1
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Lee S. Operator algebraic methods in the theory of
diffusion‐influenced
reaction kinetics. B KOREAN CHEM SOC 2021. [DOI: 10.1002/bkcs.12448] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Sangyoub Lee
- Professor Sangyoub Lee, Department of Chemistry Seoul National University Seoul South Korea
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2
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Lee K, Lee S. Interplay of reactive interference and crowding effects in the diffusion-influenced reaction kinetics. J Chem Phys 2020; 153:044129. [PMID: 32752726 DOI: 10.1063/5.0016269] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
We investigate the interplay of reactive interference and crowding effects in the irreversible diffusion-influenced bimolecular reactions of the type A+B→P+B by using the Brownian dynamics simulation method. It is known that the presence of nonreactive crowding agents retards the reaction rate when the volume fraction of the crowding agents is large enough. On the other hand, a high concentration of B is known to increase the reaction rate more than expected from the mass action law, although the B's may also act as crowders. Therefore, it would be interesting to see which effect dominates when the number density of B as well as the number density of the crowders increases. We will present an approximate theory that provides a reasonable account for the Brownian dynamics simulation results.
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Affiliation(s)
- Kyusup Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Sangyoub Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
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3
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Gopich IV. Multisite reversible association in membranes and solutions: From non-Markovian to Markovian kinetics. J Chem Phys 2020; 152:104101. [PMID: 32171220 DOI: 10.1063/1.5144282] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The role of diffusion on the kinetics of reversible association to a macromolecule with two inequivalent sites is studied. Previously, we found that, in the simplest possible description, it is not sufficient to just renormalize the rate constants of chemical kinetics, but one must introduce direct transitions between the bound states in the kinetic scheme. The physical reason for this is that a molecule that just dissociated from one site can directly rebind to the other rather than diffuse away into the bulk. Such a simple description is not valid in two dimensions because reactants can never diffuse away into the bulk. In this work, we consider a variety of more sophisticated implementations of our recent general theory that are valid in both two and three dimensions. We compare the predicted time dependence of the concentrations for a wide range of parameters and establish the range of validity of various levels of the general theory.
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Affiliation(s)
- Irina V Gopich
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA
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4
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Yang M. Steady‐State Fluorescence Intensity of Diffusion‐Influenced Reversible Excited Acid–Base Reactions. B KOREAN CHEM SOC 2020. [DOI: 10.1002/bkcs.11923] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Mino Yang
- Department of ChemistryChungbuk National University Cheongju Chungbuk 28644 South Korea
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5
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Chew WX, Kaizu K, Watabe M, Muniandy SV, Takahashi K, Arjunan SNV. Surface reaction-diffusion kinetics on lattice at the microscopic scale. Phys Rev E 2019; 99:042411. [PMID: 31108654 DOI: 10.1103/physreve.99.042411] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2018] [Indexed: 01/06/2023]
Abstract
Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method (MLM) can model these processes at the microscopic scale by tracking individual molecules, represented as hard spheres, on fine lattice voxels. Although MLM is simple to implement and is generally less computationally demanding than off-lattice approaches, its accuracy and consistency in modeling surface reactions have not been fully verified. Using the Spatiocyte scheme, we study the accuracy of MLM in diffusion-influenced surface reactions. We derive the lattice-based bimolecular association rates for two-dimensional (2D) surface-surface reaction and one-dimensional (1D) volume-surface adsorption according to the Smoluchowski-Collins-Kimball model and random walk theory. We match the time-dependent rates on lattice with off-lattice counterparts to obtain the correct expressions for MLM parameters in terms of physical constants. The expressions indicate that the voxel size needs to be at least 0.6% larger than the molecule to accurately simulate surface reactions on triangular lattice. On square lattice, the minimum voxel size should be even larger, at 5%. We also demonstrate the ability of MLM-based schemes such as Spatiocyte to simulate a reaction-diffusion model that involves all dimensions: three-dimensional (3D) diffusion in the cytoplasm, 2D diffusion on the cell membrane, and 1D cytoplasm-membrane adsorption. With the model, we examine the contribution of the 2D reaction pathway to the overall reaction rate at different reactant diffusivity, reactivity, and concentrations.
