:mo>#</mml:mo><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>l</mml:mi><mml:mi>l</mml:mi><mml:mi>s</mml:mi><mml:mo> </mml:mo><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mo> </mml:mo><mml:mi>l</mml:mi><mml:mi>y</mml:mi><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mn>720</mml:mn><mml:mo>±</mml:mo><mml:mn>80</mml:mn></mml:mrow></mml:math></inline-formula> ParB molecules per cell. (<bold>B</bold>) <italic>Top</italic>, a Western blot of a swarmer cell lysate of CJW3010 strain (in which <italic>parA-yfp</italic> replaces <italic>parA</italic> at the native location in the chromosome) and indicated amounts of purified ParA<sub>G16V</sub>-YFP-His6 using a monoclonal antibody against GFP (JL-8). <italic>Bottom</italic>, the ODs of the bands corresponding to ParA<sub>G16V</sub>-YFP-His6 standards were quantified (black circles) and fit with a linear function to create a calibration curve (black line). Red circle represents the calculated amount of ParA-YFP in the cell lysate. This measurement was repeated three times. The number of ParA-YFP per cell was calculated using the formula <inline-formula><mml:math id="inf4"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>A</mml:mi><mml:mo>−</mml:mo><mml:mi>Y</mml:mi><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo> </mml:mo><mml:mi>a</mml:mi><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mo> </mml:mo><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mo> </mml:mo><mml:mi>l</mml:mi><mml:mi>y</mml:mi><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mo>×</mml:mo><mml:mi>A</mml:mi><mml:mi>v</mml:mi><mml:mi>o</mml:mi><mml:mi>g</mml:mi><mml:mi>a</mml:mi><mml:mi>d</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mo> </mml:mo><mml:mi>n</mml:mi><mml:mi>u</mml:mi><mml:mi>m</mml:mi><mml:mi>b</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>A</mml:mi><mml:mo>−</mml:mo><mml:mi>Y</mml:mi><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo> </mml:mo><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>u</mml:mi><mml:mi>l</mml:mi><mml:mi>r</mml:mi><mml:mo> </mml:mo><mml:mi>w</mml:mi><mml:mi>e</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>h</mml:mi><mml:mi>t</mml:mi><mml:mo>×</mml:mo><mml:mo>#</mml:mo><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>l</mml:mi><mml:mi>l</mml:mi><mml:mi>s</mml:mi><mml:mo> </mml:mo><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mo> </mml:mo><mml:mi>l</mml:mi><mml:mi>y</mml:mi><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mn>170</mml:mn><mml:mo>±</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></inline-formula> ParA-YFP molecules per cell.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.007">http://dx.doi.org/10.7554/eLife.02758.007</ext-link></p></caption><graphic xlink:href="elife02758fs004"/></fig><fig id="fig1s5" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.008</object-id><label>Figure 1—figure supplement 5.</label><caption><title>His<sub>6</sub>-ParB forms a dimer in solution.</title><p>Purified His6-ParB was subjected to HPLC size exclusion chromatography (SEC) coupled with UV, on-line laser light scattering (LS) and refractive index (RI) detectors (SEC-UV/LS/RI) to measure its absolute MW. The dashed lines indicate the elution profile of His6-ParB from an RI detector while the dots are MW calculated from LS measurements at 1-s intervals. The MW measurement showed an average MW of 69 kDa, which is consistent with His6-ParB (monomeric MW = 34 kDa) forming a dimer in solution under this experimental condition.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.008">http://dx.doi.org/10.7554/eLife.02758.008</ext-link></p></caption><graphic xlink:href="elife02758fs005"/></fig><fig id="fig1s6" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.009</object-id><label>Figure 1—figure supplement 6.</label><caption><title>Fluorescence-based quantification of ParA-YFP abundance in <italic>C. crescentus</italic> cells.</title><p>Purified ParA<sub>G16V</sub>-YFP-His6 molecules were immobilized on a poly-Lysine-coated cover slip and imaged by stream acquisition using 2-s integration time. ParA<sub>G16V</sub>-YFP-His6 molecules were observed as immobile diffraction-limited spots. Shown in (<bold>A</bold>) are time lapse sequences representing the three most observed spot behaviors: (i) one-step photobleaching, (ii) two-step photobleaching and (iii) blinking. (<bold>B</bold>) Intensity profiles of single diffraction-limited spots shown in (<bold>A</bold>) showing 1-step photobleaching, 2-step photobleaching and blinking of YFP molecules. <italic>ΔI</italic> was calculated as the difference between the averaged fluorescence intensities before and after each stepwise photobleaching. (<bold>C</bold>) Histogram showing the magnitude of fluorescence loss following 1-step photobleaching (<italic>n</italic> = 219). The mean of a Gaussian fit to the histogram gives the fluorescence value of a single YFP molecule. (<bold>D</bold>) Number of YFP molecules per cell as a function of cell length. Swarmer cells from CJW3010 strain, which expresses <italic>parA-yfp</italic> from the native promoter of <italic>parA</italic>, were imaged on the same pad as wild-type swarmer cells. The number of YFP molecule per cell was calculated by dividing single-cell YFP fluorescence values by single YFP fluorescence. The cells were color-coded based on the YFP count using 50 as a cut-off (blue: <italic>parA-yfp</italic>-expressing cells, <italic>n</italic> = 251; red: wild-type, <italic>n</italic> = 248). The black lines represent linear fits to the red (y1 = 1.6x; autofluorescence in wild type cells on average equals to 1.6 YFP molecules per 1 µm cell length) and blue (y2 = 56x; fluorescence in <italic>parA-yfp</italic> cells on average equals to 56 YFP molecules per 1 µm cell length) data points, respectively. Typically, <italic>C. crescentus</italic> is ∼2.3 µm in length when <italic>parS</italic> translocation commences. Thus, there are 2.3 × (56–1.6) = 120 ParA-YFP molecules at the beginning of <italic>parS</italic> translocation.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.009">http://dx.doi.org/10.7554/eLife.02758.009</ext-link></p></caption><graphic xlink:href="elife02758fs006"/></fig><fig id="fig1s7" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.010</object-id><label>Figure 1—figure supplement 7.</label><caption><title>Estimation of the relative abundance of ParA and ParB in vivo.</title><p>(<bold>A</bold>) Cultures (1.5 ml) of CJW3010 (<italic>parA-yfp</italic>-expressing) and MT174 (<italic>gfp-parB</italic>-expressing) cells at OD<sub>660</sub> = 0.25 were harvested and lysed by boiling in equal volumes of SDS buffer followed by sonication. Duplicates of 10 µl ParA-YFP lysate were resolved on the same gel as GFP-ParB lysates (in varied volumes as indicated) and subjected to Western blot analysis using the JL-08 monoclonal α-GFP antibody (Clontech). The first lane separated by the dashed line was moved from a different region of the same blot for easier comparison. (<bold>B</bold>) All bands were quantified using ImageJ and the intensities of the GFP-ParB bands were plotted as a function of volume of lysate loaded. The solid line represents the best linear fit, which we used to calculate that 10 µl of ParA-YFP lysate (the red dot represents the mean intensity of two lanes on the same blot) contained approximately the same amount of GFP fusion molecules as those in ∼3 µl of GFP-ParB lysate. In other words, assuming that YFP/GFP fusions do not affect protein levels, the ParA:ParB ratio in swarmer/early stalked cell stage is approximately 1:3. This method estimated that there are 720 ÷ 3 = 240 ParA molecules per cell.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.010">http://dx.doi.org/10.7554/eLife.02758.010</ext-link></p></caption><graphic xlink:href="elife02758fs007"/></fig><fig id="fig1s8" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.011</object-id><label>Figure 1—figure supplement 8.</label><caption><title>Maximum lengths of different possible ParA polymer configurations.</title><p>(<bold>A</bold>) A surface representation of the <italic>Thermus thermophilus</italic> Soj dimer crystal structure showing the dimensions of the dimer along the x- and y- axes (<xref ref-type="bibr" rid="bib54">Leonard et al., 2005</xref>). The red areas represent the positions of arginine 182 which corresponds to arginine 195 in <italic>C. crescentus</italic> ParA and which has been shown to be critical for DNA-binding (<xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>). (<bold>B</bold>) Bottom view of the <italic>T. thermophilus</italic> Soj dimer showing the dimensions of the dimer along the x- and z- axes. (<bold>C</bold>) Three possible polymer configurations considering polymerization along the x-, y- and z-axes of a ParA dimer. The maximal achievable length of each polymer (<italic>L</italic>) was calculated as the product of the physiological abundance of ParA (90 dimers) and the unit length of a ParA dimer along each axis.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.011">http://dx.doi.org/10.7554/eLife.02758.011</ext-link></p></caption><graphic xlink:href="elife02758fs008"/></fig></fig-group></p><p>The absence of peaks at lower elution volumes (including the void volume) suggests that ParA does not form oligomers larger than dimers upon ATP binding under our experimental conditions (<xref ref-type="fig" rid="fig1">Figure 1A</xref>). Electron microscopy (EM) analysis of ParA (1 µM) in the presence (or absence) of Mg-ATP revealed no evidence of filament formation (data not shown).</p></sec><sec id="s2-2"><title>DNA binding switches ParA to an ATP hydrolysis-competent state</title><p>Next, we determined the biochemical conditions that affect the ATPase cycle of <italic>C. crescentus</italic> ParA in vitro using an NADH-coupled ATPase assay (<xref ref-type="bibr" rid="bib18">De La Cruz et al., 2000</xref>). In such an assay, ADP produced by ParA ATPase activity is constantly converted to ATP by a pyruvate kinase, continuously replenishing ATP and thus avoiding substrate depletion and potential product inhibition. We determined the specific ATPase activity by measuring the ADP production rate (in µM h<sup>−1</sup>) and by dividing the result by the concentration of ParA (in µM). By itself, ParA had a very weak ATPase activity that was below the baseline of our assay (0.5 hr<sup>−1</sup>).</p><p>Like other ParA orthologs, <italic>C. crescentus</italic> ParA is known to have an affinity for DNA (<xref ref-type="bibr" rid="bib20">Easter and Gober, 2002</xref>; <xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>). Addition of increasing concentrations of non-specific DNA resulted in a dose-dependent increase of ParA ATPase activity in vitro (<xref ref-type="fig" rid="fig1">Figure 1B</xref>). Fitting a Michaelis–Menten curve to the data gave a maximum activity <italic>k</italic><sub>cat</sub> = 6.7 hr<sup>−1</sup> and a half saturating DNA concentration <italic>K</italic><sub><italic>DNA</italic></sub> = 0.15 mg/ml. Note that DNA failed to stimulate the ATPase activity of the ParA<sub>R195E</sub> mutant (<xref ref-type="fig" rid="fig1">Figure 1C</xref>), which can still dimerize upon ATP binding (<xref ref-type="fig" rid="fig1">Figure 1A</xref>), but does not bind DNA (<xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>). This suggests that the DNA-dependent activation of ParA ATPase activity requires direct binding between ParA and DNA. In the presence of near saturating concentration of DNA (1.5 mg/ml), the ATPase activity was linearly dependent on ParA concentration (<xref ref-type="fig" rid="fig1">Figure 1D</xref>). ATPase activity was dependent on the concentration of ATP (<xref ref-type="fig" rid="fig1">Figure 1E</xref>), resulting in a <italic>K</italic><sub><italic>M</italic></sub> of 150 µM.</p></sec><sec id="s2-3"><title>A high concentration of ParB is required to stimulate ParA ATPase activity</title><p>We estimated the concentration of DNA in <italic>C. crescentus</italic> cells to be about 17 mg/ml ('Materials and methods’), which is above the <italic>K</italic><sub><italic>DNA</italic></sub> value of 0.15 mg/ml. This suggests that the DNA concentration inside cells is sufficient to stimulate ParA ATPase activity. However, this ATPase activity of 6.7 hr<sup>−1</sup> remains slow relative to the time scale of ParB/<italic>parS</italic> migration towards the distal pole, which occurs in the minute range (<xref ref-type="bibr" rid="bib84">Shebelut et al., 2010</xref>; <xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>; <xref ref-type="bibr" rid="bib35">Hong and McAdams, 2011</xref>). We therefore anticipated that further stimulation by ParB would be required to obtain significant ATPase activity from ParA. Indeed, ParB (60 µM) further increased ParA ATPase activity by about 10-fold in a DNA-dependent fashion (<xref ref-type="fig" rid="fig1">Figure 1C</xref>). The increased activity was likely due to an interaction between ParB and ParA (as opposed to a contaminating ATPase activity in the ParB preparation) since substitution of ParB by the ParB<sub>L12A</sub> mutant (purified under the same conditions as ParB, <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1D</xref>), which is unable to interact with ParA (<xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>), failed to stimulate ATPase activity (<xref ref-type="fig" rid="fig1s2">Figure 1—figure supplement 2</xref>). The synergistic effect of ParB and DNA on ParA ATPase activity indicates that significant ATP turnover only occurs when ParA, ParB and DNA interact.</p><p>In the presence of DNA, ParA ATPase activity depended on ParB concentrations (<xref ref-type="fig" rid="fig1">Figure 1F</xref>) with a surprisingly high apparent <italic>K</italic><sub><italic>ParB</italic></sub> of 80 µM. Equimolar concentrations (3 µM) of ParA and ParB had virtually no effect on ATP turnover; instead much higher concentrations of ParB than ParA were required to obtain significant ATPase stimulation (<xref ref-type="fig" rid="fig1">Figure 1F</xref>). This is in marked contrast to the <italic>B. subtilis</italic> ParABS system in which equimolar concentrations (2 µM) of Soj (ParA) and Spo0J (ParB) are sufficient for a 70-fold activation of Soj ATPase activity in the presence of DNA (<xref ref-type="bibr" rid="bib82">Scholefield et al., 2011</xref>).</p><p>Inside cells, there are two pools of ParB molecules: the free pool that diffuses in the cytoplasm and the associated pool that is bound to the <italic>parS</italic> region. In <italic>C. crescentus</italic>, the high concentration of ParB required for substantial ParA ATPase rate may restrict the ParB-dependent stimulation of ATP hydrolysis to the ParB molecules associated with the <italic>parS</italic> locus. To test this idea, we measured the concentration of <italic>parS</italic>-associated ParB and diffusing ParB inside cells using a strain (MT174) in which native <italic>parB</italic> has been substituted by a functional <italic>parB-gfp</italic> fusion (<xref ref-type="bibr" rid="bib90">Thanbichler and Shapiro, 2006</xref>). Quantitative analysis of the GFP-ParB fluorescent signal ('Materials and methods') showed that GFP-ParB/<italic>parS</italic> foci contain ∼80% of the total GFP-ParB signal in the cells while the remaining ∼20% correspond to diffusing GFP-ParB plus a potential degradation product (<xref ref-type="fig" rid="fig1s3">Figure 1—figure supplement 3A–D</xref>). This distribution of GFP-ParB signal does not vary with cell lengths (<xref ref-type="fig" rid="fig1s3">Figure 1—figure supplement 3E</xref>). Using quantitative Western blotting ('Materials and methods', <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1C</xref>, <xref ref-type="fig" rid="fig1s4">Figure 1—figure supplement 4A</xref>), we determined the total amount of ParB to be about 720 ± 80 molecules/cell (<xref ref-type="table" rid="tbl1">Table 1</xref>), or ∼360 dimers/cell since <italic>C. crescentus</italic> ParB dimerizes in solution (<xref ref-type="fig" rid="fig1s5">Figure 1—figure supplement 5</xref>).<table-wrap id="tbl1" position="float"><object-id pub-id-type="doi">10.7554/eLife.02758.012</object-id><label>Table 1.</label><caption><p>Estimation of ParA and ParB concentrations inside cells</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.012">http://dx.doi.org/10.7554/eLife.02758.012</ext-link></p></caption><table frame="hsides" rules="groups"><thead><tr><th/><th>Molecules per cell</th><th>Mole x 10<sup>−21</sup></th><th>Volume (fL)</th><th>Concentration (μM)</th></tr></thead><tbody><tr><td>ParB</td><td>720 ± 80</td><td align="char" char=".">1.2</td><td align="char" char=".">0.25</td><td align="char" char=".">1.8</td></tr><tr><td>ParB (diffusing)</td><td>140</td><td align="char" char=".">0.2</td><td align="char" char=".">0.25</td><td align="char" char=".">0.8</td></tr><tr><td>ParB (<italic>parS</italic>-associated)</td><td>580</td><td align="char" char=".">1</td><td align="char" char=".">0.002</td><td align="char" char=".">500</td></tr><tr><td>ParA</td><td>180 ± 30</td><td align="char" char=".">0.3</td><td align="char" char=".">0.25</td><td align="char" char=".">1.2</td></tr></tbody></table><table-wrap-foot><fn><p>This table summarizes the abundance and concentrations of ParA and ParB in swarmer/early stalked <italic>C. crescentus</italic> cells. Subcellular distribution of ParB was determined by quantitative fluorescence measurements in cells expressing GFP-ParB (MT174, <xref ref-type="fig" rid="fig1s3">Figure 1—figure supplement 3</xref>). ParB abundance was determined by quantitative Western blotting (<xref ref-type="fig" rid="fig1s4">Figure 1—figure supplement 4A</xref>). The result showing dimerization of purified ParB in solution is shown in <xref ref-type="fig" rid="fig1s5">Figure 1—figure supplement 5</xref>. ParA abundance shown here is the average value determined by three independent methods: (1) Quantitative Western blotting of ParA-YFP abundance in CJW3010 cells in which <italic>parA-yfp</italic> functionally replaces wild-type <italic>parA</italic> in the chromosome (<xref ref-type="fig" rid="fig1s4">Figure 1—figure supplement 4B</xref>), (2) Calibrated fluorescence measurement (<xref ref-type="fig" rid="fig1s6">Figure 1—figure supplement 6</xref>) and (3) Comparison between ParB-GFP and ParA-YFP amounts by quantitative Western blotting (<xref ref-type="fig" rid="fig1s7">Figure 1—figure supplement 7</xref>). The cell volume represents the cytoplasmic volume calculated from a cryoelectron tomograph of a swarmer cell (<xref ref-type="bibr" rid="bib14">Briegel et al., 2008</xref>). The volume occupied by <italic>parS</italic>-associated ParB molecules was inferred from super-resolution PALM images of cells expressing mEos3.2-ParB (CJW4978 strain, <xref ref-type="fig" rid="fig1s3">Figure 1—figure supplement 3F</xref>).