Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neurons

Abstract

Voltage-sensitive dye imaging (VSDi) has revealed fundamental properties of neocortical processing at macroscopic scales. Since for each pixel VSDi signals report the average membrane potential over hundreds of neurons, it seems natural to use a mean-field formalism to model such signals. Here, we present a mean-field model of networks of Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based synaptic interactions. We study a network of regular-spiking (RS) excitatory neurons and fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism, together with a semi-analytic approach to the transfer function of AdEx neurons to describe the average dynamics of the coupled populations. We compare the predictions of this mean-field model to simulated networks of RS-FS cells, first at the level of the spontaneous activity of the network, which is well predicted by the analytical description. Second, we investigate the response of the network to time-varying external input, and show that the mean-field model predicts the response time course of the population. Finally, to model VSDi signals, we consider a one-dimensional ring model made of interconnected RS-FS mean-field units. We found that this model can reproduce the spatio-temporal patterns seen in VSDi of awake monkey visual cortex as a response to local and transient visual stimuli. Conversely, we show that the model allows one to infer physiological parameters from the experimentally-recorded spatio-temporal patterns.

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References

  1. Angelucci, A., Levitt, J.B., Walton, E.J., Hupe, J.M., Bullier, J., Lund, J.S. (2002). Circuits for local and global signal integration in primary visual cortex. Journal of Neuroscience, 22(19), 8633–8646.

    CAS  PubMed  Google Scholar 

  2. Amit, D.J., & Brunel, N. (1997). Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cerebral Cortex, 7, 237–252.

    CAS  Article  PubMed  Google Scholar 

  3. Arieli, A., Sterkin, A., Grinvald, A., Aertsen, A., An, J.H. (1996). Dynamics of ongoing activity: explanation of the large variability in evoked cortical responses. Science (New York, N.Y.), 273, 1868–71.

    CAS  Article  Google Scholar 

  4. Arieli, A., Grinvald, A., Slovin, H. (2002). Dural substitute for long-term imaging of cortical activity in behaving monkeys and its clinical implications. Journal of Neuroscience Methods, 114, 119–133.

    Article  PubMed  Google Scholar 

  5. Augustin, M., Ladenbauer, J., Baumann, F., Obermayer, K. (2016). Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: comparison and implementation. arXiv:1611.07999.

  6. Berger, T., Borgdorff, A., Crochet, S., Neubauer, F.B., Lefort, S., Fauvet, B., Ferezou, I., Carleton, A., Lüscher, H.R., Petersen, C.C.H. (2007). Combined voltage and calcium epifluorescence imaging in vitro and in vivo reveals subthreshold and suprathreshold dynamics of mouse barrel cortex. Journal of Neurophysiology, 97, 3751–3762.

    CAS  Article  PubMed  Google Scholar 

  7. Brette, R., & Gerstner, W. (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of Neurophysiology 3637–3642.

  8. Bringuier, V., Chavane, F., Glaeser, L., Fregnac, Y. (1999). Horizontal propagation of visual activity in the synaptic integration field of area 17 neurons. Science, 283, 695–699.

    CAS  Article  PubMed  Google Scholar 

  9. Brunel, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of Computational Neuroscience, 8, 183–208.

    CAS  Article  PubMed  Google Scholar 

  10. Brunel, N., & Hakim, V. (1999). Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Computation, 11, 1621–1671.

    CAS  Article  PubMed  Google Scholar 

  11. Brunel, N., & Wang, X.J. (2003). What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance. Journal of Neurophysiology, 90, 415–430.

    Article  PubMed  Google Scholar 

  12. Buzás, P., Kovács, K., Ferecskó, A.S., Budd, J.M.L., Eysel, U.T., Kisvárday, Z.F. (2006). Model-based analysis of excitatory lateral connections in the visual cortex. The Journal of Comparative Neurology, 499, 861–81.

    Article  PubMed  Google Scholar 

  13. Chemla, S., & Chavane, F. (2010). A biophysical cortical column model to study the multi-component origin of the VSDI signal. NeuroImage, 53, 420–438.

    CAS  Article  PubMed  Google Scholar 

  14. Chemla, S., & Chavane, F. (2016). Effects of gabaa kinetics on cortical population activity: computational studies and physiological confirmations. Journal of Neurophysiology, 115, 2867–2879.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  15. Chen, Y., Geisler, W.S., Seidemann, E. (2006). Optimal decoding of correlated neural population responses in the primate visual cortex. Nature Neuroscience, 9, 1412–1420.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  16. Chen, Y., Geisler, W.S., Seidemann, E. (2008). Optimal temporal decoding of neural population responses in a reaction-time visual detection task. Journal of Neurophysiology, 99, 1366–1379.

