Relative spike timing in stochastic oscillator networks of the Hermissenda eye

Abstract

The role of relative spike timing on sensory coding and stochastic dynamics of small pulse-coupled oscillator networks is investigated physiologically and mathematically, based on the small biological eye network of the marine invertebrate Hermissenda. Without network interactions, the five inhibitory photoreceptors of the eye network exhibit quasi-regular rhythmic spiking; in contrast, within the active network, they display more irregular spiking but collective network rhythmicity. We investigate the source of this emergent network behavior first analyzing the role of relative input to spike–timing relationships in individual cells. We use a stochastic phase oscillator equation to model photoreceptor spike sequences in response to sequences of inhibitory current pulses. Although spike sequences can be complex and irregular in response to inputs, we show that spike timing is better predicted if relative timing of spikes to inputs is accounted for in the model. Further, we establish that greater noise levels in the model serve to destroy network phase-locked states that induce non-monotonic stimulus rate-coding, as predicted in Butson and Clark (J Neurophysiol 99:146–154, 2008a; J Neurophysiol 99:155–165, 2008b). Hence, rate-coding can function better in noisy spiking cells relative to non-noisy cells. We then study how relative input to spike–timing dynamics of single oscillators contribute to network-level dynamics. Relative timing interactions in the network sharpen the stimulus window that can trigger a spike, affecting stimulus encoding. Also, we derive analytical inter-spike interval distributions of cells in the model network, revealing that irregular Poisson-like spike emission and collective network rhythmicity are emergent properties of network dynamics, consistent with experimental observations. Our theoretical results generate experimental predictions about the nature of spike patterns in the Hermissenda eye.