</p></fn></table-wrap-foot></table-wrap></p><p>The <italic>C. crescentus</italic> chromosome carries two <italic>parS</italic> sites separated by 42 nucleotides (<xref ref-type="bibr" rid="bib59">Livny et al., 2007</xref>; <xref ref-type="bibr" rid="bib91">Toro et al., 2008</xref>). Each site has the potential of binding two ParB molecules. Yet, our measurements indicate that about 580 molecules of ParB (80% of the total 720 ParB molecules) are associated to the <italic>parS</italic> DNA regions (<xref ref-type="table" rid="tbl1">Table 1</xref>). This is consistent with the notion that upon binding to a <italic>parS</italic> site, ParB spreads to flanking DNA regions to form a large ParB/<italic>parS</italic> assembly (<xref ref-type="bibr" rid="bib77">Rodionov and Yarmolinsky, 2004</xref>; <xref ref-type="bibr" rid="bib68">Murray et al., 2006</xref>; <xref ref-type="bibr" rid="bib12">Breier and Grossman, 2007</xref>). Assuming that the ParB/<italic>parS</italic> assembly is localized within a radius of 78 nm (based on super-resolution microscopy results, <xref ref-type="fig" rid="fig1s3">Figure 1—figure supplement 3F</xref>), we estimated a local concentration of ParB to be at least 500 µM at the ParB/<italic>parS</italic> complex (<xref ref-type="table" rid="tbl1">Table 1</xref>). Based on our in vitro measurements (<xref ref-type="fig" rid="fig1">Figure 1F</xref>), we expect robust activation of ParA ATPase activity by <italic>parS</italic>-associated ParB inside cells and negligible stimulatory effect by the diffusing ParB (∼1 µM).</p><p>From these results, we conclude that in <italic>C. crescentus</italic>, only the highly concentrated ParB associated with <italic>parS</italic> (i.e., the ParB/<italic>parS</italic> complex) is capable of stimulating ParA ATPase activity, unlike in <italic>B. subtilis</italic> where even the low concentration of diffusing ParB is likely sufficient to stimulate ATP hydrolysis (<xref ref-type="bibr" rid="bib82">Scholefield et al., 2011</xref>). This explains why ParA (Soj) is mostly monomeric and has a diffused localization in vegetative <italic>B. subtilis</italic> cells because monomers cannot bind DNA (<xref ref-type="bibr" rid="bib82">Scholefield et al., 2011</xref>). Conversely, in <italic>C. crescentus</italic>, ParA can accumulate in a DNA-bound ParA-ATP dimeric form away from the partition complex. Thus, the difference in ParB concentrations required for stimulation of ParA ATPase activity provides an explanation for the difference in ParA localization and possibly function between <italic>B. subtilis</italic> and <italic>C. crescentus</italic> ('Discussion').</p></sec><sec id="s2-4"><title>The partition complex does not follow a linear trajectory during ParA-dependent translocation</title><p>Apart from the biochemical cycle of ParA (summarized in <xref ref-type="fig" rid="fig1">Figure 1G</xref>), a key element of the translocation mechanism is the organization of ParA inside the cells. In the prevailing spindle-like model of segregation in <italic>C. crescentus</italic> (<xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib5">Banigan et al., 2011</xref>; <xref ref-type="bibr" rid="bib85">Shtylla and Keener, 2012</xref>), ParA-ATP dimers form a filament bundle that depolymerizes upon interaction with ParB/<italic>parS</italic>, pulling the partition complex toward the new pole. If the partition complex tracks the end of a ParA filament bundle during translocation, we expected that the trajectory of the migrating ParB/<italic>parS</italic> complex would follow a line, reflecting the shape of the underlying ParA filament bundle. So far, the translocation of the partition complex has been characterized along only one cell dimension, the long cell axis (<xref ref-type="bibr" rid="bib84">Shebelut et al., 2010</xref>). Along the cell length, <italic>parS</italic>/ParB motion is known to consist of distinct steps, beginning with a slow, ParA-independent phase during which the two sister partition complexes are separated presumably by ‘bulk’ segregation mechanisms (such as DNA replication, transcription, entropic unmixing, etc). This is followed by a fast, ParA-dependent phase, and completed by the anchoring of the partition complex at the new pole through a physical interaction between ParB and the PopZ matrix (<xref ref-type="bibr" rid="bib10">Bowman et al., 2008</xref>; <xref ref-type="bibr" rid="bib21">Ebersbach et al., 2008</xref>; <xref ref-type="bibr" rid="bib84">Shebelut et al., 2010</xref>).</p><p>To acquire two-dimensional (2D) trajectories (i.e., along both short and long cell axes) at high temporal resolution, we tracked the motion of the partition complex (labeled with GFP-ParB) inside cells at 20-s intervals (<xref ref-type="fig" rid="fig2">Figure 2A</xref>). Plotting the distance of the segregating complex from the old pole as a function of time for each cell showed the multiphasic movement of the segregating GFP-ParB/<italic>parS</italic> reported before (<xref ref-type="bibr" rid="bib84">Shebelut et al., 2010</xref>), with the sequential slow, fast and anchored phases (<xref ref-type="fig" rid="fig2">Figure 2B</xref>). We found that the period of the slow, ParA-independent phase increased with faster image acquisition rates (data not shown), indicating sensitivity to phototoxicity. In contrast, the fast, ParA-dependent phase was insensitive to changes in time intervals between image acquisitions (data not shown). We measured that the partition complex covered a distance of 1.0 ± 0.2 µm along the cell length (mean ± standard deviation, SD, <italic>n</italic> = 141 cells) (<xref ref-type="fig" rid="fig2">Figure 2C</xref>) within 4.7 ± 1.2 min (<xref ref-type="fig" rid="fig2">Figure 2D</xref>) during this fast ParA-dependent phase, with an average velocity (run length/run period) of 220 ± 50 nm/min (<xref ref-type="fig" rid="fig2">Figure 2E</xref>).<fig id="fig2" position="float"><object-id pub-id-type="doi">10.7554/eLife.02758.013</object-id><label>Figure 2.</label><caption><title>Two-dimensional dynamics of the partition complex.</title><p>(<bold>A</bold>) Representative 2-D trajectory (Δ<italic>t</italic> = 20 s) of duplicated GFP-ParB/<italic>parS</italic> complexes in a CJW4762 cell. Positions of each partition complex detected in consecutive frames were joined with solid lines while dotted lines were used to connect positions interrupted by frame(s) with failed localization. (<bold>B</bold>) Trajectory of GFP-ParB/<italic>parS</italic> complexes in (<bold>A</bold>) along the long cell axis (black, old pole-proximal ParB/<italic>parS</italic> complex; for the distal partition complex: blue, ‘slow’ phase, red, ‘fast’ phase, and green, the anchored phase). <italic>x</italic><sub><italic>0</italic></sub> is the position of the distal partition complex at the moment the second GFP-ParB/<italic>parS</italic> spot appeared in a cell. <italic>x</italic><sub><italic>finish</italic></sub> is the position of the distal partition complex at the moment it became anchored at the new pole. <italic>x</italic><sub><italic>start</italic></sub> is the position when the partition complex transitions from the ‘slow’ phase into the ‘fast’ phase. Run length is the distance between <italic>x</italic><sub><italic>finish</italic></sub> and <italic>x</italic><sub><italic>start</italic></sub> along the long cell axis. Run period is the time taken to travel from <italic>x</italic><sub><italic>start</italic></sub> to <italic>x</italic><sub><italic>finish</italic></sub> along the long axis. Also shown is a table summarizing the mean ± SD values for <italic>x</italic><sub><italic>0</italic></sub>, <italic>x</italic><sub><italic>start</italic></sub> and <italic>x</italic><sub><italic>finish</italic></sub>. There were more counts for <italic>x</italic><sub><italic>start</italic></sub> and <italic>x</italic><sub><italic>finish</italic></sub> (<italic>n</italic> = 141) than for <italic>x</italic><sub><italic>0</italic></sub> (<italic>n</italic> = 96) because in some cells the GFP-ParB/<italic>parS</italic> complex had already duplicated prior image acquisition. These values were used to define the start position for the ParB/<italic>parS</italic> complex in our computer simulations and the fast phase in the analysis. (<bold>C</bold>) Histogram showing the distribution of run lengths (<italic>n</italic> = 141). (<bold>D</bold>) Histogram showing the distribution of run periods (<italic>n</italic> = 141). (<bold>E</bold>) Histogram showing the distribution of translocation speeds of partitioning ParB/<italic>parS</italic> complexes during the fast phase (<italic>n</italic> = 141). (<bold>F</bold>) Histogram showing the distribution of short-axis displacements of segregating partition complexes during the slow (blue), fast (red) and pole-anchored (green) phases.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.013">http://dx.doi.org/10.7554/eLife.02758.013</ext-link></p></caption><graphic xlink:href="elife02758f002"/></fig></p><p>Surprisingly, the partition complex did not follow a straight line (or smooth curve) during the fast translocation phase (<xref ref-type="fig" rid="fig2">Figure 2A</xref>). Moreover, when we examined its motion along the short cell axis, we found that the displacement distributions were virtually identical for the fast and slow phases (<xref ref-type="fig" rid="fig2">Figure 2F</xref>). These observations are at odds with the idea that a ParA filament bundle serves as a stable bridge guiding the movement of the partitioning complex across the cell. That is, unless the ParA filament bundle rapidly moves across the cell width, which is highly unlikely given the large size of the presumed ParA bundle. We therefore considered two alternative explanations. First, during the process of translocation, the partitioning complex detaches from the ParA filament bundle and diffuses before reattaching to the ParA filament bundle. Second, ParA-ATP does not form a filamentous structure inside the chromosome-packed cell; instead ParA-ATP dimers bind to the chromosomal DNA away from the ParB/<italic>parS</italic> complexes.</p></sec><sec id="s2-5"><title>ParA displays a wide spatial distribution along the cell width</title><p>Since the distance covered during the fast, ParA-dependent phase is about 1-µm long (<xref ref-type="fig" rid="fig2">Figure 2C</xref>), we would expect this distance to approximate the length of the ParA filament bundle if such structure were involved in the transport mechanism. To examine whether the cellular concentration of ParA could accommodate the formation of a micron-long filament bundle, we determined the number of ParA molecules per cell using three independent methods: quantitative Western blotting (<xref ref-type="fig" rid="fig1s4">Figure 1—figure supplement 4B</xref>), calibrated fluorescence microscopy (<xref ref-type="fig" rid="fig1s6">Figure 1—figure supplement 6</xref>), and stoichiometric comparison with ParB (<xref ref-type="fig" rid="fig1s7">Figure 1—figure supplement 7</xref>). Each method gave a similar result with an average of about 180 ParA molecules or 90 ParA dimers per cell (<xref ref-type="table" rid="tbl1">Table 1</xref>). ParA2 from <italic>Vibrio cholerae</italic> has been shown to polymerize on DNA in vitro, forming a nucleoprotein filament with a dimension of 4.4 dimer units per helical pitch of 12 nm (<xref ref-type="bibr" rid="bib39">Hui et al., 2010</xref>). If we assume that ParA forms a similar nucleoprotein filament inside <italic>C. crescentus</italic>, this filament would be at most 240 nm in length. Even if we ignore DNA binding and consider that ParA dimers polymerize back-to-back along their largest dimension (as determined from the crystal structure of the <italic>Thermus thermophilus</italic> Soj/ParA dimer; <xref ref-type="bibr" rid="bib54">Leonard et al., 2005</xref>), the filament could be at most 580 nm long (<xref ref-type="fig" rid="fig1s8">Figure 1—figure supplement 8</xref>). Thus, the cellular concentration of ParA appears too low to accommodate the formation of even a single micron-long filament.</p><p>To gain further insight into the spatial arrangement of ParA, we performed photo-activated localization microscopy (PALM). For this, we generated a functional <italic>parA-dendra2</italic> fusion ('Materials and methods'), which replaced the native <italic>parA</italic> in the chromosome without disrupting the operon structure. In addition, to increase emitter density, we generated a second strain in which ParA-Dendra2 was expressed from a xylose-inducible promoter on the chromosome in addition to being expressed from the native promoter. To specifically examine ParA-Dendra2 localization prior to <italic>parS</italic> replication and segregation, cells in G1 cell cycle phase (swarmer cells) were isolated and imaged by 2D PALM at an averaged localization precision of 18 nm in both the x- and y-directions. Consistent with epifluorescence images (<xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>; <xref ref-type="bibr" rid="bib84">Shebelut et al., 2010</xref>), ParA-Dendra2 was asymmetrically distributed along the long cell axis (<xref ref-type="fig" rid="fig3">Figure 3A</xref>). However, we found no evidence of a filament-like localization. Rather, ParA-Dendra2 was widely distributed along the short cell axis (<xref ref-type="fig" rid="fig3">Figure 3A</xref>). We also imaged cells at a later stage of the cell cycle, and observed strong accumulation of ParA-Dendra2 at the cell pole (<xref ref-type="fig" rid="fig3">Figure 3A</xref>), consistent with the new-pole localization of ParA accumulation following ParB/<italic>parS</italic> segregation due to ParA's interaction with the polarity factors TipN and PopZ (<xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>; <xref ref-type="bibr" rid="bib50">Laloux and Jacobs-Wagner, 2013</xref>).<fig-group><fig id="fig3" position="float"><object-id pub-id-type="doi">10.7554/eLife.02758.014</object-id><label>Figure 3.</label><caption><title>Subdiffraction visualization of ParA-Dendra2 in live cells.</title><p>(<bold>A</bold>) Representative super-resolution PALM images of cells producing ParA-Dendra2 at native levels in place of ParA (strain CJW4915), ParA-Dendra2 at xylose-inducible levels in addition to ParA-Dendra2 expressed from the native promoter (CJW5154), crescentin-Dendra2 at native levels (CJW4902) and ribosome-associated L1-Dendra2 at native levels (CJW5156). Synthesis of ParA-Dendra2 in CJW5154 cells was induced with 0.3% xylose for 1 hr before swarmer cells were isolated for imaging. Scale bar = 1 µm. (<bold>B</bold>) Positional distributions of single emitters along the short-cell axis for cells expressing ParA-Dendra2 (CJW5154, green), crescentin-Dendra2 (CJW4902, blue) and L1-Dendra2 (CJW5156, red). For each cell, a 0.5–0.8 μm segment containing at least 600 emitters was selected. Emitter positions along the short cell axis were calculated relative to the mean position. Additional super-resolution microscopy images and analysis are presented in <xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1</xref>.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.014">http://dx.doi.org/10.7554/eLife.02758.014</ext-link></p></caption><graphic xlink:href="elife02758f003"/></fig><fig id="fig3s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.015</object-id><label>Figure 3—figure supplement 1.</label><caption><title>Comparison of ParA and crescentin localization by super-resolution imaging.</title><p>(<bold>A</bold>) <italic>Left</italic>, super-resolution image of CJW5154 cells producing ParA-Dendra2 from both the native and xylose promoters. Cells were imaged at 100 frames/s for 30 s using a custom-built microscope setup equipped with a sCMOS camera (<xref ref-type="bibr" rid="bib37">Huang et al., 2013</xref>). ParA-Dendra2 synthesis was induced with 0.3% xylose for 1 hr before swarmer cells were isolated for imaging. The data set was processed using a sCMOS-specific algorithm (<xref ref-type="bibr" rid="bib37">Huang et al., 2013</xref>). <italic>Right</italic>, line profiles of emitter positions in the white boxes show the spread of ParA-Dendra2 across the cell width near the new pole (i and ii) and the distribution of ParA-Dendra2 localized at the cell pole (iii). (<bold>B</bold>) Same as <bold>A</bold>, except for the CJW4902 strain, which produces crescentin-Dendra2 from the native <italic>creS</italic> promoter, were imaged. Scale bars = 500 nm. For visualization purpose, the upper bounds in the color map have been adjusted for <bold>A</bold> and <bold>B</bold> separately. AU, arbitrary units.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.015">http://dx.doi.org/10.7554/eLife.02758.015</ext-link></p></caption><graphic xlink:href="elife02758fs009"/></fig></fig-group></p><p>For comparison, we also imaged crescentin-Dendra2 in <italic>C. crescentus</italic> cells. Crescentin is a bacterial intermediate filament protein that assembles into an inner membrane-associated filamentous structure in <italic>C. crescentus</italic> (<xref ref-type="bibr" rid="bib2">Ausmees et al., 2003</xref>) and is responsible for <italic>C. crescentus</italic>' characteristic crescent-shaped morphology. When crescentin is fused to a fluorescent protein, the crescentin fusion fails to attach to the cell membrane (resulting in loss of cell curvature) but still polymerizes into a single filamentous structure (<xref ref-type="bibr" rid="bib2">Ausmees et al., 2003</xref>). PALM visualization of crescentin-Dendra2 indeed revealed a clear filament-like localization (<xref ref-type="fig" rid="fig3">Figure 3A</xref>), indicating that our method can identify protein filaments. As a second control, we imaged L1-Dendra2-tagged ribosomes using PALM. In <italic>C. crescentus</italic>, ribosomes spread throughout the cytoplasm, as shown by both cryo-electron tomography and conventional epifluorescence microscopy (<xref ref-type="bibr" rid="bib13">Briegel et al., 2006</xref>; <xref ref-type="bibr" rid="bib66">Montero Llopis et al., 2010</xref>). Super-resolution images of L1-Dendra2-labeled ribosomes were consistent with these observations, showing near homogenous cytoplasmic localization (<xref ref-type="fig" rid="fig3">Figure 3A</xref>). Importantly, the localization of ParA-Dendra2 (spread along the cell width <italic>σ</italic> = 146 nm) was similar to L1-Dendra2-labeled ribosomes (<italic>σ</italic> = 150 nm) but not to crescentin-Dendra2 (<italic>σ</italic> = 32 nm) (<xref ref-type="fig" rid="fig3">Figure 3B</xref>). We obtained similar super-resolution images whether we used a commercial N-STORM microscope (see above) or a custom-built microscope (<xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1</xref>).</p><p>Altogether, these results suggest that ParA does not form a thin filamentous structure. Instead, they support a model in which the asymmetric ParA cloud observed by epifluorescence microscopy consists of sparse ParA-ATP dimers (or small oligomers) bound to the chromosome away from the ParB/<italic>parS</italic> complex.