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A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length t. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems. [ABSTRACT FROM AUTHOR]

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green's function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as "black-box" simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates.We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D. [ABSTRACT FROM AUTHOR]

In the quest towards coarse-grained potentials and new water models, we present an extension of the force matching technique to parameterize an all-atom force field for rigid water. The methodology presented here allows to improve the matching procedure by first optimizing the weighting exponents present in the objective function. A new gauge for unambiguously evaluating the quality of the fit has been introduced; it is based on the root mean square difference of the distributions of target properties between reference data and fitted potentials. Four rigid water models have been parameterized; the matching procedure has been used to assess the role of the ghost atom in TIP4P-like models and of electrostatic damping. In the former case, burying the negative charge inside the molecule allows to fit better the torques. In the latter, since short-range interactions are damped, a better fit of the forces is obtained. Overall, the best performing model is the one with a ghost atom and with electrostatic damping. The approach shown in this paper is of general validity and could be applied to any matching algorithm and to any level of coarse graining, also for non-rigid molecules. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Random packing of spheres inside fractal collectors of dimension 2 < d < 3 is studied numerically using Random Sequential Adsorption (RSA) algorithm. The paper focuses mainly on the measurement of random packing saturation limit. Additionally, scaling properties of density autocorrelations in the obtained packing are analyzed. The RSA kinetics coefficients are also measured. Obtained results allow to test phenomenological relation between random packing saturation density and collector dimension. Additionally, performed simulations together with previously obtained results confirm that, in general, the known dimensional relations are obeyed by systems having non-integer dimension, at least for d < 3. [ABSTRACT FROM AUTHOR]

Accurate modelling and simulation of dynamic cellular events require two main ingredients: an adequate description of key chemical reactions and simulation of such chemical events in reasonable time spans. Quite logically, posing the right model is a crucial step for any endeavour in Computational Biology. However, more often than not, it is the associated computational costs which actually limit our capabilities of representing complex cellular behaviour. In this paper, we propose a methodology aimed at representing chains of chemical reactions by much simpler, reduced models. The abridgement is achieved by generation of model-specific delay distribution functions, consecutively fed to a delay stochastic simulation algorithm. We show how such delay distributions can be analytically described whenever the system is solely composed of consecutive first-order reactions, with or without additional 'backward' bypass reactions, yielding an exact reduction. For models including other types of monomolecular reactions (constitutive synthesis, degradation, or 'forward' bypass reactions), we discuss why one must adopt a numerical approach for its accurate stochastic representation, and propose two alternatives for this. In these cases, the accuracy depends on the respective numerical sample size. Our model reduction methodology yields significantly lower computational costs while retaining accuracy. Quite naturally, computational costs increase alongside network size and separation of time scales. Thus, we expect our model reduction methodologies to significantly decrease computational costs in these instances. We anticipate the use of delays in model reduction will greatly alleviate some of the current restrictions in simulating large sets of chemical reactions, largely applicable in pharmaceutical and biological research. [ABSTRACT FROM AUTHOR]

The stochastic integral ensuring the Newton-Leibnitz chain rule is essential in stochastic energetics. Marcus canonical integral has this property and can be understood as the Wong-Zakai type smoothing limit when the driving process is non-Gaussian. However, this important concept seems not well-known for physicists. In this paper, we discuss Marcus integral for non-Gaussian processes and its computation in the context of stochastic energetics. We give a comprehensive introduction to Marcus integral and compare three equivalent definitions in the literature. We introduce the exact pathwise simulation algorithm and give the error analysis. We show how to compute the thermodynamic quantities based on the pathwise simulation algorithm. We highlight the information hidden in the Marcus mapping, which plays the key role in determining thermodynamic quantities. We further propose the tau-leaping algorithm, which advance the process with deterministic time steps when tau-leaping condition is satisfied. The numerical experiments and its efficiency analysis show that it is very promising. [ABSTRACT FROM AUTHOR]

In this paper, we describe the way to set up the floppy-box Monte Carlo (FBMC) method [L. Filion, M. Marechal, B. van Oorschot, D. Pelt, F. Smallenburg, and M. Dijkstra, Phys. Rev. Lett. 103, 188302 (2009)] to predict crystal-structure candidates for colloidal particles. The algorithm is explained in detail to ensure that it can be straightforwardly implemented on the basis of this text. The handling of hard-particle interactions in the FBMC algorithm is given special attention, as (soft) short-range and semi-long-range interactions can be treated in an analogous way. We also discuss two types of algorithms for checking for overlaps between polyhedra, the method of separating axes and a triangular-tessellation based technique. These can be combined with the FBMC method to enable crystal-structure prediction for systems composed of highly shape-anisotropic particles. Moreover, we present the results for the dense crystal structures predicted using the FBMC method for 159 (non)convex faceted particles, on which the findings in [J. de Graaf, R. van Roij, and M. Dijkstra, Phys. Rev. Lett. 107, 155501 (2011)] were based. Finally, we comment on the process of crystal-structure prediction itself and the choices that can be made in these simulations. [ABSTRACT FROM AUTHOR]

