Abstract

One of the most rigorous quantitative definitions of complexity is the notion of algorithmic complexity, discovered independently by Kolmogorov and Chaitin. It is based on the idea that the length of the shortest algorithmic description of a set of data can tell us about the complexity of the data. Here we will employ this principle to measure the physical complexity of a structure, with a particular focus on self-assembling biological structures. Self-assembly is a widespread process in biology, and is essential in the formation of structures such as DNA , protein complexes, and viruses. By minimising the information required to specify the building blocks and interactions that give rise to a structure, we obtain a quantitative measure of the structure’s complexity. Using a genetic algorithm with the building blocks as a genotype and the assembled structure as a phenotype we can investigate a number of questions, including how modularity and symmetry arises in evolution. We then apply this approach to study the evolution, assembly and classification of protein complexes and discover new fundamental organising principles, which result in a periodic table of protein complexes.