</p></sec><sec id="s2-6"><title>Modeling suggests that diffusion and ParA/ParB interplay are not sufficient to drive directed translocation</title><p>How can the properties we observed lead to a robust directional motion of ParB/<italic>parS</italic> complex toward the new pole? We considered the possibility that ParB/<italic>parS</italic> is simply diffusing and that its binding to the DNA-bound ParA-ATP dimers results in a biased diffusion along the ParA-ATP dimer gradient, as we previously suggested (<xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>). This mechanism would be similar to the Brownian ratchet proposed for the P1 and F plasmids (<xref ref-type="bibr" rid="bib40">Hwang et al., 2013</xref>; <xref ref-type="bibr" rid="bib93">Vecchiarelli et al., 2013</xref>, <xref ref-type="bibr" rid="bib95">2014</xref>). In this proposed mechanism (hereafter referred to as ‘diffusion-binding’ mechanism, <xref ref-type="fig" rid="fig4">Figure 4A</xref>), the DNA serves as a matrix to tether ParA-ATP dimers and the partition complex diffuses until it binds to one or more DNA-bound ParA-ATP dimers. Stimulation of ATP hydrolysis results in monomerization of ParA, causing the release of the ParB/<italic>parS</italic> complex and a local depletion of DNA-bound ParA-ATP dimers. The partition complex then encounters new DNA-bound ParA-ATP dimers by diffusion, reinitiating the biochemical cycle. The hypothesis is that repeated cycles of this process would result in biased diffusion of ParB/<italic>parS</italic> toward a higher concentration of ParA-ATP dimers.<fig-group><fig id="fig4" position="float"><object-id pub-id-type="doi">10.7554/eLife.02758.016</object-id><label>Figure 4.</label><caption><title>The DNA-relay model results in robust translocation of the ParB/<italic>parS</italic> complex.</title><p>(<bold>A</bold>) <italic>Left</italic>, graphical representation of the ‘diffusion-binding’ model: the diffusing ParB/<italic>parS</italic> complex (green disk) interacts with DNA-immobilized ParA-ATP dimers (filled red disks), stimulates ATPase activity, resulting in the dissociation of ParA from the DNA (open red disks). <italic>Right</italic>, graphical representation of the ‘DNA-relay model’: same as in (<bold>A</bold>) except that DNA-bound ParA-ATP dimers fluctuate randomly according to the movement of the associated DNA. When the ParB/<italic>parS</italic> complex is associated with one or more DNA-bound ParA-ATP dimers, it experiences the elastic force governing the dynamics of the DNA loci associated with ParA dimers. (<bold>B</bold>) Averaged positions of the simulated ParB/<italic>parS</italic> complex as a function of time. (<bold>C</bold>) Fraction of trajectories that completed translocation as a function of time. A summary of all parameters used in the simulations is presented in <xref ref-type="table" rid="tbl2">Table 2</xref>. Additional experiments performed to obtain these parameter values are presented in <xref ref-type="fig" rid="fig4s1 fig4s2">Figure 4—figure supplements 1 and 2</xref>.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.016">http://dx.doi.org/10.7554/eLife.02758.016</ext-link></p></caption><graphic xlink:href="elife02758f004"/></fig><fig id="fig4s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.017</object-id><label>Figure 4—figure supplement 1.</label><caption><title>Average ParA-YFP fluorescence profiles during ParB/parS segregation.</title><p>Cells expressing ParA-YFP and CFP-ParB (CJW3367 strain) were imaged, analyzed with MicrobeTracker and SpotFinderY, and sorted based on the distance of the translocating partition complex from the new pole at 100-nm intervals. Shown in the figure are the average fluorescence profiles of ParA-YFP between the translocating CFP-ParB/<italic>parS</italic> partition complex and the new pole (red curves) of cells sorted into the 2.0 ± 0.05 and 1.6 ± 0.05 µm groups. The grey bars mark the average distance of the partition complex from the new pole.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.017">http://dx.doi.org/10.7554/eLife.02758.017</ext-link></p></caption><graphic xlink:href="elife02758fs010"/></fig><fig id="fig4s2" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.02758.018</object-id><label>Figure 4—figure supplement 2.</label><caption><title>Estimation of the diffusion coefficient of the ParB/<italic>parS</italic> complex, <italic>D</italic><sub><italic>PC</italic></sub>.</title><p>(<bold>A</bold>) Three segments were identified in the trajectories of GFP-ParB/<italic>parS</italic> when the partition complexes were not engaged in the fast, ParA-dependent movement (see ‘Materials and methods’ for details). (<bold>B</bold>) The displacement along the long cell axis within each segment was collected from all cells and the distributions were plotted. Closed circles indicate data while solid lines indicate Gaussian fits to displacement distributions for each of the segments. (<bold>C</bold>) Mean square displacement (MSD) was plotted for each of the segments (closed circles). Solid lines represent linear fits (<italic>MSD</italic> = <italic>D</italic><sub><italic>PC</italic></sub> <italic>t</italic> + <italic>C</italic>, with a variable offset <italic>C</italic>, as described previously [<xref ref-type="bibr" rid="bib4">Bakshi et al., 2011</xref>; <xref ref-type="bibr" rid="bib25">English et al., 2011</xref>]) to the data points.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.018">http://dx.doi.org/10.7554/eLife.02758.018</ext-link></p></caption><graphic xlink:href="elife02758fs011"/></fig></fig-group></p><p>To test this hypothetical mechanism, we developed a 'diffusion-binding' model ('Materials and methods') that was constrained by experimentally-determined parameters (<xref ref-type="table" rid="tbl2">Table 2</xref>) to best reflect the in vivo situation. The ParB-rich partition complex was modeled as a sphere with a radius of 50 nm to simulate the interaction radius of the partition complex that we estimated from our super-resolution images (<xref ref-type="fig" rid="fig1s3">Figure 1—figure supplement 3</xref>). The ParB sphere was allowed to interact with multiple DNA-bound ParA-ATP dimers at any given time to reflect the high number of ParB molecules (i.e., ParA binding sites) within the partition complex (<xref ref-type="table" rid="tbl1">Table 1</xref>, <xref ref-type="fig" rid="fig1s3">Figure 1—figure supplement 3</xref>). The rate constant of ParB-stimulated ATPase activity was 0.03 s<sup>−1</sup>, as measured in our biochemical study (<xref ref-type="fig" rid="fig1">Figure 1F</xref>). The concentration of ParA-ATP dimers was 90 per cell (<xref ref-type="table" rid="tbl1">Table 1</xref>). Their spatial distribution was modeled to reproduce the gradient of ParA-ATP dimers bound to the DNA matrix inside cells. The shape of the ParA gradient was determined by quantitative analysis of cells expressing ParA-YFP at different stages of segregation (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1</xref>). The diffusion coefficient of the partition complex (<italic>D</italic><sub><italic>PC</italic></sub>) was estimated to be 0.0001 μm<sup>2</sup> s<sup>−1</sup> from tracking the motion of detached GFP-ParB/<italic>parS</italic> prior to the directed ParA-dependent phase (<xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2</xref> and 'Materials and methods').<table-wrap id="tbl2" position="float"><object-id pub-id-type="doi">10.7554/eLife.02758.019</object-id><label>Table 2.</label><caption><p>Default parameters and values used in simulations of mathematical models</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.019">http://dx.doi.org/10.7554/eLife.02758.019</ext-link></p></caption><table frame="hsides" rules="groups"><thead><tr><th>Model</th><th colspan="2">Parameter</th><th>Value</th><th>Comments</th><th>Source</th></tr></thead><tbody><tr><td>1, 2, 3</td><td>Time step of simulations</td><td>Δ<italic>t</italic></td><td>0.001 s</td><td>No significant differences with simulations using smaller steps</td><td/></tr><tr><td>1, 2, 3</td><td>Number of simulated trajectories</td><td><italic>n</italic><sub><italic>runs</italic></sub></td><td>1024</td><td/><td/></tr><tr><td>1, 2, 3</td><td>Duration of simulations</td><td><italic>t</italic><sub><italic>fin</italic></sub></td><td>2000 s</td><td>∼3 × time scale of translocation</td><td/></tr><tr><td rowspan="2">1, 2, 3</td><td>Cell length</td><td><italic>l</italic><sub><italic>0</italic></sub></td><td>2.6 µm</td><td rowspan="2">Average cell length and width of cells with first appearance of 2 ParB foci</td><td rowspan="2">This study</td></tr><tr><td>Cell width</td><td><italic>w</italic><sub><italic>0</italic></sub></td><td>0.4 µm</td></tr><tr><td rowspan="2">1, 2, 3</td><td rowspan="2">Initial coordinates of ParB/<italic>parS</italic> complex, relative to the long cell axis(0 = old pole; <italic>l</italic><sub><italic>0</italic></sub> = new pole) and short axis (cell walls at −w<sub>0</sub>/2 and w<sub>0</sub>/2)</td><td><italic>x</italic><sub><italic>0</italic></sub></td><td>0.8 µm</td><td rowspan="2">Average coordinate of the distal ParB focus in cells at the first appearance of 2 ParB foci</td><td rowspan="2">This study</td></tr><tr><td><italic>y</italic><sub><italic>0</italic></sub></td><td>0.0 µm</td></tr><tr><td>1, 2, 3</td><td>Start of ‘fast’ phase (used only in analysis of the simulations)</td><td><italic>x</italic><sub><italic>start</italic></sub></td><td>1.5 µm</td><td>Calculated from <italic>x</italic><sub><italic>finish</italic></sub> - run length (from <xref ref-type="fig" rid="fig2">Figure 2D</xref>)</td><td>This study</td></tr><tr><td>1, 2, 3</td><td>End point of translocation</td><td><italic>x</italic><sub><italic>finish</italic></sub></td><td>2.5 µm</td><td>Average coordinate at which distal ParB focus became anchored</td><td>This study</td></tr><tr><td>1, 2, 3</td><td>Radius of the disk for ParB/<italic>parS</italic> complex</td><td><italic>R</italic><sub><italic>ParB</italic></sub></td><td>50 nm</td><td>Value close to an estimate from super-resolution images</td><td>This study</td></tr><tr><td>2, 3</td><td>Radius of the disk for ParA dimer</td><td><italic>R</italic><sub><italic>ParA</italic></sub></td><td>2 nm</td><td>Value close to the dimension of the crystal structure of a Soj dimer (PDB: 2BEK)</td><td>(<xref ref-type="bibr" rid="bib54">Leonard et al., 2005</xref>)</td></tr><tr><td>2, 3</td><td>Number ParA dimers</td><td><italic>n</italic><sub><italic>ParA</italic></sub></td><td>90</td><td>Average of three measurements by different techniques</td><td>This study</td></tr><tr><td>2, 3</td><td>Rate of ParB-stimulated hydrolysis of ATP by ParA dimers</td><td><italic>k</italic><sub><italic>cat</italic></sub></td><td>0.03 s<sup>−1</sup></td><td>Best fit value to ParB dependence curve</td><td>This study</td></tr><tr><td>2, 3</td><td>Rate of ParA dimer rebinding to the DNA</td><td><italic>k</italic><sub><italic>db</italic></sub></td><td>0.03 s<sup>−1</sup></td><td>Results do not depend on the exact values (0.01–1 s<sup>−1</sup> range tested)</td><td/></tr><tr><td>2, 3</td><td>Spatial distribution of DNA-bound ParA dimers</td><td><italic>P</italic><sub><italic>ParA-DNA</italic></sub></td><td><xref ref-type="disp-formula" rid="equ7">Equation 6</xref></td><td>Measured from ParA-YFP fluorescence profile during segregation</td><td>This study</td></tr><tr><td>1, 2, 3</td><td>Diffusion coefficient of the translocating ParB/<italic>parS</italic> complex</td><td><italic>D</italic><sub><italic>PC</italic></sub></td><td>0.0001 µm<sup>2</sup>s<sup>−1</sup></td><td>Estimated from non-directional phases of ParB trajectories</td><td>This study</td></tr><tr><td>3</td><td>Diffusion coefficient of DNA-bound ParA dimers</td><td><italic>D</italic><sub><italic>A</italic></sub></td><td>0.01 µm<sup>2</sup>s<sup>−1</sup></td><td>Calculated from the time-dependent generalized diffusion coefficient</td><td>(<xref ref-type="bibr" rid="bib99">Weber et al., 2010</xref>; <xref ref-type="bibr" rid="bib45">Javer et al., 2013</xref>)</td></tr><tr><td rowspan="2">3</td><td rowspan="2">Standard deviations of fluctuating DNA-bound ParA dimers used to define elastic constants (1/<italic>σ</italic><sup><italic>2</italic></sup> <italic>= k</italic><sub><italic>sp</italic></sub><italic>/kT</italic>)</td><td><italic>σ</italic><sub><italic>long</italic></sub></td><td>0.06 µm</td><td rowspan="2">Measured from the positional fluctuation of the <italic>groESL</italic>, 139_lac and 165_lac DNA loci.</td><td rowspan="2">This study</td></tr><tr><td><italic>σ</italic><sub><italic>short</italic></sub></td><td>0.04 µm</td></tr></tbody></table><table-wrap-foot><fn><p>Model 1: diffusion, Model 2: diffusion-binding, Model 3: DNA-relay.</p></fn></table-wrap-foot></table-wrap></p><p>We generated over 1000 trajectories in virtual cells using Brownian dynamics simulation. We focused our analysis of the simulated trajectories to the region between 1.5 µm (<italic>x</italic><sub><italic>start</italic></sub>) and 2.5 µm (<italic>x</italic><sub><italic>finish</italic></sub>) from the old pole of virtual cells since this 1-µm region corresponds to the active, ParA-dependent motion (fast phase) in real cells (<xref ref-type="fig" rid="fig2">Figure 2B</xref>). We found that the averaged trajectory showed little (if any) net translocation toward the new pole (<xref ref-type="fig" rid="fig4">Figure 4B</xref>). In fact, none of the simulated trajectories were able to cross this 1-µm region within 30 min (<xref ref-type="fig" rid="fig4">Figure 4C</xref>; <xref ref-type="other" rid="video1">Video 1</xref> for a representative trajectory). This is in marked contrast to experimental observations where most cells complete translocation of ParB/<italic>parS</italic> within that time frame (<xref ref-type="fig" rid="fig2">Figure 2D</xref>, <xref ref-type="fig" rid="fig4">Figure 4C</xref>). Moreover, the diffusion-binding model did not work better than a simple diffusion model ('Materials and methods') in which the partition complex diffuses without interacting with ParA-ATP dimers (<xref ref-type="fig" rid="fig4">Figure 4B,C</xref>; <xref ref-type="other" rid="video2">Video 2</xref>).<media content-type="glencoe play-in-place height-250 width-310" id="video1" mime-subtype="avi" mimetype="video" xlink:href="elife02758v001.avi"><object-id pub-id-type="doi">10.7554/eLife.02758.020</object-id><label>Video 1.</label><caption><title>Example of a simulated trajectory for the diffusion-binding model.</title><p>Trajectories were generated by Brownian dynamics simulations with time step <italic>dt</italic> = 1 ms and the following parameters: diffusion coefficient of the partition complex <italic>D</italic><sub><italic>PC</italic></sub> = 0.0001 µm<sup>2</sup> s<sup>−1</sup>, total number of ParA dimers <italic>n</italic><sub><italic>ParA</italic></sub> = 90, ParB-stimulated rate of ParA ATPase activity <italic>k</italic><sub><italic>ca</italic>t</sub> = 0.03 s<sup>−1</sup>, rate constant for DNA-binding <italic>k</italic><sub><italic>DB</italic></sub> = 0.03 s<sup>−1</sup>. The partition complex and ParA-ATP dimers are shown as green and red spheres, respectively. Shown here is a representative trajectory in absolute cell coordinate (0 µm = old pole; 2.5 µm = new pole) as a function of time in a virtual cell.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.020">http://dx.doi.org/10.7554/eLife.02758.020</ext-link></p></caption></media><media content-type="glencoe play-in-place height-250 width-310" id="video2" mime-subtype="avi" mimetype="video" xlink:href="elife02758v002.avi"><object-id pub-id-type="doi">10.7554/eLife.02758.021</object-id><label>Video 2.</label><caption><title>Example of a simulated trajectory for the diffusion model.</title><p>Trajectories were generated by Brownian dynamics simulations with time step <italic>dt</italic> = 1 ms and a diffusion coefficient of partition complex <italic>D</italic><sub><italic>PC</italic></sub> = 0.0001 µm<sup>2</sup> s<sup>−1</sup>. The partition complex is shown in green. Shown here is a representative trajectory in absolute cell coordinate (0 µm = old pole; 2.5 µm = new pole) as a function of time in a virtual cell.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.021">http://dx.doi.org/10.7554/eLife.02758.021</ext-link></p></caption></media></p><p>The diffusion-binding model did not lead to directional motion, indicating that diffusion of the ParB/<italic>parS</italic> complex coupled with its biochemical interplay with DNA-bound ParA-ATP dimers does not create a Brownian ratchet. This is because this mechanism is only governed by the diffusion of the partition complex. There is no force involved and nothing prevents the partition complex from diffusing in the wrong direction when the interaction between ParB and ParA is lost following ATP hydrolysis (<xref ref-type="other" rid="video2">Video 2</xref>). The transient interactions with DNA-bound ParA-ATP dimers only intermittently stall the motion of the partition complex. These results suggested that something was missing from the diffusion-binding model.</p></sec><sec id="s2-7"><title>Adding chromosome dynamics to the model results in translocation properties similar to those observed in vivo</title><p>So far, our diffusion-binding model only considered the chromosome as a static matrix for the attachment of ParA-ATP dimers. Although chromosomal loci keep their average physical position inside bacterial cells (<xref ref-type="bibr" rid="bib97">Viollier et al., 2004</xref>; <xref ref-type="bibr" rid="bib101">Wiggins et al., 2010</xref>), they are mobile and exhibit discernible motion independent of chromosome segregation (<xref ref-type="bibr" rid="bib26">Espeli et al., 2008</xref>; <xref ref-type="bibr" rid="bib99">Weber et al., 2010</xref>; <xref ref-type="bibr" rid="bib31">Hadizadeh Yazdi et al., 2012</xref>; <xref ref-type="bibr" rid="bib45">Javer et al., 2013</xref>). This suggests that the DNA-bound ParA-ATP dimers inside cells are not static; instead, they fluctuate locally due to their associations with a dynamic DNA matrix.</p><p>To realistically describe chromosome dynamics in our model, we tracked the dynamics of a LacI-CFP-labeled chromosomal locus (<italic>groESL</italic>) positioned near the middle of the <italic>C. crescentus</italic> cell prior to replication and segregation. We performed time-lapse imaging at 2-s interval and only analyzed cells with a single fluorescent locus to eliminate motions due to segregation. Each locus (<italic>n</italic> = 641) moved randomly around an equilibrium position within individual cells (<xref ref-type="fig" rid="fig5">Figure 5A</xref>). To measure temporal fluctuations in position at the single-cell level, we determined the deviations of the locus position from the equilibrium point (i.e., mean position for each trajectory) at each time-point. The distribution of <italic>groESL</italic> position deviations was well approximated by an asymmetric two-dimensional (2-D) Gaussian distribution (<xref ref-type="fig" rid="fig5">Figure 5B</xref>). This indicates that the DNA locus moves in an asymmetric 2-D harmonic potential, which implies elastic dynamics. This is consistent with the recent proposal that bacterial chromosomes behave like elastic filaments (<xref ref-type="bibr" rid="bib101">Wiggins et al., 2010</xref>).<fig id="fig5" position="float"><object-id pub-id-type="doi">10.7554/eLife.02758.022</object-id><label>Figure 5.</label><caption><title>Chromosomal loci exhibit elastic dynamics.