Computational model of a tripartite synapse in developing somatosensory cortex, including a presynaptic neuron, a postsynaptic neuron, and an astrocyte.
The code was developed and tested on Linux with Python 3.7. The prerequisites include numpy, scipy, and tqdm. To install these libraries on Linux type in terminal:
pip3 install -r requirements.txt
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The command
python run_pairings.pywill run the t-LTD induction protocol, thus 20 simulations with the different temporal differences of post-pre pairing protocol (-10 ms, -20 ms,..., -200 ms) and saves the data to separate folders (altogether 77.8 GB). Please, modify the path where to save the data, if needed. Note that the temporal differences of the post-pre pairings are implemented in the code as positive values, whereas they have negative values in the article. The reason for this is that we set the postsynaptic stimuli to occur at fixed time points in all the simulations whereas the presynaptic stimuli occurred in varying time points after the postsynaptic stimuli depending on temporal difference used, and not the other way around. -
The command
python run_before_and_after_pairings.pywill run the protocols before (baseline) and after t-LTD induction and saves the data to separate folders (altogether 9.9 GB). Please, modify the path where to save the data, if needed. Baseline protocol is run only once, but the protocol after t-LTD induction is run 20 times, thus once for each corresponding temporal difference in the t-LTD induction protocol. The protocol after t-LTD induction needs the actual end values of f_pre from the t-LTD induction protocol, and the values are given in run_before_and_after_pairings.py file. If you modify the model, you need to change these values in the code to the values your model gives after running run_pairings.py.
Plotting can be done with the given example MATLAB code: plotting_post_pre_pairing_data.m. It will plot in separate figures, the inputs, the saved model state variables, and the other saved output variables for a certain temporal difference of the post-pre pairing protocol. You can easily modify the path to your data to plot also the simulation results from the protocols before and after t-LTD induction.
In addition to the above two python files, the model includes presynaptic (preneuron.py) and postsynaptic (postneuron.py) neurons and an astrocyte (astrocyte.py). More details of the model are given below. Description of the whole model is given in the article and its appendix.
Please, cite our article when using our code:
Tiina Manninen, Ausra Saudargiene, and Marja-Leena Linne. Astrocyte-mediated spike-timing-dependent long-term depression modulates synaptic properties in the developing cortex. PLoS Comput. Biol. 2020. DOI: 10.1371/journal.pcbi.1008360
This work is licensed under the MIT License.
PRESYNAPTIC NEURON MODEL: Layer 4 spiny stellate cell of barrel cortex
Currents in axon: Ca_NHVA (high-voltage-activated N-type Ca), K, Na, GluN2C/D-containing NMDAR
Models adopted:
HH model including K and Na channels - from L4 spiny stellate cell model (Lavzin et al., 2012)
Ca_NHVA channel - from pyramidal cell model (Safiulina et al., 2010)
NMDAR (Erreger et al., 2005; Clarke and Johnson, 2008)
CaN signaling (Fiala et al., 1996)
Glutamate release by presynaptic neuron (Combined and modified from Tsodyks et al., 1998; Lee et al., 2009; De Pitta et al., 2011; De Pitta and Brunel, 2016)
HH model:
Lavzin M, Rapoport S, Polsky A, Garion L, Schiller J (2012). Nonlinear dendritic processing determines angular tuning of barrel cortex neurons in vivo. Nature 490:397-401. https://doi.org/10.1038/nature11451 https://senselab.med.yale.edu/ModelDB/ShowModel.cshtml?model=146565#tabs-1
Ca_NHVA channel:
Safiulina VF, Caiati MD, Sivakumaran S, Bisson G, Migliore M, Cherubini E (2010). Control of GABA release at mossy fiber-CA3 connections in the developing hippocampus. Front Synaptic Neuroscience 2:1. https://doi.org/10.3389/neuro.19.001.2010 https://senselab.med.yale.edu/ModelDB/ShowModel.cshtml?model=126814#tabs-1
NMDAR:
Erreger K, Dravid SM, Banke TG, Wyllie DJA, Traynelis SF (2005). Subunit-specific gating controls rat NR1/NR2A and NR1/NR2B NMDA channel kinetics and synaptic signalling profiles. J Physiol 563.2: 345–358. https://doi.org/10.1113/jphysiol.2004.080028
Clarke RJ, Johnson JW (2008). Voltage-dependent gating of NR1/2B NMDA receptors. J Physiol 586.23: 5727–5741. https://doi.org/10.1113/jphysiol.2008.160622
CaN signaling:
Fiala JC, Grossberg S, Bullock D (1996). Metabotropic glutamate receptor activation in cerebellar Purkinje cells as substrate for adaptive timing of the classically conditioned eye-blink response. J Neurosci 16(11):3760–3774. https://doi.org/10.1523/JNEUROSCI.16-11-03760.1996