The spatial direct method with gradient-based diffusion is an accelerated stochastic reaction-diffusion simulation algorithm that treats diffusive transfers between neighboring subvolumes based on concentration gradients. This recent method achieved a marked improvement in simulation speed and reduction in the number of time-steps required to complete a simulation run, compared with the exact algorithm, by sampling only the net diffusion events, instead of sampling all diffusion events. Although the spatial direct method with gradient-based diffusion gives accurate means of simulation ensembles, its gradient-based diffusion strategy results in reduced fluctuations in populations of diffusive species. In this paper, we present a new improved algorithm that is able to anticipate all possible microscopic fluctuations due to diffusive transfers in the system and incorporate this information to retain the same degree of fluctuations in populations of diffusing species as the exact algorithm. The new algorithm also provides a capability to set the desired level of fluctuation per diffusing species, which facilitates adjusting the balance between the degree of exactness in simulation results and the simulation speed. We present numerical results that illustrate the recovery of fluctuations together with the accuracy and efficiency of the new algorithm. [ABSTRACT FROM AUTHOR]

In biochemical reaction systems dominated by delays, the simulation speed of the stochastic simulation algorithm depends on the size of the wait queue. As a result, it is important to control the size of the wait queue to improve the efficiency of the simulation. An improved accelerated delay stochastic simulation algorithm for biochemical reaction systems with delays, termed the improved delay-leaping algorithm, is proposed in this paper. The update method for the wait queue is effective in reducing the size of the queue as well as shortening the storage and access time, thereby accelerating the simulation speed. Numerical simulation on two examples indicates that this method not only obtains a more significant efficiency compared with the existing methods, but also can be widely applied in biochemical reaction systems with delays. [ABSTRACT FROM AUTHOR]

In recent years, computer simulations have become increasingly useful when trying to understand the complex dynamics of biochemical networks, particularly in stochastic systems. In such situations stochastic simulation is vital in gaining an understanding of the inherent stochasticity present, as these models are rarely analytically tractable. However, a stochastic approach can be computationally prohibitive for many models. A number of approximations have been proposed that aim to speed up stochastic simulations. However, the majority of these approaches are fundamentally serial in terms of central processing unit (CPU) usage. In this paper, we propose a novel simulation algorithm that utilises the potential of multi-core machines. This algorithm partitions the model into smaller sub-models. These sub-models are then simulated, in parallel, on separate CPUs. We demonstrate that this method is accurate and can speed-up the simulation by a factor proportional to the number of processors available. [ABSTRACT FROM AUTHOR]

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems. [ABSTRACT FROM AUTHOR]

The hydrodynamic interaction is an essential effect to consider in Brownian dynamics simulations of polymer and nanoparticle dilute solutions. Several mathematical approaches can be used to build Brownian dynamics algorithms with hydrodynamic interaction, the most common of them being the exact but time demanding Cholesky decomposition and the Chebyshev polynomial expansion. Recently, Geyer and Winter [J. Chem. Phys. 130, 1149051 (2009)] have proposed a new approximation to treat the hydrodynamic interaction that seems quite efficient and is increasingly used. So far, a systematic comparison among those approaches has not been clearly made. In this paper, several features and the efficiency of typical implementations of those approaches are evaluated by using bead-and-spring chain models. The different sensitivity to the bead overlap detected for the different implementations may be of interest to select the suitable algorithm for a given simulation. [ABSTRACT FROM AUTHOR]

This paper examines the benefits of Michaelis-Menten model reduction techniques in stochastic tau-leaping simulations. Results show that although the conditions for the validity of the reductions for tau-leaping remain the same as those for the stochastic simulation algorithm (SSA), the reductions result in a substantial speed-up for tau-leaping under a different range of conditions than they do for SSA. The reason of this discrepancy is that the time steps for SSA and for tau-leaping are determined by different properties of system dynamics. [ABSTRACT FROM AUTHOR]

The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit τ-leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, τ. This method is acceptable providing the leap condition, that no propensity function changes 'significantly' during any time-step, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next time-step. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical examples to demonstrate the effectiveness of our new method. [ABSTRACT FROM AUTHOR]

Typical multiscale biochemical models contain fast-scale and slow-scale reactions, where 'fast' reactions fire much more frequently than 'slow' ones. This feature often causes stiffness in discrete stochastic simulation methods such as Gillespie's algorithm and the Tau-Leaping method leading to inefficient simulation. This paper proposes a new strategy to automatically detect stiffness and identify species that cause stiffness for the Tau-Leaping method, as well as two stiffness reduction methods. Numerical results on a stiff decaying dimerization model and a heat shock protein regulation model demonstrate the efficiency and accuracy of the proposed methods for multiscale biochemical systems. [ABSTRACT FROM AUTHOR]

