Temporal Pattern Discrimination in the Cat's Retinal Cells and Markov System Models

Markov system theory is applied to temporal pattern sensitivity in nervous systems. First, a Markov system model is given to describe the temporal pattern sensitivity in single neurons with one input and one output. This is next extended to a two-input-one-output system. In both cases the behavior of input-output relations is estimated by using Shannon's information theory in single- and multiple-access channels. The interaction mechanisms between excitatory and inhibitory input sequences in single neurons is also described. Finally, to characterize temporal pattern sensitivity in the visual pathway, the Markov system approach is introduced using three types of statistical spot stimuli with different second-order statistics (correlations between adjacent interstimulus intervals: type 1 with positive, type 2 with negative correlation, and type 3 with independent intervals) but identical first-order statistics (mean, variance, and histogram in the interstimulus intervals). The differences in responses to these three types of stimuli, i.e., the difference in interspike interval distribution, can be used to classify cat ganglion cells into two groups, type L and type N. A type L cell has an identical histogram in interspike intervals for all three stimuli (no sensitivity to the temporal pattern); on the other hand, a type N cell has different histograms depending on the type of stimulus and is therefore highly sensitive to the temporal pattern. The type N cells are thus able to encode the information given by the correlation of interstimulus intervals by varying the distribution function of interspike intervals of the output spike train. Type L and type N units can be considered to correspond to X and Y cells, respectively, which aspect is discussed with relation to the classification of ganglion cell types in general. Different features between type L and type N cells were simulated by using the Markov system model having 2 × 2 state transition matrixes. By giving distinctive features to the state transition matrices, the interspike interval histograms of the model could be made to agree well with those of type L and type N cells; the model reproduced the sensitive and nonsensitive responses to temporal pattern at the retinal level.