Particle-Based Stochastic Simulators

Andrews, Steven S.

doi:10.1007/978-1-4614-7320-6_191-2

Cited by 15 publications

(20 citation statements)

References 17 publications

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“…Instead, simulations are the only method currently available for producing data that can test these theories quantitatively. Furthermore, Smoldyn is essentially the only adequate simulator at present because on-lattice simulators introduce substantial artifacts [43] and other offlattice simulators are substantially less accurate for simulations at the necessary size scale [44].…”

Section: Discussionmentioning

confidence: 99%

Effects of surfaces and macromolecular crowding on bimolecular reaction rates

Andrews

2019

Preprint

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Biological cells are complex environments that are densely packed with macromolecules and subdivided by membranes, both of which affect the rates of chemical reactions. It is well known that crowding reduces the volume available to reactants, which increases reaction rates, and also inhibits reactant diffusion, which decreases reaction rates. This work investigates these effects quantitatively using analytical theory and particle-based simulations. A reaction rate equation based on these two processes turned out to be inconsistent with simulation results. However, also accounting for diffusion inhibition by the surfaces of nearby obstacles led to perfect agreement for reactions near impermeable planar membranes and improved agreement for reactions in crowded spaces. These results help elucidate reaction dynamics in confined spaces and improve prediction of in vivo reaction rates from in vitro ones.

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Section: Discussionmentioning

confidence: 99%

Effects of surfaces and macromolecular crowding on bimolecular reaction rates

Andrews

2019

Preprint

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“…During the subsequent production run of length similar to eq , we record the two main observables: (i) the concentration profile ( ) as the radial distribution function (RDF) of A molecules relative to the B molecule in the centre, and (ii) the number of reactions (2) that were performed in each integration step, yielding the reaction frequency and thus the macroscopic reaction rate constant = / . Observing the (46) and (47)] for the parameters given in Table I. The separation of molecule centres is given in units of the reaction radius , and the potential energy is given in terms of the thermal energy ; the shaded region marks the reaction sphere in which reaction (2) can occur.…”

Section: A Simulation Setup and Protocolmentioning

confidence: 99%

“…For the soft repulsive and the LJ potentials [Eqs. (46) and (47) For slow reactions, ≪ 1, the concentration profile at leading order in is expected to equal the equilibrium distribution, 0 ( ) = e − ( ) , subject to the specific boundary condition ( → ∞) = [Eq. (37)].…”

Section: B Concentration Profilesmentioning

confidence: 99%

Diffusion-influenced reaction rates in the presence of pair interactions

Dibak

Fröhner

Noé

et al. 2019

The Journal of Chemical Physics

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The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi's volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction-diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction-diffusion equation in the steady state and derive semi-analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion-limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions. arXiv:1908.07764v1 [cond-mat.soft]

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“…However, because of these additional details, microscopic particle methods are more computationally demanding than RDME methods. In a recent performance benchmark of the microscopic methods [41], Smoldyn required the shortest runtime when simulating the wellknown Michaelis-Menten reaction-diffusion kinetics.…”

Section: Introductionmentioning

confidence: 99%

pSpatiocyte: a high-performance simulator for intracellular reaction-diffusion systems

et al. 2020

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Background: Studies using quantitative experimental methods have shown that intracellular spatial distribution of molecules plays a central role in many cellular systems. Spatially resolved computer simulations can integrate quantitative data from these experiments to construct physically accurate models of the systems. Although computationally expensive, microscopic resolution reaction-diffusion simulators, such as Spatiocyte can directly capture intracellular effects comprising diffusion-limited reactions and volume exclusion from crowded molecules by explicitly representing individual diffusing molecules in space. To alleviate the steep computational cost typically associated with the simulation of large or crowded intracellular compartments, we present a parallelized Spatiocyte method called pSpatiocyte. Results: The new high-performance method employs unique parallelization schemes on hexagonal close-packed (HCP) lattice to efficiently exploit the resources of common workstations and large distributed memory parallel computers. We introduce a coordinate system for fast accesses to HCP lattice voxels, a parallelized event scheduler, a parallelized Gillespie's direct-method for unimolecular reactions, and a parallelized event for diffusion and bimolecular reaction processes. We verified the correctness of pSpatiocyte reaction and diffusion processes by comparison to theory. To evaluate the performance of pSpatiocyte, we performed a series of parallelized diffusion runs on the RIKEN K computer. In the case of fine lattice discretization with low voxel occupancy, pSpatiocyte exhibited 74% parallel efficiency and achieved a speedup of 7686 times with 663552 cores compared to the runtime with 64 cores. In the weak scaling performance, pSpatiocyte obtained efficiencies of at least 60% with up to 663552 cores. When executing the Michaelis-Menten benchmark model on an eight-core workstation, pSpatiocyte required 45-and 55-fold shorter runtimes than Smoldyn and the parallel version of ReaDDy, respectively. As a high-performance application example, we study the dual phosphorylation-dephosphorylation cycle of the MAPK system, a typical reaction network motif in cell signaling pathways. Conclusions: pSpatiocyte demonstrates good accuracies, fast runtimes and a significant performance advantage over well-known microscopic particle methods in large-scale simulations of intracellular reaction-diffusion systems. The source code of pSpatiocyte is available at https://spatiocyte.org.

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Particle-Based Stochastic Simulators

Cited by 15 publications

References 17 publications

Effects of surfaces and macromolecular crowding on bimolecular reaction rates

Effects of surfaces and macromolecular crowding on bimolecular reaction rates

Diffusion-influenced reaction rates in the presence of pair interactions

pSpatiocyte: a high-performance simulator for intracellular reaction-diffusion systems

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