# Simulation of Somatic Evolution Through the Introduction of Random Mutation to the Rules of Conway’s Game of Life

## TL;DR

This paper uses a modified version of Conway’s Game of Life to simulate somatic evolution and tumor-like growth through random mutations in cellular rules.

## Contribution

A novel CA model introduces random mutations to GOL rules, simulating somatic evolution and tumor growth dynamics.

## Key findings

- Accumulated mutations in GOL rules lead to unregulated growth resembling tumor tissues.
- The overcrowding threshold is the most critical mutated rule for tumor-like transitions.
- Fitter subclones outcompete and replace wildtype cells in the simulation.

## Abstract

Conway’s Game of Life (GOL), and related cellular automata (CA) models, have served as interesting simulations of complex behaviors resulting from simple rules of interactions between neighboring cells, that sometime resemble the growth and reproduction of living things. Thus, CA has been applied towards understanding the interaction and reproduction of single-cell organisms, and the growth of larger, disorganized tissues such as tumors. Surprisingly, however, there have been few attempts to adapt simple CA models to recreate the evolution of either new species, or subclones within a multicellular, tumor-like tissue.

In this article, I present a modified form of the classic Conway’s GOL simulation, in which the three integer thresholds that define GOL (number of neighboring cells, below which a cell will “die of loneliness”; number of neighboring cells, above which a cell will die of overcrowding; and number of neighboring cells that will result in spontaneous birth of a new cell within an empty lattice location) are occasionally altered with a randomized mutation of fractional magnitude during new “cell birth” events. Newly born cells “inherit” the current mutation state of a neighboring parent cell, and over the course of 10,000 generations these mutations tend to accumulate until they impact the behaviors of individual cells, causing them to transition from the sparse, small patterns of live cells characteristic of GOL into a more dense, unregulated growth resembling a connected tumor tissue.

The mutation rate and mutation magnitude were systematically varied in repeated randomized simulation runs, and it was determined that the most important mutated rule for the transition to unregulated, tumor-like growth was the overcrowding threshold, with the spontaneous birth and loneliness thresholds being of secondary importance. Spatial maps of the different “subclones” of cells that spontaneously develop during a typical simulation trial reveal that cells with greater fitness will overgrow the lattice and proliferate while the less fit, “wildtype” GOL cells die out and are replaced with mutant cells.

This simple modeling approach can be easily modified to add complexity and more realistic biological details, and may yield new understanding of cancer and somatic evolution.

The online version contains supplementary material available at 10.1007/s12195-024-00828-9.