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Scher Y, Kumar A, Santhanam MS, Reuveni S. Continuous gated first-passage processes. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:108101. [PMID: 39208840 DOI: 10.1088/1361-6633/ad7530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2024] [Accepted: 08/29/2024] [Indexed: 09/04/2024]
Abstract
Gated first-passage processes, where completion depends on both hitting a target and satisfying additional constraints, are prevalent across various fields. Despite their significance, analytical solutions to basic problems remain unknown, e.g. the detection time of a diffusing particle by a gated interval, disk, or sphere. In this paper, we elucidate the challenges posed by continuous gated first-passage processes and present a renewal framework to overcome them. This framework offers a unified approach for a wide range of problems, including those with single-point, half-line, and interval targets. The latter have so far evaded exact solutions. Our analysis reveals that solutions to gated problems can be obtained directly from the ungated dynamics. This, in turn, reveals universal properties and asymptotic behaviors, shedding light on cryptic intermediate-time regimes and refining the notion of high-crypticity for continuous-space gated processes. Moreover, we extend our formalism to higher dimensions, showcasing its versatility and applicability. Overall, this work provides valuable insights into the dynamics of continuous gated first-passage processes and offers analytical tools for studying them across diverse domains.
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Affiliation(s)
- Yuval Scher
- School of Chemistry, Center for the Physics & Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular & Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
| | - Aanjaneya Kumar
- Department of Physics, Indian Institute of Science Education and Research, Dr Homi Bhabha Road, Pune 411008, India
| | - M S Santhanam
- Department of Physics, Indian Institute of Science Education and Research, Dr Homi Bhabha Road, Pune 411008, India
| | - Shlomi Reuveni
- School of Chemistry, Center for the Physics & Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular & Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
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Bebon R, Godec A. Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime. PHYSICAL REVIEW LETTERS 2023; 131:237101. [PMID: 38134782 DOI: 10.1103/physrevlett.131.237101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Revised: 10/18/2023] [Accepted: 10/31/2023] [Indexed: 12/24/2023]
Abstract
We derive general bounds on the probability that the empirical first-passage time τ[over ¯]_{n}≡∑_{i=1}^{n}τ_{i}/n of a reversible ergodic Markov process inferred from a sample of n independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct nonasymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.
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Affiliation(s)
- Rick Bebon
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077 Göttingen, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077 Göttingen, Germany
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Scher Y, Reuveni S. Gated reactions in discrete time and space. J Chem Phys 2021; 155:234112. [PMID: 34937380 DOI: 10.1063/5.0072393] [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
How much time does it take for two molecules to react? If a reaction occurs upon contact, the answer to this question boils down to the classic first-passage time problem: find the time it takes for the two molecules to meet. However, this is not always the case as molecules switch stochastically between reactive and non-reactive states. The reaction is then said to be "gated" by the internal states of the molecules involved, which could have a dramatic influence on kinetics. A unified, continuous-time, approach to gated reactions on networks was presented in a recent paper [Scher and Reuveni, Phys. Rev. Lett. 127, 018301 (2021)]. Here, we build on this recent advancement and develop an analogous discrete-time version of the theory. Similar to continuous-time, we employ a renewal approach to show that the gated reaction time can always be expressed in terms of the corresponding ungated first-passage and return times, which yields formulas for the generating function of the gated reaction-time distribution and its corresponding mean and variance. In cases where the mean reaction time diverges, we show that the long-time asymptotics of the gated problem is inherited from its ungated counterpart. However, when molecules spend most of their time non-reactive, an interim regime of slower power-law decay emerges prior to the terminal asymptotics. The discretization of time also gives rise to resonances and anti-resonances, which were absent from the continuous-time picture. These features are illustrated using two case studies that also demonstrate how the general approach presented herein greatly simplifies the analysis of gated reactions.
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Affiliation(s)
- Yuval Scher
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Mark Ratner Institute for Single Molecule Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Shlomi Reuveni
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Mark Ratner Institute for Single Molecule Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
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Scher Y, Reuveni S. Unified Approach to Gated Reactions on Networks. PHYSICAL REVIEW LETTERS 2021; 127:018301. [PMID: 34270310 DOI: 10.1103/physrevlett.127.018301] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2021] [Revised: 03/20/2021] [Accepted: 06/02/2021] [Indexed: 06/13/2023]
Abstract
For two molecules to react they first have to meet. Yet, reaction times are rarely on par with the first-passage times that govern such molecular encounters. A prime reason for this discrepancy is stochastic transitions between reactive and nonreactive molecular states, which results in effective gating of product formation and altered reaction kinetics. To better understand this phenomenon we develop a unifying approach to gated reactions on networks. We first show that the mean and distribution of the gated reaction time can always be expressed in terms of ungated first-passage and return times. This relation between gated and ungated kinetics is then explored to reveal universal features of gated reactions. The latter are exemplified using a diverse set of case studies which are also used to expose the exotic kinetics that arises due to molecular gating.
