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MBE Advance Access originally published online on November 10, 2004
Molecular Biology and Evolution 2005 22(3):630-638; doi:10.1093/molbev/msi048
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Molecular Biology and Evolution vol. 22 no. 3 © Society for Molecular Biology and Evolution 2004; all rights reserved.

Research Article

Prediction of Site-Specific Amino Acid Distributions and Limits of Divergent Evolutionary Changes in Protein Sequences

Markus Porto*, H. Eduardo Roman{dagger},1, Michele Vendruscolo{ddagger} and Ugo Bastolla§

* Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 8, 64289 Darmstadt, Germany; {dagger} Dipartimento di Fisica and INFN, Università di Milano, Via Celoria 16, 20133 Milano, Italy; {ddagger} Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK; § Centro de Astrobiología (INTA-CSIC), 28850 Torrejón de Ardoz, Spain

E-mail: porto{at}fkp.tu-darmstadt.de; bastollau{at}inta.es.

We derive an analytic expression for site-specific stationary distributions of amino acids from the structurally constrained neutral (SCN) model of protein evolution with conservation of folding stability. The stationary distributions that we obtain have a Boltzmann-like shape, and their effective temperature parameter, measuring the limit of divergent evolutionary changes at a given site, can be predicted from a site-specific topological property, the principal eigenvector of the contact matrix of the native conformation of the protein. These analytic results, obtained without free parameters, are compared with simulations of the SCN model and with the site-specific amino acid distributions obtained from the Protein Data Bank. These results also provide new insights into how the topology of a protein fold influences its designability, i.e., the number of sequences compatible with that fold. The dependence of the effective temperature on the principal eigenvector decreases for longer proteins, as a possible consequence of the fact that selection for thermodynamic stability becomes weaker in this case.

Key Words: Amino acid distributions • Boltzmann parameters • divergent evolutionary changes • principal eigenvector of the contact matrix • structurally constrained neutral evolution


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