The accurate prediction of absolute protein-ligand binding free energies is one of the grand challenge problems of computational science. Binding free energy measures the strength of binding between a ligand and a protein, and an algorithm that would allow its accurate prediction would be a powerful tool for rational drug design. Here we present the development of a new method that allows for the absolute binding free energy of a protein-ligand complex to be calculated from first principles, using a single simulation. Our method involves the use of a novel reaction coordinate that swaps a ligand bound to a protein with an equivalent volume of bulk water. This water-swap reaction coordinate is built using an identity constraint, which identifies a cluster of water molecules from bulk water that occupies the same volume as the ligand in the protein active site. A dual topology algorithm is then used to swap the ligand from the active site with the identified water cluster from bulk water. The free energy is then calculated using replica exchange thermodynamic integration. This returns the free energy change of simultaneously transferring the ligand to bulk water, as an equivalent volume of bulk water is transferred back to the protein active site. This, directly, is the absolute binding free energy. It should be noted that while this reaction coordinate models the binding process directly, an accurate force field and sufficient sampling are still required to allow for the binding free energy to be predicted correctly. In this paper we present the details and development of this method, and demonstrate how the potential of mean force along the water-swap coordinate can be improved by calibrating the soft-core Coulomb and Lennard-Jones parameters used for the dual topology calculation. The optimal parameters were applied to calculations of protein-ligand binding free energies of a neuraminidase inhibitor (oseltamivir), with these results compared to experiment. These results demonstrate that the water-swap coordinate provides a viable and potentially powerful new route for the prediction of protein-ligand binding free energies. [ABSTRACT FROM AUTHOR]

We propose the thermodynamic integration along a spatial reaction coordinate using the molecular dynamics simulation combined with the three-dimensional reference interaction site model theory. This method provides a free energy calculation in solution along the reaction coordinate defined by the Cartesian coordinates of the solute atoms. The proposed method is based on the blue moon algorithm which can, in principle, handle any reaction coordinate as far as it is defined by the solute atom positions. In this article, we apply the present method to the complex formation process of the crown ether 18-Crown-6 (18C6) with the potassium ion in an aqueous solution. The separation between the geometric centers of these two molecules is taken to be the reaction coordinate for this system. The potential of mean force (PMF) becomes the maximum at the separation between the molecular centers being ∼4 Å, which can be identified as the free energy barrier in the process of the molecular recognition. In a separation further than the free energy barrier, the PMF is slightly reduced to exhibit a plateau. In the region closer than the free energy barrier, approach of the potassium ion to the center of 18C6 also decreases the PMF. When the potassium ion is accommodated at the center of 18C6, the free energy is lower by -5.7 ± 0.7 kcal/mol than that at the above mentioned plateau or converged state. By comparing the results with those from the free energy calculation along the coupling parameters obtained in our previous paper [T. Miyata, Y. Ikuta, and F. Hirata, J. Chem. Phys. 133, 044114 (2010)], it is found that the effective interaction in water between 18C6 and the potassium ion vanishes beyond the molecular-center-separation of 10 Å. Furthermore, the conformation of 18C6 is found to be significantly changed depending upon the 18C6-K+ distance. A proper conformational sampling and an accurate solvent treatment are crucial for realizing the accurate PMF, and we believe that the proposed method is useful to evaluate the PMF in a solution. A discussion upon the PMF in terms of the three-dimensional distribution function for the solvent is also presented. [ABSTRACT FROM AUTHOR]

The use of discrete variable representation (DVR) basis sets within ab initio molecular dynamics calculations allows the latter to be performed with converged energies and, more importantly, converged forces. In this paper, we show how to carry out ab initio molecular dynamics calculations in the isothermal-isobaric ensemble with fully flexible simulation boxes within the DVR basis set framework. In particular, we derive the appropriate DVR based expression for the pressure tensor when the electronic structure is represented using Kohn-Sham density functional theory, and we examine the convergence of this expression as a function of the basis set size. An illustrative example using 64 silicon atoms in a fully flexible box using a combination of the Martyna-Tobias-Klein [Martyna et al., J. Chem. Phys. 101, 4177 (1994)] and Car-Parrinello [Car and Parinello, Phys. Rev. Lett. 55, 2471 (1985)] algorithms is presented to demonstrate the efficacy of the approach. [ABSTRACT FROM AUTHOR]

The weighted stochastic simulation algorithm (wSSA) was developed by Kuwahara and Mura [J. Chem. Phys. 129, 165101 (2008)] to efficiently estimate the probabilities of rare events in discrete stochastic systems. The wSSA uses importance sampling to enhance the statistical accuracy in the estimation of the probability of the rare event. The original algorithm biases the reaction selection step with a fixed importance sampling parameter. In this paper, we introduce a novel method where the biasing parameter is state-dependent. The new method features improved accuracy, efficiency, and robustness. [ABSTRACT FROM AUTHOR]