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Affiliation(s)
- Wei-Xiang Chew
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan.,Department of Physics, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia
| | - Kazunari Kaizu
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
| | - Masaki Watabe
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
| | - Sithi V Muniandy
- Department of Physics, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia
| | - Koichi Takahashi
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
| | - Satya N V Arjunan
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
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6
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Abstract
A formalism is developed to describe how diffusion alters the kinetics of coupled reversible association-dissociation reactions in the presence of conformational changes that can modify the reactivity. The major difficulty in constructing a general theory is that, even to the lowest order, diffusion can change the structure of the rate equations of chemical kinetics by introducing new reaction channels (i.e., modifies the kinetic scheme). Therefore, the right formalism must be found that allows the influence of diffusion to be described in a concise and elegant way for networks of arbitrary complexity. Our key result is a set of non-Markovian rate equations involving stoichiometric matrices and net reaction rates (fluxes), in which these rates are coupled by a time-dependent pair association flux matrix, whose elements have a simple physical interpretation. Specifically, each element is the probability density that an isolated pair of reactants irreversibly associates at time t via one reaction channel on the condition that it started out with the dissociation products of another (or the same) channel. In the Markovian limit, the coupling of the chemical rates is described by committors (or splitting/capture probabilities). The committor is the probability that an isolated pair of reactants formed by dissociation at one site will irreversibly associate at another site rather than diffuse apart. We illustrate the use of our formalism by considering three reversible reaction schemes: (1) binding to a single site, (2) binding to two inequivalent sites, and (3) binding to a site whose reactivity fluctuates. In the first example, we recover the results published earlier, while in the second one we show that a new reaction channel appears, which directly connects the two bound states. The third example is particularly interesting because all species become coupled and an exchange-type bimolecular reaction appears. In the Markovian limit, some of the diffusion-modified rate constants that describe new transitions become negative, indicating that memory effects cannot be ignored.
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Affiliation(s)
- Irina V. Gopich
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Attila Szabo
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA
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7
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Delayed fluorescence after reversible triplet ionization. COMPUT THEOR CHEM 2017. [DOI: 10.1016/j.comptc.2016.11.019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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8
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Ha J, Kim M, Lee S. Excluded Volume Effects on the Kinetics of Diffusion-influenced Reversible Bimolecular Reactions: A + B ⇄ C + B. B KOREAN CHEM SOC 2016. [DOI: 10.1002/bkcs.10870] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Jimin Ha
- Department of Chemistry; Seoul National University; Seoul 151-747 South Korea
| | - Minjung Kim
- Department of Chemistry; Seoul National University; Seoul 151-747 South Korea
| | - Sangyoub Lee
- Department of Chemistry; Seoul National University; Seoul 151-747 South Korea
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9
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Ivanov KL, Lukzen NN, Doktorov AB. On the time dependence of rate coefficients of irreversible reactions between reactants with anisotropic reactivity in liquid solutions. J Chem Phys 2016. [DOI: 10.1063/1.4960174] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Affiliation(s)
- Konstantin L. Ivanov
- International Tomography Center, Siberian Branch of the Russian Academy of Science, Novosibirsk 630090, Russia
- Novosibirsk State University, Novosibirsk 630090, Russia
| | - Nikita N. Lukzen
- International Tomography Center, Siberian Branch of the Russian Academy of Science, Novosibirsk 630090, Russia
- Novosibirsk State University, Novosibirsk 630090, Russia
| | - Alexander B. Doktorov
- Novosibirsk State University, Novosibirsk 630090, Russia
- Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Science, Novosibirsk 630090, Russia
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Kipriyanov AA, Kipriyanov AA, Doktorov AB. The general theory of multistage geminate reactions of isolated pairs of reactants. III. Two-stage reversible dissociation in geminate reaction A + A↔ C↔ B + B. J Chem Phys 2016; 144:144110. [DOI: 10.1063/1.4945626] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Ivanov KL, Sadovsky VM, Lukzen NN. Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors. J Chem Phys 2015; 143:084110. [PMID: 26328821 DOI: 10.1063/1.4928648] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical "microreactor," i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the "pole" of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting experimental data for magnetic field effects on RP recombination in confined space and (ii) for describing kinetics of chemical reactions, which occur predominantly on the surfaces of biomembranes, i.e., lipid peroxidation reactions.
