Coding of time-varying signals in spike trains of linear and half-wave rectifying neurons

The encoding of time-varying stimuli in linear and half-wave rectifying neurons is studied. The information carried in single spike trains is assessed by reconstructing part of the stimulus using mean square estimation methods. For the class of models considered here, the mean square error in the reconstructions and estimates of the rate of information transmission are computed analytically. The optimal encoding of stimuli having statistical properties of natural images predicts a change in the temporal filtering characteristics with mean firing rate. This change relates to those observed experimentally at the early stages of visual processing. The transmission of information by model neurons is shown to be fundamentally limited to a maximum of 1.13 bit/spike and it is conjectured that nonlinear processing is necessary to explain higher rates which have been observed experimentally in certain preparations. In spite of the fact that single neurons might not transmit information efficiently, a substantial part of a time-varying stimulus can be recovered from single spike trains. In particular, our results demonstrate that a small number of 'noisy' neurons can carry precise temporal information in their spike trains.