A convergent reaction-diffusion master equation

Isaacson, Samuel A.

doi:10.1063/1.4816377

Cited by 87 publications

(112 citation statements)

References 54 publications

(140 reference statements)

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“…To model iPOLYMER, we spatially discretized the well-known continuous-space Doi model of stochastic reaction-diffusion 56,57 , and obtained a physically valid approximation based on the reaction-diffusion master equation (RDME) 58–62 . This led to a Markov process model that describes the time evolution of the location of each basic or aggregate molecule at a resolution of one voxel in the system.…”

Section: Methodsmentioning

confidence: 99%

Intracellular production of hydrogels and synthetic RNA granules by multivalent molecular interactions

et al. 2017

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Non-membrane bound, hydrogel-like entities, such as RNA granules, nucleate essential cellular functions through their unique physico-chemical properties. However, these intracellular hydrogels have not been as extensively studied as their extracellular counterparts, primarily due to technical challenges in probing these materials in situ. Here, by taking advantage of a chemically inducible dimerization paradigm, we developed iPOLYMER, a strategy for rapid induction of protein-based hydrogels inside living cells. A series of biochemical and biophysical characterizations, in conjunction with computational modeling, revealed that the polymer network formed in the cytosol resembles a physiological hydrogel-like entity that behaves as a size-dependent molecular sieve. We studied several properties of the gel and functionalized it with RNA binding motifs that sequester polyadenine-containing nucleotides to synthetically mimic RNA granules. Therefore, we here demonstrate that iPOLYMER presents a unique and powerful approach to synthetically reconstitute hydrogel-like structures including RNA granules in intact cells.

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Section: Methodsmentioning

confidence: 99%

Intracellular production of hydrogels and synthetic RNA granules by multivalent molecular interactions

et al. 2017

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“…A problematic aspect of relying on mesh-dependent rate functions is that different approaches lead to different expressions, and they are dependent on the nature of the voxels, the geometry, and the test problem. Another approach to the problem was recently taken by Isaacson,91 where he constructs a new and convergent form of the RDME based on a discretization of a particle tracking model. 92 Here, the mesoscopic model is formulated in such a way as to converge to a specific microscopic, continuum model per construction.…”

Section: The Rdme On Small Length Scalesmentioning

confidence: 99%

Perspective: Stochastic algorithms for chemical kinetics

Gillespie

Hellander²,

Petzold³

2013

The Journal of Chemical Physics

295

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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“…Dividing by δr and taking the limit as before we obtain 24) with second order accuracy in space. Employing once again the fact that Π(r,t) = 4πr 2 f (r,t), we recover the Smoluchowski equation under a potential [56],…”

Section: Radial Random Walk With Spherical Symmetry Under a Potentialmentioning

confidence: 99%

“…Most of these systems are non-homogeneous in space and have a low number of molecules, so its modeling is based on stochastic reaction-diffusion theory at mesoscopic scales. However, unlike the case of homogeneous reaction theory [6,46], the connection between the reaction-diffusion phenomena at different microscopic, mesoscopic and macroscopic scales is still a matter of recent research [5,17,22,23,24]. Our model contribution in this front is to unify the theory of reversible diffusion-influenced reactions [1,26,52] with the different approaches to model reversible reactions taken by several simulation packages , like Smoldyn, FPKMC, eGFRD [3,13,58] and others [14,21,51,59,65,69].…”

Section: Introductionmentioning

confidence: 99%

A discrete stochastic formulation for reversible bimolecular reactions via diffusion encounter

Razo

Qian

2016

Communications in Mathematical Sciences

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Abstract. The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory. As there is a clear corresponding stochastic process, the mathematical description takes both Kolmogorov forward equation for the evolution of the probability distribution function and the stochastic sample trajectories. This dual description is a fundamental characteristic of stochastic processes and allows simple particle based simulations to accurately match the expected statistical behavior. However, in the traditional theory using the back-reaction boundary condition to model reversible reactions with geminate recombinations, several subtleties arise: It is unclear what the underlying stochastic process is, which causes complications in producing accurate simulations; and it is non-trivial how to perform an appropriate discretization for numerical computations. In this work, we derive a discrete stochastic model that recovers the classical models and their boundary conditions in the continuous limit. In the case of reversible reactions, we recover the back-reaction boundary condition, unifying the back-reaction approach with those of current simulation packages. Furthermore, all the complications encountered in the continuous models become trivial in the discrete model. Our formulation brings to attention the question: With computations in mind, can we develop a discrete reaction kinetics model that is more fundamental than its continuous counterpart?

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A convergent reaction-diffusion master equation

Cited by 87 publications

References 54 publications

Intracellular production of hydrogels and synthetic RNA granules by multivalent molecular interactions

Intracellular production of hydrogels and synthetic RNA granules by multivalent molecular interactions

Perspective: Stochastic algorithms for chemical kinetics

A discrete stochastic formulation for reversible bimolecular reactions via diffusion encounter

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