GLOBAL MEASURE OF MOLECULAR FLEXIBILITY AND SHAPE FLUCTUATIONS ABOUT CONFORMATIONAL MINIMA

A method to characterize conformations adopted by chain and cyclic molecules, and to assess their degree of flexibility toward folding, is developed and applied. The procedure constructs a function A0 from some simple geometric and topological properties of molecular chains. This function provides a global descriptor of the essential shape features of the molecular fold. The descriptor takes a maximum value of 1 for a completely linear or planar structure and a minimum value of 0 for an entangled or globular backbone. In this sense, the function proposed measures the compactness and degree of folding of a configuration. When one monitors the changes in this function along computer-simulated molecular dynamics trajectories, it is possible to assess the differential stability of conformations as a function of time, temperature, and other factors. Molecules that are stable over time toward adopting conformations with radically different folds are characterized as rigid. Consequently, the procedure provides also a quantitative measure of rigidity and flexibility toward folding. In other words, the fluctuations of A0 provide a quantitative measure of stability whereas the value of A0 gives a measure of the actual type of instant folding pattern. The description is characteristic of the given conformation and not relative to the initial nuclear geometry for the dynamics. The procedure is illustrated by comparing conformations of hexane and cyclohexane at various temperatures and contrasting the dynamics of hexane and decane, both starting from similar conformational minima.