Fluctuations in molecular size, entanglement complexity, and anisometry along molecular dynamics trajectories of short α‐helices

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Abstract
We present a detailed study of the intrinsic shape stability of short flexible polypeptide chains by using a number of distinct descriptors. Some large‐scale structural features found in macromolecular folding—unfolding dynamics can be monitored in terms of molecular size and compactness. Similarly, one could employ descriptors of anisometry to that purpose. In addition, we have recently proposed a new family of global, absolute shape descriptors to quantify the complexity of the self‐entanglements in a polymer, or, loosely, its “degree of folding.” This latter aspect of the molecular shape is characterized by combining simple geometrical and topological properties of the α‐carbon backbone. The resulting descriptor, the probability of observing a rigid backbone as a projected curve exhibiting N overcrossings, has been employed already for the analysis of molecular dynamics of linear hydrocarbons and aliphatic carboxylic acids. In this work, three distinct properties of a molecular chain are monitored simultaneously, for the first lime, along computer‐simulated dynamic trajectories: size, anisotropy, and entanglements. The systems studied are a series of 3 polypeptide helices: 10‐polyalanine, 10‐polyvaline, and 10‐polyglycine. Constant temperature trajectories have been computed for these helices, at thermal equilibrium with a simulated external bath, with temperatures ranging from 300 to 700 K. The differential structural stability of the helices is assessed from the various viewpoints. Even though the systems are simple, they contain some of the essential features expected in polypeptides of relevance to structural biology. The results show that the, descriptors of anisometry and entanglements are rather independent. For instance, it is found that, contrary to intuition the unfolding of helices may involve nonhelical “coil” configurations that are both self‐entangled and prolate. The simultaneous study of independent shape descriptors provides a new picture of the nature of conformations found during dynamics trajectories. The resulting description characterizes a polymer conformation in a absolute terms, and not relative to an ad hoc reference structure. The proposed approach gives some insights into the stability of secondary structural motifs in proteins and the mechanisms involved into their formation or unfolding. © 1995 John Wiley & Sons, Inc.

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