Evolutionary Dynamics in a Simple Model of Self-Assembly

TL;DR

This paper explores how simple models of tile-based self-assembly evolve under genetic algorithms, revealing complex dynamics and insights into symmetry preferences in protein structures.

Contribution

It introduces an evolvable model of self-assembly with a genotype-phenotype map, analyzing how evolutionary parameters affect structure formation.

Findings

Rich evolutionary dynamics depend on parameters like mutation rate and population size.

The model's genome space can be fully characterized in some cases.

The study explains the emergence of symmetry preferences in protein tetramers.

Abstract

We investigate the evolutionary dynamics of an idealised model for the robust self-assembly of two-dimensional structures called polyominoes. The model includes rules that encode interactions between sets of square tiles that drive the self-assembly process. The relationship between the model's rule set and its resulting self-assembled structure can be viewed as a genotype-phenotype map and incorporated into a genetic algorithm. The rule sets evolve under selection for specified target structures. The corresponding, complex fitness landscape generates rich evolutionary dynamics as a function of parameters such as the population size, search space size, mutation rate, and method of recombination. Furthermore, these systems are simple enough that in some cases the associated model genome space can be completely characterised, shedding light on how the evolutionary dynamics depends on the detailed structure of the fitness landscape. Finally, we apply the model to study the emergence of the preference for dihedral over cyclic symmetry observed for homomeric protein tetramers.