CRW-ActinBranchingUnlimited Arp2-3Full title: Correlated Random Walkers
Authors: L. Edelstein-Keshet
Contributors: D. Jahn
Date: 19.02.2021
Software: Morpheus (open-source). Download from https://morpheus.gitlab.io
Model ID: https://identifiers.org/morpheus/M2000
Reference: L. Edelstein-Keshet: Mathematical Models in Cell Biology
Comment: Particles moving left and right (as well as up) to mimic actin filament barbed ends as in the paper: Grimm HP, Verkhovsky AB, Mogilner A, Meister JJ. Analysis of actin dynamics at the leading edge of crawling cells: implications for the shape of keratocyte lamellipodia. European Biophysics Journal. 2003 Oct 1;32(6):563-77. Initialize with a few close to y = 0, assign them random left or right directions. Asymmetric "cell division" is used to create branches at some constant probability. One daughter goes left, one goes right. This simulation mimics the "unlimited Arp2/3 scenario" where branching is not limited, and where branching takes place only close to the filament barbed ends. The trajectory of the particles represents the actin filaments. The cell x coordinate modulo the size of the x range is also kept, so that the cell trajectories "wrap around" (so we see "the filaments" of ends that wandered off the edge of the domain).2The barbed ends are assumed to grow left and right along a "motile cell edge" (not explicitly modeled). The actin filaments are depicted by the trails formed by barbed ends. Those are shown in the analysis, but not modeled explicitly otherwise.rand_uni(0,1)<0.0002The "death" rate represents capping of an actin filament that prevents a barbed end from growing further. Those ends are essentially "dead".rand_uni(0,1)<0.002if(daughter==1,-1,1)nd+1The "division" represents an event where the actin filament branches (via the Arp2/3 complex). Here the branching is assumed to take place right at the barber end. Each branching results in one daughter branch going left and a second going right. This is implemented using the asymmetric cell division of Morpheus.mod(cell.center.x,size.x)This modified x-coordinate is used for the wrap-around domain, so that particles that leave the domain edge are given a coordinate modulo the domain length. This method is used to insure that the trails (a.k.a. actin flaments) of all the particles are shown on the same periodic domain.26Initate all the barbed ends close to the lower part of the domain, so we can watch them move up.Plot the actual locations of the barbed ends and assign them each the "branch order" (i.e. number of divisions) that they belong to.Draw the "trails" left by the particles, i.e. the branched structure of the actin filaments.