Empirical scale of side-chain conformational entropy in protein folding

Abstract

A major effect in the energetics of protein folding is the loss of conformational entropy of the side-chains. The definition of entropy as the Boltzmann sampling over all states (S = -R sigma p(i) ln p(i)) requires evaluation of the probability (p(i)) of the system being in rotameric state i. The principle of this paper is to obtain an estimate of p(i) from the observed distribution of exposed side-chain rotamers in 50 non-homologous protein crystal structures. However because of limited data we show that for all side-chains except Asn, Asp and Glu the side-chain distribution is independent of burial and accordingly all data were pooled in the calculation of p(i). For Asn, Asp and Glu side-chains with relative accessibility > 60% were used. The scale includes effects due to the symmetry of side-chains such as Phe and the free rotation of side-chain amide, carboxyl and hydroxyl groups. An empirical scale for the loss of side-chain conformational entropy during protein folding is thereby obtained. Values of the change in free energy due to entropy (-T delta S) on burying a side-chain range from 0 for Ala, Gly and Pro to +2.1 kcal/mol for Gln (T = 300 K). We explore the consistency of a simple model for protein folding that includes side-chain entropy, main-chain entropy, hydrophobicity and hydrogen bonding. The stability of site-directed mutations is discussed in terms of conformational entropy.