Complexity of classical dynamics of molecular systems. I. Methodology

Multiscale complex network of protein conformational fluctuations in single-molecule time series

Conformational dynamics of proteins can be interpreted as itinerant motions as the protein traverses from one state to another on a complex network in conformational space or, more generally, in state space. Here we present a scheme to extract a multiscale state space network (SSN) from a single-molecule time series. Analysis by this method enables us to lift degeneracy--different physical states having the same value for a measured observable--as much as possible. A state or node in the network is defined not by the value of the observable at each time but by a set of subsequences of the observable over time. The length of the subsequence can tell us the extent to which the memory of the system is able to predict the next state. As an illustration, we investigate the conformational fluctuation dynamics probed by single-molecule electron transfer (ET), detected on a photon-by-photon basis. We show that the topographical features of the SSNs depend on the time scale of observation; the longer the time scale, the simpler the underlying SSN becomes, leading to a transition of the dynamics from anomalous diffusion to normal Brownian diffusion.

Water network dynamics at the critical moment of a peptide’s β-turn formation: A molecular dynamics study

All-atom molecular dynamics simulations for a single molecule of Leu-Enkephalin in aqueous solution have been used to study the role of the water network during the formation of beta-turns. We give a detailed account of the intramolecular hydrogen bonding, the water-peptide hydrogen bonding, and the orientation and residence times of water molecules focusing on the short critical periods of transition to the stable beta-turns. These studies suggest that, when intramolecular hydrogen bonding between the first and fourth residue of the beta-turn is not present, the disruption of the water network and the establishment of water bridges constitute decisive factors in the formation and stability of the beta-turn. Finally, we provide possible explanations and mechanisms for the formations of different kinds of beta-turns.