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Information coding and oscillatory activity in synfire neural networks with and without inhibitory coupling

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Abstract

When a population spike (pulse-packet) propagates through a feedforward network with random excitatory connections, it either evolves to a sustained stable level of synchronous activity or fades away (Diesmann et al. in Nature 402:529–533 1999; Cateau and Fukai Neur Netw 14:675–685 2001). Here I demonstrate that in the presence of noise, the probability of the survival of the pulse-packet (or, equivalently, the firing rate of output neurons) reflects the intensity of the input. Furthermore, inhibitory coupling between layers can result in quasi- periodic alternation between several levels of firing activity. These results are obtained by analyzing the evolution of pulse-packet activity as a Markov chain. For the Markov chain analysis, the output of the chain is a linear mapping of the input into a lower-dimensional space, and the eigenvalues and eigenvectors of the transition matrix determine the dynamics of the evolution. Synchronous propagation of firing activity in successive pools of neurons are simulated in networks of integrate-and-fire and compartmental model neurons, and, consistent with the discrete Markov process, the activation of each pool is observed to be predominantly dependent upon the number of cells that fired in the previous pool. Simulation results agree with the numerical solutions of the Markov model. When inhibitory coupling between layers are included in the Markov model, some eigenvalues become complex numbers, implying oscillatory dynamics. The quasiperiodic dynamics is validated with simulation with leaky integrate-and-fire neurons. The networks demonstrate different modes of quasiperiodic activity as the inhibition or excitation parameters of the network are varied.

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References

  1. Abeles M (1991) Corticonics: neuronal circutes of cerebral cortex. Cambridge University Press, Cambridge, UK

  2. Aihara K, Matsumoto G (1986) Chaotic oscillation and bifurcation in squid giant axons. In: Holden AV (ed) Chaos. Manchester University Press, Manchester, UK, pp 257–269

  3. Anderson JS, Lampl I, Gillespie DC, Ferster D (2000) The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. Science 290:1968–1972

    Google Scholar 

  4. Aviel Y, Pavlov E, Abeles M, Horn D (2002) Synfire chain in a balanced network. Neurocomputing 44:285–292

    Google Scholar 

  5. Babloyantz A, Lourenco C (1994) Computation with chaos: a paradigm for cortical activity. Proc Natl Acad Sci USA 91:9027–9031

    Google Scholar 

  6. Basar E (ed) (1990) Chaos in brain function. Springer, Berlin Heidelberg New York

  7. Calvin WH, Stevens CF (1968) Synaptic noise and other sources of randomness in motoneuron interspike intervals. J Neurophysiol 31:574–587

    Google Scholar 

  8. Cateau H, Fukai T (2001) Fokker-Planck approach to the pulse packet propagation in synfire chain. Neural Netw 14:675–685

    Google Scholar 

  9. Date A, Bienenstock E, Geman S (1998) On the temporal resolution of neural activity. Technical Report, Division of Applied Mathematics, Brown University, Providence, RI. http://www.dam.brown.edu/people/elie/papers/temp_res.ps

  10. Destexhe A, Mainen ZF, Sejnowski TJ (1994) An efficient method for computing synaptic conductances based on a kinetic model of receptor binding. Neural Comput 6:10–14

    Google Scholar 

  11. Destexhe A, Pare D (1999) Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J Neurophysiol 81:1531–1547

    Google Scholar 

  12. Diesmann M, Gewaltig MO, Aertsen A (1999) Stable propagation of synchronous spiking in cortical neural networks. Nature 402:529–533

    Google Scholar 

  13. Engel AK, Fries P, Singer W (2001) Dynamic predictions: oscillations and synchrony in top-down processing. Nat Rev Neurosci 2:704–716

    Google Scholar 

  14. Freeman WJ (1987) Simulation of chaotic EEG patterns with a dynamic model of olfactory system. Biol Cybern 56:139:150

    Google Scholar 

  15. Freeman WJ (2000) A proposed name for aperiodic brain activity: stochastic chaos. Neural Netw 13:11–13

    Google Scholar 

  16. Gewaltig MO, Diesmann M, Aertsen A (2001) Propagation of cortical synfire activity: survival probability in single trials and stability in the mean. Neural Netw 14:657–673

