Passage-time coding with a timing kernel inferred from irregular cortical spike sequences

Abstract

In vivo cortical neurons exhibit highly irregular spike sequences. However, the computational implications of this irregular firing with respect to neural codings are not yet fully understood. Recently, we formulated neuronal firing as a stochastic process to translate the firing rate determined by synaptic input into an irregular sequence of inter-spike intervals (ISIs). We previously determined that steady-state distributions of ISIs obey a power-law in the majority of neurons recorded from the sensorimotor cortex of a rat performing a forelimb-movement task. This observation led us to a hypothesis for a neural code with irregular spiking, which we termed as ‘constrained maximization of firing-rate entropy’ (CMFE). This hypothesis asserts that noisy neuronal activity maximizes steady-state firing-rate entropy under the joint constraints of energy consumption and uncertainty over output spike trains. CMFE previously assumed that the values of the rate parameters in two successive ISIs are random and uncorrelated with each other. However, this is an oversimplification and is unrealistic. In addition, the CMFE hypothesis seems to contradict our perception that the firing-rate distribution is dependent on external stimuli. Therefore, it is necessary to explore a rate-coding scheme that can resolve these issues. In this study, we review the concept of CMFE and extend it to incorporate the correlated nature of a firing rate sequence in a biological nervous system. We introduced passage-time coding of stimulus with the timing kernel inferred from irregular cortical spike sequences in our previous study. We showed how the timing kernel determines the amount of information in spike sequences.