An information-theoretic analysis of the coding of a periodic synaptic input by integrate-and-fire neurons
Introduction
The aim of this paper is to analyse the information contained in the response of neurons to noisy periodic synaptic input [8], [3]. The analysis is carried out for the leaky integrate-and-fire neuron in the Gaussian approximation, both for the case where the neuron receives only excitatory input and where inhibition plays a substantial role, including the case of balanced input in which excitatory and inhibitory inputs are equal [10], [11], [1]. In the situation in which the neuron only receives excitatory input, it is known that the synchronization of the output of a leaky integrate-and-fire neuron is greater than its input over a wide range of parameters [3]. However, it does not necessarily follow that an organism that uses such information will be able to benefit from this increased synchronization. The amount of sensory information that can be extracted depends not only upon the synchronization of the output spikes but also upon their spiking rate. In order to examine the amount of information that the output spikes carry about the stimulus, the mutual information between the input phase of the stimulus and the timing of output spikes is analysed. This study extends previous results [8], [3] for excitatory inputs by including the effect of inhibitory inputs, thereby more closely modelling biological neural systems. The study also address the role of stochastic resonance in such neural systems, by analysing the mutual information in the situation where the input is subthreshold (i.e. in the situation where there would be no output in the absence of noise).
Section snippets
Methods
The leaky integrate-and-fire neuron is used, in which the membrane potential receives from its presynaptic inputs both excitatory and inhibitory contributions that sum linearly and it decays in time with a characteristic time constant (the membrane time constant). When the membrane potential reaches a threshold, an output spike is generated and the membrane potential is reset to its resting value. The analysis is carried out in the Gaussian approximation [2], which is accurate in the limit of a
Results
The results of the leaky integrate-and-fire neuron receiving different numbers N of excitatory inputs has been analyzed and are plotted in Fig. 1. The amplitudes of the individual postsynaptic inputs are chosen to scale inversely with the number of inputs, N. The parameters are given in the figure caption and are chosen to ensure that the neuron is in a “subthreshold” regime, i.e. the equilibrium value of the membrane potential (without the spike generation mechanism) is below the
Discussion and conclusions
The question of how much information a spiking neuron is capable of extracting from its input and transmitting in its output is a central one in neural processing. This paper provides an intuitive and straightforward derivation of the mutual information between the phase of a periodic stimulus and the timing of the output spikes, and it is calculated for the leaky integrate-and-fire neural model. This measure of the mutual information can be applied to experimental data—all that is required is
Acknowledgements
This work was funded by The Bionic Ear Institute and the National Health and Medical Research Council (NHMRC, Project Grant No. 990816) of Australia.
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