Cellular Extensions Optimally Find Targets

Persistent random walk for airineme search process. If the protrusion is persistent, then it could miss the target by wrong directions. On the contrary, if the protrusion is too diffusive, it twines too much to reach the target in given time.

Does the nature really favor optimality? Yes, it is when cells form the stripe patterns during zebrafish development. Sometimes on the yellow stripe, a black pigment cell is misallocated. In order to fix it, a different type of black pigment cells, called xantoblasts, extend long and thin protrusions called airinemes to reach the misallocated cell. One important parameter of this search process is the angular diffusion, which determines the “curviness” of airinemes. In our upcoming paper, we have shown that the search process has the “optimal” angular diffusion in the sense of the search probability. Interestingly, the theoretical optimal value coincides with the experimental estimation.

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.