Exact Solution of the Reversible Diffusion-Influenced Reaction for an Isolated Pair in Three Dimensions

Kim, Hyojoon; Shin, Kye Jung

doi:10.1103/physrevlett.82.1578

Cited by 127 publications

(173 citation statements)

References 12 publications

(21 reference statements)

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“…, and (2.12) independent of and is derived in (22). A system of three nonlinear equations is solved for coefficients in the arguments of the exponential and the complementary error function erfc in a sum with five terms.…”

Section: A Pair Of Moleculesmentioning

confidence: 99%

Flexible single molecule simulation of reaction–diffusion processes

Hellander

Lötstedt

2011

Journal of Computational Physics

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An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green's function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from its distribution function. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.

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Section: A Pair Of Moleculesmentioning

confidence: 99%

Flexible single molecule simulation of reaction–diffusion processes

Hellander

Lötstedt

2011

Journal of Computational Physics

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“…1,2,7,8 For the case of an isolated pair, exact expressions for Green's functions (GF) in the time domain, describing irreversible and reversible reactions in one, two, and three space dimensions, have been obtained. 6,[9][10][11] GF play a particular role in the theoretical description, because they can be used to derive other important quantities, for a) prustelt@niaid.nih.gov b) mms@niaid.nih.gov instance, survival probabilities and time-dependent reaction rate coefficients. Moreover, they can be employed to calculate the time evolution for any given initial distribution.…”

Section: Introductionmentioning

confidence: 99%

The area reactivity model of geminate recombination

Prüstel

Meier‐Schellersheim

2014

The Journal of Chemical Physics

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We investigate the reversible diffusion-influenced reaction of an isolated pair in the context of the area reactivity model that describes the reversible binding of a single molecule in the presence of a binding site in terms of a generalized version of the Feynman-Kac equation in two dimensions. We compute the corresponding exact Green's function in the Laplace domain for both the initially unbound and bound molecule. We discuss convolution relations that facilitate the calculation of the binding and survival probabilities. Furthermore, we calculate an exact analytical expression for the Green's function in the time domain by inverting the Laplace transform via the Bromwich contour integral and derive expressions for the binding and survival probability in the time domain as well. We numerically confirm the accuracy of the obtained expressions by propagating the generalized Feynman-Kac equation in the time domain. Our results should be useful for comparing the area reactivity model with the contact reactivity model. [http://dx

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“…10 These results were used to obtain general reaction rates, but did not involve any assessment of the spatial distribution of molecules generated by stochastic effects. Many algorithmic developments, based on Smoluchowski's work and related work by Kim and Shin 11 tackled efficient implementations of general Brownian dynamics (BD), [12][13][14] among these is a recent technique known as Green's function reaction dynamics (GFRD) (Ref. 14) which propagates the Brownian dynamics of molecules starting from an initial δ function in space instead of a uniform distribution.…”

Section: Introductionmentioning

confidence: 99%

Towards a minimal stochastic model for a large class of diffusion-reactions on biological membranes

Chevalier

El-Samad²

2012

The Journal of Chemical Physics

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Diffusion of biological molecules on 2D biological membranes can play an important role in the behavior of stochastic biochemical reaction systems. Yet, we still lack a fundamental understanding of circumstances where explicit accounting of the diffusion and spatial coordinates of molecules is necessary. In this work, we illustrate how time-dependent, non-exponential reaction probabilities naturally arise when explicitly accounting for the diffusion of molecules. We use the analytical expression of these probabilities to derive a novel algorithm which, while ignoring the exact position of the molecules, can still accurately capture diffusion effects. We investigate the regions of validity of the algorithm and show that for most parameter regimes, it constitutes an accurate framework for studying these systems. We also document scenarios where large spatial fluctuation effects mandate explicit consideration of all the molecules and their positions. Taken together, our results derive a fundamental understanding of the role of diffusion and spatial fluctuations in these systems. Simultaneously, they provide a general computational methodology for analyzing a broad class of biological networks whose behavior is influenced by diffusion on membranes.

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Exact Solution of the Reversible Diffusion-Influenced Reaction for an Isolated Pair in Three Dimensions

Cited by 127 publications

References 12 publications

Flexible single molecule simulation of reaction–diffusion processes

Flexible single molecule simulation of reaction–diffusion processes

The area reactivity model of geminate recombination

Towards a minimal stochastic model for a large class of diffusion-reactions on biological membranes

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