Monte Carlo Trajectories Research Articles

A Mode Evolution Metric to Extract Reaction Coordinates for Biomolecular Conformational Transitions.

The complex, multidimensional energy landscape of biomolecules makes the extraction of suitable, nonintuitive collective variables (CVs) that describe their conformational transitions challenging. At present, dimensionality reduction approaches and machine learning (ML) schemes are employed to obtain CVs from molecular dynamics (MD)/Monte Carlo (MC) trajectories or structural databanks for biomolecules. However, minimum sampling conditions to generate reliable CVs that accurately describe the underlying energy landscape remain unclear. Here, we address this issue by developing a Mode evolution Metric (MeM) to extract CVs that can pinpoint new states and describe local transitions in the vicinity of a reference minimum from nonequilibrated MD/MC trajectories. We present a general mathematical formulation of MeM for both statistical dimensionality reduction and machine learning approaches. Application of MeM to MC trajectories of model potential energy landscapes and MD trajectories of solvated alanine dipeptide reveals that the principal components which locate new states in the vicinity of a reference minimum emerge well before the trajectories locally equilibrate between the associated states. Finally, we demonstrate a possible application of MeM in designing efficient biased sampling schemes to construct accurate energy landscape slices that link transitions between states. MeM can help speed up the search for new minima around a biomolecular conformational state and enable the accurate estimation of thermodynamics for states lying on the energy landscape and the description of associated transitions.

Revised Centrality Measures Tell a Robust Story of Ion Conduction in Solids.

The three most commonly used centrality measures in network theory have been adapted to consider ion conduction time rather than the number of steps. Flow-IN centrality highlights sites with the largest flow of ions from the nearest neighbor sites. Return-flow centrality highlights sites with a fast rate of first returns for the conducting ion. Flow-through centrality highlights which sites support significant flow of conducting ions and appears more robust to removal of the most central vertices. Exploring these centrality measures with the sample system of proton conduction in yttrium doped barium zirconate shows flow-through centrality to provide a robust picture with high contrast between sites involved in the most probable long-range periodic conduction paths and kinetic Monte Carlo trajectories versus sites rarely visited. The flow-through centrality, including all paths further highlights that when the most central proton site is filled, the remaining highest flow-through centrality sites are nearby, corroborating earlier studies suggesting proton pair motion. Finally, while both return-flow and flow-through centrality measure images deteriorate with noise, image restoration is possible when a detailed balance is used to calculate the smaller rate constant in a forward/backward pair.

Dynamical triplet unraveling : A quantum Monte Carlo algorithm for reversible dynamics

We introduce a quantum Monte Carlo method to simulate the reversible dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator which, as opposed to most quantum Monte Carlo methods, makes it possible to access the dynamics at longer times. The Monte Carlo trajectories are realised through a piece-wise stochastic-deterministic reversible evolution where free dynamics is interspersed with two-process quantum jumps. The dynamical sign problem is bypassed via the so-called deadweight approximation, which stabilizes the many-body phases at longer times. We benchmark our method by simulating spin excitation propagation in the XXZ model and dynamical confinement in the quantum Ising chain, and show how to extract dynamical information from the Laplace representation.

Global diffusion of hydrogen molecules in the heterogeneous structure of polymer electrolytes for fuel cells: Dynamic Monte Carlo combined with molecular dynamics calculations.

Using our recently developed dynamic Monte Carlo (MC) method [Nagai et al., J. Chem. Phys. 156, 154506 (2022)], we investigated the global diffusion of hydrogen molecules over structural heterogeneities of polymer electrolyte membranes in fuel cells. The three-dimensional position-dependent free energies and the diffusion constants of the hydrogen molecules, required by the present dynamic MC calculations, were taken from our previous study [Nagai et al., J. Chem. Phys. 156, 044507 (2022)] and newly evaluated in this work, respectively. The calculations enabled evaluating the hydrogen dynamics over long-time scales, including global diffusion constants. Based on the calculated global diffusion constants and free energies, the permeability of hydrogen molecules was estimated via the solubility-diffusion model. The estimated values were in good agreement with the reported experimental data, thus validating the present methodology. The analysis of the Monte Carlo trajectories indicated that the main permeation paths are located in the polymer and interfacial phases, although the water phase may make a non-negligible contribution to mass transport.