</title><p>(<bold>A</bold>) Representative trajectory of a LacI-CFP-labeled <italic>groESL</italic> locus tracked in live CJW2966 cells showing the dynamics of a chromosomal locus. The DNA locus was imaged every 2 s for 180 s. The displacements were colored as a function of time and overlaid with the cell outline (green). The zoomed trajectory in the inset shows the magnitude of displacements. To induce LacI-CFP expression, cells were incubated for 1 hr with 0.03% xylose prior to imaging. (<bold>B</bold>) <italic>Left</italic>, two-dimensional distribution of the <italic>groESL</italic> locus positions relative to the mean position of each trajectory. The scatter plots were generated from locus positions of 641 trajectories while the mesh surface is the best 2-D asymmetrical Gaussian fit (with <italic>σ</italic><sub><italic>long</italic></sub> = 0.06 µm and <italic>σ</italic><sub><italic>short</italic></sub> = 0.04 µm). The lower plane is a heatmap of the experimental data. <italic>Right</italic>, the same data set is represented as 1-D distributions of the <italic>groESL</italic> locus positions relative to the mean position of each trajectory along the long and short cell axes in single cells. Experimental data (filled circles, long axis; open circles, short axis) and Gaussian fits (solid line, long axis; dashed line, short axis) are shown. (<bold>C</bold>) 1-D distributions of the 139_lac and 165_lac locus positions (<xref ref-type="bibr" rid="bib97">Viollier et al., 2004</xref>) relative to the mean position of each trajectory along the long and short cell axes in single cells. <italic>Left</italic>, asymmetrical Gaussian fit gives <italic>σ</italic><sub><italic>long</italic></sub> = 0.06 µm and <italic>σ</italic><sub><italic>short</italic></sub> = 0.03 µm for the 139_lac locus in which the <italic>lac</italic> operators are inserted at position 1599540 on the <italic>C. crescentus</italic> chromosome (CJW5466 strain). <italic>Right</italic>, asymmetrical Gaussian fit gives <italic>σ</italic><sub><italic>long</italic></sub> = 0.05 µm and <italic>σ</italic><sub><italic>short</italic></sub> = 0.03 µm for the 165_lac locus in which the <italic>lac</italic> operators are inserted at position 2481399 on the <italic>C. crescentus</italic> chromosome (CJW5468 strain).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.022">http://dx.doi.org/10.7554/eLife.02758.022</ext-link></p></caption><graphic xlink:href="elife02758f005"/></fig></p><p>Gaussian fitting along long and short cell axes yielded standard deviations <italic>σ</italic><sub><italic>long</italic></sub> = 0.064 ± 0.002 µm (best fit ± error of fitting) and <italic>σ</italic><sub><italic>short</italic></sub> = 0.038 ± 0.001 µm (<xref ref-type="fig" rid="fig5">Figure 5B</xref>), which were converted (using <xref ref-type="disp-formula" rid="equ3">Equation 2</xref>, 'Materials and methods') into effective spring constants (<italic>k</italic><sub><italic>sp</italic></sub>) of 0.001 pN/nm and 0.003 pN/nm along the long and short axes, respectively. We also measured the fluctuations of two other chromosomal loci (139_lac and 165_lac) at positions 1599540 and 2481399 on the chromosomal map (<xref ref-type="bibr" rid="bib97">Viollier et al., 2004</xref>) and observed similar elastic behaviors (<xref ref-type="fig" rid="fig5">Figure 5C</xref>). We used the mean <italic>σ</italic><sub><italic>long</italic></sub> and <italic>σ</italic><sub><italic>short</italic></sub> values of these three chromosomal loci (<xref ref-type="table" rid="tbl2">Table 2</xref>) to quantitatively incorporate the intrinsic fluctuating motion of DNA-bound ParA-ATP dimers into the diffusion-binding model. Simulation of this revised model, named the ‘DNA-relay’ model hereafter (<xref ref-type="fig" rid="fig4">Figure 4A</xref>), showed that considering the DNA as a dynamic matrix has a dramatic effect, yielding fast and robust translocation of partition complexes (<xref ref-type="fig" rid="fig4">Figure 4B,C</xref>; <xref ref-type="other" rid="video3">Video 3</xref>).<media content-type="glencoe play-in-place height-250 width-310" id="video3" mime-subtype="avi" mimetype="video" xlink:href="elife02758v003.avi"><object-id pub-id-type="doi">10.7554/eLife.02758.023</object-id><label>Video 3.</label><caption><title>Example of a simulated trajectory for the DNA-relay model.</title><p>Trajectories were generated by Brownian dynamics simulations with time step <italic>dt</italic> = 1 ms and following parameters: diffusion coefficient of partition complex <italic>D</italic><sub><italic>PC</italic></sub> = 0.0001 µm<sup>2</sup> s<sup>−1</sup>, total number of ParA dimers <italic>n</italic><sub><italic>ParA</italic></sub> = 90, ParB-stimulated rate of ATPase activity <italic>k</italic><sub><italic>ca</italic>t</sub> = 0.03 s<sup>−1</sup>, rate constant for DNA binding <italic>k</italic><sub><italic>DB</italic></sub> = 0.03 s<sup>−1</sup> and spring constant <italic>k</italic><sub><italic>sp</italic></sub>/<italic>kT</italic> = 1/σ<sup>2</sup> = 280 μm<sup>−2</sup>. The partition complex and ParA-ATP dimers are shown as green and red spheres, respectively. Shown here is a representative trajectory in absolute cell coordinate (0 µm = old pole; 2.5 µm = new pole) as a function of time in a virtual cell.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.023">http://dx.doi.org/10.7554/eLife.02758.023</ext-link></p></caption></media></p><p>The ability of the DNA-relay model to reproduce the experimental results (<xref ref-type="fig" rid="fig4">Figure 4B,C</xref>) is particularly remarkable given that the model was grounded on experimentally measured data (<xref ref-type="table" rid="tbl2">Table 2</xref>) and did not rely on parameter optimization. In this model, the DNA-bound ParA-ATP dimers fluctuate around the equilibrium point of the underlying DNA loci. When the partition complex catches DNA-bound ParA-ATP dimers in a stretched out-of-equilibrium state, it experiences the elastic force, which moves the complex toward the equilibrium point until ATP hydrolysis releases it. Repetition of the process results in a <italic>relay</italic> of the partition complex from one chromosomal region to another. Directionality arises from the presence of the ParA-ATP dimer gradient. Since there are more DNA-bound ParA-ATP dimers toward the new pole, the partition complex will tend to encounter these DNA-bound ParA-ATP dimers as they stretch toward the partition complex. This results in a net force and hence translocation relay toward the new pole.</p><p>From our estimate of diffusion coefficient of the partition complex (<italic>D</italic><sub><italic>PC</italic></sub> = 0.0001 μm<sup>2</sup> s<sup>−1</sup>, see <xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2</xref>) and its velocity during ParA-dependent phase (<italic>v</italic> = 0.003 µm/s, <xref ref-type="fig" rid="fig2">Figure 2E</xref>), one can estimate that the partition complex experiences a force <italic>F</italic> = <italic>v</italic> (<italic>kT</italic>/<italic>D</italic><sub><italic>PC</italic></sub>) = 0.1 pN (where <italic>k</italic> is the Boltzmann constant and <italic>T</italic> is the absolute temperature). This is in good agreement with the characteristic elastic force generated from chromosomal locus dynamics, which can be estimated as <italic>F</italic> = <italic>k</italic><sub><italic>sp</italic></sub> <italic>σ</italic><sub><italic>long</italic></sub> = 0.06 pN (where <italic>k</italic><sub><italic>sp</italic></sub> is the measured spring constant and <italic>σ</italic><sub><italic>long</italic></sub> is the standard deviation of the DNA locus from equilibrium). Thus, one or more interactions with DNA-bound ParA dimers provide sufficient force to account for the observed partitioning velocity, providing further support for the DNA-relay mechanism.</p></sec><sec id="s2-8"><title>The ParB-bound <italic>parS</italic> region transiently decompacts during translocation</title><p>The elastic force in the DNA-relay mechanism implies that the partition complex is under tension when it is bound to DNA-associated ParA-ATP dimers (i.e., during ParA-dependent translocation). We found evidence supporting this notion when we examined the fluorescent GFP-ParB/<italic>parS</italic> signal. The GFP-ParB/<italic>parS</italic> signal formed a diffraction-limited focus when located close to the cell poles, that is, before or after segregation when GFP-ParB/<italic>parS</italic> was not interacting with ParA. However, the fluorescent signal associated with the segregating GFP-ParB/<italic>parS</italic> region (i.e., interacting with DNA-bound ParA dimers) frequently adopted an extended configuration (<xref ref-type="fig" rid="fig6">Figure 6A</xref>), consistent with a force decompacting the <italic>parS</italic> region. We confirmed that this extended conformation was not due to rapid motions of GFP-ParB/<italic>parS</italic> during image acquisition as it was readily observed in formaldehyde-fixed cells (<xref ref-type="fig" rid="fig6">Figure 6B</xref>).<fig id="fig6" position="float"><object-id pub-id-type="doi">10.7554/eLife.02758.024</object-id><label>Figure 6.</label><caption><title>The ParB/<italic>parS</italic> complex transiently adopts an extended conformation during the fast segregation phase.</title><p>(<bold>A</bold>) A fraction of GFP-ParB/<italic>parS</italic> complexes (red arrows) adopts extended conformation that appears as non-diffraction limited spots in fluorescent images of live CJW4762 cells. (<bold>B</bold>) Same as (<bold>A</bold>) except that cells were fixed with 4% formaldehyde prior imaging. (<bold>C</bold>) The aspect ratio (AR) of CFP-ParB/<italic>parS</italic> complexes in live CJW3367 cells was calculated as the ratio of the longest dimension, <italic>l</italic>, to the shortest dimension, <italic>d</italic>, for each partition complex signal. A representative cell is shown with the fluorescent CFP-ParB/<italic>parS</italic> signals outlined in yellow. (<bold>D</bold>) The propensity of a CFP-ParB/<italic>parS</italic> partition complex (PC) to display a decompacted conformation is shown with respect to cellular position. Individual CFP-ParB/<italic>parS</italic> complexes were binned according to their relative positions in the cell with old pole = 0 and new pole = 1 (see ‘Materials and methods’ for pole discrimination). The fraction of CFP-ParB/<italic>parS</italic> complexes with AR &gt;1.5 in each bin are shown. (<bold>E</bold>) <italic>Top</italic>, representative time-lapse sequence (4-s intervals) showing de-compaction and recoiling of a segregating partition complex (marked by GFP-ParB) in a CJW4762 cell. <italic>Bottom</italic>, ARs of the anchored (red) and segregating (blue) ParB/<italic>parS</italic> complexes as a function of time is shown. For all the experiments indicated above, the expression of ParB fusion proteins was induced with 0.03% xylose in M2G for 60–75 min prior to synchronization and imaging. All scale bars = 1 µm.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.024">http://dx.doi.org/10.7554/eLife.02758.024</ext-link></p></caption><graphic xlink:href="elife02758f006"/></fig></p><p>To quantify these observations, we used a filtering-based algorithm to identify fluorescent objects (CFP-ParB/<italic>parS</italic> complexes) in each cell (<xref ref-type="bibr" rid="bib69">Parry et al., 2014</xref>). Analyzing only cells in which the CFP-ParB/<italic>parS</italic> complex has duplicated and separated, we measured the aspect ratio (AR) of each partition complex (<xref ref-type="fig" rid="fig6">Figure 6C</xref>), a metric that has also been used to distinguish between compacted and decompacted states of chromatin loci in eukaryotic nuclei (<xref ref-type="bibr" rid="bib96">Verdaasdonk et al., 2013</xref>). A perfectly round CFP-ParB/<italic>parS</italic> signal is expected to have an AR of 1 while a stretched signal has an AR score greater than 1 (<xref ref-type="fig" rid="fig6">Figure 6C</xref>). We visually correlated a subset of the spots with their AR and verified that an AR cutoff of 1.5 reliably discriminated between the compacted and decompacted conformations. Using this AR cutoff, we found that the frequency of decompacted conformation (AR &gt;1.5) is low near the new and old poles (<xref ref-type="fig" rid="fig6">Figure 6D</xref>), where the ParB/<italic>parS</italic> complexes are expected to either be anchored by PopZ or diffuse locally (<xref ref-type="fig" rid="fig2">Figure 2A</xref>). However, the frequency of decompacted CFP-ParB/<italic>parS</italic> signals increased as the partition complex moved away from the old pole (<xref ref-type="fig" rid="fig6">Figure 6D</xref>). Thus, the frequency of decompacted CFP-ParB/<italic>parS</italic> signals correlated with the concentration of ParA-ATP dimers, suggesting that the stretched conformation adopted by the partition complex is triggered by ParB interacting with ParA-ATP dimers bound to the dynamic DNA. Furthermore, the AR of the segregating partition complex appeared to fluctuate over time (<xref ref-type="fig" rid="fig6">Figure 6E</xref>), consistent with the partition complex dynamically responding to fluctuating pulling forces.</p></sec><sec id="s2-9"><title>The proper range of ATPase activity is important for efficient and robust translocation</title><p>The DNA-relay model suggests that the ParABS system utilizes intrinsic DNA dynamics inside cells to translocate a cargo. It also suggests that the role of a ParA-ATP dimer is to provide a timed and reversible connection between the partition complex and the dynamic DNA. According to the model, a fluctuating DNA locus is captured out-of-equilibrium by the partition complex (via ParA-ATP dimers). As the DNA locus returns to its equilibrium, it brings the partition complex along. The association time between ParB/<italic>parS</italic> and the DNA-bound ParA-ATP dimer—which is defined by ParB-stimulated ATP hydrolysis rate (<italic>k</italic><sub><italic>cat</italic></sub>)—is critical for this mechanism to work efficiently. Under optimal conditions, the partition complex would be released immediately once equilibrium is reached to catch the next out-of-equilibrium DNA-bound ParA-ATP dimer. This would result in an apparent relay of the partition complex from one DNA-bound ParA-ATP dimer to another. A back-of-the-envelope calculation ('Materials and methods') estimates that the optimal attachment time would be 36 s. Thus, the optimal rate of ATP hydrolysis, which is the inverse of this optimal attachment time, should be about 0.03 s<sup>−1</sup>. This value is in remarkably good agreement with the ParB-induced ATP hydrolysis rate (<italic>k</italic><sub>cat</sub> = 0.03 s<sup>−1</sup>) we obtained from our biochemical data (<xref ref-type="fig" rid="fig1">Figure 1F</xref>).</p><p>We expect that if the ATP hydrolysis were too slow, the partition complex would remain bound to a ParA-ATP dimer too long, slowing down progression. Conversely, too high ATP hydrolysis rate would result in premature release of the complex (before it reached the equilibrium point), under-utilizing the potential of the elastic force. To examine how the performance of the DNA-relay model depends on <italic>k</italic><sub><italic>cat</italic></sub>, we varied the <italic>k</italic><sub><italic>cat</italic></sub> values in our simulations. We found that for the estimated <italic>D</italic><sub><italic>PC</italic></sub> = 0.0001 μm<sup>2</sup> s<sup>−1</sup> (<xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2</xref>), decreasing or increasing <italic>k</italic><sub><italic>cat</italic></sub> by 10-fold negatively impacts the speed and robustness of translocation (<xref ref-type="fig" rid="fig7">Figure 7A,B</xref>). This suggests that the hydrolysis rate has been optimized during evolution for the proposed DNA-relay mechanism.<fig id="fig7" position="float"><object-id pub-id-type="doi">10.7554/eLife.02758.025</object-id><label>Figure 7.</label><caption><title>Appropriate ParB-stimulated ParA ATPase rates are important for the robustness of the DNA-relay model.</title><p>(<bold>A</bold>) Averaged trajectories of the partition complex along the long cell axis during the fast ParA-dependent phase were simulated using varied ParB-stimulated ParA ATPase rates (<italic>k</italic><sub><italic>cat</italic></sub>) and a fixed diffusion coefficient for the ParB/<italic>parS</italic> complex (<italic>D</italic><sub><italic>PC</italic></sub>) of 0.0001 μm<sup>2</sup>/s. (<bold>B</bold>) Same data set as (<bold>A</bold>), except that for each <italic>k</italic><sub><italic>cat</italic></sub>, the fraction of trajectories that completed translocation are shown as a function of time.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.025">http://dx.doi.org/10.7554/eLife.02758.025</ext-link></p></caption><graphic xlink:href="elife02758f007"/></fig></p></sec></sec><sec id="s3" sec-type="discussion"><title>Discussion</title><p>Central to the mechanism of ParABS-dependent transport is the origin of the translocation force. We did not find any evidence supporting a eukaryotic-like filament-based mechanism. Rather, our experiments and simulations collectively suggest a DNA-relay mechanism, in which the DNA-associated ParA-ATP dimers serve as transient tethers that harness the intrinsic dynamics of the chromosome to relay the partition complex from one DNA region to another. In this model, the translocation force is derived from the elastic property of the chromosome. Elastic dynamics may be inherent to highly compacted and ordered DNA as they have also been observed for chromosomal loci in eukaryotic nuclei (<xref ref-type="bibr" rid="bib96">Verdaasdonk et al., 2013</xref>) as well as in nucleoids isolated from lysed <italic>E. coli</italic> cells (<xref ref-type="bibr" rid="bib16">Cunha et al., 2005</xref>). Furthermore, a modeling study has shown that the <italic>E. coli</italic> chromosome behaves like a spring filament based on the positional distribution of chromosomal loci across cells (<xref ref-type="bibr" rid="bib101">Wiggins et al., 2010</xref>).</p><p>A recent theoretical study suggests that a ParA gradient with ParB binding alone may generate a thermodynamic force (called chemophoresis) (<xref ref-type="bibr" rid="bib88">Sugawara and Kaneko, 2011</xref>). While such force may contribute, it is not clear whether the in vivo conditions (e.g., ParA concentration, cargo size, time scale) can result in a thermodynamic force large enough to account for the translocation kinetics observed inside cells. On the other hand, we show here that the DNA-relay mechanism is sufficient to produce the sub-piconewton force that we estimated for ParA-dependent translocation.