    Google Scholar 

  17. Gray CM, Konig P, Engel AK, Singer W (1989) Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338:334–337

    Google Scholar 

  18. Hansel D, Sompolinsky H (1992) Synchronization and computation in chaotic neural network. Phys Rev Lett 68:718–721

    Google Scholar 

  19. Hansel D, Van Vreeswijk C (2002) How noise contributes to contrast invariance of orientation tuning in cat visual cortex. J Neurosci 22:5118–5128

    Google Scholar 

  20. Herrmann M, Hertz JA, Prügel-Bennett A (1995) Analysis of synfire chain networks. Netw Comput Neural Syst 6:403–414

    Google Scholar 

  21. Hertz JA, Prügel-Bennett A (1996) Learning synfire chains: turning noise into signal. Int J Neural Syst 7:445–450

    Google Scholar 

  22. Hines M (1994) The NEURON simulation program. In: Skrzypek J (ed) Neural network simulation environments. Kluwer, Norwell, MA, pp 147–163

  23. Holt GR, Softky WR, Koch C, Douglas RJ (1996) Comparison of discharge variability in vitro and in vivo in cat visual cortex neurons. J Neurophysiol 75:1806–1814

    Google Scholar 

  24. Litvak V, Sompolinsky H, Segev I, Abeles M (2000) On the transmission of rate code in long feed-forward networks with excitatory-inhibitory balance. In: Computational neuroscience meeting, Brugge, 16–20 July 2000

  25. Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons. Science 268:1503–1506

    Google Scholar 

  26. Markov AA (1907) Investigation of a noteworthy case of dependent trials. Izv Ros Akad Nauk 1:61–80

    Google Scholar 

  27. Maršálek P, Koch C, Maunsell J (1996) On the relationship between synaptic input and spike output jitter in individual neurons. Proc Natl Acad Sci USA 94:735–740

    Google Scholar 

  28. Meyer D (1994) Sensitivity of the stationary distribution of a Markov chain. SIAM J Matrix Anal Appl 15:715–728

    Google Scholar 

  29. Miller JP (1994) Neural coding. Neurons cleverer than we thought? Curr Biol 4:818–820

    Google Scholar 

  30. Miller R (1996) Cortico-thalamic interplay and the security of operation of neural assemblies and temporal chains in the cerebral cortex. Biol Cybern 73:129–137

    Google Scholar 

  31. Prut Y, Vaadia E, Bergman H, Haalman I, Slovin H, Abeles M (1998) Spatiotemporal structure of cortical activity: properties and behavioral relevance. J Neurophysiol 79:2857–2874

    Google Scholar 

  32. Salinas E, Sejnowski TJ (2001) Correlated neuronal activity and the flow of neural information. Nat Rev Neurosci 2:539–550

    Google Scholar 

  33. 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 

  34. Sompolinsky H, Crisanti A, Sommers HJ (1988) Chaos in random neural networks. Phys Rev Lett 61:259–262

    Google Scholar 

  35. Tsuda I (1992) Dynamic link of memory – chaotic memory map in nonequilibrium neural networks. Neural Netw 5:313–326

    Google Scholar 

  36. van Rossum MC, Turrigiano GG, Nelson SB (2002) Fast propagation of firing rates through layered networks of noisy neurons. J Neurosci 22:1956–1966

    Google Scholar 

  37. van Vreeswijk C, Sompolinsky H (1998) Chaotic balanced state in a model of cortical circuits. Neural Comput 15:1321–1371

    Google Scholar 

  38. Varela F, Lachaux JP, Rodriguez E, Martinerie J (2001) The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci 2:229–239

    Google Scholar 

  39. Yazdanbakhsh A, Babadi B, Rouhani S, Arabzadeh E, Abbasian A (2002) New attractor states for synchronous activity in synfire chains with inhibitory and excitatory coupling. Biol Cybern 86:367–378

    Google Scholar 

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Authors and Affiliations

  1. School of Intelligent Systems, Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran

    Farshad Moradi

  2. Computation and Neural Systems, 139-74 California Institute of Technology, Pasadena, CA, 91125

    Farshad Moradi

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  1. Farshad Moradi
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Correspondence to Farshad Moradi.

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Acknowledgements The author wishes to thank S. Rohani, A. Abbasian, V. Jayaraman, P. Wilken, and especially E. Winfree for their revision of the manuscript and constructive comments.

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Moradi, F. Information coding and oscillatory activity in synfire neural networks with and without inhibitory coupling. Biol. Cybern. 91, 283–294 (2004). https://doi.org/10.1007/s00422-004-0499-x

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