Dynamic Monte Carlo calculation generating particle trajectories that satisfy the diffusion equation for heterogeneous systems with a position-dependent diffusion coefficient and free energy.

A series of new Monte Carlo (MC) transition probabilities was investigated that could produce molecular trajectories statistically satisfying the diffusion equation with a position-dependent diffusion coefficient and potential energy. The MC trajectories were compared with the numerical solution of the diffusion equation by calculating the time evolution of the probability distribution and the mean first passage time, which exhibited excellent agreement. The method is powerful when investigating, for example, the long-distance and long-time global transportation of a molecule in heterogeneous systems by coarse-graining them into one-particle diffusive molecular motion with a position-dependent diffusion coefficient and free energy. The method can also be applied to many-particle dynamics.

A systematic analysis of phase stability in refractory high entropy alloys utilizing linear and non-linear cluster expansion models

The phase segregation behavior of three key refractory high entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr) is studied using first-principles calculations. Several linear and non-linear methods are utilized to generate surrogate models for three key refractory high entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr) via the cluster expansion formalism. The characteristics of each of the generated models is explored and the regression methods are compared. Finally, these surrogate models are utilized to generate Monte Carlo trajectories in order to explore the link between phase segregation and previously documented mechanical degradation in these materials.Phase segregation and intermetallic phases documented in the experimental literature are reproduced in all three high entropy alloys. NbTiVZr forms vanadium and zirconium clusters at lower temperatures (250 K) which disperse into the single-phase matrix by 1000 K. HfNbTaTiZr forms HfZr, NbTa, and possibly TiZr intermetallic phases at lower temperatures (250 K). Unlike the other HEAs studied here, HfNbTaTiZr does not lose short-range ordering in the solid state until around 3500 K, which is above its melting temperature. AlHfNbTaTiZr forms NbTa and AlHfTiZr phases at lower temperatures (250 K), which are not observed at higher temperatures (1000 K).

Identifying ‘win-win-win’ futures from inequitable value chain trade-offs: A system dynamics approach

ContextThere is growing recognition that food systems must adapt to become more sustainable and equitable. Consequently, in developing country contexts, there is increasing momentum away from traditional producer-facing value chain upgrades towards efforts to increase both the availability and affordability of nutritious foods at the consumer level. However, such goals must navigate the inherent complexities of agricultural value chains, which involve multiple interactions, feedbacks and unintended consequences, including important but often surprising trade-offs between producers and consumers. Objective and methodsBased around the 'Loop' horticultural aggregation scheme of Digital Green in Bihar, India, we develop a system dynamics modelling framework to survey the value chain trade-offs emerging from upgrades that aim to improve the availability of fruits and vegetables in small retail-oriented markets. We model the processes of horticultural production, aggregation, marketing, and retailing – searching for futures that are ‘win-win-win’ for: (i) the availability of fruits and vegetables in small retail markets, (ii) the profits of farmers participating in aggregation, and (iii) the sustainability of the initial scheme for Digital Green as an organisation. We simulate two internal upgrades to aggregation and two upgrades to the wider enabling environment through a series of 5000 Monte Carlo trajectories – designed to explore the plausible future dynamics of the three outcome dimensions relative to the baseline. ResultsWe find that ‘win-win-win’ futures cannot be achieved by internal changes to the aggregation scheme alone, emerging under a narrow range of scenarios that boost supplies to the small retail market whilst simultaneously supporting the financial takeaways of farmers. In contrast, undesirable producer versus consumer trade-offs emerge as unintended consequences of scaling-up aggregation and the introduction of market-based cold storage. SignificanceThis approach furthers ongoing efforts to capture complex value chain processes, outcomes and upgrades within system dynamics modelling frameworks, before scanning the horizon of plausible external scenarios, internal dynamics and unintended trade-offs to identify ‘win-win-win’ futures for all.