</p><p>The dynamic nature of chromosomes seem to be a universal feature of active cells (<xref ref-type="bibr" rid="bib61">Marshall et al., 1997</xref>; <xref ref-type="bibr" rid="bib99">Weber et al., 2010</xref>, <xref ref-type="bibr" rid="bib100">2012</xref>; <xref ref-type="bibr" rid="bib45">Javer et al., 2013</xref>; <xref ref-type="bibr" rid="bib96">Verdaasdonk et al., 2013</xref>; <xref ref-type="bibr" rid="bib103">Zidovska et al., 2013</xref>). Since many ParA-like proteins involved in positioning of various large cytoplasmic cargos (chromosomal regions, plasmids, chemotaxis clusters) have a conserved and functionally important DNA-binding surface (<xref ref-type="bibr" rid="bib34">Hester and Lutkenhaus, 2007</xref>; <xref ref-type="bibr" rid="bib15">Castaing et al., 2008</xref>; <xref ref-type="bibr" rid="bib70">Ptacin et al., 2010</xref>; <xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>; <xref ref-type="bibr" rid="bib75">Roberts et al., 2012</xref>), the DNA dynamics may also be exploited in these systems to achieve active partitioning.</p><p>Another common property of all ParABS systems examined biochemically so far is the relatively low ParA ATPase activity, even after ParB stimulation. Our data suggest that ATPase activity is near-optimal for cargo translocation via the DNA-relay mechanism (<xref ref-type="fig" rid="fig7">Figure 7</xref>).</p><p>ParA-like proteins have been implicated in other biological functions besides partitioning (<xref ref-type="bibr" rid="bib90">Thanbichler and Shapiro, 2006</xref>; <xref ref-type="bibr" rid="bib67">Murray and Errington, 2008</xref>). For example, <italic>B. subtilis</italic> Soj controls DNA replication initiation in vegetative cells (<xref ref-type="bibr" rid="bib67">Murray and Errington, 2008</xref>). While this distinct function involves interactions with other cellular components (e.g., DnaA), biochemical evidence suggests that differential regulation of ParA dimeric states by ParB also plays an important role. As shown here, <italic>C. crescentus</italic> ParA ATPase activity requires high concentration of ParB (<xref ref-type="fig" rid="fig1">Figure 1F</xref>), which insulates ParA-ATP dimers from premature turnover by diffusing ParB and restricts stimulation of ATP hydrolysis to the ParB-rich partition complex. In contrast, in <italic>B. subtilis</italic>, a low concentration of Spo0J (ParB) is sufficient to stimulate Soj ATPase activity, such that even diffusing Spo0J promotes ATP hydrolysis (<xref ref-type="bibr" rid="bib82">Scholefield et al., 2011</xref>). As a consequence, in <italic>C. crescentus</italic>, ParA accumulates as a cloud of DNA-bound ParA-ATP dimers, primed for the transport of the ParB/<italic>parS</italic> complex, whereas in <italic>B. subtilis</italic>, Soj mostly exists in a replication-inhibitory monomeric form that cannot bind the DNA (<xref ref-type="bibr" rid="bib82">Scholefield et al., 2011</xref>). Consistent with this notion, a mere overproduction of Soj, which should tip the balance toward the Soj dimer state, results in cloud-like localization of Soj and Spo0J/<italic>parS</italic> translocation in the receding wave of the Soj cloud (<xref ref-type="bibr" rid="bib62">Marston and Errington, 1999</xref>; <xref ref-type="bibr" rid="bib71">Quisel et al., 1999</xref>). Thus, a common biochemical framework can be tuned to generate different system behaviors.</p><p>In conclusion, we present a new physical mechanism for intracellular transport in which the chromosome plays a mechanical function. We anticipate that other facilitating or prohibiting elements (e.g., replication, transcription, and entropy-driven polymer separation, chromosome topology and glassy cytoplasm) (<xref ref-type="bibr" rid="bib47">Jun and Mulder, 2006</xref>; <xref ref-type="bibr" rid="bib52">Le et al., 2013</xref>; <xref ref-type="bibr" rid="bib98">Wang et al., 2013</xref>; <xref ref-type="bibr" rid="bib69">Parry et al., 2014</xref>), which were not considered in our DNA-relay model, have an influence on chromosome partitioning. Further quantitative knowledge of these effects will allow us to build upon our DNA-relay model to gain a more comprehensive understanding of chromosome segregation in bacteria.</p></sec><sec id="s4" sec-type="materials|methods"><title>Materials and methods</title><sec id="s4-1"><title>Strains, protein fusion functionality and culture conditions</title><p>Strains used in this study and methods of strains construction are detailed in Table S1 in <xref ref-type="supplementary-material" rid="SD1-data">Supplementary file 1</xref>. Oligonucleotide primers used in this study are tabulated in Table S2, which is presented in <xref ref-type="supplementary-material" rid="SD2-data">Supplementary file 2</xref> together with methods of plasmids construction. Synchrony, conjugation, transformation and transduction with the bacteriophage ΦCR30 were performed as previously described (<xref ref-type="bibr" rid="bib24">Ely, 1991</xref>). <italic>C. crescentus</italic> strains were grown at 30°C in the defined minimal M2G medium (0.87 g/l Na<sub>2</sub>HPO<sub>4</sub>, 0.54 g/l KH<sub>2</sub>PO<sub>4</sub>, 0.50 g/l NH<sub>4</sub>Cl, 0.2% [wt/vol] glucose, 0.5 mM MgSO<sub>4</sub>, 0.5 mM CaCl<sub>2</sub>, 0.01 mM FeSO<sub>4</sub>) unless otherwise stated. Since none of the <italic>C. crescentus</italic> strains used in this study contained replicative plasmids, antibiotics were omitted when cells were grown for the purpose of imaging. For all experiments, cells were harvested from exponentially growing cultures.</p><p>ParA and ParB are essential for viability in <italic>C. crescentus</italic> (<xref ref-type="bibr" rid="bib65">Mohl and Gober, 1997</xref>). The <italic>parA-dendra2</italic> (this study), <italic>parA-eyfp</italic> (<xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>) and e<italic>gfp-parB</italic> (<xref ref-type="bibr" rid="bib90">Thanbichler and Shapiro, 2006</xref>) fusions used in this study support viability when expressed as the only copy, indicating that they are functional. We previously showed that <italic>parA-eyfp</italic> is functional (<xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>). In the M2G medium at 30°C, the doubling times for the strains expressing <italic>parA-dendra2</italic> or e<italic>gfp-parB</italic> are 133 ± 2 min and 142 ± 2 min, respectively, as compared to 133 ± 2 min for wild-type CB15N grown under the same condition. For the strains in which the synthesis of ParA and ParB protein fusions was induced from the xylose-inducible promoter (pXyl) as a second copy, cells were grown in the presence of 0.03% xylose for 60–75 min (fluorescent ParB fusions) or 0.3% xylose for 1 hr (ParA-Dendra2). Under these inducing conditions, the localization of these second-copy fusions was visually undistinguishable from that of single copies (data not shown).</p></sec><sec id="s4-2"><title>Purification of ParA derivatives</title><p>For the purification of ParA or ParA<sub>R195E</sub>, BL21(DE3) cells carrying pET24HT-ParA or pET24HT-ParA(R195E) were grown in Luria Broth supplemented with 50 µg/ml kanamycin to an OD<sub>600</sub> = 0.6, chilled to 18°C before IPTG (1 mM) was added to induce His6-ParA synthesis overnight at 18°C. Cells were collected by centrifugation at 5000<italic>×g</italic> for 20 min and stored at −80°C. The cell pellet was resuspended in buffer A1 (100 mM Hepes/KOH, 100 mM KCl, 1 mM EDTA and 10% glycerol) supplemented with EDTA-free Roche protease inhibitor, 1 mM DTT, 0.5 mM Mg-ATP, 1 kU DNase I and 0.5 mg/ml lysozyme. The cell suspension was incubated on ice for 30 min before 4 M KCl was added to a final concentration of 1 M (to dissociate ParA from the DNA). Following sonication, the sample was clarified by centrifugation at 100,000×<italic>g</italic> for 30 min. One molar imidazole (pH 7) was added to the clarified lysate to a final concentration of 40 µM. The supernatant was then passed through a Ni-NTA column (Qiagen, Germany) thrice by gravity flow. The resin was washed with 30 column volumes of buffer A2 (25 mM Hepes/KOH pH 7.4, 450 mM KCl, 50 mM potassium glutamate [KGlu], 1 mM MgSO4, 40 mM imidazole, 1 mM DTT and 100 µM MgATP) before elution was carried out with 50 ml of buffer A3 (25 mM Hepes/KOH pH 7.4, 450 mM KCl, 50 mM KGlu, 1 mM MgSO4, 300 mM imidazole, 1 mM DTT and 100 µM MgATP). Eluent was collected in 1-ml fractions. Fractions containing high concentrations of protein (determined by Bradford assay using Bovine IgG as standards) were pooled. The pooled sample usually had ∼2–2.5 mg/ml protein content as determined by Bradford assay. TEV protease was diluted into the sample at ∼1:30 (wt/wt) ratio and incubated at room temperature for 2 hr to remove the 6 × His tag. The cleavage efficiency was approximately 90–95%. The sample was then concentrated approximately twofold using Amicon Ultra-14 (MWCO = 10 kDa) and subjected to gel filtration fractionation on a Superdex 75 16/60 column (GE Healthcare Life Sciences, Pittsburgh, PA) at 1 ml/min flow rate in buffer A4 (25 mM HEPES/KOH pH 7.5, 200 mM KGlu, 1 mM MgSO<sub>4</sub>, 1 mM DTT, 100 µM Mg-ATP and 5% glycerol). Residual His-tagged proteins were removed by passing the sample through a HisTrap HP column (GE Healthcare Life Sciences) in buffer A4 supplemented with 40 mM imidazole. A pooled sample was concentrated to ∼1.5 mg/ml and subjected to dialysis against buffer A4 supplemented with 20% glycerol overnight at 4°C, and stored in small aliquots at −80°C.</p><p>Polyhistidine-tagged ParA<sub>G16V</sub>-YFP was purified using Ni<sup>2+</sup> column as described for wild-type protein with the following modifications. To remove the imidazole, we induced ParA<sub>G16V</sub>-YFP-His6 precipitation by dialyzing the sample into buffer A3 and re-solubilized the precipitated protein (which we isolated by centrifugation) in buffer A1 supplemented with 1 M KCl and 1 mM DTT.</p></sec><sec id="s4-3"><title>Purification of ParB variants</title><p>BL21(DE3)/pET21b-ParB cells or BL21(DE3)/pET21b-ParB(L12A) cells grown up to OD<sub>600</sub> = 0.6 were incubated with 1 mM IPTG for 4 hr at 37°C. Cells were collected by centrifugation at 5000<italic>×g</italic> for 10 min at 4°C and frozen at −80°C. Cells were resuspended in buffer B1 (50 mM Hepes/KOH pH 7.0, 25 NaCl, 0.1 mM mM EDTA, 5 mM MgCl<sub>2</sub> and 1 mM DTT) supplemented with 1 kU DNase I and Roche EDTA-free protease inhibitor. Cell lysis was induced by passing the sample through a French press twice at 16,000 psi. Following 30 min incubation on ice, the sample was clarified by two rounds of centrifugation at 50,000<italic>×g</italic> for 25 min. The clarified lysate was injected into an HiPrep SP 16/10 column (GE Healthcare Life Sciences) equilibrated in buffer B1 at 2 ml/ml and washed with four column volumes (CV) of buffer B1 before a gradient (50–500 mM NaCl) was developed over 20 CV with buffer B2 (50 mM Hepes/KOH pH 7.0, 1 M NaCl, 0.1 mM EDTA, 5 mM MgCl<sub>2</sub> and 1 mM DTT). Fractions containing ParB-His6 were pooled and imidazole was added to ∼15 mM before incubating the sample with NiNTA resin (Qiagen) for 1 hr. The mixture was poured into the column to remove unbound proteins. The resin was washed with more than 20 CV of buffer B3 (25 mM Hepes/KOH pH 7.0, 300 mM NaCl, 5 mM MgCl<sub>2</sub>, 40 mM imidazole and 1 mM DTT) followed by 2 CV of buffer B3 minus imidazole, and eluted with buffer B4 (25 mM Hepes/KOH pH 7.0, 300 mM NaCl, 5 mM MgCl<sub>2</sub>, 300 mM imidazole and 1 mM DTT). Fractions containing ParB-His6 were pooled and subjected to dialysis in 100 × sample volume of buffer B5 (25 Tris/HCl pH 7.5, 50 mM NaCl, 5 mM MgSO<sub>4</sub>, 0.1 mM EDTA and 1 mM DTT) overnight at 4°C. The sample was clarified at 30,000 <italic>× g</italic> for 15 min prior to injection into an HiPrep Heparin 16/10 column equilibrated in buffer B5 at 1.5 ml/min. The column was washed with 5 CV of buffer B5 before a gradient (50–250 mM NaCl) was developed over 20 CV with buffer B6 (25 Tris/HCl pH 7.5, 1000 mM NaCl, 5 mM MgSO<sub>4</sub>, 0.1 mM EDTA and 1 mM DTT). Fractions containing ParB-His6 were concentrated in a Amicon-15 unit and chromatographed over a Superdex 75 16/60 column equilibrated in buffer B7 (25 mM Hepes/KOH pH 7.5, 150 mM KGlu, 5 mM MgSO<sub>4</sub>, 0.1 mM EDTA and 1 mM DTT) at a flow rate of 0.75 ml per min. Pooled samples were subjected to dialysis with two changes of 1 l of buffer B7 + 20% glycerol and stored at −80°C in small aliquots.</p></sec><sec id="s4-4"><title>Gel filtration analysis</title><p>ParA samples in buffer A4 + 20% glycerol were incubated with 25 mM EDTA for 1 hr at 37°C before their buffer was exchanged with buffer C (25 mM Hepes/KOH pH 7.5, 150 mM KGlu, 2.5 mM EDTA and 1 mM DTT) using a spin column to remove ATP. The samples were mixed with 2.5 mM Mg-ATP (for ‘+ATP’ reactions) or buffer (for ‘−ATP’ reactions), incubated at room temperature for 10 min, and centrifuged at 16,000<italic>×g</italic> for 30 s. 50-microliter samples of ParA at approximately 50 µM were injected into a Superdex 75 10/300 GL column (GE Healthcare Life Sciences) equilibrated with 25 mM Hepes/KOH pH 7.5, 150 mM KGlu, 5 mM MgSO<sub>4</sub>, 2 mM Mg-ATP, 0.1 mM EDTA and 1 mM DTT for the +ATP reactions or 25 mM Hepes/KOH pH 7.5, 150 mM KGlu, 2.5 mM EDTA and 1 mM DTT for the −ATP reactions at a flow rate of 0.6 ml/min. The elution profiles were monitored at an absorbance of 280 nm.</p></sec><sec id="s4-5"><title>SEC-UV/LS/RI analysis</title><p>To examine whether ParB forms dimers in solution, we performed a size exclusion chromatography (SEC) coupled with UV, on-line laser light scattering (LS) and refractive index (RI) detectors (SEC-UV/LS/RI). Specifically, purified His6-ParB (pre-filtered through a 0.22 µm filter) was applied on a Superose 6, 10/30, HR SEC column (GE Healthcare Life Sciences) equilibrated in 100 mM HEPES, pH 7.4, 150 mM NaCl, 1 mM DTT buffer and chromatographed at a flow rate of 0.3 ml/min. Elution from SEC was monitored by a photodiode array (PDA) UV/VIS detector (996 PDA, Waters Corp., Milford, MA), differential refractometer (OPTI-Lab, or OPTI-rEx Wyatt Corp., Santa Barbara, CA), and static, multi-angle laser light scattering detector (DAWN-EOS, Wyatt Corp.). The Millennium software (Waters Corp.) controlled the HPLC <italic>Alliance</italic> 2965 (Waters Corp.) system, to which the column was connected to, and data collection from the multi-wavelength UV/VIS detector, while the ASTRA software (Wyatt Corp.) collected data from the refractive index detector, the light scattering detectors, and recorded the UV trace at 280 nm sent from the PDA detector. Data collection and analyses were carried out at the Keck Foundation Biotechnology Resource Laboratory, Yale University.</p></sec><sec id="s4-6"><title>ATPase assay</title><p>The ATPase activity of ParA and ParA<sub>R195E</sub> was measured using an ATP/NADH-linked assay (<xref ref-type="bibr" rid="bib18">De La Cruz et al., 2000</xref>), which we modified for a 96-well plate format. Reactions (100 μl) containing the appropriate concentrations of ParA, ParB and salmon sperm DNA (Invitrogen), 5 × NADH enzyme mix (310 µM NADH, 100 U/ml of lactic dehydrogenase, 500 U/ml pyruvate kinase, and 2.5 mM phosphoenolpyruvate), 25 mM Hepes/KOH (pH 7.4), 10 mM MgSO<sub>4</sub>, 150 mM KGlu, 5% glycerol and 1 mM DTT were mixed with 2.5 mM ATP unless mentioned otherwise. Absorbance measurements at 340 nm were taken in Corning UV Transparent Flat Bottom 96-well plates in a Synergy 2 plate reader (BioTek, Winooski, VT) at 30°C at 1-min intervals. Initial velocities were calculated from a linear regression of each time course and corrected for spontaneous ATP hydrolysis and NADH oxidation. We also ran parallel control experiments to account for residual ATPase in ParB protein preparations. A standard curve with known amounts of NADH was obtained and used to convert the rate of ADP production from absorbance/time to concentration/rate.</p></sec><sec id="s4-7"><title>Determination of ParA and ParB concentrations in <italic>C. crescentus</italic> by quantitative Western blotting</title><p>We first estimated the number of ParB and ParA molecules by quantitative Western blotting of cell lysates. For ParB, swarmer cells of <italic>C. crescentus</italic> CB15N were isolated by differential centrifugation (<xref ref-type="bibr" rid="bib27">Evinger and Agabian, 1977</xref>) and resuspended in M2G medium to an OD<sub>660</sub> of 0.5. One milliliter of cell culture was pelleted and used to make a cell lysate for Western blotting. The cell lysate was separated on an Any-kD Mini-PROTEAN TGX Precast Gel (Biorad, Hercules, CA), proteins were transferred to a nitrocellulose membrane that was probed with 1:50,000 dilution of anti-ParB polyclonal antibody (Proteintech Group, Chicago, IL) and 1:10,000 dilution of anti-rabbit secondary antibody (Biorad). Signals were developed with an enhanced chemiluminescence reagent (GE Healthcare Life Sciences) and detected by exposing the membrane to a Kodak film (Carestream Health, Rochester, NY) or using a Typhoon PhosphoImager (GE Healthcare Life Sciences). The intensities of bands were quantified using ImageJ and compared against a standard curve generated from known amounts of ParB-His6 probed on the same blots. Since, at low concentrations, we lost significant amount of ParB-His6 presumably due to nonspecific binding of the protein to the wall of the plastic tubes, the ParB-His6 standard stock was prepared by diluting purified ParB-His6 in SDS buffer denatured cell lysates made from strain MT174 (which produces GFP-ParB instead of native ParB). After normalizing for the fraction of lysate loaded, we calculated the number of ParB molecules in the CB15N lysate by dividing the ParB amount by the molecular weight of ParB and by multiplying by the Avogadro number. In parallel, the number of cells used to prepare the cell lysate used for the Western blots was determined by serial dilution followed by quantification of colony forming unit (CFU) on an agar plate containing PYE medium. Using lysates made from four different pellets, we determined that swarmer cells contain 720 ± 80 (mean ± SD) ParB molecules (or 360 ParB dimers) per cell.</p><p>The number of ParA molecules per cell was determined using the same protocol as described for ParB with the following modifications. In the absence of high quality anti-ParA antibody, we used JL-8 anti-GFP antibody (Clontech, Mountain View, CA) to quantify the amount of ParA-YFP in a <italic>C. crescentus</italic> strain (CJW3010) in which <italic>parA</italic> has been cleanly replaced by a <italic>parA-yfp</italic> fusion at the native chromosomal location (<xref ref-type="bibr" rid="bib81">Schofield et al., 2010</xref>). Varying amount of purified ParA-YFP-His6 (added to cell lysate prepared from wild-type cells) was used to create a calibration curve. We used 1,000 × dilution of JL-8 as primary antibody and 10,000 × dilution of goat anti-mouse secondary antibody (Biorad). Since the dynamics of ParB/<italic>parS</italic> segregation in the ParA-YFP-producing CJW3010 strain is indistinguishable from that of the wild-type, we assume that wild-type cells contain similar concentration of ParA molecules.</p><p>To convert the number of molecules per cell to concentration, we divided the number of molecules per cell by the Avogadro number and the estimated volume of a typical swarmer cell. The cytoplasmic volume of a swarmer cell, 0.25 fL, was obtained by cryo-tomography from 3D segmentation of a <italic>C. crescentus</italic> swarmer cell (<xref ref-type="bibr" rid="bib13">Briegel et al., 2006</xref>). The concentrations of ParA and ParB were calculated using the formula = # Molecules/Avogadro Number × Volume M.