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Affiliation(s)
- Konstantin L Ivanov
- International Tomography Center, Siberian Branch, Russian Academy of Sciences, Institutskaya St. 3a, Novosibirsk 630090, Russia
| | - Vladimir M Sadovsky
- Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50/44, Krasnoyarsk 660036, Russia
| | - Nikita N Lukzen
- International Tomography Center, Siberian Branch, Russian Academy of Sciences, Institutskaya St. 3a, Novosibirsk 630090, Russia
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12
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Yang M. Effects of Coulombic Interaction in Diffusion-influenced Reversible Proton Transfer Kinetics of Photoexcited Acids. B KOREAN CHEM SOC 2015. [DOI: 10.1002/bkcs.10385] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Mino Yang
- Department of Chemistry; Chungbuk National University; Cheongju 361-763 Korea
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13
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Szymańska P, Kochańczyk M, Miękisz J, Lipniacki T. Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022702. [PMID: 25768526 DOI: 10.1103/physreve.91.022702] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2014] [Indexed: 06/04/2023]
Abstract
We investigate the kinetics of the ubiquitous phosphorylation-dephosphorylation cycle on biological membranes by means of kinetic Monte Carlo simulations on the triangular lattice. We establish the dependence of effective macroscopic reaction rate coefficients as well as the steady-state phosphorylated substrate fraction on the diffusion coefficient and concentrations of opposing enzymes: kinases and phosphatases. In the limits of zero and infinite diffusion, the numerical results agree with analytical predictions; these two limits give the lower and the upper bound for the macroscopic rate coefficients, respectively. In the zero-diffusion limit, which is important in the analysis of dense systems, phosphorylation and dephosphorylation reactions can convert only these substrates which remain in contact with opposing enzymes. In the most studied regime of nonzero but small diffusion, a contribution linearly proportional to the diffusion coefficient appears in the reaction rate. In this regime, the presence of opposing enzymes creates inhomogeneities in the (de)phosphorylated substrate distributions: The spatial correlation function shows that enzymes are surrounded by clouds of converted substrates. This effect becomes important at low enzyme concentrations, substantially lowering effective reaction rates. Effective reaction rates decrease with decreasing diffusion and this dependence is more pronounced for the less-abundant enzyme. Consequently, the steady-state fraction of phosphorylated substrates can increase or decrease with diffusion, depending on relative concentrations of both enzymes. Additionally, steady states are controlled by molecular crowders which, mostly by lowering the effective diffusion of reactants, favor the more abundant enzyme.
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Affiliation(s)
- Paulina Szymańska
- College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw, 02-089 Warsaw, Poland
| | - Marek Kochańczyk
- Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland
| | - Jacek Miękisz
- Institute of Applied Mathematics and Mechanics, University of Warsaw, 02-097 Warsaw, Poland
| | - Tomasz Lipniacki
- Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland and Department of Statistics, Rice University, Houston, Texas 77005, USA
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14
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Kipriyanov AA, Doktorov AB. General theory of the multistage geminate reactions of the isolated pairs of reactants. II. Detailed balance and universal asymptotes of kinetics. J Chem Phys 2014; 141:144105. [DOI: 10.1063/1.4897257] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Alexey A. Kipriyanov
- Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia and Novosibirsk State University, Novosibirsk 630090, Russia
| | - Alexander B. Doktorov
- Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia and Novosibirsk State University, Novosibirsk 630090, Russia
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15
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Kim M, Lee S, Kim JH. Concentration effects on the rates of irreversible diffusion-influenced reactions. J Chem Phys 2014; 141:084101. [PMID: 25172999 DOI: 10.1063/1.4893340] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We formulate a new theory of the effects of like-particle interactions on the irreversible diffusion-influenced bimolecular reactions of the type A + B → P + B by considering the evolution equation of the triplet ABB number density field explicitly. The solution to the evolution equation is aided by a recently proposed method for solving the Fredholm integral equation of the second kind. We evaluate the theory by comparing its predictions with the results of extensive computer simulations. The present theory provides a reasonable explanation of the simulation results.