Parallel simulation of drift–diffusion–recombination by cellular automata and global random walk algorithm

We suggest in this paper a parallel implementation of cellular automation and global random walk algorithms for solving drift–diffusion–recombination problems which in contrast to the classical random walk on spheres (RWS) methods calculate the solution in any desired family of m prescribed points. The method uses only N trajectories in contrast to mN trajectories in the conventional RWS algorithm. The idea is based on the adjoint symmetry property of the Green function and a double randomization approach. The synchronous multi-particle cellular automaton model of drift–diffusion–recombination is based on known cellular automata. The global RWS and cellular automaton models are tested against the exact solutions of the equation. The accuracy and computer time of both algorithms is analyzed. Parallel codes for the Monte Carlo and cellular automaton algorithms are implemented. The domain decomposition method is employed for the cellular automaton parallel implementation. The global random walk algorithm is parallelized by the Monte Carlo trajectories distribution among the cluster cores. The efficiency of the parallel codes is studied.

A Systematic Analysis of Phase Stability in Refractory High Entropy Alloys Utilizing Linear and Non-Linear Cluster Expansion Models

The phase segregation behavior of three key refractory high entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr) is studied using first-principles calculations. Several linear and non-linear methods are utilized to generate surrogate models for three key refractory high entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr) via the cluster expansion formalism. The characteristics of each of the generated models is explored and the regression methods are compared. Finally, these surrogate models are utilized to generate Monte Carlo trajectories in order to explore the link between phase segregation and previously documented mechanical degradation in these materials.Phase segregation and intermetallic phases documented in the experimental literature are reproduced in all three high entropy alloys. NbTiVZr forms vanadium and zirconium clusters at lower temperatures (250 K) which disperse into the single-phase matrix by 1000 K. HfNbTaTiZr forms HfZr, NbTa, and possibly TiZr intermetallic phases at lower temperatures (250 K). Unlike the other HEAs studied here, HfNbTaTiZr does not lose short-range ordering in the solid state until around 3500 K, which is above its melting temperature. AlHfNbTaTiZr forms NbTa and AlHfTiZr phases at lower temperatures (250 K), which are not observed at higher temperatures (1000 K).

On the possibility of track length based Monte-Carlo algorithms for stationary drift-diffusion systems with sources and sinks

The problem of constructing Monte-Carlo solutions of drift-diffusion systems corresponding to Fokker–Planck equations with sources and sinks is revisited. Firstly, a compact formalism is introduced for the specific problem of stationary solutions. This leads to identification of the dwell time as the key quantity to characterize the system and to obtain a proper normalization for statistical analysis of numerical results. Secondly, the question of appropriate track length estimators for drift-diffusion systems is discussed for a 1D model system. It is found that a simple track length estimator can be given only for pure drift motion without diffusion. The stochastic nature of the diffusive part cannot be appropriately described by the path length of simulation particles. Further analysis of the usual situation with inhomogeneous drift and diffusion coefficients leads to an error estimate based on particle trajectories. The result for limits in grid cell size and time step used for the construction of Monte-Carlo trajectories resembles the Courant-Friedrichs-Lewy and von Neumann conditions for explicit methods.

Particle-Based Monte-Carlo Simulations of Steady-State Mass Transport at Intermediate Péclet Numbers

Abstract Conventional approaches for simulating steady-state distributions of dilute particles under diffusive and advective transport involve solving the diffusion and advection equations in at least two dimensions. Here, we present an alternative computational strategy by combining a particle-based rather than a field-based approach with the initialisation of particles in proportion to their flux. This method allows accurate prediction of the steady state and is applicable even at intermediate and high Péclet numbers ( P e > 1 ) $ (Pe \gt 1)$ where traditional particle-based Monte-Carlo methods starting from randomly initialised particle distributions fail. We demonstrate that generating a flux of particles according to a predetermined density and velocity distribution at a single fixed time and initial location allows for accurate simulation of mass transport under flow. Specifically, upon initialisation in proportion to their flux, these particles are propagated individually and detected by summing up their Monte-Carlo trajectories in predefined detection regions. We demonstrate quantitative agreement of the predicted concentration profiles with the results of experiments performed with fluorescent particles in microfluidic channels under continuous flow. This approach is computationally advantageous and readily allows non-trivial initial distributions to be considered. In particular, this method is highly suitable for simulating advective and diffusive transport in microfluidic devices, for instance in the context of diffusive sizing.