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Affiliation(s)
- Yuval Scher
- School of Chemistry, Center for the Physics & Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular & Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
| | - Shlomi Reuveni
- School of Chemistry, Center for the Physics & Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular & Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
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Bressloff PC, Karamched BR, Lawley SD, Levien E. Diffusive transport in the presence of stochastically gated absorption. Phys Rev E 2017; 96:022102. [PMID: 28950455 DOI: 10.1103/physreve.96.022102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2017] [Indexed: 11/07/2022]
Abstract
We analyze a population of Brownian particles moving in a spatially uniform environment with stochastically gated absorption. The state of the environment at time t is represented by a discrete stochastic variable k(t)∈{0,1} such that the rate of absorption is γ[1-k(t)], with γ a positive constant. The variable k(t) evolves according to a two-state Markov chain. We focus on how stochastic gating affects the attenuation of particle absorption with distance from a localized source in a one-dimensional domain. In the static case (no gating), the steady-state attenuation is given by an exponential with length constant sqrt[D/γ], where D is the diffusivity. We show that gating leads to slower, nonexponential attenuation. We also explore statistical correlations between particles due to the fact that they all diffuse in the same switching environment. Such correlations can be determined in terms of moments of the solution to a corresponding stochastic Fokker-Planck equation.
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Affiliation(s)
- Paul C Bressloff
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USA
| | - Bhargav R Karamched
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USA
| | - Sean D Lawley
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USA
| | - Ethan Levien
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USA
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Berezhkovskii AM, Bezrukov SM. Effect of stochastic gating on channel-facilitated transport of non-interacting and strongly repelling solutes. J Chem Phys 2017; 147:084109. [PMID: 28863525 DOI: 10.1063/1.4986902] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ligand- or voltage-driven stochastic gating-the structural rearrangements by which the channel switches between its open and closed states-is a fundamental property of biological membrane channels. Gating underlies the channel's ability to respond to different stimuli and, therefore, to be functionally regulated by the changing environment. The accepted understanding of the gating effect on the solute flux through the channel is that the mean flux is the product of the flux through the open channel and the probability of finding the channel in the open state. Here, using a diffusion model of channel-facilitated transport, we show that this is true only when the gating is much slower than the dynamics of solute translocation through the channel. If this condition breaks, the mean flux could differ from this simple estimate by orders of magnitude.
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Affiliation(s)
- Alexander M Berezhkovskii
- Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Sergey M Bezrukov
- Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
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Berezhkovskii AM, Shvartsman SY. Diffusive flux in a model of stochastically gated oxygen transport in insect respiration. J Chem Phys 2016; 144:204101. [PMID: 27250273 DOI: 10.1063/1.4950769] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.
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Affiliation(s)
- Alexander M Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Stanislav Y Shvartsman
- Department of Chemical and Biological Engineering and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA
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Bressloff PC, Lawley SD. Stochastically gated diffusion-limited reactions for a small target in a bounded domain. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062117. [PMID: 26764642 DOI: 10.1103/physreve.92.062117] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2015] [Indexed: 06/05/2023]
Abstract
We calculate the reaction rate for stochastically gated ligands diffusing in a two-dimensional and a three-dimensional bounded domain with a single small target. Each ligand independently switches between an open and a closed state according to a two-state Markov process; a reaction between ligand and target can only occur when the former is an open state. In the large-time limit the reaction-rate is an exponentially decaying function of time, whose rate of decay is given by the principal eigenvalue of the Laplacian. We calculate the principal eigenvalue using matched asymptotics and determine the leading-order reduction in the reaction rate due to stochastic gating. We also develop a probabilistic interpretation of the reaction rate in terms of the first-passage time density to the target.
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Affiliation(s)
- Paul C Bressloff
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USA
| | - Sean D Lawley
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USA
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Rojo F, Wio HS, Budde CE. Narrow-escape-time problem: the imperfect trapping case. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:031105. [PMID: 23030864 DOI: 10.1103/physreve.86.031105] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2012] [Revised: 08/14/2012] [Indexed: 06/01/2023]
Abstract
We present a master equation approach to the narrow escape time (NET) problem, i.e., the time needed for a particle contained in a confining domain with a single narrow opening to exit the domain for the first time. We introduce a finite transition probability, ν, at the narrow escape window, allowing the study of the imperfect trapping case. Ranging from 0 to ∞, ν allowed the study of both extremes of the trapping process: that of a highly deficient capture and situations where escape is certain ("perfect trapping" case). We have obtained analytic results for the basic quantity studied in the NET problem, the mean escape time, and we have studied its dependence in terms of the transition (desorption) probability over (from) the surface boundary, the confining domain dimensions, and the finite transition probability at the escape window. Particularly we show that the existence of a global minimum in the NET depends on the "imperfection" of the trapping process. In addition to our analytical approach, we have implemented Monte Carlo simulations, finding excellent agreement between the theoretical results and simulations.
