Molecular dynamics at low time resolution

Renormalization group theory of molecular dynamics

Large scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have enabled large scale calculations, macroscopic analyses are still not realizable. Here, we present renormalized molecular dynamics (RMD), a renormalization group of MD in thermal equilibrium derived by using the Migdal–Kadanoff approximation. The RMD method improves the computational efficiency drastically while retaining the advantage of MD. The computational efficiency is improved by a factor of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{n(D+1)}$$\end{document}2n(D+1) over conventional MD where D is the spatial dimension and n is the number of applied renormalization transforms. We verify RMD by conducting two simulations; melting of an aluminum slab and collision of aluminum spheres. Both problems show that the expectation values of physical quantities are in good agreement after the renormalization, whereas the consumption time is reduced as expected. To observe behavior of RMD near the critical point, the critical exponent of the Lennard-Jones potential is extracted by calculating specific heat on the mesoscale. The critical exponent is obtained as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu =0.63\pm 0.01$$\end{document}ν=0.63±0.01. In addition, the renormalization group of dissipative particle dynamics (DPD) is derived. Renormalized DPD is equivalent to RMD in isothermal systems under the condition such that Deborah number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$De\ll 1$$\end{document}De≪1.

Exploring multi-dimensional coordinate-dependent diffusion dynamics on the energy landscape of protein conformation change

We explore the multi-dimensional diffusion dynamics of protein conformational change. We found in general that the diffusion is anisotropic and inhomogeneous. The directional and positional dependence of diffusion have significant impacts on the protein conformational kinetics: the dominant kinetic path of conformational change is shifted from the naively expected steepest decent gradient paths. The kinetic transition state is shifted away from the transition state. The effective kinetic free energy barrier height, determining the kinetic rate of the conformational change, is shifted away from the one estimated from the thermodynamic free energy barrier. The shift of the transition state in position and value will modify the phi value analysis for identification of hot residues and interactions responsible for conformational dynamics. Ongoing and future experiments can test the predictions of the model.

Microscopically computing free-energy profiles and transition path time of rare macromolecular transitions

We introduce a rigorous method to microscopically compute the observables which characterize the thermodynamics and kinetics of rare macromolecular transitions for which it is possible to identify a priori a slow reaction coordinate. In order to sample the ensemble of statistically significant reaction pathways, we define a biased molecular dynamics (MD) in which barrier-crossing transitions are accelerated without introducing any unphysical external force. In contrast to other biased MD methods, in the present approach the systematic errors which are generated in order to accelerate the transition can be analytically calculated and therefore can be corrected for. This allows for a computationally efficient reconstruction of the free-energy profile as a function of the reaction coordinate and for the calculation of the corresponding diffusion coefficient. The transition path time can then be readily evaluated within the dominant reaction pathways approach. We illustrate and test this method by characterizing a thermally activated transition on a two-dimensional energy surface and the folding of a small protein fragment within a coarse-grained model.

Fluctuations in the ensemble of reaction pathways

The dominant reaction pathway is a rigorous framework to microscopically compute the most probable trajectories, in nonequilibrium transitions. In the low-temperature regime, such dominant pathways encode the information about the reaction mechanism and can be used to estimate nonequilibrium averages of arbitrary observables. On the other hand, at sufficiently high temperatures, the stochastic fluctuations around the dominant paths become important and have to be taken into account. In this work, we develop a technique to systematically include the effects of such stochastic fluctuations, to order k(B)T. This method is used to compute the probability for a transition to take place through a specific reaction channel and to evaluate the reaction rate.