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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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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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Yogurtcu ON, Johnson ME. Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates. J Chem Phys 2016; 143:084117. [PMID: 26328828 DOI: 10.1063/1.4929390] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
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 (ka) and diffusion (D) parameters ka/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 multi-parametric 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 ka/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.
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Affiliation(s)
- Osman N Yogurtcu
- Department of Biophysics, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Margaret E Johnson
- Department of Biophysics, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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Echeverria C, Kapral R. Diffusional correlations among multiple active sites in a single enzyme. Phys Chem Chem Phys 2015; 16:6211-6. [PMID: 24562416 DOI: 10.1039/c3cp55252g] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Simulations of the enzymatic dynamics of a model enzyme containing multiple substrate binding sites indicate the existence of diffusional correlations in the chemical reactivity of the active sites. A coarse-grain, particle-based, mesoscopic description of the system, comprising the enzyme, the substrate, the product and solvent, is constructed to study these effects. The reactive and non-reactive dynamics is followed using a hybrid scheme that combines molecular dynamics for the enzyme, substrate and product molecules with multiparticle collision dynamics for the solvent. It is found that the reactivity of an individual active site in the multiple-active-site enzyme is reduced substantially, and this effect is analyzed and attributed to diffusive competition for the substrate among the different active sites in the enzyme.
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Affiliation(s)
- Carlos Echeverria
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada.
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Del Razo MJ, Pan W, Qian H, Lin G. Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction–Diffusion. J Phys Chem B 2014; 118:7037-46. [DOI: 10.1021/jp5030125] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Wenxiao Pan
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Hong Qian
- University of Washington, Seattle, Washington 98195-3925, United States
| | - Guang Lin
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
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Schofield J, Inder P, Kapral R. Modeling of solvent flow effects in enzyme catalysis under physiological conditions. J Chem Phys 2012; 136:205101. [PMID: 22667589 DOI: 10.1063/1.4719539] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
A stochastic model for the dynamics of enzymatic catalysis in explicit, effective solvents under physiological conditions is presented. Analytically-computed first passage time densities of a diffusing particle in a spherical shell with absorbing boundaries are combined with densities obtained from explicit simulation to obtain the overall probability density for the total reaction cycle time of the enzymatic system. The method is used to investigate the catalytic transfer of a phosphoryl group in a phosphoglycerate kinase-ADP-bis phosphoglycerate system, one of the steps of glycolysis. The direct simulation of the enzyme-substrate binding and reaction is carried out using an elastic network model for the protein, and the solvent motions are described by multiparticle collision dynamics which incorporates hydrodynamic flow effects. Systems where solvent-enzyme coupling occurs through explicit intermolecular interactions, as well as systems where this coupling is taken into account by including the protein and substrate in the multiparticle collision step, are investigated and compared with simulations where hydrodynamic coupling is absent. It is demonstrated that the flow of solvent particles around the enzyme facilitates the large-scale hinge motion of the enzyme with bound substrates, and has a significant impact on the shape of the probability densities and average time scales of substrate binding for substrates near the enzyme, the closure of the enzyme after binding, and the overall time of completion of the cycle.
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Affiliation(s)
- Jeremy Schofield
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
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Popov AV, Gould EA, Salvitti MA, Hernandez R, Solntsev KM. Diffusional effects on the reversible excited-state proton transfer. From experiments to Brownian dynamics simulations. Phys Chem Chem Phys 2011; 13:14914-27. [PMID: 21761033 DOI: 10.1039/c1cp20952c] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We have studied an excited state proton transfer (ESPT) from the cationic "super" photoacid N-methyl 6-hydroxyquinolinium perfluorobutane sulfonate to non-aqueous solvents using picosecond and nanosecond time-resolved fluorescence spectroscopy. Upon the photoinduced adiabatic deprotonation from the hydroxyl moiety, a quinolinium zwitterion with a highly anisotropic charge distribution is formed. Due to the complexity of the resultant photodissociated system, the typical description of the reversible ESPT within the framework of the Spherically Symmetric Diffusion Problem (SSDP) is not possible. Additional complications are caused by the presence of a counteranion particle which affects the proton mobility. To better understand the ESPT process, we have performed extensive Brownian dynamics (BD) simulations of this three-body system as a tool to reveal the nature of the nonstationary interaction potentials and to elucidate the role of a counterion in the diffusion and reactive properties of the proton. Moreover, our results demonstrated that the anisotropy of the potential force can be taken into account after adapting this force for use in the SSDP. The results of both BD simulations and SSDP calculation with the adapted force field were used to fit the experimental kinetics of this three-body problem adequately.
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Affiliation(s)
- Alexander V Popov
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA.
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Chen JX, Kapral R. Mesoscopic dynamics of diffusion-influenced enzyme kinetics. J Chem Phys 2011; 134:044503. [DOI: 10.1063/1.3528004] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Park K, Shin KJ, Kim H. Excited-State Reversible Geminate A*+B↔C*+D Reaction in Two Dimensions. Chem Asian J 2010. [DOI: 10.1002/asia.200900585] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Park K, Shin KJ, Kim H. Excited-state reversible geminate recombination in two dimensions. J Chem Phys 2009; 131:154105. [PMID: 20568845 DOI: 10.1063/1.3242273] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Excited-state reversible geminate recombination with two different lifetimes and quenching is investigated in two dimensions. From the exact Green function in the Laplace domain, analytic expressions of two-dimensional survival and binding probabilities are obtained at short and long times. We find that a new pattern of kinetic transition occurs in two dimensions. The long-time effective survival probabilities show a pattern of (ln t)(-1)-->constant-->e(t) depending on the rate constants while the effective binding probabilities show t(-1)(ln t)(-2)-->t(-1)-->e(t).
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Affiliation(s)
- Kihyun Park
- Department of Chemistry, Seoul National University, Seoul 151-747, Republic of Korea
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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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Sung BJ, Yethiraj A. Molecular-dynamics simulations for nonclassical kinetics of diffusion-controlled bimolecular reactions. J Chem Phys 2005; 123:114503. [PMID: 16392569 DOI: 10.1063/1.2035081] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular-dynamics simulations are presented for the diffusion-controlled bimolecular reaction A+B<==>C in two and three dimensions. The reactants and solvent molecules are modeled as spheres interacting via continuous potential-energy functions. The interaction potential between two reactants contains a deep well that results in a reaction. When the solvent concentration is low and the reactant dynamics is essentially ballistic, the system reaches equilibrium rapidly, and the reaction follows classical kinetics with exponential decay to the equilibrium. When the solvent concentration is high the particles enter the normal diffusion regime quickly and nonclassical behavior is observed, i.e., the reactant concentrations approach equilibrium as t(-d/2) where d is the dimensionality of space. When the reaction well depth is large, however, the reaction becomes irreversible within the simulation time. In this case the reactant concentrations decay as t(-d/4). Interestingly this behavior is also observed at intermediate times for reversible reactions.
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Affiliation(s)
- Bong June Sung
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison 53706, USA
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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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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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Gopich IV, Szabo A. Kinetics of reversible diffusion influenced reactions: The self-consistent relaxation time approximation. J Chem Phys 2002. [DOI: 10.1063/1.1482701] [Citation(s) in RCA: 82] [Impact Index Per Article: 3.7] [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: 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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