Multiscale Simulation of Stochastic Reaction-Diffusion Networks

Engblom, Stefan; Hellander, Andreas; Lötstedt, Per

doi:10.1007/978-3-319-62627-7_3

Cited by 4 publications

(7 citation statements)

References 136 publications

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“…We replaced the constant concentration term [B] (33) with the time varying term [E](t) in the equation. For the dilute case (φ = 0) in Figure 8c, there is a good agreement for the simulated k(t) with the Collins-Kimball rate coefficient (3). As φ increases to 0.3 and 0.5, the overall reaction rate decreases, and thus progressively diverges from the Collins-Kimball rate.…”

Section: Effects Of Excluded Volume On Bimolecular Reactionsupporting

confidence: 52%

“…In the intracellular environment, macromolecules can be heterogeneously distributed in space and react stochastically at low concentrations. The conventional mass action-based approach is insufficient to describe the reaction-diffusion (RD) behavior of the macromolecules and thus, it is necessary to incorporate space and stochasticity into the model [1][2][3][4][5][6]. Generally, we can represent space as a continuum (off-lattice) or a discretized lattice model.…”

Section: Introductionmentioning

confidence: 99%

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Reaction-diffusion kinetics on lattice at the microscopic scale

et al. 2018

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Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects in the cell such as volume exclusion and diffusion-influenced reactions. Nonetheless, schemes based on the high-resolution microscopic lattice method (MLM) can directly simulate these effects by representing each finite-sized molecule explicitly as a random walker on fine lattice voxels. The theory and consistency of MLM in simulating diffusion-influenced reactions have not been clarified in detail. Here, we examine MLM in solving diffusion-influenced reactions in 3D space by employing the Spatiocyte simulation scheme. Applying the random walk theory, we construct the general theoretical framework underlying the method and obtain analytical expressions for the total rebinding probability and the effective reaction rate. By matching Collins-Kimball and lattice-based rate constants, we obtained the exact expressions to determine the reaction acceptance probability and voxel size. We found that the size of voxel should be about 2% larger than the molecule. The theoretical framework of MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, eGFRD. MLM run time is more than an order of magnitude faster than eGFRD when diffusing macromolecules with typical concentrations observed in the cell. MLM also showed good agreements with eGFRD and mean-field models in case studies of two basic motifs of intracellular signaling, the protein production-degradation process and the dual phosphorylation-dephosphorylation cycle. In addition, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the non-classical reaction kinetics caused by anomalous diffusion of reacting molecules.

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Section: Effects Of Excluded Volume On Bimolecular Reactionsupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Reaction-diffusion kinetics on lattice at the microscopic scale

et al. 2018

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“…Overviews of deterministic, macroscopic and stochastic, mesoscopic and microscopic levels of modeling of biochemical networks are found in e.g. [29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic modeling of random walk and reactions in crowded media

2018

Self Cite

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We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic description into a previously developed internal state diffusive framework. The observables in the mesoscopic model correspond to solutions of macroscopic partial differential equations driven by stochastically varying diffusion fields in space and time. Analytical solutions and numerical experiments illustrate the framework.

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“…Therefore, different hybrid methods that couple the stochastic and deterministic modeling approaches are needed. In general, hybrid methods separate reactions and/or species into different groups of reactions and/or species, and they use the diffusion or the deterministic modeling approach to describe the dynamics of fast reactions and/or species with high copy numbers, while Markov chain representation is utilized for slow reactions and/or species with low copy numbers [6,7,8,10,13,27].…”

Section: Introductionmentioning

confidence: 99%

Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks

Altintan

Koeppl

2019

Bit Numer Math

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Cellular reactions have multi-scale nature in the sense that the abundance of molecular species and the magnitude of reaction rates can vary in a wide range. This diversity leads to hybrid models that combine deterministic and stochastic modeling approaches. To reveal this multi-scale nature, we proposed jump-diffusion approximation in a previous study. The key idea behind the model was to partition reactions into fast and slow groups, and then to combine Markov chain updating scheme for the slow set with diffusion (Langevin) approach updating scheme for the fast set. Then, the state vector of the model was defined as the summation of the random time change model and the solution of the Langevin equation. In this study, we have proved that the joint probability density function of the jump-diffusion approximation over the reaction counting process satisfies the hybrid master equation, which is the summation of the chemical master equation and the Fokker-Planck equation. To solve the hybrid master equation, we propose an algorithm using the moments of reaction counters of fast reactions given the reaction counters of slow reactions. Then, we solve a constrained optimization problem for each conditional probability density at the time point of interest utilizing the maximum entropy approach. Based on the multiplication rule for joint probability density functions, we construct the solution of the hybrid master equation. To show the efficiency of the method, we implement it to a canonical model of gene regulation.

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Multiscale Simulation of Stochastic Reaction-Diffusion Networks

Cited by 4 publications

References 136 publications

Reaction-diffusion kinetics on lattice at the microscopic scale

Reaction-diffusion kinetics on lattice at the microscopic scale

Mesoscopic modeling of random walk and reactions in crowded media

Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks

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