Assessment of molecular shape fluctuations along dynamic trajectories

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To assess the flexibility of a molecule (and to establish how it is affected by external conditions), one can analyze the nature of the configurations encountered along molecular dynamics (MD) trajectories. If the molecule is initially at a rigid conformation, then it will mostly undergo deformations which conserve the initial fold or shape. That is, a rigid molecule will exhibit very small shape fluctuations about the initial shape, whereas large fluctuations will be characteristic of flexible molecules. Establishing the persistence of molecular shape features along MD trajectories is a valuable piece of information in the analysis of dynamic phase transitions in large biomolecules, including protein folding and polymer melting. In this work, we discuss a methodology to monitor macromolecular shape along dynamic trajectories. The procedure uses descriptors which convey some global shape features, including the compactness and degree (and complexity) of entanglement in a backbone. The method is used to follow shape fluctuations in chain molecules (carboxylic acids) and cyclic molecules (cycloalkanes), with 6 up to 12 carbon atoms. The role of variable temperature and number of atoms on these fluctuations is analyzed. The results indicate a relatively constant average shape in the cyclic molecules, although the amplitude of the shape fluctuations increases with the temperature. In contrast, the shape of the chain molecules is affected largely at high temperature, where folding or “melting” becomes dominant. At low temperature, the chains are very rigid. In the high temperature regime, the shape fluctuations in chains are large and very similar to those in cycles. In other words, the distinction between configurations of cycles and chains starts to blur at high temperature, thus suggesting that chains are mostly folded into turns. The results would appear not to depend very strongly on the functional group at the end of the chain. © 1993 John Wiley & Sons, Inc.