</p></sec><sec id="s4-8"><title>Wide-field fluorescence imaging and image processing</title><p>For all microscopy observations, cells were spotted on 1% agarose pads containing M2G medium, unless specified otherwise. Images were acquired using an Eclipse Ti-U microscope (Nikon, Tokyo, Japan) with an Orca-ER camera (Hamamatsu Photonics, Hamamatsu City, Japan) and phase-contrast objective Plan Apochromat 100 × /1.40 NA (Carl Zeiss, Oberkochen, Germany) at room temperature except for time-lapse experiments (30°C). Images were acquired and processed with either MetaMorph software (Molecular Devices, Sunnyvale, CA) or MATLAB (The MathWorks, Natick, MA). Cell mesh creation and fluorescence quantification were done using the open source, MATLAB-based software MicrobeTracker (<xref ref-type="bibr" rid="bib86">Sliusarenko et al., 2011</xref>). Identification of diffraction-limited fluorescence spots was done using SpotFinder, an accessory in MicrobeTracker, unless mentioned otherwise.</p></sec><sec id="s4-9"><title>Quantification of ParB subcellular distribution</title><p>To measure the fraction of ParB molecules associated with the chromosomal <italic>parS</italic> region, we used a strain (MT174) in which the <italic>parB</italic> gene has been substituted by a functional <italic>parB-gfp</italic> fusion at the native chromosomal location without affecting the operon structure (<xref ref-type="bibr" rid="bib90">Thanbichler and Shapiro, 2006</xref>). MT174 cells and wild-type CB15N cells, both from exponential phase cultures, were spotted on the same pad and imaged. Cells were segmented using MicrobeTracker (<xref ref-type="bibr" rid="bib86">Sliusarenko et al., 2011</xref>). The signal intensity (in the GFP channel) of each cell normalized by its area was plotted as a histogram, which clearly showed two populations of cells (<xref ref-type="fig" rid="fig1s3">Figure 1—figure supplement 3B</xref>). A bimodal Gaussian model was used to fit the data. Autofluorescence in MT174 cells producing GFP-ParB was subtracted by the normalized signals detected in CB15N cells (lacking a GFP fusion). We used MicrobeTracker to quantify the fluorescence associated with segmented areas along the long cell axis. We assumed that segments with the least fluorescence concentration (fluorescence within the segment divided by the segment area) correspond to cell area far away from the GFP-ParB/<italic>parS</italic> complex and therefore their fluorescence values report the concentration of freely diffusing GFP-ParB. For each cell, we computationally ranked the fluorescence concentration within each cell segment, selected the lowest 10% of the total segments containing the lowest fluorescence concentration, calculated the average, and normalized this value to the total cell area to obtain the fluorescence value associated with the total diffusing GFP-ParB. This value was divided by the total GFP-ParB signal for that particular cell to obtain the fraction of diffusing GFP-ParB signal. The fraction of GFP-ParB in the partition complex = (1−fraction of diffusing ParB) × 100%.</p></sec><sec id="s4-10"><title>Analysis of the trajectory of the partitioning complex</title><p>To induce the expression of <italic>gfp-parB</italic>, 0.03% xylose was added to an exponential culture of CJW4762 cells for 60–75 min prior to subjecting the culture to synchrony. Isolated swarmer cells were spotted on a 1.5% agarose pad and imaged at 30-s intervals. Cell outlines were acquired using MicrobeTracker and the positions of the partition complex spots within each cell were detected and computed using SpotFinder (<xref ref-type="bibr" rid="bib86">Sliusarenko et al., 2011</xref>). The trajectory of each partition complex was built using a custom-written MATLAB script that minimizes the total displacements of the two spots between the current frame and the previous frame (<xref ref-type="supplementary-material" rid="SD3-data">Supplementary file 3</xref>). To analyze segregation, we considered only trajectories that reached the new pole. To identify the ‘fast’ translocation phase in each trajectory, we wrote a MATLAB script that first linearly interpolates and smoothes each trajectory along the long cell axis before calculating the second derivatives of the curve (<xref ref-type="supplementary-material" rid="SD4-data">Supplementary file 4</xref>). The two inflection points covering the longest distance travelled were defined as the start and end of the ‘run’ phase. All traces were inspected by eye and only traces with correctly assigned start and end points were kept (141 out of 155).</p></sec><sec id="s4-11"><title>Aspect ratio analysis of the fluorescent signal associated with the partition complex</title><p>Partition complexes were identified using a previously reported algorithm for detecting fluorescent objects (both diffraction-limited and non-diffraction limited) in images (<xref ref-type="bibr" rid="bib69">Parry et al., 2014</xref>).The output was analyzed to compute the major axis length and minor axis length for each partition complex using the regionprops function in MATLAB. The aspect ratio (or AR, the ratio between the major axis length and the minor axis length) was calculated for each partition complex. Before plotting AR as a function of cell coordinate, we oriented each cell such that zero corresponded to the old pole using the localization of ParA-YFP as a reference.</p></sec><sec id="s4-12"><title>Cleaning glass slides and cover slips for single-molecule imaging</title><p>Glass slides and cover slips used for single-molecule fluorescence microscopy were washed in the following order: 15 min sonication in 1 M KOH, 15 min sonication in milliQ H<sub>2</sub>O and 15 min sonication in 70% ethanol with 3 × milliQ H<sub>2</sub>O rinses between solution changes. Cleaned glass slides and cover slips were then dried with pressured air and used within the same day.</p></sec><sec id="s4-13"><title>Fluorescence-based quantification of ParA-YFP abundance in live <italic>C. crescentus</italic> cells</title><sec id="s4-13-1"><title>Measurement of single ParA-YFP fluorescence</title><p>Cleaned coverslips were treated with 0.1% poly-Lysine solution on one side for 30 min, washed extensively with buffer B7 supplemented with 10% glycerol and 0.5 mM DTT and dried with pressured air. To quantify the fluorescence intensity of single ParA-YFP molecules, we used a solution of ParA<sub>G16V</sub>-YFP-His6 (500 pM). This reagent was used because of its availability at the time of the experiment and the G16V mutation on ParA should not affect the fluorescent property of YFP. One hundred microliters of the ParA<sub>G16V</sub>-YFP-His6 solution was incubated on the poly-Lysine coated side of the coverlip for 10 s and washed extensively with buffer B7 supplemented with 10% glycerol and 0.5 mM DTT. Most of the wash solution was removed by contacting the side of the coverslip with a sheet of Kimwipe, leaving behind ∼1–3 µl. The coverslip was then mounted onto a cleaned glass slide and sealed. The images of the surface-immobilized YFP molecules were stream-acquired with 2-s integration time. In these images, ParA<sub>G16V</sub>-YFP-His6 molecules appeared as distinct diffraction-limited fluorescent spots. For image analysis, we centered a 9 × 9 pixel box on each diffraction limited spot and integrated the fluorescence intensity in the box over time (<xref ref-type="fig" rid="fig1s6">Figure 1—figure supplement 6A,B</xref>). To determine the fluorescence intensity of a single ParA<sub>G16V</sub>-YFP-His6 (or ParA-YFP) molecule, we analyzed only spots with a fluorescence profile that showed single-step photobleaching (<xref ref-type="fig" rid="fig1s6">Figure 1—figure supplement 6B</xref>, i). We determined the fluorescence intensity of a single YFP by calculating the difference in averaged fluorescence intensities before and after the stepwise photobleaching, <italic>ΔI</italic>. The mean fluorescence intensity of a single ParA-YFP molecule was determined from the mean of a Gaussian fit to the distribution of <italic>ΔI</italic> (<xref ref-type="fig" rid="fig1s6">Figure 1—figure supplement 6C</xref>).</p></sec><sec id="s4-13-2"><title>Measurement of total ParA-YFP fluorescence per cell</title><p>Exponential cultures of cells expressing <italic>parA-yfp</italic> from the <italic>parA</italic> native locus (CJW3010 strain) and wild type cells (CB15N which does not express <italic>yfp</italic>) at similar OD<sub>660</sub> were mixed at a 1:1 ratio before synchrony was performed to isolate swarmer cells. Wild-type cells were added to measure the fluorescence contribution from cellular autofluorescence. Swarmer cells of the two strains were then imaged on the same agarose pad using the same optical settings as those used to image single ParA-YFP molecules. Outlines of cells were obtained using MicrobeTracker. Fluorescence images were background-subtracted to remove signals from the agarose pad before further analysis. To completely capture the YFP fluorescence within each cells, we expanded the cell outline by five pixels. Cells with overlapping outlines were eliminated to prevent cross-cell ‘fluorescence contamination’. Intensities of all pixels within each cell outline were then integrated and designated as total YFP fluorescence per cell. Number of ParA-YFP molecule per cell was calculated as the ratio between the total ParA-YFP fluorescence per cell and the mean fluorescence of single ParA-YFP molecules. We distinguished <italic>parA-yfp</italic>-expressing cells from wild-type cells through fluorescence thresholding (<xref ref-type="fig" rid="fig1s6">Figure 1—figure supplement 6D</xref>). In a separate experiment, we confirmed that this classification method reliably separates the two strains with better than 99% accuracy (data not shown).</p></sec></sec><sec id="s4-14"><title>Super-resolution PALM microscopy</title><sec id="s4-14-1"><title>Sample preparation and image acquisition</title><p>Cells were spotted on a 2% agarose pad made with 0.22 µm-filtered M2G. Imaging was performed at room temperature. All images were acquired on either an N-STORM microscope (Nikon) or a custom-built setup assembled on a commercial Axio Observer D1 microscope stand (Carl Zeiss). The N-STORM microscope was equipped with a CFI Apo TIRF 100 × oil immersion objective (NA 1.49), lasers emitting at 405 nm and 561 nm (Agilent Technologies, Santa Clara, CA) and a built-in Perfect Focus system. Raw single molecule data were taken in a field of view of ∼43 × 43 µm<sup>2</sup> (256 × 256 pixels) with an Andor iXon X3 DU 897 EM-CCD camera (Andor Technology, South Windsor, CT) at a frame rate of 28.5–29 frames per second (fps). Under this acquisition condition, diffusing molecules appeared blurred and were rejected from our analysis. The custom-built microscope set up (<xref ref-type="bibr" rid="bib37">Huang et al., 2013</xref>) was equipped with a 100 × /1.46-NA oil-immersion objective (alpha Plan-Apochromat 100 × /1.46 oil, Carl Zeiss), lasers emitting at 405 nm (50 mW, CrystaLaser, Reno, Nevada) and 568 nm (Innova 300, ∼400 mW, Coherent, Santa Barbara, CA). Fluorescence was recorded with an ORCA-Flash 4.0 sCMOS camera (Hamamatsu Photonics) at a frame rate of 100 fps and a field of view of 23 × 23 μm<sup>2</sup>.</p></sec><sec id="s4-14-2"><title>Camera calibration</title><p>To allow the conversion of camera output counts from our images into units of effective photons that follow a Poisson distribution, we calibrated the offset and amplification gain of the EM-CCD camera using a Poisson calibration routine (<xref ref-type="bibr" rid="bib38">Huang et al., 2011</xref>). Briefly, the mean offset was determined from 1000 raw images using the 256 × 256 pixels region at the center of the EMCCD chip in a dark environment with no incident photons. To determine the amplification gain, we extracted the slope of the variance vs the mean scatter plot calculated from each pixel over 200 camera frames while illuminated with a stationary intensity pattern. This pattern was generated by imaging a slide containing 10–20,100-nm TetraSpeck microspheres (Invitrogen, Carlsbad, CA) in an out-of-focus plane such that an intensity pattern emerged from the overlapping point-spread-functions of the beads (<xref ref-type="bibr" rid="bib56">Lidke et al., 2005</xref>; <xref ref-type="bibr" rid="bib87">Smith et al., 2010</xref>; <xref ref-type="bibr" rid="bib38">Huang et al., 2011</xref>). The sCMOS camera was calibrated as previously described (<xref ref-type="bibr" rid="bib37">Huang et al., 2013</xref>).</p></sec><sec id="s4-14-3"><title>Analysis and reconstruction</title><p>Raw images were first corrected with the calibrated offset and gain values to convert pixel intensities into effective photon counts. The corrected images were analyzed using a previously described maximum-likelihood estimation algorithm to localize well-defined single emitters (<xref ref-type="bibr" rid="bib87">Smith et al., 2010</xref>). Log-likelihood ratio test was used to retain only fitted emitters that contain &gt;100 photons, and &gt;2.5% corresponding p-value (<xref ref-type="bibr" rid="bib38">Huang et al., 2011</xref>). The average localization precision for all dataset is approximately 19 nm (±6 nm, SD). The super-resolution images were reconstructed by placing 2D Gaussians (σ = 10 nm) on images with 9 nm pixel size. Drift corrections were performed on localized single molecule centers using cross-correlation method by assigning 500 frames for each correlation segment (<xref ref-type="bibr" rid="bib64">Mlodzianoski et al., 2011</xref>). Images taken with the sCMOS camera was analyzed with a previously published sCMOS-specific script which takes into consideration sCMOS-intrinsic-pixel-dependent readout noise and achieves optimal precision at the theoretical limit (<xref ref-type="bibr" rid="bib37">Huang et al., 2013</xref>). Images shown in <xref ref-type="fig" rid="fig3">Figure 3</xref> were generated from data acquired with the N-STORM, while those presented in <xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1</xref> were taken with the custom-built setup.</p></sec><sec id="s4-14-4"><title>Width distribution analysis</title><p>Due to the large pixel size of our images, we first expanded the bright field images from 256 × 256 pixels to 1024 × 1024 pixels using bicubic interpolation before subjecting them to MicrobeTracker analysis to obtain cell outline. We then linked each single molecule to each cell outline by using the inpolygon function in MATLAB and calculated the distance for each single molecule to the cell center line as determined from the MicrobeTracker outline. To determine the individual distribution of Dendra2 fusions inside cells along the cell width, we selected cells that contain high density of localized emitters (&gt;1000 per cell) for analysis. To analyze the distribution of emitters along the short cell axis, a 0.5–0.8 μm long segment was manually selected for each cell. These segments corresponded to regions containing the ParA ‘cloud’ in cells expressing ParA-Dendra2 or areas where the crescentin-Dendra2 filament orientation was parallel to the long cell axis. For cells expressing L1-Dendra2, the segments were randomly selected since the distribution of emitters along the long cell axis was mostly homogenous. Only segments with at least 600 emitters were analyzed to minimize statistical error. For segments that passed the selection, single emitter positions with respect to the short cell axis were then normalized to the mean of the distribution in each cell and plotted as a histogram.</p></sec></sec><sec id="s4-15"><title>Estimation of DNA concentration inside <italic>C. crescentus</italic></title><p><disp-formula id="equ1"><mml:math id="m1"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:mtext>DNA mass per </mml:mtext><mml:mi mathvariant="italic">C.</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="italic">crescentus</mml:mi><mml:mtext> chromosome</mml:mtext></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mtext>Total</mml:mtext><mml:mo> </mml:mo><mml:mi>b</mml:mi><mml:mi>p</mml:mi><mml:mo> </mml:mo><mml:mtext>per chromosome</mml:mtext><mml:mo>×</mml:mo><mml:mtext>mass per</mml:mtext><mml:mo> </mml:mo><mml:mi>b</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mn>6</mml:mn></mml:msup><mml:mo> </mml:mo><mml:mi>b</mml:mi><mml:mi>p</mml:mi><mml:mo>×</mml:mo><mml:mn>650</mml:mn><mml:mo> </mml:mo><mml:mi>D</mml:mi><mml:mi>a</mml:mi><mml:msup><mml:mrow><mml:mtext> bp</mml:mtext></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn>2.6</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mn>9</mml:mn></mml:msup><mml:mi>D</mml:mi><mml:mi>a</mml:mi><mml:mo>×</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>6.022</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mn>23</mml:mn></mml:mrow></mml:msup><mml:mi>D</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn>4.31</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>15</mml:mn></mml:mrow></mml:msup><mml:mtext>g</mml:mtext></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p><p>Thus, in vivo DNA concentration <inline-formula><mml:math id="inf1"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mtext>DNA mass</mml:mtext></mml:mrow><mml:mrow><mml:mtext>Cell volume</mml:mtext></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>4.3</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>15</mml:mn></mml:mrow></mml:msup><mml:mtext> g</mml:mtext></mml:mrow><mml:mrow><mml:mn>2.5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>13</mml:mn></mml:mrow></mml:msup><mml:mtext> ml</mml:mtext></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mn>17</mml:mn><mml:msup><mml:mrow><mml:mtext> mg ml</mml:mtext></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></p></sec><sec id="s4-16"><title>Estimation of the diffusion coefficient of the partition complex, <italic>D</italic><sub><italic>PC</italic></sub></title><p>To estimate <italic>D</italic><sub><italic>PC</italic></sub>, we analyzed the movement of the ParB/<italic>parS</italic> complex in the slow, ParA-independent phase (<xref ref-type="bibr" rid="bib84">Shebelut et al., 2010</xref>), which appears to exhibit diffusive behaviors. As shown in <xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2A</xref>, we identified three ‘segments’ within the slow phase for each cell:</p><p>‘Segment 1’ corresponds to the part of the trajectory when the ParB/<italic>parS</italic> complex has detached from the old pole but has not yet duplicated. To identify this segment, we computationally looked for the part of trajectory in which there was only one ParB/<italic>parS</italic> complex in the cell and its position was at least 320 nm from the old cell pole.</p><p>‘Segment 2’ corresponds to the part of the trajectory when the ParB/<italic>parS</italic> complex proximal to the old pole has separated from its sister but has not yet re-attached to the old pole. This segment started 1 min after two ParB/<italic>parS</italic> complexes became visibly separated (to exclude possible active splitting mechanism) and ended when the complex moved within 320 nm from the old pole.