Backbone entropy of loops as a measure of their flexibility: application to a ras protein simulated by molecular...

The flexibility of surface loops plays an important role in protein-protein and protein-peptide recognition; it is commonly studied by Molecular Dynamics or Monte Carlo stimulations. We propose to measure the relative backbone flexibility of loops by the difference in their backbone conformational entropies, which are calculated here with the local states (LS) method of Meirovitch. Thus, one can compare the entropies of loops of the same protein or, under certain simulation conditions, of different proteins. These loops should be equal in size but can differ in their sequence of amino acids residues. This methodology is applied successfully to three segments of 10 residues of a Ras protein simulated by the stochastic boundary molecular dynamics procedure. For the first time estimates of backbone entropy differences are obtained, and their correlation with B factors is pointed out; for example, the segments which consist of residues 60-65 and 112-117 have average B factors of 67 and 18 A2, respectively, and entropy difference T delta S = 5.4 +/- 0.1 kcal/mol at T = 300 K. In a large number of recent publications the entropy due to the fast motions (on the ps-ns time scale) of N-H and C-H vectors has been obtained from their order parameter, measured in nuclear magnetic resonance spin relaxation experiments. This enables one to estimate differences in the entropy of protein segments due to folding-unfolding transitions, for example. However, the vectors are assumed to be independent, and the effect of the neglected correlations is unknown; our method is expected to become an important tool for assessing this approximation. The present calculations, obtained with the LS method, suggest that the errors involved in experimental entropy differences might not be large; however, this should be verified in each case. Potential applications of entropy calculations to rational drug design are discussed.