Summary
A time-dependent, nonlinear model of neuronal interaction which was probabilistically analyzed in a previous article is shown here to be a natural generalization of the Hartline-Ratliff model of the Limulus retina. Although the primary physical variables in the model are the membrane potentials of neurons, the equations which govern the means and covariances of the membrane potentials are coupled through the average firing rates; as a consequence, the average firing rates control the selective storage and retrieval of covariance information. Motor learning in the cerebellar cortex is treated as a problem of covariance storage, and a prediction is made for the underlying synaptic plasticity: the change in synaptic strength between a parallel fiber and a Purkinje cell should be proportional to the covariance between discharges in the parallel fiber and the climbing fiber. Unlike previous proposals for synaptic plasticity, this prediction requires both facilitation and depression to occur (under different conditions) at the same synapse.
Similar content being viewed by others
References
Amassian, V. H., Giblin, D.: Periodic components in steady-state activity of cuneate neurones and their possible role in sensory coding. J. Physiol. 243, 353–385 (1974).
Bell, C., Kawasaki, T.: Relation among climbing fiber responses of nearby Purkinje cells. J. Neurophysiol. 35, 155–169 (1972).
Dickson, J. W., Gerstein, G. L.: Interactions between neurons in auditory cortex of the cat. J. Neurophysiol. 37, 1239–1261 (1974).
Eccles, J. C., Ito, M., Szentágothai, J.: The cerebellum as a neuronal machine. Berlin-Heidelberg New York: Springer 1967.
Grossberg, S.: Control enhancement, short-term memory, and constancies in reverberating neural networks. Studies in App. Math. 52, 213–257 (1973).
Hartline, H. K., Ratliff, F.: Inhibitory interaction of the receptor units in the eye of Limulus. J. Gen. Physiol. 40, 1357–1376 (1957).
Hebb, D. O.: The organization of behavior. New York: Wiley 1949.
Ito, M.: Learning control mechanisms by the cerebellum flocculo-vestibulo-ocular system. In: The nervous system, Vol. 1 (Tower, D. H., ed.). New York: Raven Press 1975.
Jeffress, L. A.: Localization of sound. In: Handbook of sensory physiology V/2: Auditory system (Keidel, W. D., Neff, W. D., eds.). Berlin-Heidelberg-New York: Springer 1975.
Julesz, B.: Foundations of cyclopean perception. Chicago: University of Chicago Press 1971.
Kalil, R. E., Chase, R.: Corticofugal influence on activity of lateral geniculate neurons in the cat. J. Neurophysiol. 33, 459–474 (1970).
Kalman, R. E., Bucy, R. S.: New results in linear filtering and prediction theory. J. Basic Engineering 83D, 95–108 (1961).
Kalman, R. E., Falb, P. L., Arbib, M. A.: Topics in mathematical system theory. New York: McGraw-Hill 1969.
Marr, D.: A theory of cerebellar cortex. J. Physiol. 202, 437–470 (1969).
Mountcastle, V. B.: The problem of sensing and neural coding. In: The neurosciences: a study program (Quarton, G. C., Melnechuk, T., Schmitt, F. O., eds.). New York: The Rockefeller University Press 1967.
Palay, S. L., Chan-Palay, W.: Cerebellar cortex: cytology and organization. Berlin-Heidelberg New York: Springer 1974.
Pfaffelhuber, E.: Correlation memory models — a first approximation in a general learning scheme. Biol. Cybernetics 18, 217–223 (1975).
Plomp, R.: Auditory psychophysics. Ann. Rev. Psychol. 26, 207–232 (1975).
Rakic, P.: Local circuit neurons. Neuroscience Res. Prog. Bull. 13, 289–446 (1975).
Ramón y Cajal, S.: Histologie du système nerveux de l'homme et des vertébrés, Tom. II. Paris: Maloine 1955. Madrid: Consejo Superior de Investigaciones Cientificas 1911.
Ratliff, F.: Studies in excitation and inhibition in the retina. New York: The Rockefeller University Press 1974.
Robinson, D. A.: Adaptive gain control of vestibulo-ocular reflex by the cerebellum. J. Neuro physiol. 39, 954–969 (1976).
Rodiek, R. W.: Maintained activity of cat retinal ganglion cells. J. Neurophysiol. 30, 1043–1071 (1967).
Ross, J.: Stereopsis by binocular delay. Nature 248, 363–364 (1974).
Sejnowski, T. J.: On global properties of neuronal interaction. Biol. Cybernetics 22, 85–95 (1976).
Sejnowski, T. J.: On the stochastic dynamics of neuronal interaction. Biol. Cybernetics 22, 203–211 (1976).
Sejnowski, T. J.: Statistical constraints on synaptic plasticity. J. Theor. Bio., in press (1977).
Snyder, D. L.: Random point processes. New York: Wiley 1975.
Stent, G. S.: A physiological mechanism for Hebb's postulate of learning. Proc. Nat. Acad. Sci. U.S.A. 70, 997–1001 (1973).
Stevens, C. F.: Neurophysiology: A primer. New York: J. Wiley 1966.
Stevens, J. K., Gerstein, G. L.: Interactions between cat lateral geniculate neurons. J. Neurophysiol. 39, 239–256 (1976).
Szentágothai, J.: Architecture of the cerebral cortex. In: Basic mechanisms of the epilepsies (Jasper, H. H., Ward, A. A., Pope, A., eds.). Boston: Little, Brown 1969.
Tsypkin, Ya. Z.: Foundations of the theory of learning systems. New York: Academic Press 1973.
Werblin, F. S., Dowling, J. E.: Organization of the retina of the mudpuppy, Necturus maculosus: II. Intracellular recording. J. Neurophysiol. 32, 339–355 (1969).
Wilson, H. R., Cowan, J. D.: Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1–24 (1972).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sejnowski, T.J. Storing covariance with nonlinearly interacting neurons. J. Math. Biol. 4, 303–321 (1977). https://doi.org/10.1007/BF00275079
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00275079