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Register a new userEfficient Bayesian estimation of Markov model transition matrices with given stationary distribution
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Added by
Benjamin Trendelkamp-Schroer
Publication date
2013
fields
Physics
and research's language is
English
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Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the convergence of expectation values of equilibrium probabilities and expectation values of stationary quantities significantly. Unfortunately the convergence of dynamic observables such as correlation functions or timescales of conformational transitions relies on direct equilibrium simulations. Markov state models are well suited to describe both, stationary properties and properties of slow dynamical processes of a molecular system, in terms of a transition matrix for a jump process on a suitable discretiza- tion of continuous conformation space. Here, we introduce statistical estimation methods that allow a priori knowledge of equilibrium probabilities to be incorporated into the estimation of dynamical observables. Both, maximum likelihood methods and an improved Monte Carlo sampling method for reversible transition ma- trices with fixed stationary distribution are given. The sampling approach is applied to a toy example as well as to simulations of the MR121-GSGS-W peptide, and is demonstrated to converge much more rapidly than a previous approach in [F. Noe, J. Chem. Phys. 128, 244103 (2008)]
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We propose a transform method from a force curve obtained by a surface force apparatus (SFA) to a density distribution of a liquid on a surface of the SFA probe. (We emphasize that the transform method is a theory for the experiment.) In the method, two-body potential between the SFA probe and the solvent sphere is modeled as the soft attractive potential with rigid wall. The model potential is more realistic compared with the rigid potential applied in our earlier work. The introduction of the model potential is the improved point of the present transform method. The transform method is derived based on the statistical mechanics of a simple liquid where the simple liquid is an ensemble of small spheres. To derive the transform method, Kirkwood superposition approximation is used. It is found that the transformation can be done by a sequential computation. It is considered that the solvation structure can be obtained more precisely by using the improved transform method.
An analytical model of mechanical stress in a polymer electrolyte membrane (PEM) of a hydrogen/air fuel cell with porous Water Transfer Plates (WTP) is developed in this work. The model considers a mechanical stress in the membrane is a result of the cell load cycling under constant oxygen utilization. The load cycling causes the cycling of the inlet gas flow rate, which results in the membrane hydration/dehydration close to the gas inlet. Hydration/dehydration of the membrane leads to membrane swelling/shrinking, which causes mechanical stress in the constrained membrane. Mechanical stress results in through-plane crack formation. Thereby, the mechanical stress in the membrane causes mechanical failure of the membrane, limiting fuel cell lifetime. The model predicts the stress in the membrane as a function of the cell geometry, membrane material properties and operation conditions. The model was applied for stress calculation in GORE-SELECT.
We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of sufficient length can be gathered to approximate stationary sampling. Instead, we consider an alternative setting where a fixed set of transitions has been collected beforehand, by a separate, possibly unknown procedure. The goal is still to estimate properties of the stationary distribution, but without additional access to the underlying system. We propose a consistent estimator that is based on recovering a correction ratio function over the given data. In particular, we develop a variational power method (VPM) that provides provably consistent estimates under general conditions. In addition to unifying a number of existing approaches from different subfields, we also find that VPM yields significantly better estimates across a range of problems, including queueing, stochastic differential equations, post-processing MCMC, and off-policy evaluation.
Motivated by an experiment in which the singlet-triplet gap in triphenylene based copolymers was effectively tuned, we used time dependent density functional theory (TDDFT) to reproduce the main results. By means of conventional and long-range corrected exchange correlation functionals, the luminescence energies and the exciton localization were calculated for a triphenylene homopolymer and several different copolymers. The phosphorescence energy of the pure triphenylene chain is predicted accurately by means of the optimally tuned long-range corrected LC-PBE functional and slightly less accurate by the global hybrid B3LYP. However, the experimentally observed fixed phosphorescence energy could not be reproduced because the localization pattern is different to the expectations: Instead of localizing on the triphenylene moiety - which is present in all types of polymers - the triplet state localizes on the different bridging units in the TDDFT calculations. This leads to different triplet emission energies for each type of polymer. Yet, there are clear indications that long-range corrected TDDFT has the potential to predict the triplet emission energies as well as the localization behavior more accurate than conventional local or semi-local functionals.
Molecular dynamics (MD) simulations are used to investigate $^1$H nuclear magnetic resonance (NMR) relaxation and diffusion of bulk $n$-C$_5$H$_{12}$ to $n$-C$_{17}$H$_{36}$ hydrocarbons and bulk water. The MD simulations of the $^1$H NMR relaxation times $T_{1,2}$ in the fast motion regime where $T_1 = T_2$ agree with measured (de-oxygenated) $T_2$ data at ambient conditions, without any adjustable parameters in the interpretation of the simulation data. Likewise, the translational diffusion $D_T$ coefficients calculated using simulation configurations are well-correlated with measured diffusion data at ambient conditions. The agreement between the predicted and experimentally measured NMR relaxation times and diffusion coefficient also validate the forcefields used in the simulation. The molecular simulations naturally separate intramolecular from intermolecular dipole-dipole interactions helping bring new insight into the two NMR relaxation mechanisms as a function of molecular chain-length (i.e. carbon number). Comparison of the MD simulation results of the two relaxation mechanisms with traditional hard-sphere models used in interpreting NMR data reveals important limitations in the latter. With increasing chain length, there is substantial deviation in the molecular size inferred on the basis of the radius of gyration from simulation and the fitted hard-sphere radii required to rationalize the relaxation times. This deviation is characteristic of the local nature of the NMR measurement, one that is well-captured by molecular simulations.
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