1
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Raja Venkatesh A, Le KH, Weld DM, Brandman O. Diffusive lensing as a mechanism of intracellular transport and compartmentalization. eLife 2024; 12:RP89794. [PMID: 38896469 PMCID: PMC11186627 DOI: 10.7554/elife.89794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/21/2024] Open
Abstract
While inhomogeneous diffusivity has been identified as a ubiquitous feature of the cellular interior, its implications for particle mobility and concentration at different length scales remain largely unexplored. In this work, we use agent-based simulations of diffusion to investigate how heterogeneous diffusivity affects the movement and concentration of diffusing particles. We propose that a nonequilibrium mode of membrane-less compartmentalization arising from the convergence of diffusive trajectories into low-diffusive sinks, which we call 'diffusive lensing,' is relevant for living systems. Our work highlights the phenomenon of diffusive lensing as a potentially key driver of mesoscale dynamics in the cytoplasm, with possible far-reaching implications for biochemical processes.
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Affiliation(s)
- Achuthan Raja Venkatesh
- Department of Biochemistry, Stanford UniversityStanfordUnited States
- Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) MohaliMohaliIndia
| | - Kathy H Le
- Department of Biochemistry, Stanford UniversityStanfordUnited States
| | - David M Weld
- Department of Physics, University of California, Santa BarbaraSanta BarbaraUnited States
| | - Onn Brandman
- Department of Biochemistry, Stanford UniversityStanfordUnited States
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2
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Ali SY, Bauri P, Mondal D. Optimizing Work Extraction in the Presence of an Entropic Potential: An Entropic Stochastic Resonance. J Phys Chem B 2024; 128:3824-3832. [PMID: 38616737 DOI: 10.1021/acs.jpcb.3c08066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/16/2024]
Abstract
We study the nontrivial thermodynamic responses of an overdamped Brownian system driven by an unbiased driving force when the particle is confined inside a bilobal irregular structure. The spatial irregularity of the confinement results in an effective entropic bistable potential along the direction of transport. We calculate the thermodynamic response functions in terms of the averaged work done and the absorbed heat over a cycle of driving. We find that the thermodynamic responses are influenced by the nonlinearity of the effective entropic potential, the frequency of the external periodic driving force, and the random thermal fluctuations in a nontrivial way. In the presence of an optimal amount of thermal noise and a favoring driving frequency, the process exhibits a resonance-like precedent in terms of both output work and absorbed heat. We explore the conditions to get best synchronized work extraction (or absorbed heat), which can be utilized as a potential quantifier of an entropic stochastic resonance phenomenon. Finally, we identify a hallmark of entropy dominance over an analogous energy-driven scenario in terms of output work.
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Affiliation(s)
- Syed Yunus Ali
- Department of Chemistry and Center for Atomic, Molecular, and Optical Sciences & Technologies, Indian Institute of Technology Tirupati, Yerpedu 517619, Andhra Pradesh, India
| | - Prashanta Bauri
- Department of Chemistry and Center for Atomic, Molecular, and Optical Sciences & Technologies, Indian Institute of Technology Tirupati, Yerpedu 517619, Andhra Pradesh, India
| | - Debasish Mondal
- Department of Chemistry and Center for Atomic, Molecular, and Optical Sciences & Technologies, Indian Institute of Technology Tirupati, Yerpedu 517619, Andhra Pradesh, India
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3
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Go BG, Jeon E, Kim YW. Active search for a reactive target in thermal environments. J Chem Phys 2024; 160:044103. [PMID: 38258927 DOI: 10.1063/5.0179968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2023] [Accepted: 12/15/2023] [Indexed: 01/24/2024] Open
Abstract
We study a stochastic process where an active particle, modeled by a one-dimensional run-and-tumble particle, searches for a target with a finite absorption strength in thermal environments. Solving the Fokker-Planck equation for a uniform initial distribution, we analytically calculate the mean searching time (MST), the time for the active particle to be finally absorbed, and show that there exists an optimal self-propulsion velocity of the active particle at which MST is minimized. As the diffusion constant increases, the optimal velocity changes from a finite value to zero, which implies that a purely diffusive Brownian motion outperforms an active motion in terms of searching time. Depending on the absorption strength of the target, the transition of the optimal velocity becomes either continuous or discontinuous, which can be understood based on the Landau approach. In addition, we obtain the phase diagram indicating the passive-efficient and the active-efficient regions. Finally, the initial condition dependence of MST is presented in limiting cases.