Glutamate release by presynaptic neuron:
Tsodyks M, Pawelzik K, Markram H (1998). Neural networks with dynamic synapses. Neural Comput 10(4):821–835. https://doi.org/10.1162/089976698300017502
Lee C-CJ, Anton M, Poon C-S, McRae GJ (2009). A kinetic model unifying presynaptic short-term facilitation and depression. J Comput Neurosci 26:459–473. https://doi.org/10.1007/s10827-008-0122-6 https://senselab.med.yale.edu/modeldb/ShowModel.cshtml?model=120184#tabs-1
De Pittà M, Volman V, Berry H, Ben-Jacob E (2011). A tale of two stories: astrocyte regulation of synaptic depression and facilitation. PLoS Comput Biol 7(12):e1002293. https://doi.org/10.1371/journal.pcbi.1002293
De Pittà M, Brunel N (2016). Modulation of synaptic plasticity by glutamatergic gliotransmission: a modeling study. Neural Plast 2016:7607924. https://doi.org/10.1155/2016/7607924
POSTSYNAPTIC NEURON MODEL: Layer 2/3 pyramidal cell of barrel cortex
Two compartmental model (Pinsky and Rinzel, 1994)
Currents in soma: K_DR (delayed rectifier K), Na, Na_P (persistent Na)
Currents in dendrite: K_A (A-type K), AMPAR, Ca_LHVA (high-voltage-activated L-type Ca), Ca_LLVA (low-voltage-activated L-type Ca), Na, GluN2B-containing NMDAR
Models adopted:
HH model including K_A, K_DR and Na, Na_P channels - from L2/3 pyramidal cell model (Sarid et al., 2007)
Ca_LHVA channel - from neocortical pyramidal cell model (Reuveni et al., 1993, Markram et al., 2015)
Ca_LLVA channel - from hippocampal CA3 pyramidal cell model (Avery and Johnston, 1996)
AMPAR (Destexhe et al., 1998)
NMDAR (Destexhe et al., 1998)
mGluR -> 2-AG reactions (Mostly from Kim et al., 2013, but added model components from De Young and Keizer, 1992; Li and Rinzel, 1994; Blackwell, 2002; Zachariou et al., 2013)
HH model:
Sarid L, Bruno R, Sakmann B, Segev I, Feldmeyer D (2007). Modeling a layer 4-to-layer 2/3 module of a single column in rat neocortex: Interweaving in vitro and in vivo experimental observations. Proc Natl Acad Sci USA 104(41): 16353-16358. https://doi.org/10.1073/pnas.0707853104
Ca_L channels:
Reuveni I, Friedman A, Amitai Y, Gutnick MJ (1993). Stepwise repolarization from Ca2+ plateaus in neocortical pyramidal cells: evidence for nonhomogeneous distribution of HVA Ca2+ channels in dendrites. J Neurosci 13(11): 4609-4621. https://doi.org/10.1523/JNEUROSCI.13-11-04609.1993
Avery RB, Johnston D (1996). Multiple channel types contribute to the low-voltage-activated calcium current in hippocampal CA3 pyramidal neurons. J Neurosci 16(18): 5567–5582. https://doi.org/10.1523/JNEUROSCI.16-18-05567.1996
Markram H, Muller E, Ramaswamy S, Reimann MW, Abdellah M, et al. (2015). Reconstruction and simulation of neocortical microcircuitry. Cell 163(2): 456-492. https://doi.org/10.1016/j.cell.2015.09.029 https://senselab.med.yale.edu/modeldb/ShowModel?model=188543#tabs-1
AMPAR and NMDAR:
Destexhe A, Mainen ZF, Sejnowski TJ (1998). Kinetic Models of Synaptic Transmission. In Book: Methods in Neuronal Modeling, Koch C and Segev I, MIT Press, Cambridge, MA.
mGluR -> 2-AG reactions:
Kim B, Hawes SL, Gillani F, Wallace LJ, Blackwell KT (2013). Signaling pathways involved in striatal synaptic plasticity are sensitive to temporal pattern and exhibit spatial specificity. PLoS Comput Biol 9(3): e1002953. https://doi.org/10.1371/journal.pcbi.1002953 http://krasnow1.gmu.edu/CENlab/publications.html
De Young GW, Keizer J (1992). A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci USA 89(20): 9895–9899. https://doi.org/10.1073/pnas.89.20.9895
Li YX, Rinzel J (1994). Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. J Theor Biol 166(4): 461–473. https://doi.org/10.1006/jtbi.1994.1041
Blackwell KT (2002). Calcium waves and closure of potassium channels in response to GABA stimulation in Hermissenda type B photoreceptors. J. Neurophysiol. 87: 776-792. https://doi.org/10.1152/jn.00867.2000
Zachariou M, Alexander SPH, Coombes S, Christodoulou C (2013). A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition. PLoS ONE 8(3): e58926. https://doi.org/10.1371/journal.pone.0058926
ASTROCYTE MODEL
Models adopted:
Calcium equations (De Young and Keizer, 1992; Li and Rinzel, 1994)
Glutamate release by astrocyte (Combined from Tsodyks et al., 1998; Lee et al., 2009; De Pitta et al., 2011; Wade et al., 2012; De Pitta and Brunel, 2016)
Wade J, McDaid L, Harkin J, Crunelli V, Kelso S (2012). Self-repair in a bidirectionally coupled astrocyte-neuron (AN) system based on retrograde signaling. Front Comput Neurosci 6:76. https://doi.org/10.3389/fncom.2012.00076