Biological networks in evolution: Theory, modeling and bioinformatics

This thesis covers a range of topics regarding the evolution of biological networks. The first set of questions revolves around the evolution of protein structures and the networks of structural relationships that define the modern protein universe. Using a graph-theoretic approach, we employ sets of protein structures found in the proteomes of individual organisms to provide evidence for a divergent model of structural evolution and against convergent models. This work motivates the use of protein structures as characters for use in the construction of prokaryotic phylogenies, and we find that the phylogenies so constructed are evolutionarily reasonable and in agreement with many other sources of phylogenetic data. The success of this dataset in phylogenetic reconstruction lends strong weight to models of the evolution of structural proteomes. We also consider the network of structural similarity for the complete structural space of a lattice polymer, and show that this space is fundamentally different from the network of structural relationships observed in real proteins. We demonstrate that the structures in this space may be sampled according to divergent evolutionary rules to recapitulate a structural network similar to that observed in the evolved protein universe. A completely physical, sequence-based model of duplication and divergence is also shown to recapitulate the features of this structural network and represents the first analysis of a physically realistic divergent evolutionary model in the context of global properties of the structural set that is evolved.; The second set of questions revolves around more general topics in evolution. We consider the nature of the protein-protein interaction networks that have been determined using high-throughput experiments and demonstrate that the topological features of this network may be explained by a simple and purely physical model of protein-protein interactions. We find a strong correlation between surface hydrophobicity and connectivity in these networks, which lends considerable weight to our model of these networks. Finally, we consider a model for semiconservatively replicating populations and demonstrate that the dynamics of these populations exhibit interesting features at high mutation rates near what is known as the "error catastrophe" when compared to conservatively replicating populations.