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Affiliation(s)
- Byeong Guk Go
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Euijin Jeon
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Yong Woon Kim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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4
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Jeon E, Go BG, Kim YW. Searching for a partially absorbing target by a run-and-tumble particle in a confined space. Phys Rev E 2024; 109:014103. [PMID: 38366428 DOI: 10.1103/physreve.109.014103] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2023] [Accepted: 11/30/2023] [Indexed: 02/18/2024]
Abstract
A random search of a partially absorbing target by a run-and-tumble particle in a confined one-dimensional space is investigated. We analytically obtain the mean searching time, which shows a nonmonotonic behavior as a function of the self-propulsion speed of the active particle, indicating the existence of an optimal speed, when the absorption strength of the target is finite. In the limit of large and small absorption strengths, respectively, asymptotes of the mean searching time and the optimal speed are found. We also demonstrate that the first-passage problem of a diffusive run-and-tumble particle in high dimensions can be mapped into a one-dimensional problem with a partially absorbing target. Finally, as a practical application exploiting the existence of the optimal speed, we propose a filtering device to extract active particles with a desired speed and evaluate how the resolution of the filtering device depends on the absorption strength.
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Affiliation(s)
- Euijin Jeon
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Byeong Guk Go
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Yong Woon Kim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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5
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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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6
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Chun HM, Hwang S, Kahng B, Rieger H, Noh JD. Heterogeneous Mean First-Passage Time Scaling in Fractal Media. PHYSICAL REVIEW LETTERS 2023; 131:227101. [PMID: 38101364 DOI: 10.1103/physrevlett.131.227101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 11/03/2023] [Indexed: 12/17/2023]
Abstract
The mean first passage time (MFPT) of random walks is a key quantity characterizing dynamic processes on disordered media. In a random fractal embedded in the Euclidean space, the MFPT is known to obey the power law scaling with the distance between a source and a target site with a universal exponent. We find that the scaling law for the MFPT is not determined solely by the distance between a source and a target but also by their locations. The role of a site in the first passage processes is quantified by the random walk centrality. It turns out that the site of highest random walk centrality, dubbed as a hub, intervenes in first passage processes. We show that the MFPT from a departure site to a target site is determined by a competition between direct paths and indirect paths detouring via the hub. Consequently, the MFPT displays a crossover scaling between a short distance regime, where direct paths are dominant, and a long distance regime, where indirect paths are dominant. The two regimes are characterized by power laws with different scaling exponents. The crossover scaling behavior is confirmed by extensive numerical calculations of the MFPTs on the critical percolation cluster in two dimensional square lattices.
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Affiliation(s)
- Hyun-Myung Chun
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
| | | | - Byungnam Kahng
- Center for Complex Systems Studies, and KENTECH Institute for Grid Modernization, Korea Institute of Energy Technology, Naju 58217, Korea
| | - Heiko Rieger
- Center for Biophysics and Department of Theoretical Physics, Saarland University, 66123 Saarbrücken, Germany
- Lebniz-Institute for New Materials INM, 66123 Saarbrücken, Germany
| | - Jae Dong Noh
- Department of Physics, University of Seoul, Seoul 02504, Korea
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7
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Grebenkov DS. Diffusion-Controlled Reactions: An Overview. Molecules 2023; 28:7570. [PMID: 38005291 PMCID: PMC10674959 DOI: 10.3390/molecules28227570] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2023] [Revised: 10/20/2023] [Accepted: 10/21/2023] [Indexed: 11/26/2023] Open
Abstract
We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski, who recognized the importance of diffusion in chemical reactions, we discuss perfect and imperfect surface reactions, their microscopic origins, and the underlying mathematical framework. Single-molecule reaction schemes, anomalous bulk diffusions, reversible binding/unbinding kinetics, and many other extensions are presented. An alternative encounter-based approach to diffusion-controlled reactions is introduced, with emphasis on its advantages and potential applications. Some open problems and future perspectives are outlined.
