Thermodynamic prediction of protein neutrality

Thermodynamic prediction of protein neutrality
Published online before print January 11, 2005
Jesse D. Bloom *, , , Jonathan J. Silberg , Claus O. Wilke , ?, D. Allan Drummond , ||, Christoph Adami , ?, and Frances H. Arnold *,
PNAS | January 18, 2005 | vol. 102
*Division of Chemistry and Chemical Engineering 210-41, Digital Life Laboratory 136-93, and ||Computation and Neural Systems, California Institute of Technology, Pasadena, CA 91125; Department of Biochemistry and Cell Biology, Rice University, Houston, TX 77005; and ?Keck Graduate Institute, 535 Watson Drive, Claremont, CA 91711
Edited by Alan R. Fersht, University of Cambridge, Cambridge, United Kingdom and approved December 3, 2004 (received for review September 10, 2004)
We present a simple theory that uses thermodynamic parameters to predict the probability that a protein retains the wild-type structure after one or more random amino acid substitutions. Our theory predicts that for large numbers of substitutions the probability that a protein retains its structure will decline exponentially with the number of substitutions, with the severity of this decline determined by properties of the structure. Our theory also predicts that a protein can gain extra robustness to the first few substitutions by increasing its thermodynamic stability. We validate our theory with simulations on lattice protein models and by showing that it quantitatively predicts previously published experimental measurements on subtilisin and our own measurements on variants of TEM1 -lactamase. Our work unifies observations about the clustering of functional proteins in sequence space, and provides a basis for interpreting the response of proteins to substitutions in protein engineering applications.
mutational robustness | protein evolution | protein stability | directed evolution | -lactamase
The ability to predict a protein's tolerance to amino acid substitutions is of fundamental importance in understanding natural protein evolution, developing protein engineering strategies, and understanding the basis of genetic diseases. Computational and experimental studies have demonstrated that both protein stability and structure affect a protein's tolerance to substitutions. Simulations have shown that more stable proteins have a higher fraction of folded mutants (1Ò4) and that some structures are encoded by more sequences than others (5Ò7). Experiments have demonstrated that proteins can be extremely tolerant to single substitutions; for example, 84% of single-residue mutants of T4 lysozyme (8) and 65% of single-residue mutants of lac repressor (9) were scored as functional. For multiple substitutions, the fraction of functional proteins decreases roughly exponentially with the number of substitutions, although the severity of this decline varies among proteins (10Ò12). Protein mutagenesis experiments have also underscored the contribution of protein stability to mutational tolerance by finding "global suppressor" substitutions that buffer a protein against otherwise deleterious substitutions by increasing its stability (13, 14).
We unify these diverse experimental and computational results into a simple framework for predicting a protein's tolerance to substitutions. A fundamental measure of this tolerance is the fraction of proteins retaining the wild-type structure after a single random substitution, often called the neutrality (15). We extend this concept to multiple substitutions by defining the m-neutrality as the fraction of proteins that fold to the wild-type structure among all sequences that differ from the wild-type sequence at m residues. Because mutants that fail to fold also generally fail to function, the m-neutrality provides an upper bound to the fraction of proteins with m substitutions that retain biochemical function. We show that a protein's m-neutrality can be accurately predicted from measurable thermodynamic parameters, and that these predictions capture the contributions of both stability and structure to determining a protein's tolerance to substitutions.
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