Protein Evolution within a Structural Space

TL;DR

This study uses lattice polymers to model protein structural space, revealing that the network of structures behaves like a random graph and that a divergent evolution model can replicate the scale-free properties of real protein structure networks.

Contribution

It introduces a lattice polymer model to analyze protein structural evolution and demonstrates that this model can reproduce key network properties of real protein structures.

Findings

Lattice structure graphs resemble random graphs.

Subgraphs also exhibit randomness under constraints.

Divergent evolution models can produce scale-free networks.

Abstract

Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural "space" might impact protein structural evolution. We approach this question using lattice polymers as a completely characterized model of this space. We develop a measure of structural comparison of lattice structures that is analgous to the one used to understand structural similarities between real proteins. We use this measure of structural relatedness to create a graph of lattice structures and compare this graph (in which nodes are lattice structures and edges are defined using structural similarity) to the graph obtained for real protein structures. We find that the graph obtained from all compact lattice structures exhibits a distribution of structural neighbors per node consistent with a random graph. We also find that subgraphs of 3500 nodes chosen either at random or according to physical constraints also represent random graphs. We develop a divergent evolution model based on the lattice space which produces graphs that, within certain parameter regimes, recapitulate the scale-free behavior observed in similar graphs of real protein structures.