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.
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.