A Reaction-Diffusion Model of Cholinergic Retinal Waves

Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability.Author Summary: Both within the visual system and more generally, two general processes describe nervous system development: first, genetically determined cues provide a coarse layout of cells and connections and second, neuronal activity removes unwanted cells and refines connections. This activity occurs not just through external stimulation, but also through correlated, spontaneously generated bursts of action potentials occurring in hyper-excitable regions of the developing nervous system prior to external stimulation. Spontaneous activity has been implicated in the maturation of many neural circuits, however exactly which features are important for this purpose is largely unknown. In order to help address this question we construct a mathematical model to understand the spatiotemporal patterns of spontaneously driven activity in the developing retina. This activity is known as retinal waves. We describe a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. This novel reaction-diffusion formulation allows us to connect wave features to underlying physiological parameters. In particular this approach is used to determine which features of the system are responsible for wave propagation and for the spatiotemporal patterns of propagating waves observed in both mice and other species.