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Affiliation(s)
- Denis S Grebenkov
- Laboratoire de Physique de la Matière Condensée, CNRS-Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
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8
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Lauber N, Tichacek O, Narayanankutty K, De Martino D, Ruiz-Mirazo K. Collective catalysis under spatial constraints: Phase separation and size-scaling effects on mass action kinetics. Phys Rev E 2023; 108:044410. [PMID: 37978605 DOI: 10.1103/physreve.108.044410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 09/07/2023] [Indexed: 11/19/2023]
Abstract
Chemical reactions are usually studied under the assumption that both substrates and catalysts are well-mixed (WM) throughout the system. Although this is often applicable to test-tube experimental conditions, it is not realistic in cellular environments, where biomolecules can undergo liquid-liquid phase separation (LLPS) and form condensates, leading to important functional outcomes, including the modulation of catalytic action. Similar processes may also play a role in protocellular systems, like primitive coacervates, or in membrane-assisted prebiotic pathways. Here we explore whether the demixing of catalysts could lead to the formation of microenvironments that influence the kinetics of a linear (multistep) reaction pathway, as compared to a WM system. We implemented a general lattice model to simulate LLPS of a collection of different catalysts and extended it to include diffusion and a sequence of reactions of small substrates. We carried out a quantitative analysis of how the phase separation of the catalysts affects reaction times depending on the affinity between substrates and catalysts, the length of the reaction pathway, the system size, and the degree of homogeneity of the condensate. A key aspect underlying the differences reported between the two scenarios is that the scale invariance observed in the WM system is broken by condensation processes. The main theoretical implications of our results for mean-field chemistry are drawn, extending the mass action kinetics scheme to include substrate initial "hitting times" to reach the catalysts condensate. We finally test this approach by considering open nonlinear conditions, where we successfully predict, through microscopic simulations, that phase separation inhibits chemical oscillatory behavior, providing a possible explanation for the marginal role that this complex dynamic behavior plays in real metabolisms.
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Affiliation(s)
- Nino Lauber
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Donostia International Physics Center, 20018 Donostia-San Sebastian, Spain
- Department of Philosophy, University of the Basque Country, 20018 Donostia-San Sebastian, Spain
| | - Ondrej Tichacek
- Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences, 160 00 Prague, Czech Republic
| | - Krishnadev Narayanankutty
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Department of Molecular Biology and Biochemistry, University of the Basque Country, 48940 Leioa, Spain
| | - Daniele De Martino
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Ikerbasque Foundation, 48009 Bilbao, Spain
| | - Kepa Ruiz-Mirazo
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Department of Philosophy, University of the Basque Country, 20018 Donostia-San Sebastian, Spain
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9
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Kischuck LT, Brown AI. Tube geometry controls protein cluster conformation and stability on the endoplasmic reticulum surface. SOFT MATTER 2023; 19:6771-6783. [PMID: 37642520 DOI: 10.1039/d3sm00694h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
The endoplasmic reticulum (ER), a cellular organelle that forms a cell-spanning network of tubes and sheets, is an important location of protein synthesis and folding. When the ER experiences sustained unfolded protein stress, IRE1 proteins embedded in the ER membrane activate and assemble into clusters as part of the unfolded protein response (UPR). We use kinetic Monte Carlo simulations to explore IRE1 clustering dynamics on the surface of ER tubes. While initially growing clusters are approximately round, once a cluster is sufficiently large a shorter interface length can be achieved by 'wrapping' around the ER tube. A wrapped cluster can grow without further interface length increases. Relative to wide tubes, narrower tubes enable cluster wrapping at smaller cluster sizes. Our simulations show that wrapped clusters on narrower tubes grow more rapidly, evaporate more slowly, and require a lower protein concentration to grow compared to equal-area round clusters on wider tubes. These results suggest that cluster wrapping, facilitated by narrower tubes, could be an important factor in the growth and stability of IRE1 clusters and thus impact the persistence of the UPR, connecting geometry to signaling behavior. This work is consistent with recent experimental observations of IRE1 clusters wrapped around narrow tubes in the ER network.
