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General description: The first ones among N identical and independently distributed (i.i.d.) Brownian trajectories that arrives to a small target have timescales that are much faster than the average arrival time of a single particle [1]. As introduced in [2], these timescales determine the activation of reaction onsets of biochemical reactions involving signal amplifications in cellular microdomains. We provide here computational codes to compute the arrival times in 1, 2 and 3 dimensions both with simulations and analytical asymptotic calculations. Example: In the example of the 2D circular domain shown in Fig.A below, when N particles are released at the initial point P0, the fastest among N has a timescale plotted in B. (In [1], we derived the asymptotics for this inverse-logarithmic relationship). In addition, we developed a framework to simulate calcium diffusion in the biological microdomain of dendritic spine. Particularly, using the extreme statistics framework, we provide a numerical code to compute the time for the first two calcium ions (among N=500, 1000) released simultaneously in the spine head to reach the base of the spine (Fig. 6 of [1]). Python and Mathematica source codes: The following .tar file contains the Python source code to run simulations and Mathematica scripts to do the analytic computations and generate plots of [1] as detailed in the readme.txt file. see also: http://bionewmetrics.org/simulating-extreme-statistics-of-escape-times-in-1-2-and-3-dimensions/ References: [1] Basnayake, K., Schuss, Z., & Holcman, D. (2019). Asymptotic formulas for extreme statistics of escape times in 1, 2 and 3-dimensions. Journal of Nonlinear Science,29(2), 461-499. [2] Schuss, Z., K. Basnayake, and D. Holcman. "Redundancy principle and the role of extreme statistics in molecular and cellular biology."Physics of life reviews28 (2019): 52-79. |
