We describe a new, computationally simple method for analyzing the dynamics of neuronal spike trains driven by external stimuli. The goal of our method is to test the predictions of simple spike-generating models against extracellularly recorded neuronal responses. Through a new statistic called the power ratio, we distinguish between two broad classes of responses: (1) responses that can be completely characterized by a variable firing rate, (for example, modulated Poisson and gamma spike trains); and (2) responses for which firing rate variations alone are not sufficient to characterize response dynamics (for example, leaky integrate-and-fire spike trains as well as Poisson spike trains with long absolute refractory periods). We show that the responses of many visual neurons in the cat retina, cat lateral geniculate nucleus, and macaque primary visual cortex fall into the second class, which implies that the pattern of spike times can carry significant information about visual stimuli. Our results also suggest that spike trains of X-type retinal ganglion cells, in particular, are very similar to spike trains generated by a leaky integrate-and-fire model with additive, stimulus-independent noise that could represent background synaptic activity.
Left: the interval map in real (untransformed) time of an on-center X ganglion cell in response to a drifting sinusoidal grating. The horizontal position of each point represents the firing time of a spike within the stimulus cycle; the vertical position represents the length of the interspike interval. Marginal sums correspond to the post-stimulus time histogram, plotted across the top of the graph, and the interspike interval histogram, plotted on the right of the graph.
Right: the interval map is recalculated with respect to a transformed time. The time transformation is chosen to make the post-stimulus time histogram flat -- i.e., time is stretched where the original firing rate is high, and time is compressed where the original firing rate is low. The diagonal band at the extreme right (blue asterisk) indicates that spike statistics are inhomogeneous, even in transformed time. This signature of inhomogeneity is not present in modulated Poisson or gamma-process spike trains (with or without a physiological refractory period), but is reproduced by the integrate-and-fire model.
As described in the paper, the interval maps constructed from responses
of neurons in the lateral geniculate and visual cortex also show inhomogeneities
inconsistent with modulated Poisson or gamma-process spike trains. However, these
inhomogeneities are different from those seen in the retina, and may represent
processes other than integrate-and-fire dynamics.