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Proteins, by virtue of their central role in most biological processes, represent one of the key subjects of the study of molecular evolution. Inherent to the indispensability of proteins for living cells is the fact that a given protein can adopt a specific three-dimensional shape that is specified solely by the proteins sequence of amino acids. Over the past several decades, structural biologists have demonstrated that the array of structures that proteins may adopt is quite astounding, and this has lead to a strong interest in understanding how protein structures change and evolve over time. In this review we consider a large body of recent work that attempts to illuminate this structure-centric picture of protein evolution. Much of this work has focused on the question of how completely new protein structures (i.e. new folds or topologies) are discovered by protein sequences as they evolve. Pursuant to this question of structural innovation has been a desire to describe and understand the observation that certain types of protein structures are far more abundant than others and how this uneven distribution of proteins implicates on the process through which new shapes are discovered. We consider a number of theoretical models that have been successful at explaining this heterogeneity in protein populations and discuss the increasing amount of evidence that indicates that the process of structural evolution involves the divergence of protein sequences and structures from one another.

A generalized computational method for folding proteins with a fully transferable potential and geometrically realistic all-atom model is presented and tested on seven different helix bundle proteins. The protocol, which includes graph-theoretical analysis of the ensemble of resulting folded conformations, was systematically applied and consistently produced structure predictions of approximately 3 Angstroms without any knowledge of the native state. To measure and understand the significance of the results, extensive control simulations were conducted. Graph theoretic analysis provides a means for systematically identifying the native fold and provides physical insight, conceptually linking the results to modern theoretical views of protein folding. In addition to presenting a method for prediction of structure and folding mechanism, our model suggests that a accurate all-atom amino acid representation coupled with a physically reasonable atomic interaction potential (that does not require optimization to the test set) and hydrogen bonding are essential features for a realistic protein model., Comment: submitted to PNAS 2005-03-16

It has recently been demonstrated that many biological networks exhibit a scale-free topology where the probability of observing a node with a certain number of edges (k) follows a power law: i.e. p(k) ~ k^-g. This observation has been reproduced by evolutionary models. Here we consider the network of protein-protein interactions and demonstrate that two published independent measurements of these interactions produce graphs that are only weakly correlated with one another despite their strikingly similar topology. We then propose a physical model based on the fundamental principle that (de)solvation is a major physical factor in protein-protein interactions. This model reproduces not only the scale-free nature of such graphs but also a number of higher-order correlations in these networks. A key support of the model is provided by the discovery of a significant correlation between number of interactions made by a protein and the fraction of hydrophobic residues on its surface. The model presented in this paper represents the first physical model for experimentally determined protein-protein interactions that comprehensively reproduces the topological features of interaction networks. These results have profound implications for understanding not only protein-protein interactions but also other types of scale-free networks., Comment: 50 pages, 17 figures

It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other systems has previously been explained using network growth models that, while motivated by biological processes, do not explicitly consider the underlying physics or biology. In the present work we explore a sequence-based model for the evolution protein structures and demonstrate that this model is able to recapitulate the scale-free nature observed in graphs of real protein structures. We find that this model also reproduces other statistical feature of the protein domain graph. This represents, to our knowledge, the first such microscopic, physics-based evolutionary model for a scale-free network of biological importance and as such has strong implications for our understanding of the evolution of protein structures and of other biological networks., Comment: 20 pages (including figures), 4 figures, to be submitted to PNAS

This paper extends Eigen's quasispecies equations to account for the semiconservative nature of DNA replication. We solve the equations in the limit of infinite sequence length for the simplest case of a static, sharply peaked fitness landscape. We show that the error catastrophe occurs when $ \mu $, the product of sequence length and per base pair mismatch probability, exceeds $ 2 \ln \frac{2}{1 + 1/k} $, where $ k > 1 $ is the first order growth rate constant of the viable ``master'' sequence (with all other sequences having a first-order growth rate constant of $ 1 $). This is in contrast to the result of $ \ln k $ for conservative replication. In particular, as $ k \to \infty $, the error catastrophe is never reached for conservative replication, while for semiconservative replication the critical $ \mu $ approaches $ 2 \ln 2 $. Semiconservative replication is therefore considerably less robust than conservative replication to the effect of replication errors. We also show that the mean equilibrium fitness of a semiconservatively replicating system is given by $ k (2 e^{-\mu/2} - 1) $ below the error catastrophe, in contrast to the standard result of $ k e^{-\mu} $ for conservative replication (derived by Kimura and Maruyama in 1966)., Comment: 15 pages, 7 figures, to be submitted to Phys. Rev. E

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., Comment: 27 pages, 7 figures