Royal Society Publishing

Real-Time Performance of a Movement-Sensitive Neuron in the Blowfly Visual System: Coding and Information Transfer in Short Spike Sequences

R. De Ruyter Van Steveninck, W. Bialek

Abstract

We develop model-independent methods for characterizing the information carried by particular features of a neural spike train as it encodes continuously varying stimuli. These methods consist, in essence, of an inverse statistical approach; instead of asking for the statistics of neural responses to a given stimulus we describe the probability distribution of stimuli that give rise to a certain short pattern of spikes. These `response-conditional ensembles' contain all the information about the stimulus that a hypothetical observer of the spike train may obtain. The structure of these distributions thus provides a quantitative picture of the neural code, and certain integrals of these distributions determine the absolute information in bits carried by a given spike sequence. These methods are applied to a movement-sensitive neuron (H1) in the visual system of the blowfly Calliphora erythrocephala. The stimulus is chosen as the time-varying angular velocity of a (spatially) random pattern, and we consider segments of the spike train of up to three spikes with specified spike-intervals. We demonstrate that, with extensive analysis, a single experiment of roughly one hour's duration is sufficient to provide reliable estimates of the relevant probability distributions. From the experimentally determined probability distributions we are able to draw several conclusions. (1) Under the conditions of our experiment, observation of a single spike carries roughly 0.36 bits of information, but spike pairs carry an interval-dependent signal that can be much larger than 0.72 bits; estimates of the total information capacity are in rough agreement with the maximum possible capacity given the signal-to-noise characteristics of the photoreceptors. (2) On average a single spike signals the occurrence of a velocity waveform that is positive (movement in the excitatory direction) at all times before the spike, whereas spike pairs can signal both positive and negative velocities, depending on the inter-spike interval. (3) Although inter-spike intervals are crucial in extracting all the coded information, the code is robust to several millisecond errors in the estimate of spike arrival times. (4) Short spike sequences give reliable information about specific features of the stimulus waveform, and this specificity can be quantified. (5) Our results suggest approximate strategies for reading the neural code -- reconstructing the stimulus from observations of the spike train -- and some preliminary reconstructions are presented. Some tentative attempts are made to relate our results to the more general questions of coding and computation in the nervous system.

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