Gillespie’s direct method (DM) [D. Gillespie, J. Chem. Phys. 81, 2340 (1977)] for exact stochastic simulation of chemical reaction systems has been widely adopted. It is easy to implement but requires large computation for relatively large systems. Recently, two more efficient methods, next reaction method (NRM) [M. A. Gibson and J. Bruck, J. Phys. Chem. A 105, 1876 (2000)] and optimized DM (ODM) [Y. Cao et al., J. Chem. Phys. 121, 4059 (2004)], have been developed to improve simulation speed. It has been demonstrated that the ODM is the state-of-the-art most efficient method for exact stochastic simulation of most practical reaction systems. In this paper, we first develop an exact stochastic simulation algorithm named ODMK that is more efficient than the ODM. We then develop an approximate method named K-skip method to further accelerate simulation. Using two chemical reaction systems, we demonstrate that our ODMK and K-skip method can save 20%–30% and 70%–80% simulation time, respectively, comparing to the ODM. We also show that our ODMK and K-skip method provide almost the same simulation accuracy as the ODM. [ABSTRACT FROM AUTHOR]

Reactions in real chemical systems often take place on vastly different time scales, with “fast” reaction channels firing very much more frequently than “slow” ones. These firings will be interdependent if, as is usually the case, the fast and slow reactions involve some of the same species. An exact stochastic simulation of such a system will necessarily spend most of its time simulating the more numerous fast reaction events. This is a frustratingly inefficient allocation of computational effort when dynamical stiffness is present, since in that case a fast reaction event will be of much less importance to the system’s evolution than will a slow reaction event. For such situations, this paper develops a systematic approximate theory that allows one to stochastically advance the system in time by simulating the firings of only the slow reaction events. Developing an effective strategy to implement this theory poses some challenges, but as is illustrated here for two simple systems, when those challenges can be overcome, very substantial increases in simulation speed can be realized. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we examine the different formulations of Gillespie’s stochastic simulation algorithm (SSA) [D. Gillespie, J. Phys. Chem. 81, 2340 (1977)] with respect to computational efficiency, and propose an optimization to improve the efficiency of the direct method. Based on careful timing studies and an analysis of the time-consuming operations, we conclude that for most practical problems the optimized direct method is the most efficient formulation of SSA. This is in contrast to the widely held belief that Gibson and Bruck’s next reaction method [M. Gibson and J. Bruck, J. Phys. Chem. A 104, 1876 (2000)] is the best way to implement the SSA for large systems. Our analysis explains the source of the discrepancy. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we consider combinations of two well-known generalized-ensemble algorithms, namely, simulated tempering and replica-exchange method. We discuss two examples of such combinations. One is the replica-exchange simulated tempering and the other is the simulated tempering replica-exchange method. In the former method, a short replica-exchange simulation is first performed and the simulated tempering weight factor is obtained by the multiple-histogram reweighting techniques. This process of simulated tempering weight factor determination is faster and simpler than that in the usual iterative process. A long simulated tempering production run is then performed with this weight factor. The latter method is a further extension of the former in which a simulated tempering replica-exchange simulation is performed with a small number of replicas. These algorithms are particularly useful for studying frustrated systems with rough energy landscape. We give the formulations of these two methods in detail and demonstrate their effectiveness taking the example of the system of a 17-residue helical peptide. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A novel theory of an equation of state based on excluded volume and formulated in two preceding papers for gases and gaseous mixtures is extended to the entire density range by considering higher (beginning from the third) approximations of the theory. The algorithm of constructing higher approximations is elaborated. Equations of state are deduced using the requirement of maximum simplicity and contain a single free parameter to be chosen by reason of convenience or simplicity or to be used as a fitting parameter with respect to the computer simulation database. In this way, precise equations of state are derived for the hard-sphere fluid in the entire density range. On the side, the theory reproduces most known earlier equations of state for hard spheres and determines their place in the hierarchy of approximations. Equations of state for van der Waals fluids are also presented, and their critical parameters are estimated. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An efficient molecular dynamics (MD) algorithm is presented in this paper for biomolecular systems, which incorporates a novel variation on the fast multipole method (FMM) coupled to the reversible reference system propagator algorithm (r-RESPA). A top-down FMM is proposed which calculates multipoles recursively from the top of the box tree instead of from the bottom in Greengard’s original FMM, in an effort to be more efficient for noncubic or nonuniform systems. In addition, the use of noncubic box subdivisions of biomolecular systems is used and discussed. Reversible RESPA based on a Trotter factorization of the Liouville propagator in generating numerical integration schemes is coupled to the top-down FMM and applied to a MD study of proteins in vacuo, and is shown to be able to use a much larger time-step than the standard velocity Verlet method for a comparable level of accuracy. Furthermore, by using the FMM it becomes possible to perform MD simulations for very large biomolecules, since memory and CPU time requirements are now nearly of order of O(N) instead of O(N2). For a protein with 9513 atoms (the photosynthetic reaction center), the efficient MD algorithm leads to 20-fold reduction in CPU time for the Coulomb interaction and approximately 15-fold reduction in total CPU time over the standard velocity Verlet algorithm with a direct evaluation of Coulomb forces. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The time evolution of species concentrations in biochemical reaction networks is often modeled using the stochastic simulation algorithm (SSA) [Gillespie, J. Phys. Chem. 81, 2340 (1977)]. The computational cost of the original SSA scaled linearly with the number of reactions in the network. Gibson and Bruck developed a logarithmic scaling version of the SSA which uses a priority queue or binary tree for more efficient reaction selection [Gibson and Bruck, J. Phys. Chem. A 104, 1876 (2000)]. More generally, this problem is one of dynamic discrete random variate generation which finds many uses in kinetic Monte Carlo and discrete event simulation. We present here a constant-time algorithm, whose cost is independent of the number of reactions, enabled by a slightly more complex underlying data structure. While applicable to kinetic Monte Carlo simulations in general, we describe the algorithm in the context of biochemical simulations and demonstrate its competitive performance on small- and medium-size networks, as well as its superior constant-time performance on very large networks, which are becoming necessary to represent the increasing complexity of biochemical data for pathways that mediate cell function. [ABSTRACT FROM AUTHOR]