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Affiliation(s)
- Minjung Kim
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Sangyoub Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Ji-Hyun Kim
- Department of Chemistry and Institute of Innovative Functional Imaging, Chung-Ang University, Seoul 156-756, South Korea
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16
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Doktorov AB, Kipriyanov AA. General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations. J Chem Phys 2014; 140:184104. [PMID: 24832250 DOI: 10.1063/1.4874001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of "effective" particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered.
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Affiliation(s)
- Alexander B Doktorov
- Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk 630090, Russia
| | - Alexey A Kipriyanov
- Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk 630090, Russia
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17
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Lukzen NN, Ivanov KL, Sadovsky VM, Kaptein R, Sagdeev RZ. Magnetic field and spin effects on the recombination of radicals on two-dimensional surfaces. DOKLADY PHYSICAL CHEMISTRY 2013. [DOI: 10.1134/s0012501613030056] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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18
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Jung W, Yang S, Sung J. Novel Chemical Kinetics for a Single Enzyme Reaction: Relationship between Substrate Concentration and the Second Moment of Enzyme Reaction Time. J Phys Chem B 2010; 114:9840-7. [DOI: 10.1021/jp1001868] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Won Jung
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea
| | - Seongeun Yang
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea
| | - Jaeyoung Sung
- Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea
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19
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Arjunan SNV, Tomita M. A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation. SYSTEMS AND SYNTHETIC BIOLOGY 2009; 4:35-53. [PMID: 20012222 PMCID: PMC2816228 DOI: 10.1007/s11693-009-9047-2] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/23/2009] [Revised: 10/06/2009] [Accepted: 10/08/2009] [Indexed: 11/25/2022]
Abstract
Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally.
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Affiliation(s)
- Satya Nanda Vel Arjunan
- Institute for Advanced Biosciences, Keio University, Baba-cho 14-1, Tsuruoka, 997-0035 Yamagata Japan
- Systems Biology Program, Graduate School of Media and Governance, Keio University, Fujisawa, 252-8520 Kanagawa Japan
| | - Masaru Tomita
- Institute for Advanced Biosciences, Keio University, Baba-cho 14-1, Tsuruoka, 997-0035 Yamagata Japan
- Systems Biology Program, Graduate School of Media and Governance, Keio University, Fujisawa, 252-8520 Kanagawa Japan
- Department of Environment and Information, Keio University, Fujisawa, 252-8520 Kanagawa Japan
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Affiliation(s)
- Soohyung Park
- Institute of Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
| | - Noam Agmon
- Institute of Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
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21
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Park S, Agmon N. Theory and Simulation of Diffusion-Controlled Michaelis−Menten Kinetics for a Static Enzyme in Solution. J Phys Chem B 2008; 112:5977-87. [DOI: 10.1021/jp075941d] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Soohyung Park
- Institute of Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
| | - Noam Agmon
- Institute of Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
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22
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Yang M. Rate kernel theory for pseudo-first-order kinetics of diffusion-influenced reactions and application to fluorescence quenching kinetics. J Chem Phys 2007; 126:214503. [PMID: 17567204 DOI: 10.1063/1.2737045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived.
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Affiliation(s)
- Mino Yang
- Department of Chemistry, Chungbuk National University, Cheongju, Chungbuk 361-763, South Korea.
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24
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Reversible Excited-State Proton Transfer: Effect of the Switching of Interaction Potential by Reaction. B KOREAN CHEM SOC 2006. [DOI: 10.5012/bkcs.2006.27.2.197] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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25
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Nonequilibrium Distribution Function Theory of Many-Particle Effects in the Reversible Reactions of the Type A+B ↔ C+B. B KOREAN CHEM SOC 2005. [DOI: 10.5012/bkcs.2005.26.12.1986] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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26
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Kipriyanov A, Fedorenko S, Doktorov A. Kinetic equations for exactly solvable models of a geminate reaction in the presence of scavengers. Chem Phys 2005. [DOI: 10.1016/j.chemphys.2005.06.022] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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27
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The analysis of the derivation principles of kinetic equations based on exactly solvable models of the bulk reaction A+B→Product. Chem Phys 2005. [DOI: 10.1016/j.chemphys.2005.06.036] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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28
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Park S, Shin KJ, Popov AV, Agmon N. Diffusion-influenced excited-state reversible transfer reactions, A*+B⇌C*+D, with two different lifetimes: Theories and simulations. J Chem Phys 2005; 123:34507. [PMID: 16080744 DOI: 10.1063/1.1948369] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report accurate Brownian simulation results for the kinetics of the pseudo-first-order diffusion-influenced excited-state reversible transfer reaction A(*) + Bright harpoon over left harpoonC(*) + D with two different lifetimes using two different propagation algorithms. The results are used to test approximate solutions for this many-particle problem. Available theories fail when one of the two reactions or (decay) rate constants is large. To remedy this situation, we develop two uniform approximations, which are based on introducing a generalized Smoluchowski term into the relaxation-time approximation. The best of these is the extended unified theory of reversible target reactions, which reduces correctly in all limits and exhibits superior agreement with simulations.