    Article  PubMed  PubMed Central  Google Scholar 

  17. Civillico, E.F., & Contreras, D. (2012). Spatiotemporal properties of sensory responses in vivo are strongly dependent on network context. Frontiers in Systems Neuroscience, 6, 25.

    Article  PubMed  PubMed Central  Google Scholar 

  18. Contreras, D., & Llinas, R. (2001). Voltage-sensitive dye imaging of neocortical spatiotemporal dynamics to afferent activation frequency. The Journal of Neuroscience: the Official Journal of the Society for Neuroscience, 21, 9403–9413.

    CAS  Google Scholar 

  19. Daley, D.J., & Vere-Jones, D. (2007). An introduction to the theory of point processes: volume II: general theory and structure, vol. 2. Springer Science & Business Media.

  20. Destexhe, A., Rudolph, M., Paré, D. (2003). The high-conductance state of neocortical neurons in vivo. Nature Reviews Neuroscience, 4, 739–751.

    CAS  Article  PubMed  Google Scholar 

  21. El Boustani, S., & Destexhe, A. (2009). A master equation formalism for macroscopic modeling of asynchronous irregular activity states. Neural Computation, 21, 46–100.

    Article  PubMed  Google Scholar 

  22. Ferezou, I., Bolea, S., Petersen, C.C.H. (2006). Visualizing the cortical representation of whisker touch: voltage-sensitive dye imaging in freely moving mice. Neuron, 50, 617–629.

    CAS  Article  PubMed  Google Scholar 

  23. Gawne, T., McClurkin, J., Richmond, B., Optican, L. (1991). Lateral geniculate neurons in behaving primates. III. Response predictions of a channel model with multiple spatial-to-temporal filters. Journal of Neurophysiology, 66, 809–823.

    CAS  Article  PubMed  Google Scholar 

  24. Gilad, A., & Slovin, H. (2015). Population responses in v1 encode different figures by response amplitude. Journal of Neuroscience, 35, 6335–6349.

    CAS  Article  PubMed  Google Scholar 

  25. Girard, P., Hupé, J. M., Bullier, J. (2001). Feedforward and feedback connections between areas V1 and V2 of the monkey have similar rapid conduction velocities. Journal of Neurophysiology, 85(3), 1328–1331.

    CAS  Article  PubMed  Google Scholar 

  26. Goodman, D.F.M., & Brette, R. (2009). The brian simulator. Frontiers in Neuroscience, 3, 192–197.

    Article  PubMed  PubMed Central  Google Scholar 

  27. Hansel, D., & Sompolinsky, H. (1996). Chaos and synchrony in a model of a hypercolumn in visual cortex. Journal of Computational Neuroscience, 3, 7–34.

    CAS  Article  PubMed  Google Scholar 

  28. Jancke, D., Chavane, F., Naaman, S., Grinvald, A. (2004). Imaging cortical correlates of illusion in early visual cortex. Nature, 428, 423–426.

    CAS  Article  PubMed  Google Scholar 

  29. Kuhn, A., Aertsen, A., Rotter, S. (2004). Neuronal integration of synaptic input in the fluctuation-driven regime. The Journal of Neuroscience: the Official Journal of the Society for Neuroscience, 24, 2345–56.

    CAS  Article  Google Scholar 

  30. Kumar, A., Schrader, S., Aertsen, A., Rotter, S. (2008). The high-conductance state of cortical networks. Neural Computation, 20, 1–43.

    Article  PubMed  Google Scholar 

  31. Latham, P.E., Richmond, B.J., Nelson, P.G., Nirenberg, S. (2000). Intrinsic dynamics in neuronal networks. I. Theory. Journal of Neurophysiology, 83, 808–827.

    CAS  Article  PubMed  Google Scholar 

  32. Ledoux, E., & Brunel, N. (2011). Dynamics of networks of excitatory and inhibitory neurons in response to time-dependent inputs. Frontiers in Computational Neuroscience, 5, 25.

    Article  PubMed  PubMed Central  Google Scholar 

  33. Markram, H., Toledo-Rodriguez, M., Wang, Y., Gupta, A., Silberberg, G., Wu, C. (2004). Interneurons of the neocortical inhibitory system. Nature Reviews. Neuroscience, 5, 793–807.

    CAS  Article  PubMed  Google Scholar 

  34. Markram, H., Muller, E., Ramaswamy, S., Reimann, M. (2015). Reconstruction and simulation of neocortical microcircuitry. Cell, 163, 456–492.

    CAS  Article  PubMed  Google Scholar 

  35. McCormick, D.A., Connors, B.W., Lighthall, J.W., Da, Prince. (1985). Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. Journal of Neurophysiology, 54, 782–806.

