MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations

Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long-timescale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large lengthscales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time- and lengthscales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported

Probability distributions of molecular observables computed from Markov models. II: Uncertainties in observables and their time-evolution

Discrete-state Markov (or master equation) models provide a useful simplified representation for characterizing the long-time statistical evolution of biomolecules in a manner that allows direct comparison with experiments as well as the elucidation of mechanistic pathways for an inherently stochastic process. A vital part of meaningful comparison with experiment is the characterization of the statistical uncertainty in the predicted experimental measurement, which may take the form of an equilibrium measurement of some spectroscopic signal, the time-evolution of this signal following a perturbation, or the observation of some statistic (such as the correlation function) of the equilibrium dynamics of a single molecule. Without meaningful error bars (which arise from both approximation and statistical error), there is no way to determine whether the deviations between model and experiment are statistically meaningful. Previous work has demonstrated that a Bayesian method that enforces microscopic reversibility can be used to characterize the statistical component of correlated uncertainties in state-to-state transition probabilities (and functions thereof) for a model inferred from molecular simulation data. Here, we extend this approach to include the uncertainty in observables that are functions of molecular conformation (such as surrogate spectroscopic signals) characterizing each state, permitting the full statistical uncertainty in computed spectroscopic experiments to be assessed. We test the approach in a simple model system to demonstrate that the computed uncertainties provide a useful indicator of statistical variation, and then apply it to the computation of the fluorescence autocorrelation function measured for a dye-labeled peptide previously studied by both experiment and simulation

Markov state models of biomolecular conformational dynamics

It has recently become practical to construct Markov state models (MSMs) that reproduce the long-time statistical conformational dynamics of biomolecules using data from molecular dynamics simulations. MSMs can predict both stationary and kinetic quantities on long timescales (e.g. milliseconds) using a set of atomistic molecular dynamics simulations that are individually much shorter, thus addressing the well-known sampling problem in molecular dynamics simulation. In addition to providing predictive quantitative models, MSMs greatly facilitate both the extraction of insight into biomolecular mechanism (such as folding and functional dynamics) and quantitative comparison with single-molecule and ensemble kinetics experiments. A variety of methodological advances and software packages now bring the construction of these models closer to routine practice. Here, we review recent progress in this field, considering theoretical and methodological advances, new software tools, and recent applications of these approaches in several domains of biochemistry and biophysics, commenting on remaining challenges

Simulation tools for particle-based reaction-diffusion dynamics in continuous space

Particle-based reaction-diffusion algorithms facilitate the modeling of the diffusional motion of individual molecules and the reactions between them in cellular environments. A physically realistic model, depending on the system at hand and the questions asked, would require different levels of modeling detail such as particle diffusion, geometrical confinement, particle volume exclusion or particle-particle interaction potentials. Higher levels of detail usually correspond to increased number of parameters and higher computational cost. Certain systems however, require these investments to be modeled adequately. Here we present a review on the current field of particle-based reaction-diffusion software packages operating on continuous space. Four nested levels of modeling detail are identified that capture incrementing amount of detail. Their applicability to different biological questions is discussed, arching from straight diffusion simulations to sophisticated and expensive models that bridge towards coarse grained molecular dynamics

Cyclization dynamics of finite-length collapsed self-avoiding polymers

We study the end-point cyclization of ideal and interacting polymers as a function of chain length N. For the cyclization time �cyc of ideal chains we recover the known scaling �cyc � N2 for different backbone models, for a self-avoiding slightly collapsed chain we obtain from Langevin simulations and scaling theory a modified scaling �cyc � N5=3. By extracting the memory kernel that governs the non-Markovian end-point kinetics, we demonstrate that the dynamics of a finite-length collapsed chain is dominated by the crossover between swollen and collapsed behavior

Effects of confinement on pattern formation in two dimensional systems with competing interactions

Template-assisted pattern formation in monolayers of particles with competing short-range attraction and long-range repulsion interactions (SALR) is studied by Monte Carlo simulations in a simple generic model [N. G. Almarza et al., J. Chem. Phys., 2014, 140, 164708]. We focus on densities corresponding to formation of parallel stripes of particles and on monolayers laterally confined between straight parallel walls. We analyze both the morphology of the developed structures and the thermodynamic functions for broad ranges of temperature T and the separation L between the walls. At low temperature stripes parallel to the boundaries appear, with some corrugation when the distance between the walls does not match the bulk periodicity of the striped structure. The stripes integrity, however, is rarely broken for any L. This structural order is lost at T = T(L) depending on L according to a Kelvin-like equation. Above the Kelvin temperature T(L) many topological defects such as breaking or branching of the stripes appear, but a certain anisotropy in the orientation of the stripes persists. Finally, at high temperature and away from the walls, the system behaves as an isotropic fluid of elongated clusters of various lengths and with various numbers of branches. For L optimal for the stripe pattern the heat capacity as a function of temperature takes the maximum at T = T(L).Peer Reviewe

ReaDDyMM: fast interacting-particle reaction-diffusion simulations using graphical processing units

AbstractReaDDy is a modular particle simulation package combining off-lattice reaction kinetics with arbitrary particle interaction forces. Here we present a graphical processing unit implementation of ReaDDy that employs the fast multiplatform molecular dynamics package OpenMM. A speedup of up to two orders of magnitude is demonstrated, giving us access to timescales of multiple seconds on single graphical processing units. This opens up the possibility of simulating cellular signal transduction events while resolving all protein copies