In this paper a new algorithm is presented that improves the efficiency of Wang and Landau algorithm or density of states (DOS) Monte Carlo simulations by employing rejected states. The algorithm is shown to have a performance superior to that of the original Wang-Landau [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)] algorithm and the more recent configurational temperature DOS algorithm. The performance of the method is illustrated in the context of results for the Lennard-Jones fluid. [ABSTRACT FROM AUTHOR]

Rigorous simulations of quantum tunneling dynamics in model systems with up to 20 coupled degrees of freedom are reported. The simulations implement an extension of the recently developed matching-pursuit/split-operator Fourier-transform method to complex-valued coherent-state representations. The resulting method recursively applies the time-evolution operator, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state representations generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We propose a fast method for the calculation of short-range interactions in molecular dynamics simulations. The so-called random-batch list method is a stochastic version of the classical neighbor-list method to avoid the construction of a full Verlet list, which introduces two-level neighbor lists for each particle such that the neighboring particles are located in core and shell regions, respectively. Direct interactions are performed in the core region. For the shell zone, we employ a random batch of interacting particles to reduce the number of interaction pairs. The error estimate of the algorithm is provided. We investigate the Lennard-Jones fluid by molecular dynamics simulations and show that this novel method can significantly accelerate the simulations with a factor of several fold without loss of the accuracy. This method is simple to implement, can be well combined with any linked cell methods to further speed up and scale up the simulation systems, and can be straightforwardly extended to other interactions, such as Ewald short-range part, and thus it is promising for large-scale molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

We perform extensive benchmark comparisons of surface hopping dynamics with numerically exact calculations for the spin-boson model over a wide range of energetic and coupling parameters as well as temperature. We find that deviations from golden-rule scaling in the Marcus regime are generally small and depend sensitively on the energetic bias between electronic states. Fewest switches surface hopping (FSSH) is found to be surprisingly accurate over a large swath of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic, at least for the case of an environment modeled with the commonly used Debye spectral density. [ABSTRACT FROM AUTHOR]

Multiple time scales in cellular chemical reaction systems often render the tau-leaping algorithm inefficient. Various model reductions have been proposed to accelerate tau-leaping simulations. However, these are often identified and deployed manually, requiring expert knowledge. This is time-consuming and prone to error. In previous work, we proposed a methodology for automatic identification and validation of model reduction opportunities for tau-leaping simulation. Here, we show how the model reductions can be automatically and adaptively deployed during the time course of a simulation. For multiscale systems, this can result in substantial speedups. [ABSTRACT FROM AUTHOR]

We propose a new exact stochastic rejection-based simulation algorithm for biochemical reactions and extend it to systems with delays. Our algorithm accelerates the simulation by pre-computing reaction propensity bounds to select the next reaction to perform. Exploiting such bounds, we are able to avoid recomputing propensities every time a (delayed) reaction is initiated or finished, as is typically necessary in standard approaches. Propensity updates in our approach are still performed, but only infrequently and limited for a small number of reactions, saving computation time and without sacrificing exactness. We evaluate the performance improvement of our algorithm by experimenting with concrete biological models. [ABSTRACT FROM AUTHOR]

Comments on the article 'A new algorithm for reverse Monte Carlo simulations,' by Fernando Luis B. da Silva and colleagues, which appeared in the 'Journal of Chemical Physics.' Comparison of the results of metropolis Monte Carlo simulations to results obtained by the reverse Monte Carlo scheme; Structural characterization of the algorithm.

