Nonlinear analysis of interspike intervals.

Theories of neural coding and neural information processing rely on a knowledge of the correlations between firing events. We present a method of analyzing experimental interspike interval (ISI) sequences from neurons for the presence of nonlinear correlations. This is accomplished by comparing nonlinear predictions on experimental data sets and on their "surrogate" data sets. These surrogates have the same linear properties as the experimental data, but are otherwise stochastic. A difference in nonlinear predictability between both sets implies that nonlinear correlations are present in the experimental data. We also examine the relationship between, on one hand, neural firing times, and on the other, the dynamical variables of the neuron and its inputs. We focus on a recently proposed method to reconstruct the dynamics of the input to a neuron via a delay embedding of the interspike intervals. We show that this method works well for the simple integrate-and-fire type neuron models when the mean sampling rate is high. However, the method does not extend to more realistic models. Our analysis suggests that this method may be applicable to a small subset of real neurons and that, in general, we should not expect to easily extract information about input stimuli to neurons using ISI embeddings