Advertisement

Journal of Computational Neuroscience

, Volume 16, Issue 2, pp 159–175 | Cite as

An Analytical Model for the ‘Large, Fluctuating Synaptic Conductance State’ Typical of Neocortical Neurons In Vivo

  • Hamish Meffin
  • Anthony N. Burkitt
  • David B. Grayden
Article

Abstract

A model of in vivo-like neocortical activity is studied analytically in relation to experimental data and other models in order to understand the essential mechanisms underlying such activity. The model consists of a network of sparsely connected excitatory and inhibitory integrate-and-fire (IF) neurons with conductance-based synapses. It is shown that the model produces values for five quantities characterizing in vivo activity that are in agreement with both experimental ranges and a computer-simulated Hodgkin-Huxley model adapted from the literature (Destexhe et al. (2001) Neurosci. 107(1): 13–24). The analytical model builds on a study by Brunel (2000) (J. Comput. Neurosci. 8: 183–208), which used IF neurons with current-based synapses, and therefore does not account for the full range of experimental data. The present results suggest that the essential mechanism required to explain a range of data on in vivo neocortical activity is the conductance-based synapse and that the particular model of spike initiation used is not crucial. Thus the IF model with conductance-based synapses may provide a basis for the analytical study of the ‘large, fluctuating synaptic conductance state’ typical of neocortical neurons in vivo.