    CAS  Article  PubMed  Google Scholar 

  36. Meirovithz, E., Ayzenshtat, I., Bonneh, Y.S., Itzhack, R., Werner-Reiss, U., Slovin, H. (2009). Population response to contextual influences in the primary visual cortex. Cerebral Cortex, 20, 1293–1304.

    Article  PubMed  Google Scholar 

  37. Muller, L., Reynaud, A., Chavane, F., Destexhe, A. (2014). The stimulus-evoked population response in visual cortex of awake monkey is a propagating wave. Nature Communications, 5, 3675.

    PubMed  PubMed Central  Google Scholar 

  38. Papoulis, A. (1991). Probability, random variables and stochastic processes. Mcgraw-Hill.

  39. Platkiewicz, J., & Brette, R. (2010). A threshold equation for action potential initiation. PLoS Computational Biology, 6, e1000850.

    Article  PubMed  PubMed Central  Google Scholar 

  40. Reinhold, K., Lien, A.D., Scanziani, M. (2015). Distinct recurrent versus afferent dynamics in cortical visual processing. Nature Neuroscience, 18.

  41. Renart, A., Brunel, N., Wang, X.J. (2004). Mean-field theory of irregularly spiking neuronal populations and working memory in recurrent cortical networks. Computational Neuroscience: A Comprehensive Approach 431–490.

  42. Reynaud, A., Masson, G.S., Chavane, F. (2012). Dynamics of local input normalization result from balanced short- and long-range intracortical interactions in area v1. The Journal of Neuroscience: the Official Journal of the Society for Neuroscience, 32, 12558–69.

    CAS  Article  Google Scholar 

  43. Shoham, D., Glaser, D.E., Arieli, A., Kenet, T., Wijnbergen, C., Toledo, Y., Hildesheim, R., Grinvald, A. (1999). Imaging cortical dynamics at high spatial and temporal resolution with novel blue voltage-sensitive dyes. Neuron, 24, 791–802.

    CAS  Article  PubMed  Google Scholar 

  44. Stettler, D. D., Das, A., Bennett, J., Gilbert, C. D. (2002). Lateral connectivity and contextual interactions in macaque primary visual cortex. Neuron, 36(4), 739–750.

    CAS  Article  PubMed  Google Scholar 

  45. Steriade, M., Timofeev, I., Grenier, F. (2001). Natural waking and sleep states: a view from inside neocortical neurons. Journal of Neurophysiology, 85, 1969–1985.

    CAS  Article  PubMed  Google Scholar 

  46. Tan, A.Y., Chen, Y., Scholl, B., Seidemann, E., Priebe, N.J. (2014). Sensory stimulation shifts visual cortex from synchronous to asynchronous states. Nature, 509, 226–229.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  47. van Vreeswijk, C., & Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science (New York, N.Y.), 274, 1724–6.

    Article  Google Scholar 

  48. Vogels, T.P., & Abbott, L.F. (2005). Signal propagation and logic gating in networks of integrate-and-fire neurons. The Journal of Neuroscience, 25, 10786–10795.

    CAS  Article  PubMed  Google Scholar 

  49. Yger, P., El Boustani, S., Destexhe, A., Yves, F. (2011). Topologically invariant macroscopic statistics in balanced networks of conductance-based integrate-and-fire neurons. Journal of Computational Neuroscience, 31, 229–245.

    Article  PubMed  Google Scholar 

  50. Zerlaut, Y., Telenczuk, B., Deleuze, C., Bal, T., Ouanounou, G., Destexhe, A. (2016). Heterogeneous firing response of mice layer V pyramidal neurons in the fluctuation-driven regime. The Journal of Physiology, 594, 3791–808.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

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Acknowledgments

Research supported by the CNRS, the ICODE excellence network, the European Community: Human Brain Project H2020-720270 and a Flag-Era JTC (SLOW-DYN) to A.D., FET Grant BrainScaleS FP7-269921 to A.D. and F.C and the ANR BalaV1 and Trajectory (ANR-13-BSV4-0014-02 to F.C). Y.Z. was supported by fellowships from the Initiative d’Excellence Paris-Saclay and the Fondation pour la Recherche Médicale (FDT 20150532751).

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Correspondence to Yann Zerlaut or Alain Destexhe.

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Experimental protocols have been approved by the Marseille Ethical Committee in Neuroscience (approval A10/01/13, official national registration French Ministry of Research). All procedures complied with the French and European regulations for animal research, as well as the guidelines from the Society for Neuroscience.

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The authors declare that they have no conflict of interest.

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Zerlaut, Y., Chemla, S., Chavane, F. et al. Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neurons. J Comput Neurosci 44, 45–61 (2018). https://doi.org/10.1007/s10827-017-0668-2

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Keywords

  • Recurrent network dynamics
  • Mean-field description
  • Adex model
  • Voltage-sensitive dye imaging