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Distributions in Protein Conformation Space: Implications for Structure Prediction and Entropy

Department of Pharmaceutical Chemistry, University of California, San Francisco, California 94143-2240

Correspondence: Address reprint requests to Irwin D. Kuntz, Dept. of Pharmaceutical Chemistry, University of California, San Francisco, CA 94143-2240. Tel.: 415-476-1937; Fax: 415-502-1411; E-mail: kuntz{at}cgl.ucsf.edu.

By considering how polymer structures are distributed in conformation space, we show that it is possible to quantify the difficulty of structural prediction and to provide a measure of progress for prediction calculations. The critical issue is the probability that a conformation is found within a specified distance of another conformer. We address this question by constructing a cumulative distribution function (CDF) for the average probability from observations about its limiting behavior at small displacements and numerical simulations of polyalanine chains. We can use the CDF to estimate the likelihood that a structure prediction is better than random chance. For example, the chance of randomly predicting the native backbone structure of a 150-amino-acid protein to low resolution, say within 6 Å, is 10^–14. A high-resolution structural prediction, say to 2 Å, is immensely more difficult (10^–57). With additional assumptions, the CDF yields the conformational entropy of protein folding from native-state coordinate variance. Or, using values of the conformational entropy change on folding, we can estimate the native state's conformational span. For example, for a 150-mer protein, equilibrium -carbon displacements in the native ensemble would be 0.3–0.5 Å based on TS of 1.42 kcal/(mol residue).

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