Gap junctions set the speed and nucleation rate of stage I retinal waves

Abstract

Spontaneous waves in the developing retina are essential in the formation of the retinotopic mapping in the visual system. From experiments in rabbits, it is known that the earliest type of retinal waves (stage I) is nucleated spontaneously, propagates at a speed of 451{+/-}91 m/sec and relies on gap junction coupling between ganglion cells. Because gap junctions (electrical synapses) have short integration times, it has been argued that they cannot set the low speed of stage I retinal waves. Here, we present a theoretical study of a two-dimensional neural network of the ganglion cell layer with gap junction coupling and intrinsic noise. We demonstrate that this model can explain observed nucleation rates as well as the comparatively slow propagation speed of the waves. From the interaction between two coupled neurons, we estimate the wave speed in the model network. Furthermore, using simulations of small networks of neurons (N[≤]260), we estimate the nucleation rate in form of an Arrhenius escape rate. These results allow for informed simulations of a realistically sized network, yielding values of the gap junction coupling and the intrinsic noise level that are in a physiologically plausible range.\n\nAuthor summaryRetinal waves are a prominent example of spontaneous activity that is observed in neuronal systems of many different species during development. Spatio-temporally correlated bursts travel across the retina at a few hundred m/sec to facilitate the maturation of the underlying neuronal circuits. Even at the earliest stage, in which the network merely consists of ganglion cells coupled by electric synapses (gap junctions), it is unclear which mechanisms are responsible for wave nucleation and transmission speed. We propose a model of gap-junction coupled noisy neurons, in which waves emerge from rare stochastic fluctuations in single cells and the waves transmission speed is set by the latency of the burst onset in response to gap-junction currents between neighboring cells.