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Affiliation(s)
- Liam T Kischuck
- Department of Physics, Toronto Metropolitan University, Toronto, Ontario, M5B 2K3, Canada.
| | - Aidan I Brown
- Department of Physics, Toronto Metropolitan University, Toronto, Ontario, M5B 2K3, Canada.
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10
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Scott ZC, Koning K, Vanderwerp M, Cohen L, Westrate LM, Koslover EF. Endoplasmic reticulum network heterogeneity guides diffusive transport and kinetics. Biophys J 2023; 122:3191-3205. [PMID: 37401053 PMCID: PMC10432226 DOI: 10.1016/j.bpj.2023.06.022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Revised: 05/17/2023] [Accepted: 06/28/2023] [Indexed: 07/05/2023] Open
Abstract
The endoplasmic reticulum (ER) is a dynamic network of interconnected sheets and tubules that orchestrates the distribution of lipids, ions, and proteins throughout the cell. The impact of its complex, dynamic morphology on its function as an intracellular transport hub remains poorly understood. To elucidate the functional consequences of ER network structure and dynamics, we quantify how the heterogeneity of the peripheral ER in COS7 cells affects diffusive protein transport. In vivo imaging of photoactivated ER membrane proteins demonstrates their nonuniform spreading to adjacent regions, in a manner consistent with simulations of diffusing particles on extracted network structures. Using a minimal network model to represent tubule rearrangements, we demonstrate that ER network dynamics are sufficiently slow to have little effect on diffusive protein transport. Furthermore, stochastic simulations reveal a novel consequence of ER network heterogeneity: the existence of "hot spots" where sparse diffusive reactants are more likely to find one another. ER exit sites, specialized domains regulating cargo export from the ER, are shown to be disproportionately located in highly accessible regions, further from the outer boundary of the cell. Combining in vivo experiments with analytic calculations, quantitative image analysis, and computational modeling, we demonstrate how structure guides diffusive protein transport and reactions in the ER.
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Affiliation(s)
| | - Katherine Koning
- Department of Chemistry and Biochemistry, Calvin University, Grand Rapids, Michigan
| | - Molly Vanderwerp
- Department of Chemistry and Biochemistry, Calvin University, Grand Rapids, Michigan
| | | | - Laura M Westrate
- Department of Chemistry and Biochemistry, Calvin University, Grand Rapids, Michigan
| | - Elena F Koslover
- Department of Physics, University of California, San Diego, La Jolla, California.