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Affiliation(s)
- Félix Rojo
- Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina
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Rojo F, Pury PA, Budde CE. Intermittent pathways towards a dynamical target. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:011116. [PMID: 21405670 DOI: 10.1103/physreve.83.011116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2010] [Indexed: 05/30/2023]
Abstract
In this paper, we investigate the quest for a single target, which remains fixed in a lattice, by a set of independent walkers. The target exhibits fluctuating behavior between a trap and an ordinary site of the lattice, whereas the walkers perform an intermittent kind of search strategy. Our searchers carry out their movements in one of two states, between which they switch randomly. One of these states (the exploratory phase) is a symmetric nearest-neighbor random walk and the other state (the relocating phase) is a symmetric next-nearest-neighbor random walk. By using the multistate continuous-time random-walk approach we are able to show that for dynamical targets, the intermittent strategy (despite the simplicity of the kinetics chosen for searching) improves detection, in comparison to displacements in a single state. We have obtained analytic results, which can be numerically evaluated, for the survival probability and for the lifetime of the target. Thus, we have studied the dependence of these quantities both in terms of the transition probability that describes the dynamics of the target and in terms of the parameter that characterizes the walkers' intermittency. In addition to our analytical approach, we have implemented Monte Carlo simulations, finding excellent agreement between the theoretical-numerical results and simulations.
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Affiliation(s)
- Félix Rojo
- FaMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba, Argentina
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Berlin YA, Burin AL, Siebbeles LDA, Ratner MA. Conformationally Gated Rate Processes in Biological Macromolecules. J Phys Chem A 2001. [DOI: 10.1021/jp004436c] [Citation(s) in RCA: 64] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yuri A. Berlin
- Department of Chemistry, Center for Nanofabrication and Molecular Self-Assembly and Materials Research Center, Northwestern University, 2145 N Sheridan Road, Evanston, Illinois 60208-3113, and IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
| | - Alexander L. Burin
- Department of Chemistry, Center for Nanofabrication and Molecular Self-Assembly and Materials Research Center, Northwestern University, 2145 N Sheridan Road, Evanston, Illinois 60208-3113, and IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
| | - Laurens D. A. Siebbeles
- Department of Chemistry, Center for Nanofabrication and Molecular Self-Assembly and Materials Research Center, Northwestern University, 2145 N Sheridan Road, Evanston, Illinois 60208-3113, and IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
| | - Mark A. Ratner
- Department of Chemistry, Center for Nanofabrication and Molecular Self-Assembly and Materials Research Center, Northwestern University, 2145 N Sheridan Road, Evanston, Illinois 60208-3113, and IRI, Radiation Chemistry Department, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
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Barzykin AV, Seki K, Tachiya M. Kinetics of diffusion-assisted reactions in microheterogeneous systems. Adv Colloid Interface Sci 2001; 89-90:47-140. [PMID: 11215811 DOI: 10.1016/s0001-8686(00)00053-1] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Abstract
This review is focused on the basic theory of diffusion-assisted reactions in microheterogeneous systems, from porous solids to self-organized colloids and biomolecules. Rich kinetic behaviors observed experimentally are explained in a unified fashion using simple concepts of competing distance and time scales of the reaction and the embedding structure. We mainly consider pseudo-first-order reactions, such as luminescence quenching, described by the Smoluchowski type of equation for the reactant pair distribution function with a sink term defined by the reaction mechanism. Microheterogeneity can affect the microscopic rate constant. It also enters the evolution equation through various spatial constraints leading to complicated boundary conditions and, possibly, to the reduction of dimensionality of the diffusion space. The reaction coordinate and diffusive motion along this coordinate are understood in a general way, depending on the problem at hand. Thus, the evolution operator can describe translational and rotational diffusion of molecules in a usual sense, it can be a discrete random walk operator when dealing with hopping of adsorbates in solids, or it can correspond to conformational fluctuations in proteins. Mathematical formulation is universal but physical consequences can be different. Understanding the principal features of reaction kinetics in microheterogeneous systems enables one to extract important structural and dynamical information about the host environments by analyzing suitably designed experiments, it helps building effective strategies for computer simulations, and ultimately opens possibilities for designing systems with controllable reactivity properties.