Adaptive low-rank approximation and denoised Monte Carlo approach for high-dimensional Lindblad equations

We present a twofold contribution to the numerical simulation of Lindblad equations. First, an adaptive numerical approach to approximate Lindblad equations using low-rank dynamics is described: a deterministic low-rank approximation of the density operator is computed, and its rank is adjusted dynamically, using an on-the-fly estimator of the error committed when reducing the dimension. On the other hand, when the intrinsic dimension of the Lindblad equation is too high to allow for such a deterministic approximation, we combine classical ensemble averages of quantum Monte Carlo trajectories and a denoising technique. Specifically, a variance reduction method based upon the consideration of a low-rank dynamics as a control variate is developed. Numerical tests for quantum collapse and revivals show the efficiency of each approach, along with the complementarity of the two approaches.

New Monte Carlo Based Technique To Study DNA-Ligand Interactions.

We present a new all-atom Monte Carlo technique capable of performing quick and accurate DNA-ligand conformational sampling. In particular, and using the PELE software as a frame, we have introduced an additional force field, an implicit solvent, and an anisotropic network model to effectively map the DNA energy landscape. With these additions, we successfully generated DNA conformations for a test set composed of six DNA fragments of A-DNA and B-DNA. Moreover, trajectories generated for cisplatin and its hydrolysis products identified the best interacting compound and binding site, producing analogous results to microsecond molecular dynamics simulations. Furthermore, a combination of the Monte Carlo trajectories with Markov State Models produced noncovalent binding free energies in good agreement with the published molecular dynamics results, at a significantly lower computational cost. Overall our approach will allow a quick but accurate sampling of DNA-ligand interactions.

Coarse‐Grained and Atomistic Simulations for the G = 4 PAMAM‐EDA Dendrimer

Extensive fully‐atomistic molecular dynamics simulations have been performed for the G = 4 generation of the dendrimer PAMAM‐EDA in water, with fully protonated and non‐protonated amine groups. Some parameters from these results have been incorporated into a coarse‐grained model suitable for Monte Carlo simulations. Satisfactory agreement is found between the dendrimer density profiles obtained from the Monte Carlo and the molecular dynamics simulations, both for the protonated and neutral molecules. The Monte Carlo and molecular dynamics trajectories have also been employed to calculate binary interactions between pairs of dendrimers. The interactions between G = 4 PAMAM‐EDA dendrimers can be satisfactorily described by a theoretically proposed Gaussian potential.

Centrality measures highlight proton traps and access points to proton highways in kinetic Monte Carlo trajectories.

A centrality measure based on the time of first returns rather than the number of steps is developed and applied to finding proton traps and access points to proton highways in the doped perovskite oxides: AZr(0.875)D(0.125)O3, where A is Ba or Sr and the dopant D is Y or Al. The high centrality region near the dopant is wider in the SrZrO3 systems than the BaZrO3 systems. In the aluminum-doped systems, a region of intermediate centrality (secondary region) is found in a plane away from the dopant. Kinetic Monte Carlo (kMC) trajectories show that this secondary region is an entry to fast conduction planes in the aluminum-doped systems in contrast to the highest centrality area near the dopant trap. The yttrium-doped systems do not show this secondary region because the fast conduction routes are in the same plane as the dopant and hence already in the high centrality trapped area. This centrality measure complements kMC by highlighting key areas in trajectories. The limiting activation barriers found via kMC are in very good agreement with experiments and related to the barriers to escape dopant traps.

