β-Sheet propensity and its correlation withparameters based on conformation

The dispersion of the main-chain and side-chain conformations in the φ, ψ, χ₁ space for all residues have been estimated in terms of three parameters corresponding to the entropy (S) of the distribution, the volume (D_V) and the area (D_A) the points are enclosed in. These parameters are inversely correlated with Chou and Fasman β-sheet propensities, P_β (Gly and Pro excluded), suggesting that residues with greater dispersion in the conformational space are weak β-sheet formers. It was also found that different residues have different relative populations in the bridging region (intervening between the helical and β-sheet regions) which may lie on the pathway for interconversion between α and β conformations. The energy barrier for this transformation, as obtained from the population of residues in the bridging region relative to the β region, is directly correlated to P_β. Residues with high P_β have branched side chains, which have greater steric interactions with the main-chain atoms resulting in a shrinking of the available conformational space (first correlation) and a steeper energy gradient beyond the allowed space (second correlation) compared with linear residues. It is proposed that if residues exist in an extended conformation when the polypeptide chain is synthesized, a stretch of residues with high P_β, because of the high energy barrier for their conversion into the α conformation, will continue to remain in the extended conformation and will ultimately constitute a β-strand in the folded structure.