Intrinsic shape stability of equilibrium motions in poly(L-alanine)

Under some conditions, an isolated macromolecular chain at a minimum energy configuration may be subject to either local or large-scale vibrational deformations that can preserve the global molecular shape features of the given minimum. We refer to this persistence of dynamical shape as intrinsic shape stability. Assessing shape stability is essential for studies of molecular recognition and binding. In this work, we present a novel approach to analyzing and quantifying shape stability. As an illustrative example, we apply the method in a quantitative study of stability in poly(L-alanine) helices of variable lengths. Our approach explores the interrelation between various independent aspects of macromolecular shape, namely, size, compactness, anisometry, and chain entanglements (or degree of folding). We associate a different shape descriptor to each aspect. In this work, we analyze the role of the chain's length on the fluctuations in shape descriptors. We show that the study of entanglements and anisometry can indicate the occurrence of conformational rearrangements that would otherwise remain hidden when monitoring only the radius of gyration. We estimate the critical number of amino acid residues for which a polypeptide, undergoing equilibrium motions, better conserves its helical shape for a given set of environmental conditions. The methodology can be applied to general configurational changes in other types of polymers.