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Predicting the Tolerance of Proteins to Random Amino Acid Substitution

Claus O. Wilke ^* , Jesse D. Bloom  , D. Allan Drummond   and Alpan Raval ^* ¶

^* Keck Graduate Institute of Applied Life Sciences, Claremont, California; Division of Chemistry and Chemical Engineering, Program in Computation and Neural Systems, Digital Life Laboratory, California Institute of Technology, Pasadena, California; and ^¶ School of Mathematical Sciences, Claremont Graduate University, Claremont, California

Correspondence: Address reprint requests to C. O. Wilke at his present address, Section of Integrative Biology, University of Texas at Austin, Texas. E-mail: cwilke{at}mail.utexas.edu.

We have recently proposed a thermodynamic model that predicts the tolerance of proteins to random amino acid substitutions. Here we test this model against extensive simulations with compact lattice proteins, and find that the overall performance of the model is very good. We also derive an approximate analytic expression for the fraction of mutant proteins that fold stably to the native structure, P_f(m), as a function of the number of amino acid substitutions m, and present several methods to estimate the asymptotic behavior of P_f(m) for large m. We test the accuracy of all approximations against our simulation results, and find good overall agreement between the approximations and the simulation measurements.

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