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Journal of Computational Neuroscience

, Volume 3, Issue 1, pp 7–34 | Cite as

Chaos and synchrony in a model of a hypercolumn in visual cortex

  • D. Hansel
  • H. Sompolinsky
Article

Abstract

Neurons in cortical slices emit spikes or bursts of spikes regularly in response to a suprathreshold current injection. This behavior is in marked contrast to the behavior of cortical neurons in vivo, whose response to electrical or sensory input displays a strong degree of irregularity. Correlation measurements show a significant degree of synchrony in the temporal fluctuations of neuronal activities in cortex. We explore the hypothesis that these phenomena are the result of the synchronized chaos generated by the deterministic dynamics of local cortical networks. A model of a “hypercolumn” in the visual cortex is studied. It consists of two populations of neurons, one inhibitory and one excitatory. The dynamics of the neurons is based on a Hodgkin-Huxley type model of excitable voltage-clamped cells with several cellular and synaptic conductances. A slow potassium current is included in the dynamics of the excitatory population to reproduce the observed adaptation of the spike trains emitted by these neurons. The pattern of connectivity has a spatial structure which is correlated with the internal organization of hypercolumns in orientation columns. Numerical simulations of the model show that in an appropriate parameter range, the network settles in a synchronous chaotic state, characterized by a strong temporal variability of the neural activity which is correlated across the hypercolumn. Strong inhibitory feedback is essential for the stabilization of this state. These results show that the cooperative dynamics of large neuronal networks are capable of generating variability and synchrony similar to those observed in cortex. Auto-correlation and cross-correlation functions of neuronal spike trains are computed, and their temporal and spatial features are analyzed. In other parameter regimes, the network exhibits two additional states: synchronized oscillations and an asynchronous state. We use our model to study cortical mechanisms for orientation selectivity. It is shown that in a suitable parameter regime, when the input is not oriented, the network has a continuum of states, each representing an inhomogeneous population activity which is peaked at one of the orientation columns. As a result, when a weakly oriented input stimulates the network, it yields a sharp orientation tuning. The properties of the network in this regime, including the appearance of virtual rotations and broad stimulus-dependent cross-correlations, are investigated. The results agree with the predictions of the mean field theory which was previously derived for a simplified model of stochastic, two-state neurons. The relation between the results of the model and experiments in visual cortex are discussed.