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11
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Guo S, Saha I, Saffarian S, Johnson ME. Structure of the HIV immature lattice allows for essential lattice remodeling within budded virions. eLife 2023; 12:e84881. [PMID: 37435945 PMCID: PMC10361719 DOI: 10.7554/elife.84881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2022] [Accepted: 07/12/2023] [Indexed: 07/13/2023] Open
Abstract
For HIV virions to become infectious, the immature lattice of Gag polyproteins attached to the virion membrane must be cleaved. Cleavage cannot initiate without the protease formed by the homo-dimerization of domains linked to Gag. However, only 5% of the Gag polyproteins, termed Gag-Pol, carry this protease domain, and they are embedded within the structured lattice. The mechanism of Gag-Pol dimerization is unknown. Here, we use spatial stochastic computer simulations of the immature Gag lattice as derived from experimental structures, showing that dynamics of the lattice on the membrane is unavoidable due to the missing 1/3 of the spherical protein coat. These dynamics allow for Gag-Pol molecules carrying the protease domains to detach and reattach at new places within the lattice. Surprisingly, dimerization timescales of minutes or less are achievable for realistic binding energies and rates despite retaining most of the large-scale lattice structure. We derive a formula allowing extrapolation of timescales as a function of interaction free energy and binding rate, thus predicting how additional stabilization of the lattice would impact dimerization times. We further show that during assembly, dimerization of Gag-Pol is highly likely and therefore must be actively suppressed to prevent early activation. By direct comparison to recent biochemical measurements within budded virions, we find that only moderately stable hexamer contacts (-12kBT<∆G<-8kBT) retain both the dynamics and lattice structures that are consistent with experiment. These dynamics are likely essential for proper maturation, and our models quantify and predict lattice dynamics and protease dimerization timescales that define a key step in understanding formation of infectious viruses.
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Affiliation(s)
- Sikao Guo
- TC Jenkins Department of Biophysics, Johns Hopkins UniversityBaltimoreUnited States
| | - Ipsita Saha
- Laboratory of Cell and Developmental Signaling, Center for Cancer Research, National Cancer Institute, National Institutes of HealthFrederickUnited States
| | - Saveez Saffarian
- Center for Cell and Genome Science, University of UtahSalt Lake CityUnited States
- Department of Physics and Astronomy, University of UtahSalt Lake CityUnited States
- School of Biological Sciences, University of UtahSalt Lake CityUnited States
| | - Margaret E Johnson
- TC Jenkins Department of Biophysics, Johns Hopkins UniversityBaltimoreUnited States
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12
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Aquino T, Le Borgne T, Heyman J. Fluid-Solid Reaction in Porous Media as a Chaotic Restart Process. PHYSICAL REVIEW LETTERS 2023; 130:264001. [PMID: 37450789 DOI: 10.1103/physrevlett.130.264001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2022] [Revised: 02/10/2023] [Accepted: 06/05/2023] [Indexed: 07/18/2023]
Abstract
Chemical and biological reactions at fluid-solid interfaces are central to a broad range of porous material applications and research. Pore-scale solute transport limitations can reduce reaction rates, with marked consequences for a wide spectrum of natural and engineered processes. Recent advances show that chaotic mixing occurs spontaneously in porous media, but its impact on surface reactions is unknown. We show that pore-scale chaotic mixing significantly increases reaction efficiency compared to nonchaotic flows. We find that reaction rates are well described in terms of diffusive first-passage times of reactants to the solid interface subjected to a stochastic restart process resulting from Lagrangian chaos. Under chaotic mixing, the shear layer at no-slip interfaces sets the restart rate and leads to a characteristic scaling of reaction efficiency with Péclet number, in excellent agreement with numerical simulations. Reaction rates are insensitive to the flow topology as long as flow is chaotic, suggesting the relevance of this process to a broad range of porous materials.
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Affiliation(s)
- Tomás Aquino
- Spanish National Research Council (IDAEA - CSIC), 08034 Barcelona, Spain
- Université de Rennes, CNRS, Géosciences Rennes, UMR 6118, 35000 Rennes, France
| | - Tanguy Le Borgne
- Université de Rennes, CNRS, Géosciences Rennes, UMR 6118, 35000 Rennes, France
| | - Joris Heyman
- Université de Rennes, CNRS, Géosciences Rennes, UMR 6118, 35000 Rennes, France
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13
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Ro S, Yi J, Kim YW. Target searches of interacting Brownian particles in dilute systems. Phys Rev E 2023; 107:064143. [PMID: 37464617 DOI: 10.1103/physreve.107.064143] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2022] [Accepted: 06/05/2023] [Indexed: 07/20/2023]
Abstract
We study the target searches of interacting Brownian particles in a finite domain, focusing on the effect of interparticle interactions on the search time. We derive the integral equation for the mean first-passage time and acquire its solution as a series expansion in the orders of the Mayer function. We analytically obtain the leading order correction to the search time for dilute systems, which are most relevant to target search problems and prove a universal relation given by the particle density and the second virial coefficient. Finally, we validate our theoretical prediction by Langevin dynamics simulations for the various types of the interaction potential.