</p><p>‘Segment 3’ corresponds to the part of the trajectory when the ParB/<italic>parS</italic> complex distal to the old pole has separated from its sister and has not engaged in the directed ‘fast’ translocation phase. This segment contained the maximum unbiased stretch of the trajectory 1 min after two ParB/<italic>parS</italic> complexes became visibly separated. We identified this segment by determining the longest part of the trajectory that remains confined within a virtual 500-nm wide box (i.e., no net directional motion).</p><p>We combined data from all trajectories for each of these three segments separately and analyzed their respective displacement distributions and mean square displacements (MSDs) (<xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2B,C</xref>). We estimated <italic>D</italic><sub><italic>PC</italic></sub> using two different approaches. First, we performed a Gaussian fitting (which is expected for normal diffusion) to the displacement distributions, which returned best fit <italic>D</italic><sub><italic>PC</italic></sub> values of 0.0007 ± 0.0001, 0.00012 ± 0.0001 and 0.00012 ± 0.0001 µm<sup>2</sup>s<sup>−1</sup> for ParB/<italic>parS</italic> motion during segments 1, 2 and 3, respectively (<xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2B</xref>). Consistent with these estimations, a linear fit to the first four time points of each MSD gave <italic>D</italic><sub><italic>PC</italic></sub> values of 0.0004 ± 0.0003, 0.0001 ± 0.0006 and 0.00008 ± 0.0001 µm<sup>2</sup>s<sup>−1</sup> for segments 1, 2 and 3, respectively (<xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2C</xref>). These values are close to the diffusion coefficient (1.5 × 10<sup>−4</sup> µm<sup>2</sup>s<sup>−1</sup>) of <italic>E. coli</italic> chromosomal <italic>ori</italic> region that we estimated from data presented in <xref ref-type="bibr" rid="bib49">Kuwada et al. (2013)</xref>. In addition, the good linear MSD fits suggest that the motions of the unattached ParB/<italic>parS</italic> complex can be approximated as a normal diffusion at a minute scale (i.e., on the time-scale of segregation). Therefore, unless specified otherwise, we used <italic>D</italic><sub><italic>PC</italic></sub> = 1 × 10<sup>−4</sup> µm<sup>2</sup>s<sup>−1</sup> (the average value for ‘Segment 2’ and ‘Segment 3’ given by the two approaches) in all simulations.</p></sec><sec id="s4-17"><title>Estimation of the diffusion coefficient of DNA-bound ParA-ATP dimers, <italic>D</italic><sub><italic>A</italic></sub></title><p>We estimated <italic>D</italic><sub><italic>A</italic></sub> from published results for generalized (i.e., time-dependent) diffusion coefficient of various chromosomal loci in <italic>E. coli</italic>, <italic>D</italic><sub><italic>app</italic></sub> ∼ (0.25–1.5) × 10<sup>−3</sup> µm<sup>2</sup>s<sup>−0.4</sup> (<xref ref-type="bibr" rid="bib100">Weber et al., 2012</xref>; <xref ref-type="bibr" rid="bib45">Javer et al., 2013</xref>). This gives an effective diffusion coefficient at 1-ms time scale (time interval used in our simulations): <italic>D</italic><sub><italic>A</italic></sub> = <italic>D</italic><sub><italic>app</italic></sub><italic>Δt</italic> <sup>−0.6</sup> ∼ (1.5–9) × 10<sup>−2</sup> µm<sup>2</sup>s<sup>−1</sup>. We used <italic>D</italic><sub><italic>A</italic></sub> value of 0.01 µm<sup>2</sup>s<sup>−1</sup> in the simulations of our DNA-relay model. As a control, we simulated the dynamics of DNA-bound ParA dimers in the absence of other factors and found that this estimated <italic>D</italic><sub><italic>A</italic></sub> value closely recapitulated the step-size and position distributions that are experimentally observed for chromosomal loci such as the LacI-labeled <italic>groESL</italic> locus (data not shown).</p></sec><sec id="s4-18"><title>Chromosomal locus tracking</title><p>CJW2966, CJW5466 and CJW5468 cells were grown at 30°C in M2G supplemented with 5 µg/ml kanamycin. Prior to imaging, synthesis of LacI-CFP was induced with 0.03% xylose (plus 20 µM IPTG to prevent adverse effects on DNA replication and cell division). After 60–80 min, cells were washed and spotted on 1.2% agarose containing M2G and 20 µM IPTG, and imaged at 2-s time intervals between frames. LacI-CFP-labeled chromosomal loci appeared as diffraction-limited spots. Their positions (relative to the long and short axes of each cell) were determined using the SpotFinder (<xref ref-type="bibr" rid="bib86">Sliusarenko et al., 2011</xref>). Only trajectories with a minimal length of five frames were considered for quantitative analysis.</p></sec><sec id="s4-19"><title>Estimation of the elastic constant of the DNA locus</title><p>To exclude differences in equilibrium position due to cell-to-cell variability, we measured deviations (<italic>Δx</italic>) from the mean position of each individual trajectory. The probability <italic>P</italic>(<italic>Δx</italic>) of a locus to fluctuate around its equilibrium point is given by:<disp-formula id="equ2"><label>(1)</label><mml:math id="m2"><mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>Δ</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>∼</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:mi>E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Δ</mml:mi><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:msup></mml:mrow></mml:math></disp-formula>where <italic>k</italic> is the Boltzmann constant<italic>, T</italic> is the absolute temperature, and <italic>E</italic>(<italic>Δx</italic>) is the energy associated with the fluctuation. For an elastic force, <italic>F</italic> = <italic>k</italic><sub><italic>sp</italic></sub> <italic>Δx</italic> and <italic>E</italic>(<italic>Δx</italic>) = <italic>k</italic><sub><italic>sp</italic></sub><italic>Δx</italic><sup>2</sup>/2 (with <italic>k</italic><sub><italic>sp</italic></sub> being the elastic constant) and the probability of observing a locus at a distance <italic>Δx</italic> from the equilibrium is a Gaussian distribution (which is what we observe in experiments):<disp-formula id="equ3"><label>(2)</label><mml:math id="m3"><mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>Δ</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>∼</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mi>Δ</mml:mi><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>k</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:msup></mml:mrow></mml:math></disp-formula></p><p>We fitted the experimental distributions separately for deviations along the short and long axes of the cell with one free parameter <italic>σ</italic> (with 1/<italic>σ</italic><sup>2</sup> = <italic>k</italic><sub><italic>sp</italic></sub>/<italic>kT</italic>), obtaining <italic>σ</italic> = 38 ± 1 nm and 64 ± 2 nm for the short and long axis, respectively. These values were used in the Brownian dynamics simulations.</p></sec><sec id="s4-20"><title>Brownian dynamics simulations</title><p>We considered three models in this study. The ‘diffusion’ model contains only the diffusion terms of the <xref ref-type="disp-formula" rid="equ4">Equation 3</xref> below. The ‘diffusion-binding’ model also includes binding and un-binding of the ParB/<italic>parS</italic> complex to the DNA-bound ParA dimers, but no force terms (i.e., immobile DNA-bound ParA dimers). The ‘DNA-relay’ model contains all terms described in <xref ref-type="disp-formula" rid="equ4">Equation 3</xref>, which takes into consideration diffusion, binding/unbinding, and elastic forces (i.e., dynamic DNA-bound ParA dimers). The parameter values used in each model are listed in the <xref ref-type="table" rid="tbl2">Table 2</xref> unless stated otherwise.</p><p>Two-dimensional Brownian dynamics (BD) simulations were performed using a second-order approximation (<xref ref-type="bibr" rid="bib11">Branka and Heyes, 1998</xref>). At each time step, the coordinates of the ParB/<italic>parS</italic> complex and DNA-bound ParA-ATP dimers were calculated as follows:<disp-formula id="equ4"><label>(3)</label><mml:math id="m4"><mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi>Δ</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mi>x</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mfrac><mml:mi>D</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:mfrac><mml:mi>F</mml:mi><mml:mi>Δ</mml:mi><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi>D</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfrac><mml:mi>F</mml:mi><mml:msup><mml:mrow><mml:mi>F</mml:mi><mml:mo>'</mml:mo></mml:mrow><mml:mrow><mml:mi>Δ</mml:mi><mml:msup><mml:mi>t</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mfrac><mml:mi>D</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:mfrac><mml:mi>F</mml:mi><mml:mo>'</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math></disp-formula></p><p>The first three terms in <xref ref-type="disp-formula" rid="equ4">Equation 3</xref> correspond to first-order approximations typically used in BD simulations (<xref ref-type="bibr" rid="bib80">Saxton, 2007</xref>), where <italic>Δt</italic> is the time step of simulations, <italic>x</italic>(<italic>t</italic><sub><italic>i</italic></sub>) is the coordinate of ParB/<italic>parS</italic> or DNA-bound ParA dimers at the previous time point, <italic>D</italic> is the diffusion coefficient for the component considered (<italic>D</italic><sub><italic>PC</italic></sub> for the ParB/<italic>parS</italic> complex or <italic>D</italic><sub><italic>A</italic></sub> for DNA-bound ParA dimers), <italic>kT</italic> is the temperature in energy units, <italic>R</italic><sub><italic>0</italic></sub> specifies the random displacement due to diffusion (i.e., random number from a Gaussian distribution with zero mean &lt;<italic>R</italic><sub><italic>0</italic></sub>&gt; = 0 and variance &lt;<italic>R</italic><sub><italic>0</italic></sub><sup>2</sup>&gt; = 2<italic>DΔt</italic>), <italic>F</italic> is the force acting on the particle considered (partition complex or DNA-bound ParA-ATP dimer). The last two terms in <xref ref-type="disp-formula" rid="equ4">Equation 3</xref> correspond to further expansion of the stochastic equations (<xref ref-type="bibr" rid="bib11">Branka and Heyes, 1998</xref>), where <italic>F’</italic> is the derivative of the force (<italic>F</italic>′ = d<italic>F</italic>/d<italic>x</italic>) and <italic>R</italic><sub><italic>1</italic></sub> is a random number specified by a Gaussian distribution (with zero mean &lt;<italic>R</italic><sub>1</sub>&gt; = 0 and variance &lt;<italic>R</italic><sub><italic>1</italic></sub><sup>2</sup>&gt; = (2/3)<italic>DΔt</italic><sup>3</sup>), which is correlated with <italic>R</italic><sub><italic>0</italic></sub>: &lt;<italic>R</italic><sub><italic>0</italic></sub> <italic>R</italic><sub><italic>1</italic></sub>&gt; = D<italic>Δt</italic><sup>2</sup>. The force terms for DNA-bound ParA and ParB/<italic>parS</italic> are:<disp-formula id="equ5"><label>(4)</label><mml:math id="m5"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>A</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mtext> and </mml:mtext><mml:msubsup><mml:mi>F</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>A</mml:mi></mml:mrow><mml:mo>'</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula><disp-formula id="equ6"><label>(5)</label><mml:math id="m6"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mo>∑</mml:mo></mml:mstyle><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>A</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mtext> and </mml:mtext><mml:msubsup><mml:mi>F</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mo>'</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>A</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>respectively, where <italic>k</italic><sub><italic>sp</italic></sub> is the spring constant, <inline-formula><mml:math id="inf2"><mml:mrow><mml:msubsup><mml:mi>x</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>A</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula> is the equilibrium point of ParA dimers bound to DNA, and <italic>n</italic><sub><italic>AB</italic></sub> is the total number of ParA dimers bound to the partition complex. Note that <xref ref-type="disp-formula" rid="equ6">Equation 5</xref> is the sum over all ParA dimers bound to the partition complex. Also, only the ratio <italic>k</italic><sub><italic>sp</italic></sub>/<italic>kT</italic> was defined as a model parameter (determined from experiment, 1/<italic>σ</italic><sup>2</sup> = <italic>k</italic><sub><italic>sp</italic></sub>/<italic>kT</italic>) since all force terms depends only on this combination of <italic>k</italic><sub><italic>sp</italic></sub> and <italic>kT</italic>.</p><p>In our models, the ParB/<italic>parS</italic> complex can be in one of two states: (1) freely diffusing (no force terms) or (2) in a complex with one or more DNA-bound ParA dimers (non-zero force terms). We modeled ParA dimers and ParB/<italic>parS</italic> complex as disks with <italic>R</italic><sub><italic>ParA</italic></sub> and <italic>R</italic><sub><italic>PC</italic></sub> equal to 2 and 50 nm, respectively. The partition complex binds to ParA every time their disks overlap. At any given time, ParA could be in one of three different states: DNA-associated, in a complex with ParB/<italic>parS</italic>, or freely diffusing. The motion of DNA-bound ParA was simulated via <xref ref-type="disp-formula" rid="equ4">Equations 3</xref> and <xref ref-type="disp-formula" rid="equ5">4</xref>. When a ParA dimer was associated with the partition complex, its coordinate increment was equal to the increment of the partition complex. The motion of freely diffusing ParA monomers was not explicitly simulated, since ParA monomers do not interact with the partition complex. The motion of freely diffusing ParA is relatively fast (<italic>D</italic><sub><italic>A-free</italic></sub> <italic>&gt;&gt; D</italic><sub><italic>A</italic></sub>) leading to a uniform random distribution across the cytoplasm within seconds. Free ParA molecules bind to DNA with uniform probability with respect to the short cell axis. However, in the long-axis direction, we emulated ParA distribution observed in cells (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1</xref>) by assuming that the probability of ParA to re-bind to DNA is a linearly increasing function between the current ParB/<italic>parS</italic> location (<italic>x</italic><sub><italic>PC</italic></sub>) and the new pole:<disp-formula id="equ7"><label>(6)</label><mml:math id="m7"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>A</mml:mi><mml:mo>−</mml:mo><mml:mi>D</mml:mi><mml:mi>N</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>2</mml:mn><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>l</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfrac><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mtext>, for </mml:mtext><mml:msub><mml:mi>x</mml:mi><mml:mi mathvariant="italic">pc</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mi>x</mml:mi><mml:mo>&lt;</mml:mo><mml:mi>l</mml:mi><mml:mtext>,</mml:mtext></mml:mrow></mml:math></disp-formula>where <italic>l</italic> is a cell length, and the coordinates are defined as <italic>x</italic> = 0 at the old ole and <italic>x</italic> = <italic>l</italic> at the new pole.</p><p>The transition of ParA between different states was modeled as a stochastic process (exponential distribution of times) with average times <italic>τ</italic><sub><italic>db</italic></sub> (for ParA<sub>free</sub> → ParA<sub>DNA-bound</sub>) and <italic>τ</italic><sub><italic>cat</italic></sub> (for ParA<sub>ParB/<italic>parS</italic></sub> <sub>bound</sub> → ParA<sub>free</sub>). The rate of ParA dissociation from the DNA upon interaction with the ParB/<italic>parS</italic> complex is equal to the maximum hydrolysis rate, <italic>τ</italic><sub><italic>cat</italic></sub> = 1/<italic>k</italic><sub><italic>cat</italic></sub> ≈ 30 s (<xref ref-type="fig" rid="fig1">Figure 1F</xref>), unless mentioned otherwise. Note that because of its slow rate, dissociation of ParA from the DNA due to the basal ATPase activity of DNA-bound ParA was neglected. Since for the plasmid P1 system, the rate of freely diffusing ParA monomers dimerizing and binding to DNA is thought to be comparable to ATP hydrolysis rate (<xref ref-type="bibr" rid="bib92">Vecchiarelli et al., 2010</xref>), we assumed that <italic>τ</italic><sub><italic>db</italic></sub> = <italic>τ</italic><sub><italic>cat</italic></sub> = 30 s for all simulations shown here. Note that varying <italic>τ</italic><sub><italic>db</italic></sub> between 1-100 s did not significantly affect the results of our simulations (data not shown).</p><p>We defined the starting conditions using experimentally measured values. At the beginning of the simulation, the partition complex was placed at <italic>x</italic>(0) = 0.8 µm (measured from the old pole, <xref ref-type="fig" rid="fig2">Figure 2B</xref>), <italic>y</italic>(0) = 0. At the start of each simulation, ParA-ATP dimers were distributed randomly using <xref ref-type="disp-formula" rid="equ7">Equation 6</xref> with <italic>x</italic><sub><italic>PC</italic></sub> = <italic>x</italic>(0). Cell boundaries were modelled as a reflective 2.5 µm × 0.4 µm rectangular. All simulations were carried out using Δ<italic>t</italic> = 1 ms for a total of 2000 s or until the partition complex crosses <italic>x</italic><sub><italic>finish</italic></sub> = 2.6 μm, which ever happened first.</p></sec><sec id="s4-21"><title>Calculation of the optimal ATP hydrolysis rate for the DNA-relay model</title><p>To estimate the optimal attachment time between the partition complex and ParA-ATP dimers, we calculated the average time (Δ<italic>t</italic>) required for the partition complex to reach an equilibrium point since its association with a DNA-bound ParA dimer. A particle under elastic force (<italic>F</italic> = <italic>k</italic><sub><italic>sp</italic></sub> Δ<italic>x</italic> where <italic>k</italic><sub><italic>sp</italic></sub> is the elastic constant) moves a distance Δ<italic>x</italic> in a viscous medium during an interval Δ<italic>t</italic>:</p><p>Δ<italic>x</italic> = <italic>v</italic> Δ<italic>t</italic> = <italic>µ F</italic> Δ<italic>t</italic> = (<italic>D</italic>/<italic>kT</italic>) <italic>k<sub>sp</sub></italic> Δ<italic>x</italic> Δ<italic>t</italic></p><p>Here <italic>v</italic> is the velocity of the particle, <italic>µ</italic> is the particle mobility linked to the diffusion coefficient <italic>D</italic><sub><italic>PC</italic></sub> as µ = <italic>D</italic><sub><italic>PC</italic></sub>/(<italic>kT</italic>), <italic>k</italic> is the Boltzmann constant and <italic>T</italic> is the absolute temperature. This allowed us to calculate the optimal time of ATP hydrolysis using <italic>σ</italic><sub><italic>long</italic></sub><sup>2</sup> = <italic>kT</italic>/<italic>k</italic><sub><italic>sp</italic></sub>:</p><p>Δ<italic>t</italic> = <italic>kT</italic>/(<italic>D</italic><sub><italic>PC</italic></sub> <italic>k</italic><sub><italic>sp</italic></sub>) = <italic>σ</italic><sub><italic>long</italic></sub><sup>2</sup>/<italic>D</italic><sub><italic>PC</italic></sub> = (0.06 µm)<sup>2</sup>/10<sup>−4</sup> µm<sup>2</sup> s<sup>−1</sup> = 36 s.