A Reaction-Diffusion Model of Cholinergic Retinal Waves

Abstract

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.

Understanding neural circuit development through theory and models

“…In the retina, spontaneous activity is generated before the retina responds to light, and has been commonly implicated in the refinement of retinotopic maps between the retina and SC or LGN [18,19]. The retina generates complex spatiotemporal waves of spontaneous activity during the first two weeks of postnatal development (in rodents) ( [20], for models see [21,22]). These propagate through the visual pathway to the SC, the thalamus, and the visual cortex [23,24,25 • ], which are themselves spontaneously active [26 • , 27].…”

Neural Field Models for Latent State Inference: Application to Large-Scale Neuronal Recordings

“…Model parameters were initialized heuristically based on observed timescales at ρ e =ρ a =15, ρ r =0.15, and σ =0.15. As in Lansdell et al (2014), lateral interactions in our model re ect an e ective coupling that combines both excitatory synaptic interactions and the putative e ect of di using excitatory neurotransmitters, which has been shown to promote late-stage glutamatergic wave propagation (Blankenship et al, 2009). The spontaneous excitation rate ρ q was set to zero, such that the spontaneous wave-initiation events are captured by the system as an extrinsic noise source.…”

“…wavefront speed, c.f. Lansdell et al 2014), remain the best-available approach to model estimation. Nevertheless, the state-space formulation of neural eld models enables Bayesian state inference from candidate neural eld models, and opens the possibility of likelihood-based parameter inference in the future.…”

“…We apply this approach to HDMEA recordings of spontaneous activity from ganglion cells in the developing mouse retina (Maccione et al, 2014), showing that the calibrated model effectively captures the non-linear excitable phenomenon of coordinated, wave-like patterns of spiking (Meister et al, 1991) that have been considered in both discrete (Hennig et al, 2009a) and eld-theoretic models before (Lansdell et al, 2014).…”

Theoretical Models of Neural Development

“…An interesting finding from both types of models is that the retinal network may be operating close to the point of a percolation phase transition, providing statistics similar to those of natural images ( Albert et al., 2008 , Hennig et al., 2009 ). Theoretical analyses have provided precise predictions for the dependence of wave behavior on model parameters (e.g., Lansdell et al., 2014 , Karvouniari et al., 2017 ).…”