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

Abstract

Introduction: 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.

Methods: 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.

Results: 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.

Conclusions: 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.

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

Keywords: Cellular automata; Game of life; Somatic evolution.

Fig. 1

Dynamics of Conway’s Game of Life with no mutation. A Final population on the 2-D lattice, showing live cells in red and dead/empty cells in blue. B Cell population as a function of generation number

Fig. 2

A Final number of generations before reaching steady-state or maximum generation number, as a function of mutation magnitude and mutation rate. B Population of live cells as a function of generation number, for mutation rate = 0.01 and mutation magnitude = 1.0. C. Final lattice map of cell population, with live cells in red and dead/empty cells in blue. D. Population of live cells as a function of generation number, for mutation rate = 0.05 and mutation magnitude of 6.0. E. Final lattice map of cell population, with live cells in red and dead/empty cells in blue

Fig. 3

A The final live cell population at the end of each simulation, as a function of mutation magnitude and mutation rate. B Final spatial map of live cell population for a mutation magnitude = 5.0 and mutation rate = 0.01. C Final spatial map of live cell population for a mutation magnitude = 0.5 and mutation rate = 0.05

Fig. 4

A The final lonely GOL threshold value averaged over the 2-D lattice, as a function of mutation magnitude and mutation rate. B A spatial map of the final lonely GOL threshold for a mutation magnitude = 1.0 and mutation rate = 0.05. C A spatial map of the final lonely GOL threshold for a mutation magnitude = 1.5 and mutation rate = 0.4

Fig. 5

A The final born GOL threshold value averaged over the 2-D lattice, as a function of mutation magnitude and mutation rate. B A spatial map of the final born GOL threshold for a mutation magnitude = 1.5 and mutation rate = 0.4. C A spatial map of the final born GOL threshold for a mutation magnitude = 1.5 and mutation rate = 0.4

Fig. 6

A The final crowded GOL threshold value averaged over the 2-D lattice, as a function of mutation magnitude and mutation rate. B A spatial map of the final crowded GOL threshold for a mutation magnitude = 6.0 and mutation rate = 0.05. C A spatial map of the final crowded GOL threshold for a mutation magnitude = 0.5 and mutation rate = 0.1