Evolutionary dynamics in a simple model of self-assembly
- The evolution of self-assembling structures in biology is hard to study: we build and explore a model that contains key features (a genome encoding interactions between physical subunits) and how evolution "learns" self-assembly rules
Proteins are complicated structures that have evolved over billions of years. To understand how evolution has "learned" the interactions between subunits that proteins need to successfully self-assemble, we need to work with a model system that includes the scientifically interesting details but is simple enough to investigate on paper or with a computer.
In a paper (here in Physical Review E; free here), we work with "polyominoes" as a model for evolving self-assembling systems. Polyominoes are shapes made up of connected square tiles (dominoes are polyominoes containing two tiles; the "tetromino" pieces in Tetris -- from which the game gets its name -- are polyominoes containing four tiles). In our model, these tiles have sticky edges, with some edges sticking to some others -- a list of numbers describes who sticks to whom. If we put tiles in a bag and shake them, some edges will stick, and a polyomino will form. We thus have the essential features of a random cell (the bag) and interactions between subunits (sticky edges) which are encoded by a genome (the list of numbers).
We then simulated evolution in a computer, with random mutations changing the "genome" and natural selection acting on the resulting polyominoes. We show how different mutation rates, population sizes, and reproductive strategies affect the evolution of model biological structures. We also show that this evolutionary model can explain the symmetries of protein structures observed in biology. We explore the surprisingly rich set of structures that the model can produce, and the different modes of evolution that can lead from simple to complex forms -- helping us understand how important structures have evolved and may go wrong through mutation. There's more work on this here and an associated interactive simulation tool here! Iain