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Affiliation(s)
- Soohyung Park
- School of Chemistry, Seoul National University, Korea
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Abstract
The absorption of a photon by a hydroxy-aromatic photoacid triggers a cascade of events contributing to the overall phenomenon of intermolecular excited-state proton transfer. The fundamental steps involved were studied over the last 20 years using a combination of theoretical and experimental techniques. They are surveyed in this sequel in sequential order, from fast to slow. The excitation triggers an intramolecular charge transfer to the ring system, which is more prominent for the anionic base than the acid. The charge redistribution, in turn, triggers changes in hydrogen-bond strengths that set the stage for the proton-transfer step itself. This step is strongly influenced by the solvent, resulting in unusual dependence of the dissociation rate coefficient on water content, temperature, and isotopic substitution. The photolyzed proton can diffuse in the aqueous solution in a mechanism that involves collective changes in hydrogen-bonding. On longer times, it may recombine adiabatically with the excited base or quench it. The theory for these diffusion-influenced geminate reactions has been developed, showing nice agreement with experiment. Finally, the effect of inert salts, bases, and acids on these reactions is analyzed.
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Affiliation(s)
- Noam Agmon
- Department of Physical Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel.
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Ivanov KL, Lukzen NN, Doktorov AB. The integral encounter theory of multistage reactions containing association-dissociation reaction stages. III. Taking account of quantum states of reactants. J Chem Phys 2004; 121:5115-24. [PMID: 15352803 DOI: 10.1063/1.1783273] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The formalism developed in Part I [K. L. Ivanov, N. N. Lukzen, A. A. Kipriyanov, and A. B. Doktorov, Phys. Chem. Chem. Phys. 6, 1706 (2004)] of the present contribution is extended to treat the reacting particles with internal quantum states. Initial spatial correlations of reactants are considered in the framework of this formalism as well.
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Popov AV, Agmon N, Gopich IV, Szabo A. Influence of diffusion on the kinetics of excited-state association–dissociation reactions: Comparison of theory and simulation. J Chem Phys 2004; 120:6111-6. [PMID: 15267495 DOI: 10.1063/1.1649935] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Several recent theories of the kinetics of diffusion influenced excited-state association--dissociation reactions are tested against accurate Brownian dynamics simulation results for a wide range of parameters. The theories include the relaxation time approximation (RTA), multiparticle kernel decoupling approximations and the so-called kinetic theory. In the irreversible limit, none of these theories reduce to the Smoluchowski result. For the pseudo-first-order target problem, we show how the RTA can be modified so that the resulting formalism does reduce correctly in the irreversible limit. We call this the unified Smoluchowski approximation, because it unites modern theories of reversible reactions with Smoluchowski's theory of irreversible reactions.
