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Protein Evolution within a Structural Space

Eric J. Deeds ^*, Nikolay V. Dokholyan  and Eugene I. Shakhnovich 

^* Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts; Department of Biochemistry and Biophysics, University of North Carolina School of Medicine, Chapel Hill, North Carolina; and Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts

Correspondence: Address reprint requests to Eugene Shakhnovich, Dept. of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138. Tel: 617-495-4130; Fax: 617-496-5948; E-mail: eugene{at}belok.harvard.edu.

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 analogous 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.

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