cortical background activity conductance-based synapses integrate-and-fire neuron analytical model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramowitz M, Stegun IA (eds.) (1972) Handbook of Mathematical Functions. Dover Publications, New York.Google Scholar
  2. Amit DJ, Brunel N (1997) Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cereb. Cortex 7: 237-252.Google Scholar
  3. Arieli A, Sterkin A, Grinvald A, Aertsen A (1996) Dynamics of ongoing activity: Explanation of the large varibality in evoked cortical responses. Science 273: 1868-1871.Google Scholar
  4. Aviel Y, Pavlov E, Abeles M, Horn D (2002) Synfire chain in a balanced network. Neurocomput. 44-46: 285-292.Google Scholar
  5. Azouz R, Gray CM (1999) Cellular mechanisms contribute to response variablity of cortical neurons in vivo. J. Neurosci. 19(6): 2209-2223.Google Scholar
  6. Bernander O, Douglas RJ, Martin KAC, Koch C (1991) Synaptic background activity influences spatiotemporal integration in single pyramidal cells. Proc. Natl. Acad. Sci. USA 88: 11569-11573.Google Scholar
  7. Brunel N (2000) Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J. Comput. Neurosci. 8: 183-208.Google Scholar
  8. Brunel N, Hakim V (1999) Fast global oscillation in networks of integrate-and-fire N with low firing rates. Neural. Comput. 11: 1621-1671.Google Scholar
  9. Brunel N, Sergi S (1998) Firing frequency of leaky integrate-and-fire neurons with synaptic current dynamics. J. Theor. Neurobiol. 195: 87-95.Google Scholar
  10. Bugmann G, Christodoulou C, Taylor JG (1997) Role of temporal integration and fluctuation detection in the highly irregular firing of a leaky integrator neuron model with partial reset. Neural Comput. 9: 985-1000.Google Scholar
  11. Burkitt AN (2000) Balanced neurons: Analysis of leaky integrateand-fire neurons with reversal potential. Biol. Cybern. 85: 247-255.Google Scholar
  12. Burkitt AN, Meffin H, Grayden DB (2003) Study of neuronal gain in a conductance-based leaky integrate-and-fire neuron model with balanced excitatory and inhibitory synaptic input. Biol. Cybern. 89: 119-125.Google Scholar
  13. Câteau H, Fukai T (2001) Fokker-Planck approach to the pulse packet propagation in synfire chain. Neural Networks 14: 675-685.Google Scholar
  14. Chance FS, Abbott LF, Reyes AD (2002) Gain modulation from background synaptic input. Neuron 35: 773-782.Google Scholar
  15. Destexhe A (2001) Simulations of in-vivo-like activity in neocortical neurons using fluctuating synaptic conductances. http://cns.iaf.cnrs-gif.fr/alain demos.html.Google Scholar
  16. Destexhe A, Paré D (1999) Impact of network activity on the integrative properties of neocortical pyrimidal neurons in vivo. J. Neurophysiol. 81: 1531-1547.Google Scholar
  17. Destexhe A, Rudolph M, Fellous J-M, Sejnowski TJ (2001) Fluctuating synaptic conductances recreate in-vivo-like activity in neocortical neurons. Neurosci. 107: 13-24.Google Scholar
  18. Doedel EJ, Paffenroth RC, Champneys AR, Fairgrieve TF, Kuznetov YA, Sandstede B, Wang X (2000) AUTO2000: Continuation and Bifurcation Software for ODE's. http://www.ama.caltech.edu/ redrod/auto2000/distribution.Google Scholar
  19. Feng J, Brown D (1998) Spike output jitter, mean firing time and coefficient of variation. J. Phys. A. 31: 1239-1252.Google Scholar
  20. Gerstein GL, Mandelbrot B (1964) Random walk models for the spike activity of a single neuron. Biophys. J. 4: 41-68.Google Scholar
  21. Gutkin BS, Ermentrout GB (1998) Dynamics of membrane excitability determine interspike interval variability: A link between spike generation mechanisms and cortical spike train statistics. Neural Comput. 10: 1047-1065.Google Scholar
  22. Häusser M, Spruston N, Stuart GJ (2000) Diversity and dynamics of dendritic signaling. Science 290: 739-744.Google Scholar
  23. Hines ML, Carnevale NT (1997) The NEURON simulation environment. Neural Comput. 9: 1179-1209.Google Scholar
  24. Johnston D, Magee JC, Colbert CM, Christie BR (1996) Active properties of neuronal dendrites. Annu. Rev. Neurosci. 19: 165-186.Google Scholar
  25. Kisley MA, Gerstein GL (1999) The continuum of operating modes for passive model neurons. Neural Comput. 11: 1139-1154.Google Scholar
  26. Lampl I, Reichova I, Ferster D (1999) Synchonous membrane potential fluctuations in neurons of the cat visual cortex. Neuron 22: 361-374.Google Scholar
  27. Longtin A, Doiron B, Bulsara, AR (2002) Noise-induced divisive gain control in neuron models. BioSys. 67: 147-156.Google Scholar
  28. Mel BW (1999) Why have dendrites? A computational perspective. In: GJ Stuart, N Spruston, M H¨usser, eds. Dendrites. Oxford Uni. Press, NY, pp. 271-289.Google Scholar
  29. Moreno R, de la Rocha J, Renart A, Parga N (2002) Response of spiking neurons to correlated input. Phys. Rev. Lett. 89(28): 288101.Google Scholar