</p></sec></sec></body><back><ack id="ack"><title>Acknowledgements</title><p>We thank Drs Enrique M De La Cruz, Wenxiang Cao and Michael J Bradley for help with setting up the NADH-linked ATPase assay, Dr Pingyong Xu for providing the template for <italic>mEos3.2</italic>, Drs Herald Herrmann-Lerdon and Nicole Foeger for providing the pET24dHT plasmid, Dr Patrick Viollier for strains carrying the 139_lac and 165_lac constructs, Jennifer R Heinritz and Dr Whitman Schofield for providing plasmid constructs, Drs Grant Jensen and Ariane Briegel for sharing unpublished calculations of the swarmer cell volume, Dr Gitte Ebersbach Charbon for providing the ParB dimerization data, staffs of the Yale University Faculty of Arts and Sciences High Performance Computing Center for support, and members of the Jacobs-Wagner laboratory for critical reading of this manuscript and for fruitful discussions.</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>JB: Discloses significant financial interest in Vutara, Inc (Salt Lake City, UT).</p></fn><fn fn-type="conflict" id="conf2"><p>The other 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>HCL, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con2"><p>IVS, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con3"><p>BGB, Conception and design, Acquisition of data, Analysis and interpretation of data</p></fn><fn fn-type="con" id="con4"><p>FH, Conception and design, Acquisition of data, Analysis and interpretation of data</p></fn><fn fn-type="con" id="con5"><p>JB, Conception and design, Drafting or revising the article</p></fn><fn fn-type="con" id="con6"><p>CJ-W, Conception and design, Analysis and interpretation of data, Drafting or revising the article</p></fn></fn-group></sec><sec sec-type="supplementary-material"><title>Additional files</title><supplementary-material id="SD1-data"><object-id pub-id-type="doi">10.7554/eLife.02758.026</object-id><label>Supplementary file 1.</label><caption><p>Strains used in this study and the methods of strains construction.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.026">http://dx.doi.org/10.7554/eLife.02758.026</ext-link></p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife02758s001.docx"/></supplementary-material><supplementary-material id="SD2-data"><object-id pub-id-type="doi">10.7554/eLife.02758.027</object-id><label>Supplementary file 2.</label><caption><p>Oligonucleotide primers used in this study and methods of plasmids construction.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.027">http://dx.doi.org/10.7554/eLife.02758.027</ext-link></p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife02758s002.docx"/></supplementary-material><supplementary-material id="SD3-data"><object-id pub-id-type="doi">10.7554/eLife.02758.028</object-id><label>Supplementary file 3.</label><caption><p>Custom-built MATLAB function (buildTrace.m) for constructing trajectories of ParB/<italic>parS</italic> complexes in single cells.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.028">http://dx.doi.org/10.7554/eLife.02758.028</ext-link></p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife02758s003.docx"/></supplementary-material><supplementary-material id="SD4-data"><object-id pub-id-type="doi">10.7554/eLife.02758.029</object-id><label>Supplementary file 4.</label><caption><p>Custom-built MATLAB function (findFastSegPhase.m) for identifying the ‘fast’ phase in the segregating trajectory.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.02758.029">http://dx.doi.org/10.7554/eLife.02758.029</ext-link></p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife02758s004.docx"/></supplementary-material></sec><ref-list><title>References</title><ref id="bib1"><element-citation 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editor</role><aff><institution>University of Warwick</institution>, <country>United Kingdom</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 “Evidence for a DNA-relay mechanism in ParABS-mediated chromosome segregation” for consideration at <italic>eLife.</italic> Your article has been favorably evaluated by Senior Editor Richard Losick and 3 reviewers, one of whom is a member of our Board of Reviewing Editors, and one of whom, Kerry Bloom (peer reviewer #3), has agreed to reveal her identity.</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>In short, we would like to receive a revised manuscript that addresses the major point raised by Reviewer # 1, to provide additional evidence for elastic dynamics in other regions of the Caulobacter chromosomes and to expand the scope of the modeling, as suggested by Reviewer #2. It will also be useful to provide additional explanations for the scenario raised by Reviewer #2 on how the separation of the <italic>parS</italic> sites at oriC on the chromosome might affect your model.</p><p>With these revisions, your work will make an important contribution to the fields of bacterial chromosome biology and bacterial cell division.</p><p><italic>Reviewer #1</italic>:</p><p>This excellent manuscript by Lim et al provides a new mechanism for DNA segregation in the bacterium Caulobacter crescentus by the ParABS system. Perhaps the most important finding is that ParA does not form filaments but that it participates in chromosome segregation through a modulation of its ATPase activity stimulated by highly concentrated ParB at <italic>ParS</italic> sequences. Through a combination of beautiful biochemical and cell biological experiments (including super resolution experiments) they establish the central thesis of the paper.</p><p>Modeling work reveals inadequacy of a diffusion-binding mechanism. The authors arrive at the conclusion that some of aspect of DNA structure itself might contribute to polar segregation of chromosomes. In short elastic dynamics of chromosomal DNA in conjunction with ParA-ATP gradient drives chromosome segregation. This is an exciting new parameter that enters their final model. In summary, the experiments are well done and support the overall conclusions and this paper deserves to be published in <italic>eLife</italic>.</p><p>Since elastic dynamics of DNA is proposed to provide chromosome segregational forces and since this is a new dimension introduced to describe DNA segregation, I would like to see if 1-2 other loci (in addition to GroESL) undergo similar elastic dynamics, to further bolster the notion that the Caulobacter chromosome behaves like an elastic filament. I do not know how easy/difficult it would be to generate a strain by integration of LacI into other loci and perform such a study in Caulobacter.</p><p><italic>Reviewer #2:</italic></p><p>This is a beautifully written paper describing interesting and important new insights into the mechanism of ParAB mediated plasmid and chromosome segregation. The experiments are superbly documented with very thorough controls. Apart from quantitatively documenting many features of the biochemistry and cell biology of the Caulobacter ParAB system, a “DNA relay” model is presented, which can explain the directional movement of the origin of replication, without the need for ParA filaments, which have been an important feature of most previous models.</p><p>My only concern/criticism is that the new model is, in principle, rather similar to that recently proposed by the Mizuuchi lab, based on in vitro experiments with a plasmid ParABS system. The main difference between the two models would seem to be the proposed role of intrinsic fluctuating motion of DNA-bound ParA-ATP dimers. Intuitively, it seems to me that the modelling would work just as well by a Mizuuchi-like process and that tethering the ParA molecules to DNA provides a matrix on which the polar gradient of ParA can be fixed. It would be interesting to see this alternative scenario modelled. The new model also does not take account of the fact that each oriC region has multiple ParB molecules bound, and that there are several separated <italic>parS</italic> sites, each of which could collide with a DNA-bound ParA dimer, facilitating the walk up the ParA gradient towards the cell pole. Perhaps the occasional “stretching” of ParB foci represents simultaneous interactions made by different <italic>parS</italic> assemblies?</p><p>My feeling therefore is that this paper is important because it reinforces the notion that filament formation by ParA may not be crucial for its function and provides strong in vivo support for a Mizuuchi-like diffusion-ratchet model (which could equally be called a DNA relay). I am less convinced by the proposed role for an elastic force.</p><p><italic>Reviewer #3:</italic></p><p>This is an excellent manuscript that describes a novel mode of chromosome segregation in <italic>C. crescentus</italic>. The paper addresses several important unanswered questions in the field, and provides significant new insights. The data are clearly presented, thorough, and the model is well-reasoned.</p><p>Specific comments:</p><p>The mode of chromosome segregation in many bacteria is poorly understood. The ParABS system has been proposed to be analogous to the eukaryotic spindle-based mechanisms using a filament of ParA to pull the ParB/<italic>parS</italic> complex along. To better understand how the system works in vivo, these investigators begin with determining the DNA-dependent ATPase activity. They find a different behavior in the <italic>C. crescentus</italic> vs. <italic>B. subtilis</italic> components that has important biological consequences.</p><p>The investigators count the number of molecules, which will be a critical parameter in the model. The counting method is well-described.</p><p>The filament model of ParA function predicts a particular trajectory of the translocation. The measured trajectory (<xref ref-type="fig" rid="fig2">Figure 2</xref>) indicates a random, fluctuating path, at odds with the current models. Furthermore, the molecular counts indicate the in vivo concentration to be too low to accommodate filament formation.</p><p>The investigators proceed to examine diffusion rates and find that at least with simple diffusion models and the measured parameters, the biased diffusion model does not lead to directional motion.</p><p>The significant discovery comes in the analysis and incorporation of chromosome dynamics into the model. The ParA complex is influenced by the fluctuations of a dynamic DNA matrix. The model is clear and the investigators have done an excellent job integrating the biochemical cycle of the ParComplex with the fluctuations of DNA into a novel mechanism that provides highly significant insight into an important biological problem.</p></body></sub-article><sub-article article-type="reply" id="SA2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.02758.031</article-id><title-group><article-title>Author response</article-title></title-group></front-stub><body><p><italic>In short, we would like to receive a revised manuscript that addresses the major point raised by Reviewer # 1, to provide additional evidence for elastic dynamics in other regions of the Caulobacter chromosomes and to expand the scope of the modeling, as suggested by Reviewer #2. It will also be useful to provide additional explanations for the scenario raised by Reviewer #2 on how the separation of the</italic> parS <italic>sites at oriC on the chromosome might affect your model</italic>.</p><p>Thank you for giving us the opportunity to submit a revised manuscript. We have added experimental evidence for the elastic dynamics of two other chromosomal regions and expanded the scope of the modeling, as requested by Reviewer 1 and 2, respectively. Regarding the multiplicity of <italic>parS</italic> sites and their separation, please note that in the <italic>C. crescentus</italic> chromosome, there are only two <italic>parS</italic> sites and they are separated by only 42 nucleotides. Fully stretched, 42 nucleotides would be at most 14 nm, making the scenario raised by Reviewer 2 unlikely. Nevertheless, we have considered this scenario and shown that it does not alter our conclusions. Please see below for details.</p><p>Reviewer #1:</p><p><italic>Since elastic dynamics of DNA is proposed to provide chromosome segregational forces and since this is a new dimension introduced to describe DNA segregation, I would like to see if 1-2 other loci (in addition to GroESL) undergo similar elastic dynamics, to further bolster the notion that the Caulobacter chromosome behaves like an elastic filament. I do not know how easy / difficult it would be to generate a strain by integration of LacI into other loci and perform such a study in Caulobacter</italic>.</p><p>We agree with the reviewer, and have imaged and analyzed the motion of two additional chromosomal loci (139_lac and 165_lac) (Viollier et al., PNAS, 2004). We found that they displayed elastic dynamics similar to the <italic>groESL</italic> locus. The results have been added to <xref ref-type="fig" rid="fig5">Figure 5</xref> (panel C). The text and figure legend have been modified accordingly.</p><p>Reviewer #2:</p><p><italic>Intuitively, it seems to me that the modelling would work just as well by a Mizuuchi-like process and that tethering the ParA molecules to DNA provides a matrix on which the polar gradient of ParA can be fixed. It would be interesting to see this alternative scenario modelled</italic>.</p><p>We apologize for not being more explicit in the original submission, but our ‘diffusion-binding’ model does test a ‘Mizuuchi-like’ process. In that model, a polar gradient of ParA-ATP dimers is fixed on a static DNA matrix exactly as proposed by the reviewer. As shown in <xref ref-type="fig" rid="fig4">Figure 4B and 4C</xref>, this diffusion-binding model does not lead to fast or robust segregation. Note that we were, at first, surprised by the results because we had the same intuition as Reviewer 2. In hindsight, the poor performance of the diffusion-binding model should be expected because in this model, the movement of the partition complex is governed by diffusion. There is no force involved and the ParA-ParB interactions only stall the partition complex without productively moving the partition complex in the ‘right’ direction.</p><p>There is nothing in this mechanism that prevents the partition complex from diffusing in the wrong direction when the interaction between ParA and ParB is lost (i.e., in the ParA-depleted region away from the ParA gradient). This can be seen in <xref ref-type="other" rid="video2">Video 2</xref>. As a result, the diffusion-binding model does not perform better than the model in which the partition complex only passively diffuses (no interaction with ParA-ATP dimers). In fact, the diffusion-binding model quantitatively performs worse than the diffusion-alone model because the only thing the ParA/ParB interaction does is to temporally stops the motion of the partition complex, slowing down its ultimate arrival at the opposite cell pole. We found that it was essential to include the elastic dynamics of the underlying DNA (which had not been considered before) to explain the translocation kinetics observed in vivo. We have revised the manuscript to be more explicit.</p><p><italic>The new model also does not take account of the fact that each oriC region has multiple ParB molecules bound, and that there are several separated parS sites, each of which could collide with a DNA-bound ParA dimer</italic>, <italic>facilitating the walk up the ParA gradient towards the cell pole. Perhaps the occasional “stretching” of ParB foci represents simultaneous interactions made by different parS assemblies?</italic></p><p>Our modeling does take into account that multiple ParB dimers bind to the <italic>parS</italic> (ori) region and that the ParB-rich partition complex can interact with more than one DNA-bound ParA-ATP dimer. The interaction radius of the ParB-rich partition complex is 50 nm, which we estimated from our super-resolution images (<xref ref-type="fig" rid="fig1s3">Figure 1–figure supplement 3</xref>). In the model, the 50-nm ParB sphere is allowed to interact with infinite number of DNA-bound ParA-ATP dimers as long as there is an overlap between the ParB sphere and the ParA-ATP dimer sphere (the dimension of which was determined from the crystal structure of a ParA homolog (Leonard et al., EMBO J, 2005)). Multiple interactions between the ParB-rich partition complex and ParA dimers can be clearly seen in <xref ref-type="other" rid="video3">Video 3</xref>. We agree that this information was not clearly described in the main text of the original submission. The text has been revised to make it clearer.</p><p>Regarding the reviewer’s concern about the multiplicity of <italic>parS</italic> sites and their separation, it is important to note that there are only 2 <italic>parS</italic> sites in the <italic>C. crescentus</italic> chromosome and they are separated by only 42 nucleotides, which can be, at most, 14 nm long. Therefore, we believe that there is only one stable ParB/<italic>parS</italic> assembly complex per chromosome in <italic>C. crescentus</italic>. This is likely to be the case in most, if not all, plasmid systems.</p><p>However, the notion of separated ParB/<italic>parS</italic> assemblies remains interesting as it may be relevant to the <italic>B. subtilis</italic> chromosome case in which 10 <italic>parS</italic> sites are spread across a ∼2 Mb-nucleotide region flanking the origin of replication (Breier and Grossman, Mol Microbiol, 2007). By epifluorescence microscopy, this region appears as a single diffraction-limited spot (Lin et al., PNAS, 1997, Glaser et al., Genes Dev, 1997), indicating that the most distal <italic>parS</italic> sites are separated by ≤ 250 nm. As suggested by the reviewer, we have expanded the ‘diffusion-binding’ model to consider the cases of two ParB/<italic>parS</italic> assemblies (two spheres of 35 nm of radius) separated by a flexible linker of varying lengths to simulate the reviewer’s scenario. The reason for using a radius of 35 nm is to make the surface area of the two ParB spheres comparable to the surface area of the single partition complex sphere (50 nm of radius) used in the original model (2·π·35<sup>2</sup> ≈ π·50<sup>2</sup>). Our simulations show that separating the <italic>parS</italic> sites by up to 400 nm had little, if any, positive effect on translocation (unpublished result), further supporting the notion that the elastic dynamics of the underlying DNA must be considered to obtain the translocation kinetics observed inside cells. Since the partition complex of <italic>C. crescentus</italic> is unlikely to form two or more ParB assemblies, we feel that these data do not belong to this manuscript. We would therefore prefer to publish these results elsewhere together with follow-up studies<italic>.</italic></p></body></sub-article></article>