A tractable genotype-phenotype map for the self-assembly of protein quaternary structure

TL;DR

This paper introduces a biologically realistic, computationally tractable genotype-phenotype map based on self-assembly of polyomino structures, revealing properties like redundancy, bias, and evolvability relevant to protein complex formation.

Contribution

The study presents a novel GP map model for self-assembling structures that captures key properties and shows similarities with other models, suggesting universal features.

Findings

Genotypes vastly outnumber phenotypes

Phenotype bias varies greatly among phenotypes

Mutational robustness scales logarithmically with redundancy

Abstract

The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here we introduce a rich, intuitive, and biologically realistic genotype-phenotype (GP) map, that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a 2D lattice and exhibits a number of properties: $\textit{redundancy}$ (genotypes vastly outnumber phenotypes), $\textit{phenotype bias}$ (genotypic redundancy varies greatly between phenotypes), $\textit{genotype component disconnectivity}$ (phenotypes consist of disconnected mutational networks) and $\textit{shape space covering}$ (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the HP lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps.