Synaptic Patterns with Intrinsic Noise

Distribution of synaptic puncta along ventral cord of C. elegans. New synapses are inserted during development to maintain the synaptic density.

How intrinsic noise affects a pattern-forming mechanism? This has been studied extensively on the reaction-diffusion (RD) equation. Brooks and Bressloff (2016) developed C. elegans synaptic site pattern forming mechanism by introducing a reaction-diffusion-advection (RDA) equation. However, it has been still unknown what is the role of intrinsic fluctuation in the RDA stochastic pattern formation. In Kim and Bressloff (2020), we address this question by carrying out a system-size expansion of the RDA master equation.