Hironori K. Nakamura

Squeezed exponential kinetics to describe a nonglassy downhill folding as observed in a lattice protein model

We previously studied the so‐called strange kinetics in the two‐dimensional lattice HP model. To further study the strange kinetics, folding processes of a 27‐mer cubic lattice protein model with Gō potential were investigated by simulating how the bundle of folding trajectories, consisting of a number of independent Monte Carlo simulations, evolves as the folding reaction proceeds, covering a wide range of temperature. Three realms of folding kinetics were observed depending on temperature. Although at temperatures where folding was two‐state‐like, the kinetics was conventional single exponential, we found that the time course data were well represented by a squeezed (or “shrunken”) exponential function, exp [−(t/τ)β] with β > 1, at temperatures lower than the folding temperature, where folding was fastest and of a nonglassy downhill type. The squeezed exponential kinetics was found to pertain to the subdiffusion on the nonglassy downhill free energy surface and presents a marked contrast both to the single exponential kinetics and to the stretched exponential kinetics that was observed at lower temperatures where folding was also downhill but topological frustration came into effect. The observed temperature dependence of the folding kinetics suggests that some small single‐domain proteins may follow the squeezed exponential kinetics at about the room temperature. Proteins 2004;55:99–106.

Population analyses of kinetic partitioning in protein folding

A simple lattice model of protein folding is studied in order to analyze the kinetic partitioning phenomena in the energy landscape perspective. By restricting the area of conformational space, it becomes possible to follow many Monte Carlo trajectories until they reach equilibrium. Alteration of population of trajectories is monitored and the relations between the energy landscape and kinetics are examined. Kinetic partitioning phenomena are categorized into different types in terms of characteristic time constants and partitioning ratio. In a specific partitioning process, refolding proceeds along the parallel pathways; the time constants have a temperature dependence similar to that observed in hen lysozyme. High‐energy conformations are classified into groups according to the probability that the trajectories starting from those conformations will reach each energy valley. The partitioning ratio is determined by the way in which the conformational space is organized into these groups. Proteins 2001;43:280–291.

Strange kinetics and complex energy landscapes in a lattice model of protein folding

Non-exponential relaxation in a simplified lattice model of folding is studied with Monte Carlo (MC) calculation. As folding proceeds, population of the native conformation approaches its equilibrium value with the stretched exponential form. As temperature increases, relaxation becomes less stretched, and for 2 sequences out of 5 tested ones, the relaxation becomes faster than exponential at high temperature. Energy landscape of the model is analyzed and flow of trajectories is followed to explain temperature dependence of kinetics. Measurement of stretched or shrunken kinetics of folding should help to understand nature of intermediates and ruggedness of the landscape.

On the model granularity to simulate protein dynamics: A biological physics view on biomolecular computing

What granularity is needed to carry out computer simulations of biomolecular reactions/motions? This is one of the central issues of the in silico biomolecular computing. In this paper, we addressed this issue by studying model granularity dependence of the native structure dynamics of protein molecules. We conducted molecular dynamics simulations employing three different protein models: the model with full atomic details and two coarse-grained models in which only Cα atoms interacting with each other through simple potentials are considered. In addition to the observed agreement among the three models in terms of isotropic thermal fluctuation, principal component analysis showed that the coarse-grained models can also reproduce the anisotropy (or directionality) of the fluctuation, particularly of collective modes having relevance to molecular function. This indicates that the dependence of the essential dynamics of a protein molecule on the model granularity is weak, although it was also shown that incorporation of the Lennard–Jones-type potential into the harmonic-potential-based coarse-grained model improves the reproducibility to some degree, and that a plastic nature of structural dynamics observed in the full atomic model transforms into an elastic one in the coarse-grained models. The coarse-grained model can be applied to a molecular motor system, which may lead to a new view of biomolecular computing in the context of biological physics.