Dynamic correlation effect in reversible diffusion-influenced reactions: Brownian dynamics simulation in three dimensions

Kim, Hyojoon; Yang, Mino; Shin, Kye Jung

doi:10.1063/1.479297

Cited by 46 publications

(16 citation statements)

References 30 publications

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“…30 Our numerical simulations represent unique tests of these theoretical results in 2D, because previous numerical tests were restricted to 3D and 1D. 33,35 For the self-consistent relaxation time approximation (SCRTA) method, 29 a pair of equations must be solved self-consistently, which cannot be done analytically in 2D, due to the lack of a steady state rate constant. Instead, we adapt the method from the original paper 29 to self-consistently solve the pair of equations where the second condition is resolved numerically rather than analytically.…”

Section: Pseudo-first-order Reversible Reactions In 2dmentioning

confidence: 99%

“…18), and derivations of binary non-Markovian kinetic equations when accounting for manybody correlations provide a general framework for quantifying sources of deviations from simple chemical kinetics, 31,32 for example. Most treatments of 3D reaction dynamics have already been tested via numerical simulation, 12,[33][34][35][36] and some predictions in 2D, 19,37 and here, we provide new simulations that highlight the effectiveness of specific theoretical approximations in describing 2D reaction dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates

Yogurtcu

Johnson

2015

The Journal of Chemical Physics

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The dynamics of association between diffusing and reacting molecular species are routinely quantified using simple rate-equation kinetics that assume both well-mixed concentrations of species and a single rate constant for parameterizing the binding rate. In two-dimensions (2D), however, even when systems are well-mixed, the assumption of a single characteristic rate constant for describing association is not generally accurate, due to the properties of diffusional searching in dimensions d ≤ 2. Establishing rigorous bounds for discriminating between 2D reactive systems that will be accurately described by rate equations with a single rate constant, and those that will not, is critical for both modeling and experimentally parameterizing binding reactions restricted to surfaces such as cellular membranes. We show here that in regimes of intrinsic reaction rate (k a ) and diffusion (D) parameters k a /D > 0.05, a single rate constant cannot be fit to the dynamics of concentrations of associating species independently of the initial conditions. Instead, a more sophisticated multiparametric description than rate-equations is necessary to robustly characterize bimolecular reactions from experiment. Our quantitative bounds derive from our new analysis of 2D rate-behavior predicted from Smoluchowski theory. Using a recently developed single particle reaction-diffusion algorithm we extend here to 2D, we are able to test and validate the predictions of Smoluchowski theory and several other theories of reversible reaction dynamics in 2D for the first time. Finally, our results also mean that simulations of reactive systems in 2D using rate equations must be undertaken with caution when reactions have k a /D > 0.05, regardless of the simulation volume. We introduce here a simple formula for an adaptive concentration dependent rate constant for these chemical kinetics simulations which improves on existing formulas to better capture non-equilibrium reaction dynamics from dilute to dense systems. C 2015 AIP Publishing LLC. [http://dx

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Section: Pseudo-first-order Reversible Reactions In 2dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates

Yogurtcu

Johnson

2015

The Journal of Chemical Physics

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“…Since θ j < h/σ, the quotient θ (30) and p ρ in (36) for φ 1 = 0 follows from (35) and (46) when γ is sufficiently small such that S 0 ≈ 1/γ…”

Section: Density On the Spherementioning

confidence: 99%

“…There is an analytical solution to (7) and (8) in [35] and also the CDF is integrated analytically there.…”

Section: Molecules In Three Dimensionsmentioning

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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“…The error due to the operator splitting is analyzed in the next section. For the reversible reaction, there is an analytical solution of (3.3) and (3.4) derived in (23). These solutions are integrated exactly, and thus there is an analytical expression for the necessary CDF.…”

Section: Solve In the Polar And Azimuthal Directions Formentioning

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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Dynamic correlation effect in reversible diffusion-influenced reactions: Brownian dynamics simulation in three dimensions

Cited by 46 publications

References 30 publications

Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates

Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates

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

Flexible single molecule simulation of reaction–diffusion processes

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