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Originally published as Genetics Published Articles Ahead of Print on November 16, 2006.

Genetics, Vol. 175, 255-266, January 2007, Copyright © 2007
doi:10.1534/genetics.106.061754

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Thermodynamics of Neutral Protein Evolution

Jesse D. Bloom*,1, Alpan Raval{dagger} and Claus O. Wilke{ddagger}

* Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, {dagger} Keck Graduate Institute of Applied Life Sciences and School of Mathematical Sciences, Claremont Graduate University, Claremont, California 91711 and {ddagger} Section of Integrative Biology and Center for Computational Biology and Bioinformatics, University of Texas, Austin, Texas 78712

1 Corresponding author: Division of Chemistry and Chemical Engineering, California Institute of Technology, Mail Code 210-41, 1200 E. California Blvd., Pasadena, CA 91125.
E-mail: jesse.bloom{at}gmail.com

Naturally evolving proteins gradually accumulate mutations while continuing to fold to stable structures. This process of neutral evolution is an important mode of genetic change and forms the basis for the molecular clock. We present a mathematical theory that predicts the number of accumulated mutations, the index of dispersion, and the distribution of stabilities in an evolving protein population from knowledge of the stability effects ({Delta}{Delta}G values) for single mutations. Our theory quantitatively describes how neutral evolution leads to marginally stable proteins and provides formulas for calculating how fluctuations in stability can overdisperse the molecular clock. It also shows that the structural influences on the rate of sequence evolution observed in earlier simulations can be calculated using just the single-mutation {Delta}{Delta}G values. We consider both the case when the product of the population size and mutation rate is small and the case when this product is large, and show that in the latter case the proteins evolve excess mutational robustness that is manifested by extra stability and an increase in the rate of sequence evolution. All our theoretical predictions are confirmed by simulations with lattice proteins. Our work provides a mathematical foundation for understanding how protein biophysics shapes the process of evolution.




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