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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Hierarchical Stochastic Simulation Algorithm for SBML Models of Genetic Circuits

This paper describes a hierarchical stochastic simulation algorithm, which has been implemented within iBioSim, a tool used to model, analyze, and visualize genetic circuits. Many biological analysis tools flatten out hierarchy before simulation, but there are many disadvantages associated with this approach. First, the memory required to represent the model can quickly expand in the process. Second, the flattening process is computationally expensive. Finally, when modeling a dynamic cellular population within iBioSim, inlining the hierarchy of the model is inefficient since models must grow dynamically over time. This paper discusses a new approach to handle hierarchy on the fly to make the tool faster and more memory-efficient. This approach yields significant performance improvements as compared to the former flat analysis method.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Constant-complexity stochastic simulation algorithm with optimal binning

At the molecular level, biochemical processes are governed by random interactions between reactant molecules, and the dynamics of such systems are inherently stochastic. When the copy numbers of reactants are large, a deterministic description is adequate, but when they are small, such systems are often modeled as continuous-time Markov jump processes that can be described by the chemical master equation. Gillespie’s Stochastic Simulation Algorithm (SSA) generates exact trajectories of these systems, but the amount of computational work required for each step of the original SSA is proportional to the number of reaction channels, leading to computational complexity that scales linearly with the problem size. The original SSA is therefore inefficient for large problems, which has prompted the development of several alternative formulations with improved scaling properties. We describe an exact SSA that uses a table data structure with event time binning to achieve constant computational complexity with respect to the number of reaction channels for weakly coupled reaction networks. We present a novel adaptive binning strategy and discuss optimal algorithm parameters. We compare the computational efficiency of the algorithm to existing methods and demonstrate excellent scaling for large problems. This method is well suited for generating exact trajectories of large weakly coupled models, including those that can be described by the reaction-diffusion master equation that arises from spatially discretized reaction-diffusion processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

Exploring the performance of spatial stochastic simulation algorithms

Since the publication of Gillespie's direct method, diverse methods have been developed to improve the performance of stochastic simulation methods and to enter the spatial realm. In this paper we discuss a spatial {tau}-leaping variant (S{tau}) that extends the basic leap method. S{tau} takes reaction and both outgoing and incoming diffusion events into account when calculating a leap candidate. A performance analysis shall reveal details on the achieved success in balancing speed and accuracy in comparison to other methods. However, performance analysis of spatial stochastic algorithms requires significant effort - it is crucial to choose suitable (benchmark) models and to carefully define model and simulation setups that take problem and simulation design spaces into account.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

An adaptive multi-level simulation algorithm for stochastic biological systems

Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms (SSA) to estimate system statistics. The Gillespie algorithm is exact, but computationally costly as it simulates every single reaction. As such, approximate stochastic simulation algorithms such as the tau-leap algorithm are often used. Potentially computationally more efficient, the system statistics generated suffer from significant bias unless tau is relatively small, in which case the computational time can be comparable to that of the Gillespie algorithm. The multi-level method [Anderson and Higham, “Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics,” SIAM Multiscale Model. Simul. 10(1), 146–179 (2012)] tackles this problem. A base estimator is computed using many (cheap) sample paths at low accuracy. The bias inherent in this estimator is then reduced using a number of corrections. Each correction term is estimated using a collection of paired sample paths where one path of each pair is generated at a higher accuracy compared to the other (and so more expensive). By sharing random variables between these paired paths, the variance of each correction estimator can be reduced. This renders the multi-level method very efficient as only a relatively small number of paired paths are required to calculate each correction term. In the original multi-level method, each sample path is simulated using the tau-leap algorithm with a fixed value of τ. This approach can result in poor performance when the reaction activity of a system changes substantially over the timescale of interest. By introducing a novel adaptive time-stepping approach where τ is chosen according to the stochastic behaviour of each sample path, we extend the applicability of the multi-level method to such cases. We demonstrate the efficiency of our method using a number of examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

HRSSA – Efficient hybrid stochastic simulation for spatially homogeneous biochemical reaction networks

This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Multiscale stochastic simulations of chemical reactions with regulated scale separation

We present a coupling of multiscale frameworks with accelerated stochastic simulation algorithms for systems of chemical reactions with disparate propensities. The algorithms regulate the propensities of the fast and slow reactions of the system, using alternating micro and macro sub-steps simulated with accelerated algorithms such as τ and R-leaping. The proposed algorithms are shown to provide significant speedups in simulations of stiff systems of chemical reactions with a trade-off in accuracy as controlled by a regulating parameter. More importantly, the error of the methods exhibits a cutoff phenomenon that allows for optimal parameter choices. Numerical experiments demonstrate that hybrid algorithms involving accelerated stochastic simulations can be, in certain cases, more accurate while faster, than their corresponding stochastic simulation algorithm counterparts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

On the rejection-based algorithm for simulation and analysis of large-scale reaction networks