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Affiliation(s)
- Sunghan Ro
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Juyeon Yi
- Department of Physics, Pusan National University, Busan 46241, Korea
| | - Yong Woon Kim
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Physics, Korea Advanced Institute of Science and Technology, Deajeon 34141, Korea
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14
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Grebenkov DS. Encounter-based approach to the escape problem. Phys Rev E 2023; 107:044105. [PMID: 37198799 DOI: 10.1103/physreve.107.044105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2023] [Accepted: 03/23/2023] [Indexed: 05/19/2023]
Abstract
We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to deal with a more general setting, in which the reactive region is surrounded by a reflecting boundary with an escape region. We derive a spectral expansion for the full propagator and investigate the behavior and probabilistic interpretations of the associated probability flux density. In particular, we obtain the joint probability density of the escape time and the number of encounters with the reactive region before escape, and the probability density of the first-crossing time of a prescribed number of encounters. We briefly discuss generalizations of the conventional Poissonian-type surface reaction mechanism described by Robin boundary condition and potential applications of this formalism in chemistry and biophysics.
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Affiliation(s)
- Denis S Grebenkov
- Laboratoire de Physique de la Matière Condensée, CNRS-Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
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15
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Dong JQ, Han WH, Wang Y, Chen XS, Huang L. Universal cover-time distribution of heterogeneous random walks. Phys Rev E 2023; 107:024128. [PMID: 36932492 DOI: 10.1103/physreve.107.024128] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 01/24/2023] [Indexed: 06/18/2023]
Abstract
The cover-time problem, i.e., the time to visit every site in a system, is one of the key issues of random walks with wide applications in natural, social, and engineered systems. Addressing the full distribution of cover times for random walk on complex structures has been a long-standing challenge and has attracted persistent efforts. Usually it is assumed that the random walk is noncompact, to facilitate theoretical treatments by neglecting the correlations between visits. The known results are essentially limited to noncompact and homogeneous systems, where different sites are on an equal footing and have identical or close mean first-passage times, such as random walks on a torus. In contrast, realistic random walks are prevailingly heterogeneous with diversified mean first-passage times. Does a universal distribution still exist? Here, by considering the most general situations of noncompact random walks, we uncover a generalized rescaling relation for the cover time, exploiting the diversified mean first-passage times that have not been accounted for before. This allows us to concretely establish a universal distribution of the rescaled cover times for heterogeneous noncompact random walks, which turns out to be the Gumbel universality class that is ubiquitous for a large family of extreme value statistics. Our analysis is based on the transfer matrix framework, which is generic in that, besides heterogeneity, it is also robust against biased protocols, directed links, and self-connecting loops. The finding is corroborated with extensive numerical simulations of diverse heterogeneous noncompact random walks on both model and realistic topological structures. Our technical ingredient may be exploited for other extreme value or ergodicity problems with nonidentical distributions.
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Affiliation(s)
- Jia-Qi Dong
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing 100190, China
| | - Wen-Hui Han
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Yisen Wang
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Xiao-Song Chen
- School of Systems Science, Beijing Normal University, Beijing 100875, China
| | - Liang Huang
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
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16
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Yang Z, Koslover EF. Diffusive exit rates through pores in membrane-enclosed structures. Phys Biol 2023; 20. [PMID: 36626849 DOI: 10.1088/1478-3975/acb1ea] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Accepted: 01/10/2023] [Indexed: 01/11/2023]
Abstract
The function of many membrane-enclosed intracellular structures relies on release of diffusing particles that exit through narrow pores or channels in the membrane. The rate of release varies with pore size, density, and length of the channel. We propose a simple approximate model, validated with stochastic simulations, for estimating the effective release rate from cylinders, and other simple-shaped domains, as a function of channel parameters. The results demonstrate that, for very small pores, a low density of channels scattered over the boundary is sufficient to achieve substantial rates of particle release. Furthermore, we show that increasing the length of passive channels will both reduce release rates and lead to a less steep dependence on channel density. Our results are compared to previously-measured local calcium release rates from tubules of the endoplasmic reticulum, providing an estimate of the relevant channel density responsible for the observed calcium efflux.
