Adaptive mesh refinement for stochastic reaction–diffusion processes

Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros

doi:10.1016/j.jcp.2010.08.035

Cited by 23 publications

(30 citation statements)

References 37 publications

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“…An alternative is to use adaptive mesh refinement [7] to increase the accuracy locally in parts of the domain. This is possible provided that all parts of the model can be formulated on the mesoscale and that the RDME can be corrected to account for errors due to small voxels.…”

Section: Discussionmentioning

confidence: 99%

Coupled Mesoscopic and Microscopic Simulation of Stochastic Reaction-Diffusion Processes in Mixed Dimensions

Hellander¹,

Hellander²,

Lötstedt³

2012

Multiscale Model. Simul.

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We present a new simulation algorithm that allows for dynamic switching between a mesoscopic and a microscopic modeling framework for stochastic reaction-diffusion kinetics. The more expensive and more accurate microscopic model is used only for those species and in those regions in space where there is reason to believe that a microscopic model is needed to capture the dynamics correctly. The microscopic algorithm is extended to simulation on curved surfaces in order to model reaction and diffusion on membranes. The accuracy of the method on and near a spherical membrane is analyzed and evaluated in a numerical experiment. Two biologically motivated examples are simulated in which the need for microscopic simulation of parts of the system arises for different reasons. First, we apply the method to a model of the phosphorylation reactions in a MAPK signaling cascade where microscale methods are necessary to resolve fast rebinding events. Then a model is considered for transport of a species over a membrane coupled to reactions in the bulk. The new algorithm attains an accuracy similar to a full microscopic simulation by handling critical interactions on the microscale, but at a significantly reduced cost by using the mesoscale framework for most parts of the biological model.

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Section: Discussionmentioning

confidence: 99%

Coupled Mesoscopic and Microscopic Simulation of Stochastic Reaction-Diffusion Processes in Mixed Dimensions

Hellander¹,

Hellander²,

Lötstedt³

2012

Multiscale Model. Simul.

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“…The extension of FLAVOR to Extended-FLAVOR provides additional control over the extent of convergence of the fast modes, affecting speedup and error. Ongoing work investigates the extensions of these methods with other variants of the HMM algorithm [25] as well as stochastic reaction-diffusion systems with variable spatial adaptivity [27]. We consider that an important line of work is to consider systems with multiple time-scales and investigate whether adaptively defined, multiple n, v, M variables can be introduced to scale propensities on multiple time-scales.…”

Section: Discussionmentioning

confidence: 99%

Multiscale stochastic simulations of chemical reactions with regulated scale separation

Koumoutsakos

Feigelman

2013

Journal of Computational Physics

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“…Stochastic simulations of pattern forming reaction-diffusion systems can be used to study the effect of noise at low molecule numbers [7,9,21,22]. Here, we propose an implementation of juxtacrine signaling inside the extended SEM framework and study the influence of added noise and intrinsic noise as a result of the number of SCEs per cell.…”

Section: Juxtacrine Signalingmentioning

confidence: 99%

SEM++: A particle model of cellular growth, signaling and migration

et al. 2014

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We present a discrete particle method to model biological processes from the sub-cellular to the inter-cellular level. Particles interact through a parametrized force field to model cell mechanical properties, cytoskeleton remodeling, growth and proliferation as well as signaling between cells. We discuss the guiding design principles for the selection of the force field and the validation of the particle model using experimental data. The proposed method is integrated into a multiscale particle framework for the simulation of biological systems.

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Adaptive mesh refinement for stochastic reaction–diffusion processes

Cited by 23 publications

References 37 publications

Coupled Mesoscopic and Microscopic Simulation of Stochastic Reaction-Diffusion Processes in Mixed Dimensions

Coupled Mesoscopic and Microscopic Simulation of Stochastic Reaction-Diffusion Processes in Mixed Dimensions

Multiscale stochastic simulations of chemical reactions with regulated scale separation

SEM++: A particle model of cellular growth, signaling and migration

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