Accelerating Systems Biology Computation: Enhanced Sampling of Spatially Realistic Stochastic Models using the Weighted Ensemble Approach

We apply the “weighted ensemble” (WE) simulation strategy, previously employed in the context of molecular dynamics and spatially homogeneous chemical kinetics simulations, to a number of three dimensional spatially resolved stochastic systems-biology models. WE is relatively easy to implement, does not require extensive hand-tuning of parameters, does not depend on the details of the underlying simulation algorithm, and can facilitate the unbiased sampling of extremely rare events.We study three systems of varying complexity and structure: a toy model in an artificial geometry with ∼10ˆ3 diffusing molecules, a spatially realistic cellular model with ∼10ˆ6 molecules, and a spatially realistic neuromuscular junction model with time-varying rate “constants” containing ∼10ˆ6 molecules. We are able to speed up the sampling of key events by many orders of magnitude and obtain unbiased estimates of event probabilities. Data is obtained using the publicly available “WESTPA” implementation of WE, which orchestrates MCell kinetic Monte Carlo trajectories of the various models.

TRAVIS - a free analyzer and visualizer for Monte Carlo and molecular dynamics trajectories

We present TRAVIS (TRajectory Analyzer and VISualizer), a free program package for analyzing and visualizing Monte Carlo and molecular dynamics trajectories [1]. The aim of TRAVIS is to collect as many analyses as possible in one program, creating a powerful tool and making it unnecessary to use many different programs for evaluating simulations. This should greatly rationalize and simplify the workflow of analyzing trajectories. TRAVIS is written in C++, open-source freeware and licensed under the terms of the GNU General Public License (GPLv3). It is easy to install (platform independent, no external libraries) and easy to use. On this poster, we present some of the algorithms that are implemented in TRAVIS - many of them widely known for a long time, but some of them also to appear in literature for the first time. All shown analyses only require a standard MD trajectory as input data. Figure 1

TRAVIS - A Free Analyzer and Visualizer for Monte Carlo and Molecular Dynamics Trajectories

We present TRAVIS ("TRajectory Analyzer and VISualizer"), a free program package for analyzing and visualizing Monte Carlo and molecular dynamics trajectories. The aim of TRAVIS is to collect as many analyses as possible in one program, creating a powerful tool and making it unnecessary to use many different programs for evaluating simulations. This should greatly rationalize and simplify the workflow of analyzing trajectories. TRAVIS is written in C++, open-source freeware and licensed under the terms of the GNU General Public License (GPLv3). It is easy to install (platform independent, no external libraries) and easy to use. In this article, we present some of the algorithms that are implemented in TRAVIS - many of them widely known for a long time, but some of them also to appear in literature for the first time. All shown analyses only require a standard MD trajectory as input data.

Stochastic simulation and analysis of biomolecular reaction networks

BackgroundIn recent years, several stochastic simulation algorithms have been developed to generate Monte Carlo trajectories that describe the time evolution of the behavior of biomolecular reaction networks. However, the effects of various stochastic simulation and data analysis conditions on the observed dynamics of complex biomolecular reaction networks have not recieved much attention. In order to investigate these issues, we employed a a software package developed in out group, called Biomolecular Network Simulator (BNS), to simulate and analyze the behavior of such systems. The behavior of a hypothetical two gene in vitro transcription-translation reaction network is investigated using the Gillespie exact stochastic algorithm to illustrate some of the factors that influence the analysis and interpretation of these data.ResultsSpecific issues affecting the analysis and interpretation of simulation data are investigated, including: (1) the effect of time interval on data presentation and time-weighted averaging of molecule numbers, (2) effect of time averaging interval on reaction rate analysis, (3) effect of number of simulations on precision of model predictions, and (4) implications of stochastic simulations on optimization procedures.ConclusionThe two main factors affecting the analysis of stochastic simulations are: (1) the selection of time intervals to compute or average state variables and (2) the number of simulations generated to evaluate the system behavior.

Real-Time Synchronization Feedbacks for Single-Atom Frequency Standards

Simple feedback loops, inspired from extremum seeking, are proposed to lock a probe frequency to the transition frequency of a single quantum system following quantum Monte-Carlo trajectories. Two specific quantum systems are addressed: a 2-level one, and a 3-level one that appears in coherence population trapping and optical pumping. For both systems, the feedback algorithm is shown to be convergent in the following sense: the probe frequency converges on average towards the system-transition one and its standard deviation can be made arbitrarily small. Closed-loop simulations illustrate robustness versus jump-detection efficiency and modeling errors.