BIEN 225 Cellular Automata Assignment

BIEN 225 Cellular Automata Assignment

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BIEN 225 – Self-Organization in Engineered and Native Tissue :

In this assignment, you expand on what you produced in HW1 to create a more physiologically relevant “Game of Life”. This will be discussed in Discussion, so please come with questions and read the paper in advance.

Please name your m-file using the following format:

HW_2_P#_LastFirst.m

Where LastFirst is your Last name and your First name, and # is the problem number. Please start each m file with the following lines:

%LAST FIRST %HW2 %P1 clearvars close all clc

In this homework, we’ll be re-creating a classic cellular automata model, similar to Conway’s Game of Life, but modified to more closely capture the dynamics of mammalian cells grown in a monolayer. In the paper “Proliferation of Anchorage-Dependent Contact-Inhibited Cells: 1. Development of Theoretical Models Based on Cellular Automata” the authors present 2 models of adherent cell proliferation, a synchronous and an asynchronous model. In the following problems you will replicate the synchronous (P1 and P2) and asynchronous models (P3). The paper is attached to the assignment on iLearn and should be used as a reference.  BIEN 225 Cellular Automata Assignment

Problem 1: You will recreate the synchronous model where cells can only proliferate in straight directions and not diagonals. Each iteration, each live cell should divide in a random “allowed” direction and not proliferate onto existing cells or off the side of the board. Cells without proliferation options should not proliferate, cells that have directions blocked off should proliferate randomly in one of the available directions. Cells do not die in this model.

To complete the assignment, create a simulation with the following parameters:

1. Exists on a 51×51 board 2. Has 4 randomly positioned cells as the initial condition 3. Iterates for 100 steps

Hint: The function randperm() can be used to create a random vector from 1 to 4 (where the numbers could correspond to directions, and you can use a system similar to the neighborhood assessment you used in Game of Life to identify which directions are allowed or forbidden for any given cell. Further, the switch/case conditional is a convenient way to take actions based on the value of a variable.  BIEN 225 Cellular Automata Assignment

Problem 2: Extend your model from Problem 1 to allow for diagonal proliferation. Cells should proliferate along the “straights” until there are no available directions and then switch to a diagonal proliferation on a random basis. Each cell should have a 20% chance of proliferating per available diagonal, but only can proliferate once per iterations. For example, a cell with 4 available directions has an 80% chance of proliferating, but the direction must be random. A cell with 3 available diagonals has a 60% chance of proliferating, etc.

Problem 3: Extend your model from Problem 2 to the asynchronous model. After each proliferation, set both the daughter (the new cells) and the parent (the original cells) cells to a random number in the range 5-10. Each cell should be set to its own random number. Each iteration, all cells should count down by 1. Cells at zero should proliferate according to the rules in Problem 1 and 2 or stay at zero otherwise. BIEN 225 Cellular Automata Assignment

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