We develop a novel method of replica-exchange molecular dynamics (REMD) simulation, mass-scaling REMD (MSREMD) method, which improves numerical stability of simulations. In addition, the MSREMD method can also simplify a replica-exchange routine by eliminating velocity scaling. As a pilot system, a Lennard-Jones fluid is simulated with the new method. The results suggest that the MSREMD method improves the numerical stability at high temperatures compared with the conventional REMD method. For the Nosé-Hoover thermostats, we analytically demonstrate that the MSREMD simulations can reproduce completely the same trajectories of the conventional REMD ones with shorter time steps at high temperatures. Accordingly, we can easily compare the computational costs of the REMD and MSREMD simulations. We conclude that the MSREMD method decreases the instability and optimizes the computational resources with simpler algorithm. [ABSTRACT FROM AUTHOR]

We have extended the multilevel summation (MLS) method, originally developed to evaluate longrange Coulombic interactions in molecular dynamics simulations [R. D. Skeel, I. Tezcan, and D. J. Hardy, J. Comput. Chem. 23, 673 (2002)], to handle dispersion interactions. While dispersion potentials are formally short-ranged, accurate calculation of forces and energies in interfacial and inhomogeneous systems require long-range methods. The MLS method offers some significant advantages compared to the particle-particle particle-mesh and smooth particle mesh Ewald methods. Unlike mesh-based Ewald methods, MLS does not use fast Fourier transforms and is thus not limited by communication and bandwidth concerns. In addition, it scales linearly in the number of particles, as compared with the O(N logN) complexity of the mesh-based Ewald methods. While the structure of the MLS method is invariant for different potentials, every algorithmic step had to be adapted to accommodate the r-6 form of the dispersion interactions. In addition, we have derived error bounds, similar to those obtained by Hardy ["Multilevel summation for the fast evaluation of forces for the simulation of biomolecules," Ph.D. thesis, University of Illinois at Urbana-Champaign, 2006] for the electrostatic MLS. Using a prototype implementation, we have demonstrated the linear scaling of the MLS method for dispersion, and present results establishing the accuracy and efficiency of the method. [ABSTRACT FROM AUTHOR]

The thermostats in molecular dynamics (MD) simulations of highly confined channel flow may have significant influences on the fidelity of transport phenomena. In this study, we exploit non-equilibrium MD simulations to generate Couette flows with different combinations of thermostat algorithms and strategies. We provide a comprehensive analysis on the effectiveness of three thermostat algorithms Nosé-Hoover chain (NHC), Langevin (LGV) and dissipative particle dynamics (DPD) when applied in three thermostat strategies, thermostating either walls (TW) or fluid (TF), and thermostating both the wall and fluid (TWTF). Our results of thermal and mechanical properties show that the TW strategy more closely resembles experimental conditions. The TF and TWTF systems also produce considerably similar behaviors in weakly sheared systems, but deviate the dynamics in strongly sheared systems due to the isothermal condition. The LGV and DPD thermostats used in the TF and TWTF systems provide vital ways to yield correct dynamics in coarse-grained systems by tuning the fluid transport coefficients. Using conventional NHC thermostat to thermostat fluid only produces correct thermal behaviors in weakly sheared systems, and breaks down due to significant thermal inhomogeneity in strongly sheared systems. [ABSTRACT FROM AUTHOR]

We put forward a simple procedure for extracting dynamical information from Monte Carlo simulations, by appropriate matching of the short-time diffusion tensor with its infinite-dilution limit counterpart, which is supposed to be known. This approach - discarding hydrodynamics interactions - first allows us to improve the efficiency of previous dynamic Monte Carlo algorithms for spherical Brownian particles. In the second step, we address the case of anisotropic colloids with orientational degrees of freedom. As an illustration, we present a detailed study of the dynamics of thin platelets, with emphasis on long-time diffusion and orientational correlations. [ABSTRACT FROM AUTHOR]

We consider several patchy particle models that have been proposed in literature and we investigate their candidate crystal structures in a systematic way. We compare two different algorithms for predicting crystal structures: (i) an approach based on Monte Carlo simulations in the isobaric-isothermal ensemble and (ii) an optimization technique based on ideas of evolutionary algorithms. We show that the two methods are equally successful and provide consistent results on crystalline phases of patchy particle systems. [ABSTRACT FROM AUTHOR]

This work presents an immersed boundary method that allows fast Brownian dynamics simulation of solutions of polymer chains and other Brownian objects in complex geometries with fluctuating hydrodynamics. The approach is based on the general geometry Ewald-like method, which solves the Stokes equation with distributed regularized point forces in O(N) or O(NlogN) operations, where N is the number of point forces in the system. Time-integration is performed using a midpoint algorithm and Chebyshev polynomial approximation proposed by Fixman. This approach is applied to the dynamics of a genomic DNA molecule driven by flow through a nanofluidic slit with an array of nanopits on one wall of the slit. The dynamics of the DNA molecule was studied as a function of the Péclet number and chain length (the base case being λ-DNA). The transport characteristics of the hopping dynamics in this device differ at low and high Péclet number, and for long DNA, relative to the pit size, the dynamics is governed by the segments residing in the pit. By comparing with results that neglect them, hydrodynamic interactions are shown to play an important quantitative role in the hopping dynamics. [ABSTRACT FROM AUTHOR]