Keywords

Visual Cortex Spike Train Synaptic Conductance Orientation Tuning Asynchronous State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Abeles M (1991) Corticonics: Neural Circuits of the Cerebral Cortex. Cambridge University Press, Cambridge.Google Scholar
  2. Amit DJ, Brunel N (1995) Global spontaneous activity and local structured (learned) delay activity in cortex. Preprint.Google Scholar
  3. Anderson PW, Stein DL (1984) Broken symmetry, emergent properties, dissipative structures, life and its origin: Are they related? In: FE Yates, ed. Self-Organizing Systems: The Emergence of Order. Plenum Press, New York.Google Scholar
  4. Bair W, Koch C, Newsome W, Britten K (1994) Power spectrum analysis of bursting cells in Area MT in the behaving monkey. J. Neurosc. 14:2870–2892.Google Scholar
  5. Ben-Yishai R, Lev Bar-Or R, Sompolinsky H (1994) Theory of orientation tuning in visual cortex. Proc. Natl. Acad. Sci. (USA) (in press).Google Scholar
  6. Bergé P, Pomeau Y, Vidal C (1984) Order within Chaos: Towards a Deterministic Approach to Turbulence. Johny Wiley and Hermann, Paris.Google Scholar
  7. Bernander Ö, Koch C, Usher M (1994) The effect of synchronized inputs at the single neuron level. Neural Comp. 6:622–641.Google Scholar
  8. Burns BD, Webb AC (1976) The spontaneous activity of neurons in the cat's cerebral cortex. Proc. R. Soc. Lond. B 194:211–213.Google Scholar
  9. Bush P, Douglas R (1991) Synchronization of bursting action potential discharge in a model network of neocortical neurons. Neural Comp. 3:19–30.Google Scholar
  10. Celebrini S, Thorpe S, Trotter Y, Imbert M (1993) Visual Neurose. 10:811–825.Google Scholar
  11. Chapman B, Zahs KR, Stryker MP (1991) Relation of cortical cell orientation selectivity to alignment of receptive fields of the geniculocortical afferents that arborize within a single orientation column in ferret visual cortex. J. Neurosci. 11:1347–1358.Google Scholar
  12. Connor JA, Walter D, McKown R (1977) Neural repetitive firing: Modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons. Biophys. J. 18:81–102.Google Scholar
  13. Connors BW, Gutnick MJ, Prince DA (1982) Electrophysiological properties of neocortical neurons in vitro. J. Neurophysiol. 48:1302–1320.Google Scholar
  14. Dean AF (1981) The variability of discharge of simple cells in cat striate cortex. Exp. Brain Res. 44:431–440.Google Scholar
  15. Douglas RJ, Mahowald MA, Martin KAC (1994) Hybrid analog-digital architectures for neuromorphic systems.Google Scholar
  16. Eckhorn R, Reitboeck HJ, Arndt M, Dicke P (1990) Feature linking among distributed assemblies: Simulations and results from cat visual cortex. Neural Comp. 2:292–306.Google Scholar
  17. Engel AK, Konig P, Kreiter AK, Singer W (1991) Interhemispheric synchronization of oscillatory neuronal responses in cat visual cortex. Science 252:1177–1180.Google Scholar
  18. Ernst U, Pawelzik K, Geisel T (1995) Synchronization induced by temporal delays in pulse coupled oscillators. Phys. Rev. Lett. 74:1570–1573.Google Scholar
  19. Fetz E, Toyama K, Smith W (1991) Synaptic interactions between cortical neurons. In: A Peters, EG Jones, eds. Cerebral Cortex. Plenum Press, New York. Vol. 9, pp. 1–80.Google Scholar
  20. Fregnac Y, Bringuier V, Baranyi A (1994) Oscillatory neuronal activity in visual cortex: A critical re-evaluation. In: G Buzsaki, R Llinas, W Singer, A Berthoz, Y Christen, eds. Temporal Coding in the Brain: Research and Perspectives in Neurosciences. Springer-Verlag, Berlin.Google Scholar
  21. Freiwald W (1993) Dynamik lokaler synchronisationen: eine elektrophysiologische untersuchung mit Stereotetroden im visuellen system der säugetiere. Diplomarbeit, Tubingen.Google Scholar
  22. Georgopoulos AP, Lurito JT, Petrides M, Schwartz AB, Massey JT (1989) Mental rotation of the neuronal population vector. Science 243:234–236.Google Scholar
  23. Georgopoulos AP, Taira M, Lukashin A (1993) Cognitive neurophysiology of the motor cortex. Science 260:47–52.Google Scholar
  24. Ginzburg I, Sompolinsky H (1994) Theory of correlations in stochastic neural networks. Phys. Rev. E 50:3171–3191.Google Scholar
  25. Gochin PM, Miller EK, Gross CG, Gerstein GL (1991) Functional interactions among neurons in inferior temporal cortex of the awake macaque. Exp. Brain Res. 84:505–516.Google Scholar
  26. Gray CM, König P, Engel AK, Singer W (1989) Oscillatory responses in cat visual cortex exhibit intercolumnar synchronization which reflects global stimulus properties. Nature 338:334–337.Google Scholar
  27. Gustafsson B, Galvan M, Grafe P, Wigstrom H (1982) Transient outward current in mammalian central neuron blocked by 4-aminopyridine. Nature 299:252–254.Google Scholar
  28. Hansel D, Sompolinsky H (1992) Synchronization and computation in a chaotic neural network. Phys. Rev. Lett. 68:718–721.Google Scholar
  29. Hansel D, Mato G, Meunier C (1995) Synchrony in excitatory neural networks. Neural Comp. 7:307–337.Google Scholar
  30. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (London) 117:500–544.Google Scholar
  31. Hubel DH, Wiesel TN (1962) Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. J. Physiol. Lond 160:106–154.Google Scholar