  30. Panzeri S, Rolls ET, Battaglia F, Lavis R (2001) Speed of feedforward and recurrent processing in multilayer networks of integrate-and-fire neurons. Network: Comput. Neural Syst. 12: 423-440.Google Scholar
  31. Paré D, Shink E, Gaudreau H, Destexhe A, Lang EJ (1998) Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons in vivo. J. Neurophysiol. 79: 1450-1460.Google Scholar
  32. Pongracz F, Firestein S, Shepard GM (1991) Electrotonic structure of olafactory sensory neurons analysed by intracellular and whole cell patch techniques. J. Neurophysiol. 65: 747-758.Google Scholar
  33. Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1992) Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge.Google Scholar
  34. Rudolph M, Destexhe A (2003a) The discharge variability of neocortical neurons during high-conductance states. Neurosci. 119: 855-873.Google Scholar
  35. Rudolph M, Destexhe A (2003b) A fast-conducting, stochastic integrative mode for neocortical neurons in vivo. J. Neurosci. 24(6): 2466-2476.Google Scholar
  36. Rudolph M, Destexhe A (2003c) Tuning neocortical pyramidal neurons between integrators and coincidence detectors. J. Comput. Neurosci. 14(3): 239-251.Google Scholar
  37. Salinas E, Sejnowski TJ (2000) Impact of correlated synaptic input on output firing rate and variability in simple neuronal models. J. Neurosci. 20: 6193-6209.Google Scholar
  38. Shadlen MN, Newsome WT (1994) Noise, neural codes and cortical organization. Curr. Opin. Neurobiol. 4: 569-579.Google Scholar
  39. Shadlen MN, Newsome WT (1998) The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding. J. Neurosci. 18: 3870-3896.Google Scholar
  40. Softky WR, Koch C (1993) The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13: 334-350.Google Scholar
  41. Spruston N, Johnston D (1992) Perforated patch-clamp analysis of the passive membrane properties of three classes of hippocampal neurons. J. Neurophysiol. 67: 508-529.Google Scholar
  42. Stevens CF, Zador AM (1998) Input synchrony and the irregular firing of cortical neurons. Nature Neurosci. 1(3): 210-217.Google Scholar
  43. Stuart G, Spruston N, Häusser M (1999) Dendrites. Oxford Unversity Press, NY.Google Scholar
  44. Tetzlaff T, Giesel T, Diesmann M (2002) The ground state of cortical feedforward networks. Neurocomput. 44-46: 673-678.Google Scholar
  45. Tiesinga PHE, José JV, Sejnowski TJ (2000) Comparison of currentdriven and conductance-driven neocortical model neurons with Hodgkin-Huxley voltage-gated channels. Phys. Rev. E 62: 8413-8419.Google Scholar
  46. Traub RD, Miles R (1991) Neuronal Networks of the Hippocampus. Cambridge University Press, Cambridge, UK.Google Scholar
  47. Treves A (1993) Mean-field analysis of neuronal spike dynamics. Network: Comput. Neural Syst. 4: 259-284.Google Scholar
  48. Troyer TW, Miller KD (1997) Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell. Neural Comput. 9: 971-983.Google Scholar
  49. Tsodyks MV, Sejnowski TJ (1995) Rapid state switching in balanced cortical network models. Network: Comput. Neural Sys. 6: 111-124.Google Scholar
  50. Tsodyks MV, Kenet T, Grinvald A, Arieli A (1999) Linking spontaneous activity of single cortical neurons and the underlying functional architecture. Science 286: 1943-1945.Google Scholar
  51. Tuckwell HC (1988a) Introduction to Theoretical Neurobiology: Vol. 1, Linear Cable Theory and Dendritic Structure. Cambridge University Press, Cambridge.Google Scholar
  52. Tuckwell HC (1988b) Introduction to Theoretical Neurobiology: Vol. 2, Nonlinear and Stochastic Theories. Cambridge University Press, Cambridge.Google Scholar
  53. Usher M, Stemmler M, Koch C, Olami Z (1994) Network amplification of local fluctuations cause high spike rate variability, fractal firing patterns and oscillatory local field potentials. Neural Comput. 6: 795-836.Google Scholar
  54. van Kampen NG (1992) Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam.Google Scholar
  55. van Rossum MCW, Turrigiano GG, Nelson SB (2002) Fast propagation of firing rates through layered networks of noisy neurons. J. Neurosci. 22: 1956-1966.Google Scholar
  56. van Vreeswijk C, Somplinsky H (1996) Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274: 1724-1726.Google Scholar
  57. van Vreeswijk C, Somplinsky H (1998) Chaotic balanced state in a model of cortical circuits. Neural Comput. 10: 1321-1371.Google Scholar
  58. Williams SR, Stuart GJ (2000) Site independence of EPSP time course is mediated by dendrtic Ih in neocortical pyramidal neurons. J. Neurophysiol. 83: 3177-3182.Google Scholar
  59. Williams SR, Stuart GJ (2002) Dependence of EPSP efficacy on synapse location in neocortical pyramidal neurons. Science 295: 1907-1910.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Hamish Meffin
    • 1
  • Anthony N. Burkitt
    • 1
  • David B. Grayden
    • 1
  1. 1.The Bionic Ear InstituteEast MelbourneAustralia

Personalised recommendations