Abstract
We examine the effects of degree of balance between inhibitory and excitatory random synaptic inputs, and of positive correlation between the inputs on the mean and variability of the output of the classical Hodgkin-Huxley (HH) model for squid giant axon, using computer simulation. The mean interspike interval (ISI) and the coefficient of variation of ISI change little as the degree of balance changes, unlike the leaky integrate-and-fire model, frequently used in stochastic network modelling as an approximation to more biophysically based models. Low correlations (up to about 0.1) between 100 excitatory inputs each firing at 100 Hz reduce the mean(ISI) to below a third of its value when the inputs are independent, and CV by a factor of 5 from a near-Poisson range to one associated with regular firing.
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References
Abbott L.F., Varela, J.A., Sen, K., and Nelson S.B. (1997). Synaptic depression and cortical gain control, Science 275, 220–223.
Brown, D. and Feng, J. (1999) Is there a problem matching real and model CV (ISI)? Neurocomputing (in press).
Feerick, S.D., Feng, J. and Brown D. Accuracy of the diffusion approximation for the Hodgkin-Huxley model (in prep.)
Feng, J. (1997). Behaviour of spike output jitter in the integrate-and-fire model, Phys. Rev. Lett 79 4505–4508.
Feng, J., and Brown D. (1998). Impact of temporal variation and the balance between excitation and inhibition on the output of the perfect integrate-and-fire model. Bio. Cyber. 78 369–376.
Feng, J., and Brown, D. Spike output jitter, mean firing time and coefficient of variation J. Phys. A: Math. Gen., 31, 1239–1252, (1998).
Feng, J. and Brown D. (1999) Impact of correlated inputs on the output of the integrate-and-fire model Neural Computation (accepted)
Hanson F.B., and Tuckwell H.C. (1983). Diffusion approximation for neuronal activity including synaptic reversal potentials. J. Theor. Neurobiol. 2 127–153.
Hertz J. (1997), Reading the information in the outcome of neural computation. in Building Blocks for Intelligent Systems, to appear.
Hodgkin, A.L. and Huxley, A.F. (1952), A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiology, 117, 500–544.
Holt G. R., Softky W.R., Koch C., and Douglas R. J. (1996). Comparison of discharge variability In Vitro and In Vivo in cat visual cortex neurons, J. of Neurophysiology, 1806–1814.
Hopfield, J.J., and Herz, A.V.M. (1995). Rapid local synchronization of action potentials: Towards computation with coupled integrate-and-fire networks. Proc. Natl. Acad. Sci. USA 92, 6655–6662.
Koch C. (1997). Computation and the single neurone, Nature, 385, 207–210.
Lánský P., Sacerdote L., and Tomassetti F. (1995). On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity Biol Cybern. 73 457–465.
Lánský P., and Musila M. (1991). Variable initial depolarization in Stein’s neuronal model with synaptic reversal potentials. Biol. Cybern. 64 285–291.
McCormick D.A., Connors B.W., Lighthall J.W., and Prince D.A. (1985). Cooperative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. J. Neurophysiol. 54, 782–805.
Mainen Z.F., and Sejnowski, T. J. (1995). Reliability of spike timing in neocortical neurones, Science 268, 1503–1506.
Mainen Z.F., and Sejnowski T. J. (1996). Influence of dendritic structure on firing pattern in model neocortical neurones, Nature 382, 363–366.
Ricciardi, L.M., and Sato, S. (1990), Diffusion process and first-passage-times problems. Lectures in Applied Mathematics and Informatics ed. Ricciardi, L.M., Manchester: Manchester University Press.
Rieke F., Warland D., de Ruyter van Steveninck R., and Bialek W. (1997), Spikes-Exploring The Neural Code. The MIT Press.
Sejnowski T. J. (1995). Time for a new neural code?, Nature, 323 21–22.
de Ruyter van Steveninck R.R., Lewen G.D., Strong S.P., Koberle, R., and Bialek W. (1997). Reproducibility and variability in neural spike trains, Science 275, 1805–18008.
Softky W., and Koch C. (1993). The highly irregular firing of cortical-cells is inconsistent with temporal integration of random EPSPs, J. Neurosic. 13 334–350.
Shadlen M.N., and Newsome W.T. (1994). Noise, neural codes and cortical organization, Curr. Opin. Neurobiol. 4, 569–579.
Troyer T.W., and Miller K.D. (1997). Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell, Neural Computation 9, 733–745.
Tuckwell H.C. (1979). Synaptic transmission in a model for stochastic neural activity. J. Theor. Biol. 77 65–81.
Tuckwell H.C., and Richter W. (1978). Neuronal interspike time distributions and the estimation fo neurophysiological and neuroanatomical parameters. J. Theor. Biol. 71 167–183.
Tuckwell H. C. (1988), Stochastic Processes in the Neurosciences. Society for industrial and applied mathematics: Philadelphia, Pennsylvania.
Wilbur W.J., and Rinzel J. (1983). A theoretical basis of large coefficient of variation and biomodality in neuronal interspike interval distribution. J. Theor. Biol. 105 345–368.
Zohary, E., Shadlen M.N., and Newsome W.T. (1994), Correlated neuronal discharge rate and its implications for psychophysical performance. Nature 370 140–143.
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Brown, D., Feng, J. (1999). Effects of correlation and degree of balance in random synaptic inputs on the output of the hodgkin-huxley model. In: Mira, J., Sánchez-Andrés, J.V. (eds) Foundations and Tools for Neural Modeling. IWANN 1999. Lecture Notes in Computer Science, vol 1606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098174
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DOI: https://doi.org/10.1007/BFb0098174
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