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Affiliation(s)
- A V Barzykin
- National Institute of Materials and Chemical Research, Tsukuba, Ibaraki, Japan.
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Benichou O, Moreau M, Oshanin G. Kinetics of stochastically gated diffusion-limited reactions and geometry of random walk trajectories. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:3388-3406. [PMID: 11088115 DOI: 10.1103/physreve.61.3388] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/1999] [Indexed: 05/23/2023]
Abstract
In this paper we study the kinetics of diffusion-limited, pseudo-first-order A+B-->B reactions in situations in which the particles' intrinsic reactivities are not constant but vary randomly in time. That is, we suppose that the particles are bearing "gates" which fluctuate in time, randomly and independently of each other, between two states-an active state, when the reaction may take place between A and B particles appearing in close contact; and a blocked state, when the reaction is completely inhibited. We focus here on two customary limiting cases of pseudo-first-order reactions-the so-called target annihilation and the Rosenstock trapping model-and consider four different particular models, such that the A particle can be either mobile or immobile or gated or ungated, and ungated or gated B particles can be fixed at random positions or move randomly. All models are formulated on a d-dimensional regular lattice, and we suppose that the mobile species perform independent, homogeneous, discrete-time lattice random walks. The model involving a single, immobile, ungated target A and a concentration of mobile, gated B particles is solved exactly. For the remaining three models we determine exactly, in the form of rigorous lower and upper bounds showing the same N dependence, the large-N asymptotical behavior of the probability that the A particle survives until the Nth step. We also realize that for all four models studied here the A particle survival probability can be interpreted as the moment generating function of some functionals of random walk trajectories, such as, e. g., the number of self-intersections, the number of sites visited exactly a given number of times, the "residence time" on a random array of lattice sites, etc. Our results thus apply to the asymptotic behavior of corresponding generating functions which are not known as yet.
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Affiliation(s)
- O Benichou
- Laboratoire de Physique Theorique des Liquides (CNRS-UMR 7600), Universite Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France
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Re MA, Budde CE. Diffusion-mediated reactions with a time-dependent absorption rate. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:1110-1120. [PMID: 11046381 DOI: 10.1103/physreve.61.1110] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/1999] [Indexed: 05/23/2023]
Abstract
Diffusion-mediated reactions models are particularly useful for the characterization of physical, chemical, and biological problems. In this paper we present a theoretical study of the absorption probability density, survival probability, and reaction rate for diffusion-mediated reactions models with a time-dependent finite absorption rate (an extension of a model usually referred to as the "imperfect trap model"). The results are obtained by means of the formalism of continuous time random walk on a lattice and considering a general reaction dynamics upon encounter of the reactives. First jump probability densities are included to take initial conditions into account. Previous results presented by Collins and Kimball [J. Colloid. Sci. 4, 425 (1949)] and Noyes [J. Chem. Phys. 22, 1349 (1954)] are reobtained for the particular case of a time-independent absorptivity. Short and long time behaviors are analyzed resulting, in particular, in that the long time behavior of the absorption probability density exhibits the same time dependence as the first passage time density. The results obtained are illustrated by considering a one-dimensional model with consequent discussion.
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Affiliation(s)
- MA Re
- Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Ciudad Universitaria, 5010 Cordoba, Argentina
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Shushin AI. Specific Features of Kinetics of Stochastically Gated, Diffusion-Controlled Reactions. J Phys Chem A 1999. [DOI: 10.1021/jp9836729] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- A. I. Shushin
- Institute of Chemical Physics, Russian Academy of Sciences, 117977, GSP-1 Kosygin str 4, Moscow, Russia
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Makhnovskii YA, Berezhkovskii AM, Sheu SY, Yang DY, Kuo J, Lin SH. Stochastic gating influence on the kinetics of diffusion-limited reactions. J Chem Phys 1998. [DOI: 10.1063/1.475460] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Jung Y, Hyeon C, Shin S, Lee S. Effects of a quantum-mechanically driven two-state gating mode on the diffusion-influenced bimolecular reactions. J Chem Phys 1997. [DOI: 10.1063/1.475284] [Citation(s) in RCA: 4] [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)
- John L. Spouge
- National Center for Biotechnology Information, National Library of Medicine, Bethesda, Maryland 20894
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Berezhkovskii AM, Yang DY, Lin SH, Makhnovskii YA, Sheu SY. Smoluchowski-type theory of stochastically gated diffusion-influenced reactions. J Chem Phys 1997. [DOI: 10.1063/1.473722] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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