Accelerated stochastic and hybrid methods for spatial simulations of reaction–diffusion systems

Rossinelli, Diego; Bayati, Basil; Koumoutsakos, Petros

doi:10.1016/j.cplett.2007.11.055

Cited by 45 publications

(63 citation statements)

References 19 publications

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“…To that end, Rossinelli et al 75 have proposed a combination of tau-leaping, hybrid tau-leaping and deterministic diffusion. Iyengar et al 76 and Marquez-Lago and Burrage 77 have introduced and compared additional implementations of spatial tau-leaping.…”

Section: B Algorithms For Spatial Stochastic Simulationmentioning

confidence: 99%

Perspective: Stochastic algorithms for chemical kinetics

Gillespie

Hellander²,

Petzold³

2013

The Journal of Chemical Physics

297

341

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We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discretestochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not wellmixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes. © 2013 AIP Publishing LLC.[http://dx

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Section: B Algorithms For Spatial Stochastic Simulationmentioning

confidence: 99%

Perspective: Stochastic algorithms for chemical kinetics

Gillespie

Hellander²,

Petzold³

2013

The Journal of Chemical Physics

297

341

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“…The numerical experiments of Sec. III E, along with previous work such as the use of tau-leap 21 and R-leap 22 in spatial models, show the feasibility of spatial stochastic simulations but do not, we think, exhaust the avenues for their acceleration.…”

Section: Discussionmentioning

confidence: 99%

An exact accelerated stochastic simulation algorithm

Mjolsness

Orendorff

Chatelain

et al. 2009

The Journal of Chemical Physics

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An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm ͑SSA͒, is proposed. The present "ER-leap" algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 2 / 3 power of the number of reaction events in a Galton-Watson process.

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“…[37][38][39] For systems with diffusion, the tau-leaping method for the RDME is also known as the spatial tau-leaping scheme. Assuming that the step τ satisfies the leap condition, the spatial tau-leaping method applied on the interval [t,t + τ] gives…”

Section: Spatial Tau-leaping Methodsmentioning

confidence: 99%

“…35 Nonetheless, ISSA is often prohibitively slow as it simulates all individual chemical reactions and diffusive transfer events. 36 To overcome this difficulty approximation techniques, such as the tau-leaping scheme 16 were extended to the heterogeneous setting [37][38][39] and hybrid techniques were designed to improve the computational cost of stochastic simulation of reaction-diffusion systems. 38,40,41 For example, Marquez and Burrage 37 proposed a strategy combining the binomial tau-leaping spatial method with the Inhomogeneous Stochastic Simulation Algorithm to approximate the solution of stochastic models of heterogeneous biochemical systems, Koh and Blackwell 39,42 used gradient-based diffusion and tau-leaping for simulating such systems and Lampoudi et al 41 developed a multinomial tau-leaping algorithm.…”

Section: Introductionmentioning

confidence: 99%

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

Padgett

Ilie

2016

AIP Advances

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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.

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Accelerated stochastic and hybrid methods for spatial simulations of reaction–diffusion systems

Cited by 45 publications

References 19 publications

Perspective: Stochastic algorithms for chemical kinetics

Perspective: Stochastic algorithms for chemical kinetics

An exact accelerated stochastic simulation algorithm

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

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