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Affiliation(s)
- Alexander V Popov
- Department of Physical Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
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Ivanov KL, Lukzen NN, Kipriyanov AA, Doktorov AB. The integral encounter theory of multistage reactions containing association–dissociation reaction stages : Part I. Kinetic equations. Phys Chem Chem Phys 2004. [DOI: 10.1039/b308267a] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Ivanov KL, Lukzen NN, Doktorov AB. The integral encounter theory of multistage reactions containing association–dissociation reaction stages : Part II. The kinetics of reversible excitation binding. Phys Chem Chem Phys 2004. [DOI: 10.1039/b308268g] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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34
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Kim JH, Lee S. Effects of chain stiffness on the quenching of an excited polymer by small quenchers. J Chem Phys 2003. [DOI: 10.1063/1.1624056] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Affiliation(s)
- A. V. Popov
- Department of Physical Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
| | - A. I. Burshtein
- Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel
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Sung J, Silbey RJ. Exact dynamics of a continuous time random walker in the presence of a boundary: beyond the intuitive boundary condition approach. PHYSICAL REVIEW LETTERS 2003; 91:160601. [PMID: 14611387 DOI: 10.1103/physrevlett.91.160601] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2003] [Indexed: 05/24/2023]
Abstract
We derive the exact dynamics of a random walker with arbitrary non-Markovian transport and reaction rate distribution at a boundary, and present exact solutions in the continuum limit. We find that the ultimate escape probability of the particle is independent of the transport mechanism in contradiction to the long-standing belief based on the conventional approach. We also find a phase transition in the relaxation kinetics associated with the heterogeneity of the transport media.
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Affiliation(s)
- Jaeyoung Sung
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Popov AV, Gladkikh VS, Burshtein AI. Stern−Volmer Law in Competing Theories and Approximations. J Phys Chem A 2003. [DOI: 10.1021/jp030007d] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- A. V. Popov
- Department of Physical Chemistry and the Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel
| | - V. S. Gladkikh
- Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel
| | - A. I. Burshtein
- Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel
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Popov AV, Agmon N. Three-dimensional simulations of reversible bimolecular reactions. III. The pseudo-unimolecular ABCD reaction. J Chem Phys 2003. [DOI: 10.1063/1.1570816] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Park J, Kim H, Shin KJ. Excluded volume effect on diffusion-influenced reactions in one dimension. J Chem Phys 2003. [DOI: 10.1063/1.1570409] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ivanov KL, Lukzen NN, Morozov VA, Doktorov AB. Integral encounter theories of multistage reactions. IV. Account of internal quantum states of reactants. J Chem Phys 2002. [DOI: 10.1063/1.1516214] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Popov AV, Agmon N. Three-dimensional simulations of reversible bimolecular reactions. II. The excited-state target problem with different lifetimes. J Chem Phys 2002. [DOI: 10.1063/1.1496455] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Popov AV, Agmon N. Three-dimensional simulations of reversible bimolecular reactions: The simple target problem. J Chem Phys 2001. [DOI: 10.1063/1.1412609] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Pines D, Pines E. Direct observation of power-law behavior in the asymptotic relaxation to equilibrium of a reversible bimolecular reaction. J Chem Phys 2001. [DOI: 10.1063/1.1379572] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sung J, Park H, Lee S. Green's function approach to nonclassical reaction kinetics in fractal media. PHYSICAL REVIEW LETTERS 2001; 86:2463-2466. [PMID: 11289955 DOI: 10.1103/physrevlett.86.2463] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/1999] [Indexed: 05/23/2023]
Abstract
We present an accurate description for the mean field kinetics of the reversible recombination reaction occurring in fractal media, which is in good agreement with Monte Carlo simulation results from an intermediate to a long time region. The central dynamic quantity is the Green's function for the generalized diffusion equation that is defined in a hypothetical space whose dimensionality is given by the fracton dimension d. An exact expression for the Green's function that is valid for arbitrary values of d is presented.
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Affiliation(s)
- J Sung
- School of Chemistry and Molecular Engineering and Center for Molecular Catalysis, Seoul National University, Seoul 151-747, South Korea
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Kwac K, Yang M, Shin KJ. Excited-state reversible association–dissociation reaction: Renormalized kinetic theory in configuration space. J Chem Phys 2001. [DOI: 10.1063/1.1344612] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lee J, Sung J, Lee S. Excluded volume effects on the diffusion-influenced reaction: The many-particle kernel approach. J Chem Phys 2000. [DOI: 10.1063/1.1318738] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Sung J, Lee S. Relations among the modern theories of diffusion-influenced reactions. II. Reduced distribution function theory versus modified integral encounter theory. J Chem Phys 2000. [DOI: 10.1063/1.480780] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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50
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Sung J, Lee S. Relations among the modern theories of diffusion-influenced reactions. I. Reduced distribution function theory versus memory function theory of Yang, Lee, and Shin. J Chem Phys 1999. [DOI: 10.1063/1.480366] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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