Stochastic simulation for in silico studies of large biochemical networks requires a great amount of computational time. We recently proposed a new exact simulation algorithm, called the rejection-based stochastic simulation algorithm (RSSA) [Thanh et al., J. Chem. Phys. 141(13), 134116 (2014)], to improve simulation performance by postponing and collapsing as much as possible the propensity updates. In this paper, we analyze the performance of this algorithm in detail, and improve it for simulating large-scale biochemical reaction networks. We also present a new algorithm, called simultaneous RSSA (SRSSA), which generates many independent trajectories simultaneously for the analysis of the biochemical behavior. SRSSA improves simulation performance by utilizing a single data structure across simulations to select reaction firings and forming trajectories. The memory requirement for building and storing the data structure is thus independent of the number of trajectories. The updating of the data structure when needed is performed collectively in a single operation across the simulations. The trajectories generated by SRSSA are exact and independent of each other by exploiting the rejection-based mechanism. We test our new improvement on real biological systems with a wide range of reaction networks to demonstrate its applicability and efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Final Technical Report "Multiscale Simulation Algorithms for Biochemical Systems"

Biochemical systems are inherently multiscale and stochastic. In microscopic systems formed by living cells, the small numbers of reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical characteristics is the stochastic simulation algorithm (SSA, Gillespie, 1976), a numerical simulation procedure that is essentially exact for chemical systems that are spatially homogeneous or well stirred. Despite recent improvements, as a procedure that simulates every reaction event, the SSA is necessarily inefficient for most realistic problems. There are two main reasons for this, both arising from the multiscale nature of the underlying problem: (1) stiffness, i.e. the presence of multiple timescales, the fastest of which are stable; and (2) the need to include in the simulation both species that are present in relatively small quantities and should be modeled by a discrete stochastic process, and species that are present in larger quantities and are more efficiently modeled by a deterministic differential equation (or at some scale in between). This project has focused on the development of fast and adaptive algorithms, and the fun- damental theory upon which they must be based, for the multiscale simulation of biochemical systems. Areas addressed by this project include: (1) Theoretical and practical foundations for ac- celerated discrete stochastic simulation (tau-leaping); (2) Dealing with stiffness (fast reactions) in an efficient and well-justified manner in discrete stochastic simulation; (3) Development of adaptive multiscale algorithms for spatially homogeneous discrete stochastic simulation; (4) Development of high-performance SSA algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Multi-level methods and approximating distribution functions

Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

The time dependent propensity function for acceleration of spatial stochastic simulation of reaction–diffusion systems

The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Advanced Dynamically Adaptive Algorithms for Stochastic Simulations on Extreme Scales

The focus of the project is the development of mathematical methods and high-performance computational tools for stochastic simulations, with a particular emphasis on computations on extreme scales. The core of the project revolves around the design of highly efficient and scalable numerical algorithms that can adaptively and accurately, in high dimensional spaces, resolve stochastic problems with limited smoothness, even containing discontinuities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Advanced Dynamically Adaptive Algorithms for Stochastic Simulations on Extreme Scales

The focus of the project is the development of mathematical methods and high-performance com- putational tools for stochastic simulations, with a particular emphasis on computations on extreme scales. The core of the project revolves around the design of highly e cient and scalable numer- ical algorithms that can adaptively and accurately, in high dimensional spaces, resolve stochastic problems with limited smoothness, even containing discontinuities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Simulation of biochemical reactions with time-dependent rates by the rejection-based algorithm

We address the problem of simulating biochemical reaction networks with time-dependent rates and propose a new algorithm based on our rejection-based stochastic simulation algorithm (RSSA) [Thanh et al., J. Chem. Phys. 141(13), 134116 (2014)]. The computation for selecting next reaction firings by our time-dependent RSSA (tRSSA) is computationally efficient. Furthermore, the generated trajectory is exact by exploiting the rejection-based mechanism. We benchmark tRSSA on different biological systems with varying forms of reaction rates to demonstrate its applicability and efficiency. We reveal that for nontrivial cases, the selection of reaction firings in existing algorithms introduces approximations because the integration of reaction rates is very computationally demanding and simplifying assumptions are introduced. The selection of the next reaction firing by our approach is easier while preserving the exactness.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations

The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766–1793 (1996); ibid. 56, 1794–1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The small-voxel tracking algorithm for simulating chemical reactions among diffusing molecules

Simulating the evolution of a chemically reacting system using the bimolecular propensity function, as is done by the stochastic simulation algorithm and its reaction-diffusion extension, entails making statistically inspired guesses as to where the reactant molecules are at any given time. Those guesses will be physically justified if the system is dilute and well-mixed in the reactant molecules. Otherwise, an accurate simulation will require the extra effort and expense of keeping track of the positions of the reactant molecules as the system evolves. One molecule-tracking algorithm that pays careful attention to the physics of molecular diffusion is the enhanced Green's function reaction dynamics (eGFRD) of Takahashi, Tănase-Nicola, and ten Wolde [Proc. Natl. Acad. Sci. U.S.A. 107, 2473 (2010)]. We introduce here a molecule-tracking algorithm that has the same theoretical underpinnings and strategic aims as eGFRD, but a different implementation procedure. Called the small-voxel tracking algorithm (SVTA), it combines the well known voxel-hopping method for simulating molecular diffusion with a novel procedure for rectifying the unphysical predictions of the diffusion equation on the small spatiotemporal scale of molecular collisions. Indications are that the SVTA might be more computationally efficient than eGFRD for the problematic class of non-dilute systems. A widely applicable, user-friendly software implementation of the SVTA has yet to be developed, but we exhibit some simple examples which show that the algorithm is computationally feasible and gives plausible results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics

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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating the solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Adaptive hybrid simulations for multiscale stochastic reaction networks

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