  32. König P, Engel AK, Roelfsema PR, Singer W (1995) How precise is neuronal synchronization. Neural Comp. 7:469–486.Google Scholar
  33. Krüger J, Aiple F (1988) Multimicroelectrode investigation of monkey striate cortex: Spike train correlations in the infragranular layers. J. Neurophysiol. 60:798–827.Google Scholar
  34. Llinas RR (1988) The intrinsic electrophysiology properties of mammalian neurons: Insights into central nervous system function. Science 242:1654–1664.Google Scholar
  35. Lukashin AV, Georgopoulos AP (1994) Directional operations in the motor cortex modeled by a neural network of spiking neurons. Biol. Cybern. 71:79–85.Google Scholar
  36. Martin KAC (1988) From single cells to simple circuits in the cerebral cortex. Q. J. Exp. Physiol. 73:637–702.Google Scholar
  37. Mason A, Nicoll A, Stratford K (1991) Synaptic transmission between individual pyramidal neurons of the rat visual cortex in vitro. J. Neurosc. 11:72–84.Google Scholar
  38. Murthy VN, Fetz EE (1994) Effects of input synchrony on the firing rate of a three-conductance cortical neuron model. Neural Comp. 6:1111–1126.Google Scholar
  39. Noda H, Adey WR (1970) Firing variability in cat association cortex during sleep and wakefulness. Brain Res. 18:513–526.Google Scholar
  40. Nowak LG, Munk MHJ, Nelson JI, James AC, Bullier J (1995) The structural basis of cortical synchronization. I. Three types of interhemispheric coupling. J. Neurophysiol. 74:2379–2400. The structural basis of cortical synchronization. II. Effects of cortical lesions. J. Neurophysiol. 74:2401–2414.Google Scholar
  41. Rush ME, Rinzel J (1994) The potassium A-current, low firing rates and rebound excitation in Hodgkin-Huxley models. Bulletin of Mathematical Biology 57:899–929.Google Scholar
  42. Schiller PH, Finlay BL, Volmann SF (1976) Short-term response variability of monkey striate neurons. Brain Res. 105:347–349.Google Scholar
  43. Shadlen MN, Newsome WT (1994) Noise, neural codes and cortical organization. Current Opinion in Neurobiol. 4:569–579.Google Scholar
  44. Shepard RN, Metzler J (1971) Mental rotation of three-dimensional objects. Science 171:701–703.Google Scholar
  45. Shevelev IA, Sharaev GA, Lazareva NA, Novikova RV, Tikhomirov AS (1993) Dynamics of orientation tuning in the cat striate cortex neurons. Neuroscience 56:865–876.Google Scholar
  46. Sillito AM, Kemp JA, Milson JA, Berardi N (1980) A re-evaluation of the mechanisms underlying simple cell orientation selectivity. Brain Res. 194:517–520.Google Scholar
  47. Softky W, Koch C (1993) The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSP's. J. Neurosc. 13:334–350.Google Scholar
  48. Somers DC, Nelson SB, Sur M (1995) An emergent model of orientation selectivity in cat visual cortical simple cells. J. Neurosc. 15:5448–5465.Google Scholar
  49. Stafstrom CE, Schwindt PC, Crill WE (1982) Negative slope conductance due to a persistent subthreshold sodium current in cat neocortical neurons in vitro. Brain Res. 236:221–226.Google Scholar
  50. Storm JF (1993) Functional diversity of K + currents in hippocampal pyramidal neurons. Seminars in The Neurosciences 5:79–92.Google Scholar
  51. Tolhurst DJ, Movshon JA, Dean AF (1983) The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vision Res. 23:775–786.Google Scholar
  52. Ts'o DY, Gilbert CD, Wiesel TN (1986) Relationship between horizontal interactions and functional architecture in cat striate cortex as revealed by cross-correlation analysis. J. Neurophysiol. 6:1160–1170.Google Scholar
  53. Tsodyks M, Sejnowski T (1995) Rapid state switching in balanced cortical network models. Network 6:111–124.Google Scholar
  54. Tsumoto T, Eckart W, Creutzfeldt OD (1979) Modification of orientation sensitivity of cat visual cirtex neurons by removal of GABA-mediated inhibition. Exp. Brain Res. 34:351–363.Google Scholar
  55. Usher M, Stemmler M, Koch C, Olami Z (1994) Network amplification of local fluctuations causes high spike rate variability, fractal firing patterns and oscillatory local field potentials. Neural Computation 6:795–836.Google Scholar
  56. Van Vreeswijk C, Abbott LF, Ermentrout GB (1995) Inhibition, not excitation synchronizes coupled neurons. J. Comp. Neurosci. 1:313–321.Google Scholar
  57. Van Vreeswijk C, Sompolinsky H (1995) Theory of randomly connected networks with excitation-inhibition balance. Abstract in Cortical Dynamics. Jerusalem.Google Scholar
  58. Vogels R, Spileers W, Orban GA (1989) The response variability of striate cortical neurons in the behaving monkey. Exp. Brain Res. 77:432–436.Google Scholar
  59. Woergotter F, Koch C (1991) A detailed model of the primary visual pathway in the cat: Comparison of afferent excitatory and intracortical inhibitory connection schemes for orientation selectivity. J. Neurosc. 11:1959–1979.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • D. Hansel
    • 1
  • H. Sompolinsky
    • 2
  1. 1.Centre de Physique Théorique, UPR014-CNRS, Ecole PolytechniquePalaiseauFrance
  2. 2.Racah Institute of Physics and Center for Neural Computation, The Hebrew UniversityJerusalemIsrael

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