Recording from Two Neurons: Second-Order Stimulus Reconstruction from Spike Trains and Population Coding

Abstract

We study the reconstruction of visual stimuli from spike trains, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. If the reconstructed stimulus is to be represented by a Volterra series and correlations between spikes are to be taken into account, first order expansions are insufficient and we have to go to second order, at least. In this case higher order correlation functions have to be manipulated, whose size may become prohibitively large. We therefore develop a Gaussian-like representation for fourth order correlation functions, which works exceedingly well in the case of the fly. The reconstructions using this Gaussian-like representation are very similar to the reconstructions using the experimental correlation functions. The overall contribution to rotational stimulus reconstruction of the second order kernels -measured by a chi-squared averaged over the whole experiment -is only about 8% of the first order contribution. Yet if we introduce an instant-dependent chi-square to measure the contribution of second order kernels at special events, we observe an up to 100% improvement. As may be expected, for translational stimuli the reconstructions are rather poor. The Gaussian-like representation could be a valuable aid in population coding with large number of neurons.

Temporal Encoding in a Nervous System

“…Figures 6– 9). This is in general agreement with results from the H1 neurons of flies as well as auditory receptor neurons in locusts [9], [65], [77]. In the study of de Ruyter van Steveninck and Bialek it was shown that the mean stimulus preceding short patterns of spikes in the H1 neurons of flies was impossible to predict from combinations of the mean stimulus preceding single spikes (their Figures 5G and 12).…”

Nonlinear decoding of a complex movie from the mammalian retina

“…A large body of work dissects nonlinearities in stimulus processing, from nonlinear summation in the receptive field or during adaptation, to essential spike generation nonlinearities. Consequently, one would expect nonlinear decoding to outperform linear, but reports to that effect are scarce [ 11 , 41 ]. In theory the results of a nonlinear encoding process can be linearly decodable [ 42 , 43 ], yet whether this is true of real neurons under rich stimulation is still unclear.…”

Modular Acquisition and Stimulation System for Timestamp-Driven Neuroscience Experiments

“…The system described in this paper (source code at [8]) can be applied to neuroscience research both on in vivo or in vitro experiments requiring deterministic timing and synchronous stimuli generation, such as the study of neural coding on the visual system of flies [21]. It can also be applied to experiments in neuroethology, for example on the analysis of electrocommunication signals produced by pulse-type electric fish [22,23,24,25].…”