In recent years there has been substantial growth in the development of algorithms for characterizing rare events in stochastic biochemical systems. Two such algorithms, the state-dependent weighted stochastic simulation algorithm (swSSA) and the doubly weighted SSA (dwSSA) are extensions of the weighted SSA (wSSA) by H. Kuwahara and I. Mura [J. Chem. Phys. 129, 165101 (2008)]. The swSSA substantially reduces estimator variance by implementing system state-dependent importance sampling (IS) parameters, but lacks an automatic parameter identification strategy. In contrast, the dwSSA provides for the automatic determination of state-independent IS parameters, thus it is inefficient for systems whose states vary widely in time. We present a novel modification of the dwSSA-the state-dependent doubly weighted SSA (sdwSSA)-that combines the strengths of the swSSA and the dwSSA without inheriting their weaknesses. The sdwSSA automatically computes state-dependent IS parameters via the multilevel cross-entropy method. We apply the method to three examples: a reversible isomerization process, a yeast polarization model, and a lac operon model. Our results demonstrate that the sdwSSA offers substantial improvements over previous methods in terms of both accuracy and efficiency. [ABSTRACT FROM AUTHOR]

The vibrational energy transfer from the excited carbonyl stretch mode in N-deuterated N-methylacetamide (NMA-d), both in isolation and in a heavy water cluster, is studied with nonequilibrium molecular dynamics (NEMD) simulations, employing a quantum mechanical/molecular mechanical (QM/MM) force field at the semiempirical PM3 level. The nonequilibrium ensemble of vibrationally excited NMA-d is prepared by perturbing the positions and velocities of the carbonyl C and O atoms and its NEMD trajectories are obtained with a leap-frog algorithm properly modified for the initial perturbation. In addition to the time-domain analysis of the kinetic and potential energies, a novel method for the spectral analysis of the atomic kinetic energies is developed, in terms of the spectral density of kinetic energy, which provides the time-dependent changes of the frequency-resolved kinetic energies without the complications of normal mode analysis at every MD time step. Due to the QM description of the solute electronic structure, the couplings among the normal modes are captured more realistically than with classical force fields. The energy transfer in the isolated NMA-d is found to proceed first from the carbonyl bond to other modes with time scales of 3 ps or less, and then among the other modes over 3-21 ps. In the solvated NMA-d, most of the excess energy is first transferred to other intramolecular modes within 5 ps, which is subsequently dissipated to solvent with 7-19 ps time scales. The contribution of the direct energy transfer from the carbonyl bond to solvent was only 5% with ∼7 ps time scale. Solvent reorganization that leads to destabilization of the electrostatic interactions is found to be crucial in the long time relaxation of the excess energy, while the water intramolecular modes do not contribute significantly. Detailed mode-specific energy transfer pathways are deduced for the isolated and solvated NMA-d and they show that the energy transfer in NMA-d is a highly cooperative process among the intramolecular modes and there is no single dominant pathway with more than 30% of transient contribution. [ABSTRACT FROM AUTHOR]

Variability and fluctuations among genetically identical cells under uniform experimental conditions stem from the stochastic nature of biochemical reactions. Understanding network function for endogenous biological systems or designing robust synthetic genetic circuits requires accounting for and analyzing this variability. Stochasticity in biological networks is usually represented using a continuous-time discrete-state Markov formalism, where the chemical master equation (CME) and its kinetic Monte Carlo equivalent, the stochastic simulation algorithm (SSA), are used. These two representations are computationally intractable for many realistic biological problems. Fitting parameters in the context of these stochastic models is particularly challenging and has not been accomplished for any but very simple systems. In this work, we propose that moment equations derived from the CME, when treated appropriately in terms of higher order moment contributions, represent a computationally efficient framework for estimating the kinetic rate constants of stochastic network models and subsequent analysis of their dynamics. To do so, we present a practical data-derived moment closure method for these equations. In contrast to previous work, this method does not rely on any assumptions about the shape of the stochastic distributions or a functional relationship among their moments. We use this method to analyze a stochastic model of a biological oscillator and demonstrate its accuracy through excellent agreement with CME/SSA calculations. By coupling this moment-closure method with a parameter search procedure, we further demonstrate how a model's kinetic parameters can be iteratively determined in order to fit measured distribution data. [ABSTRACT FROM AUTHOR]

