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The Impact of Synaptic Unreliability on the Information Transmitted by Spiking Neurons

Anthony Zador
Salk Institute MNL/S
La Jolla, CA 92037
zador@salk.edu

J. Neurophysiology, in press

Running Title: Synaptic Unreliability and Information. (M.S. #J-757-7)

Address Correspondence To:
Anthony Zador
Salk Institute
La Jolla, CA 92037

Phone: (619) 453-4100 tex2html_wrap_inline1075 1404
Fax: (619) 450-2172
Electronic Mail: zador@salk.edu
Keywords: Information theory, synaptic unreliability, cortical processing

Synaptic unreliability and information (M.S. #J-757-7)

Abstract

The spike generating mechanism of cortical neurons is highly reliable, able to produce spikes with a precision of a few milliseconds or less. The excitatory synapses driving these neurons are by contrast much less reliable, subject both to release failures and quantal fluctuations. This suggests that synapses represent the primary bottleneck limiting the faithful transmission of information through cortical circuitry.

How does the capacity of a neuron to convey information depend on the properties of its synaptic drive? We address this question rigorously in an information theoretic framework. We consider a model in which a population of independent unreliable synapses provides the drive to an integrate-and-fire neuron. Within this model, the mutual information between the synaptic drive and the resulting output spike train can be computed exactly from distributions that depend only on a single variable, the interspike interval. The reduction of the calculation to dependence on only a single variable greatly reduces the amount of data required to obtain reliable information estimates.

We consider two factors that govern the rate of information transfer: the synaptic reliability, and the number of synapses connecting each presynaptic axon to its postsynaptic target (i.e. the connection redundancy, which constitutes a special form of input synchrony). The information rate is a smooth function of both mechanisms; no sharp transition is observed from an ``unreliable'' to a ``reliable'' mode. Increased connection redundancy can compensate for synaptic unreliability, but only under the assumption that the fine temporal structure of individual spikes carries information. If only the number of spikes in some relatively long time window carries information (a ``mean rate'' code), an increase in the fidelity of synaptic transmission results in a seemingly paradoxical decrease in the information available in the spike train. This suggests that the fine temporal structure of spike trains can be used to maintain reliable transmission with unreliable synapses.


Introduction

A pyramidal neuron in the cortex receives excitatory synaptic inputs from tex2html_wrap_inline1077-tex2html_wrap_inline1079 other neurons [Shepherd, 1990]. When an action potential invades the presynaptic terminal of one of these synapses, it sometimes triggers the release of a vesicle of glutamate, which causes current to flow into the postsynaptic dendrite. Some of this current then propagates, passively or actively, to the spike generator, where it may contribute to the triggering of an action potential.

The postsynaptic neuron can be viewed as an input-output element that converts the input spike trains from many presynaptic neurons into a single output spike train. This input-output transformation is the basic computation performed by neurons. It is the foundation upon which cortical processing is based.

The computational strategies available to a neuronal circuit depend upon the fidelity of its components. For example, the computational power of a single integrate-and-fire neuron depends on the effective noise of the currents driving the spike generator [Zador and Pearlmutter, 1996]. In the cortex, the transformation of somatic current into an output spike train appears to be highly reliable ([Mainen and Sejnowski, 1995]; see also [Bryant and Segundo, 1976]), in marked contrast to the unreliability of synaptic transmission [Allen and Stevens, 1994, Dobrunz and Stevens, 1997, Stratford et al., 1996]. In this paper, we use simple biophysical models of spike transduction and stochastic synaptic release to explore the implications of synaptic unreliability on information transmission and neural coding in the cortex. Our goal is to provide a quantitative answer to the question: How much information can the output spike train provide about the synaptic inputs? Our answer will be cast in an information-theoretic framework.




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