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Affiliation(s)
- Zitao Yang
- La Jolla Country Day School, La Jolla, CA 92037, United States of America
| | - Elena F Koslover
- Department of Physics, University of California, San Diego, La Jolla, CA 92093, United States of America
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17
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Punia B, Chaudhury S. Theoretical insights into the full description of DNA target search by subdiffusing proteins. Phys Chem Chem Phys 2022; 24:29074-29083. [PMID: 36440504 DOI: 10.1039/d2cp04934a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
DNA binding proteins (DBPs) diffuse in the cytoplasm to recognise and bind with their respective target sites on the DNA to initiate several biologically important processes. The first passage time distributions (FPTDs) of DBPs are useful in quantifying the timescales of the most-probable search paths in addition to the mean value of the distribution which, strikingly, are decades of order apart in time. However, extremely crowded in vivo conditions or the viscoelasticity of the cellular medium among other factors causes biomolecules to exhibit anomalous diffusion which is usually overlooked in most theoretical studies. We have obtained approximate analytical expressions of a general FPTD and the two characteristic timescales that are valid for any single subdiffusing protein searching for its target in vivo. Our results can be applied to single-particle tracking experiments of target search.
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Affiliation(s)
- Bhawakshi Punia
- Department of Chemistry, Indian Institute of Science Education and Research, Dr Homi Bhabha Road, Pune, Maharashtra, India.
| | - Srabanti Chaudhury
- Department of Chemistry, Indian Institute of Science Education and Research, Dr Homi Bhabha Road, Pune, Maharashtra, India.
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18
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Benkhadaj Z, Grebenkov DS. Encounter-based approach to diffusion with resetting. Phys Rev E 2022; 106:044121. [PMID: 36397494 DOI: 10.1103/physreve.106.044121] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2022] [Accepted: 09/27/2022] [Indexed: 06/16/2023]
Abstract
An encounter-based approach consists in using the boundary local time as a proxy for the number of encounters between a diffusing particle and a target to implement various surface reaction mechanisms on that target. In this paper, we investigate the effects of stochastic resetting onto diffusion-controlled reactions in bounded confining domains. We first discuss the effect of position resetting onto the propagator and related quantities; in this way, we retrieve a number of earlier results but also provide complementary insights into them. Second, we introduce boundary local time resetting and investigate its impact. Curiously, we find that this type of resetting does not alter the conventional propagator governing the diffusive dynamics in the presence of a partially reactive target with a constant reactivity. In turn, the generalized propagator for other surface reaction mechanisms can be significantly affected. Our general results are illustrated for diffusion on an interval with reactive end points. Further perspectives and some open problems are discussed.
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Affiliation(s)
| | - Denis S Grebenkov
- Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, IP Paris, 91128 Palaiseau, France
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19
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Everlasting impact of initial perturbations on first-passage times of non-Markovian random walks. Nat Commun 2022; 13:5319. [PMID: 36085151 PMCID: PMC9463153 DOI: 10.1038/s41467-022-32280-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Accepted: 07/25/2022] [Indexed: 11/09/2022] Open
Abstract
Persistence, defined as the probability that a signal has not reached a threshold up to a given observation time, plays a crucial role in the theory of random processes. Often, persistence decays algebraically with time with non trivial exponents. However, general analytical methods to calculate persistence exponents cannot be applied to the ubiquitous case of non-Markovian systems relaxing transiently after an imposed initial perturbation. Here, we introduce a theoretical framework that enables the non-perturbative determination of persistence exponents of Gaussian non-Markovian processes with non stationary dynamics relaxing to a steady state after an initial perturbation. Two situations are analyzed: either the system is subjected to a temperature quench at initial time, or its past trajectory is assumed to have been observed and thus known. Our theory covers the case of spatial dimension higher than one, opening the way to characterize non-trivial reaction kinetics for complex systems with non-equilibrium initial conditions.