We present a method called local environment kinetic Monte Carlo (LE-KMC) method for efficiently performing off-lattice, self-learning kinetic Monte Carlo (KMC) simulations of activated processes in material systems. Like other off-lattice KMC schemes, new atomic processes can be found on-the-fly in LE-KMC. However, a unique feature of LE-KMC is that as long as the assumption that all processes and rates depend only on the local environment is satisfied, LE-KMC provides a general algorithm for (i) unambiguously describing a process in terms of its local atomic environments, (ii) storing new processes and environments in a catalog for later use with standard KMC, and (iii) updating the system based on the local information once a process has been selected for a KMC move. Search, classification, storage and retrieval steps needed while employing local environments and processes in the LE-KMC method are discussed. The advantages and computational cost of LE-KMC are discussed. We assess the performance of the LE-KMC algorithm by considering test systems involving diffusion in a submonolayer Ag and Ag-Cu alloy films on Ag(001) surface. [ABSTRACT FROM AUTHOR]

We develop near-field (NF), a very efficient finite-difference time-dependent (FDTD) approach for simulating electromagnetic systems in the near-field regime. NF is essentially a time-dependent version of the quasistatic frequency-dependent Poisson algorithm. We assume that the electric field is longitudinal, and hence propagates only a set of time-dependent polarizations and currents. For near-field scales, the time step (dt) is much larger than in the usual Maxwell FDTD approach, as it is not related to the velocity of light; rather, it is determined by the rate of damping and plasma oscillations in the material, so dt = 2.5 a.u. was well converged in our simulations. The propagation in time is done via a leapfrog algorithm much like Yee's method, and only a single spatial convolution is needed per time step. In conjunction, we also develop a new and very accurate 8 and 9 Drude-oscillators fit to the permittivity of gold and silver, desired here because we use a large time step. We show that NF agrees with Mie-theory in the limit of small spheres and that it also accurately describes the evolution of the spectral shape as a function of the separation between two gold or silver spheres. The NF algorithm is especially efficient for systems with small scale dynamics and makes it very simple to introduce additional effects such as embedding. [ABSTRACT FROM AUTHOR]

A multigrid algorithm has been developed enabling more efficient solution of the cluster size distribution for N-component nucleation from the Becker-Döring equations. The theoretical derivation is valid for an arbitrary number of condensing components, making the simulation of many-component nucleating systems feasible. A steady state ternary nucleation problem is defined to demonstrate its efficiency. The results are used as a validation for existing nucleation theories. The non-steady state ternary problem provides useful insight into the initial stages of the nucleation process. We observe that for the ideal mixture the main nucleation flux bypasses the saddle point. [ABSTRACT FROM AUTHOR]

An efficient first-principles electronic dynamics method is introduced in this article. The approach we put forth relies on incrementally constructing a time-dependent Fock/Kohn-Sham matrix using active space density screening method that reduces the cost of computing two-electron repulsion integrals. An adaptive stepsize control algorithm is developed to optimize the efficiency of the electronic dynamics while maintaining good energy conservation. A selected set of model dipolar push-pull chromophore molecules are tested and compared with the conventional method of direct formation of the Fock/Kohn-Sham matrix. While both methods considered herein take on identical dynamical simulation pathways for the molecules tested, the active space density screening algorithm becomes much more computationally efficient. The adaptive stepsize control algorithm, when used in conjunction with the dynamically active space method, yields a factor of ∼3 speed-up in computational cost as observed in electronic dynamics using the time dependent density functional theory. The total computational cost scales nearly linear with increasing size of the molecular system. [ABSTRACT FROM AUTHOR]

Stochastic simulation of reaction-diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies. [ABSTRACT FROM AUTHOR]

We have developed a treecode-based O(Nlog N) algorithm for the generalized Born (GB) implicit solvation model. Our treecode-based GB (tGB) is based on the GBr6 [J. Phys. Chem. B 111, 3055 (2007)], an analytical GB method with a pairwise descreening approximation for the R6 volume integral expression. The algorithm is composed of a cutoff scheme for the effective Born radii calculation, and a treecode implementation of the GB charge-charge pair interactions. Test results demonstrate that the tGB algorithm can reproduce the vdW surface based Poisson solvation energy with an average relative error less than 0.6% while providing an almost linear-scaling calculation for a representative set of 25 proteins with different sizes (from 2815 atoms to 65456 atoms). For a typical system of 10k atoms, the tGB calculation is three times faster than the direct summation as implemented in the original GBr6 model. Thus, our tGB method provides an efficient way for performing implicit solvent GB simulations of larger biomolecular systems at longer time scales. [ABSTRACT FROM AUTHOR]

A method to generate reactive trajectories, namely equilibrium trajectories leaving a metastable state and ending in another one is proposed. The algorithm is based on simulating in parallel many copies of the system, and selecting the replicas which have reached the highest values along a chosen one-dimensional reaction coordinate. This reaction coordinate does not need to precisely describe all the metastabilities of the system for the method to give reliable results. An extension of the algorithm to compute transition times from one metastable state to another one is also presented. We demonstrate the interest of the method on two simple cases: A one-dimensional two-well potential and a two-dimensional potential exhibiting two channels to pass from one metastable state to another one. [ABSTRACT FROM AUTHOR]