Active Brownian Crawler model

Written in MATLAB

By Jack Treado, Yale University, 2021

Getting started

The main file that runs the simulation is the function activeBrownianCrawler.m.

The code can be tuned from directed, pseudopod motion (left) to random, focal adhesion-like motion (right).

Inputs

The main function is defined as follows:

function activeBrownianCrawler(NV,calA0,Kl,Kb,v0,Dr,Ds,NT,dt,NFRAMES,seed,savestr)

• NV: integer number of vertices that make up the deformable particle (DP)
• calA0: initial preferred shape parameter
  • Defined as where and are the preferred perimeter and area of the cell, respectively.
• Kl: mechanical constant for perimeter
• Kb: mechanical constant for curvature
• v0: crawling speed
• Dr: cell-based director diffusion coefficient
• Ds: "foot size", spread of velocity distribution to nearby vertices
• NT: number of time steps to simulate
• dt: time step size
  • Note that total time will be ttotal = NT * dt
• NFRAMES: total number of "frames" to be saved during simulation.
  • Frame count rounds down, i.e. if there are NT = 8 time steps and you ask for NFRAMES = 3, you will only print out 2 frames total
• seed: integer seed for random number generator, must be integer > 0.
• savestr: string variable, path to file with saved data from simulation. Data saved in .mat file format, see MATLAB documentation on MAT-files.

Outputs

All simulation data is saved in the file named in the savestr variable. See this section for a detailed list of outputs.

Running Locally

To run locally on your machine, call the MATLAB function from the MATLAB command line with relevant inputs. The left example was run with

>> activeBrownianCrawler(32, 1.3, 1.0, 0.0, 0.05, 0.01, 0.2, 1e6, 0.005, 200, 1, 'test.mat');

and the right-hand example with

>> activeBrownianCrawler(32, 1.3, 1.0, 0.0, 0.05, 0.1, 0.1, 1e6, 0.005, 200, 1, 'test.mat');

To draw the simulation frame-by-frame, see the script abc_draw.m. The simulation code is replicated exactly, but the shape of the deformable particle is drawn in a figure window. An animated simulation can be saved to a .gif file if the makeAMovie variable on line 79 is set to 1.

Running on the cluster

Section in progress...

Matfile Data

Data in the MAT-file named in the savestr can be either loaded into the workspace using

load(savestr);

or loaded into a struct using

outputStruct = load(savestr);

The saved data can then be accessed as struct member variables using the . operator, e.g. outputStruct.NV.

All inputs to the function are saved in the MAT-file with their same name. Other variables are:

• frameList: time step of each frame.
  • Note: time (in simulation units) of each frame is frameList(tt) * dt.
• cList: center-of-mass position at each frame
• fList: center-of-mass net force at each frame
• vList: center-of-mass velocity at each frame
• UList: shape energy at each frame
• calAList: shape parameter at each frame
• abpCList: position of active brownian particle with steps drawn from ABC ensemble
• abpVList: velocity of active brownian particle with steps drawn from ABC ensemble