Dobramysl U, Holcman D
Wellcome Trust/Cancer Research UK Gurdon Institute, University of Cambridge, Tennis Court Rd, Cambridge CB2 1QN, United Kingdom.
Ecole Normale Supérieure, 46 rue d'Ulm, 75005 Paris, France.
J Comput Phys. 2018 Feb 15;355:22-36. doi: 10.1016/j.jcp.2017.10.058.
Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid tracking Brownian trajectories in the entire infinite space. Instead, we generate particles near the absorbing windows, computed from the analytical expression of the exit probability. When the Brownian particles are generated by a steady-state gradient at a single point, we compute asymptotically the fluxes to small absorbing holes distributed on the boundary of half-space and on a disk in two dimensions, which agree with stochastic simulations. We also derive an expression for the splitting probability between small windows using the matched asymptotic method. Finally, when there are more than two small absorbing windows, we show how to reconstruct the position of the source from the diffusion fluxes. The present approach provides a computational first principle for the mechanism of sensing a gradient of diffusing particles, a ubiquitous problem in cell biology.
能否根据布朗粒子向位于区域边界上的小吸收窗口的稳态通量来恢复源的位置？为了解决这个问题，我们开发了一种数值方法，以避免在整个无限空间中追踪布朗轨迹。相反，我们根据退出概率的解析表达式在吸收窗口附近生成粒子。当布朗粒子由单点处的稳态梯度生成时，我们渐近地计算向二维半空间边界和圆盘上分布的小吸收孔的通量，这与随机模拟结果相符。我们还使用匹配渐近方法推导了小窗口之间分裂概率的表达式。最后，当有两个以上的小吸收窗口时，我们展示了如何根据扩散通量重建源的位置。本方法为感知扩散粒子梯度的机制提供了一种计算第一原理，这是细胞生物学中一个普遍存在的问题。
