First-Passage Time Distribution and Non-Markovian Diffusion Dynamics of Protein Folding

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described in terms of an order parameter given by the fraction of native conformations. The non-Markovian diffusion dynamics is analyzed in detail and an expression for the mean first-passage time (MFPT) from non-native unfolded states to native folded state is obtained. It was found that the MFPT has a V-shaped dependence on the temperature. We also find that the MFPT is shortened as one increases the gap between the energy of the native and average non-native folded states relative to the fluctuations of the energy landscape. The second- and higher-order moments are studied to infer the first-passage time (FPT) distribution. At high temperature, the distribution becomes close to a Poisson distribution, while at low temperatures the distribution becomes a L\'evy-like distribution with power-law tails, indicating a non-self-averaging intermittent behavior of folding dynamics. We note the likely relevance of this result to single-molecule dynamics experiments, where a power law (L\'evy) distribution of the relaxation time of the underlined protein energy landscape is observed.Comment: 26 pages, 10 figure

Diffusion Dynamics, Moments, and Distribution of First Passage Time on the Protein-Folding Energy Landscape, with Applications to Single Molecules

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We obtain information for the first passage-time (FPT) distribution and its moments. The results show a dynamic transition temperature below which the FPT distribution develops a power-law tail, a signature of the intermittency phenomena of the folding dynamics. We also discuss the possible application of the results to single-molecule dynamics experiments

Molecular dynamics simulation of polymer helix formation using rigid-link methods

Molecular dynamics simulations are used to study structure formation in simple model polymer chains that are subject to excluded volume and torsional interactions. The changing conformations exhibited by chains of different lengths under gradual cooling are followed until each reaches a state from which no further change is possible. The interactions are chosen so that the true ground state is a helix, and a high proportion of simulation runs succeed in reaching this state; the fraction that manage to form defect-free helices is a function of both chain length and cooling rate. In order to demonstrate behavior analogous to the formation of protein tertiary structure, additional attractive interactions are introduced into the model, leading to the appearance of aligned, antiparallel helix pairs. The simulations employ a computational approach that deals directly with the internal coordinates in a recursive manner; this representation is able to maintain constant bond lengths and angles without the necessity of treating them as an algebraic constraint problem supplementary to the equations of motion.Comment: 15 pages, 14 figure

Glassy phases in Random Heteropolymers with correlated sequences

We develop a new analytic approach for the study of lattice heteropolymers, and apply it to copolymers with correlated Markovian sequences. According to our analysis, heteropolymers present three different dense phases depending upon the temperature, the nature of the monomer interactions, and the sequence correlations: (i) a liquid phase, (ii) a ``soft glass'' phase, and (iii) a ``frozen glass'' phase. The presence of the new intermediate ``soft glass'' phase is predicted for instance in the case of polyampholytes with sequences that favor the alternation of monomers. Our approach is based on the cavity method, a refined Bethe Peierls approximation adapted to frustrated systems. It amounts to a mean field treatment in which the nearest neighbor correlations, which are crucial in the dense phases of heteropolymers, are handled exactly. This approach is powerful and versatile, it can be improved systematically and generalized to other polymeric systems