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20
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Abstract
Despite having been studied for decades, first passage processes remain an active area of research. In this contribution we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We obtain analytic expressions for the joint distribution of the hitting time and the hitting angle in two and three dimensions. For certain configurations we observe a ``diffusive echo", i.e. two well-defined maxima in the first passage time distribution to a targeted position on the absorbing boundary. This effect, which results from the interplay between the starting location and the environmental constraints, may help to significantly increase the efficiency of the random search by generating a high, sustained flux to the targeted position over a short period. Finally, we examine the corresponding one-dimensional system for which there is no well-defined echo. In a confined system, the flux integrated over all target positions always displays a shoulder. This does not, however, guarantee the presence of an echo in the joint distribution.
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Affiliation(s)
| | - Julian Talbot
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Sorbonne Universités, France
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21
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Ro S, Kim YW. Optimal searcher distribution for parallel random target searches. Phys Rev E 2022; 106:024101. [PMID: 36109972 DOI: 10.1103/physreve.106.024101] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2022] [Accepted: 06/27/2022] [Indexed: 06/15/2023]
Abstract
We consider a problem of finding a target located in a finite d-dimensional domain, using N independent random walkers, when partial information about the target location is given as a probability distribution. When N is large, the first-passage time sensitively depends on the initial searcher distribution, which invokes the question of the optimal searcher distribution that minimizes the first-passage time. Here, we analytically derive the equation for the optimal distribution and explore its limiting expressions. If the target volume can be ignored, the optimal distribution is proportional to the target distribution to the power of one third. If we consider a target of a finite volume and the probability of the initial overlapping of searchers with the target cannot be ignored in the large N limit, the optimal distribution has a weak dependence on the target distribution, with its variation being proportional to the logarithm of the target distribution. Using Langevin dynamics simulations, we numerically demonstrate our predictions in one and two dimensions.
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Affiliation(s)
- Sunghan Ro
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Yong Woon Kim
- Department of Physics, Korea Advanced Institute of Science and Technology, Deajeon 34141, Korea and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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22
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Chen A, Qiu H, Tian T, Zhou T. Generalized fluctuation-dissipation theorem for non-Markovian reaction networks. Phys Rev E 2022; 105:064409. [PMID: 35854490 DOI: 10.1103/physreve.105.064409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2021] [Accepted: 05/23/2022] [Indexed: 06/15/2023]
Abstract
Intracellular biochemical networks often display large fluctuations in the molecule numbers or the concentrations of reactive species, making molecular approaches necessary for system descriptions. For Markovian reaction networks, the fluctuation-dissipation theorem (FDT) has been well established and extensively used in fast evaluation of fluctuations in reactive species. For non-Markovian reaction networks, however, the similar FDT has not been established so far. Here, we present a generalized FDT (gFDT) for a large class of non-Markovian reaction networks where general intrinsic-event waiting-time distributions account for the effect of intrinsic noise and general stochastic reaction delays represent the impact of extrinsic noise from environmental perturbations. The starting point is a generalized chemical master equation (gCME), which describes the probabilistic behavior of an equivalent Markovian reaction network and identifies the structure of the original non-Markovian reaction network in terms of stoichiometries and effective transition rates (extensions of common reaction propensity functions). From this formulation follows directly the solution of the linear noise approximation of the stationary gCME for all the components in the non-Markovian reaction network. While the gFDT can quickly trace noisy sources in non-Markovian reaction networks, example analysis verifies its effectiveness.
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Affiliation(s)
- Aimin Chen
- School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
| | - Huahai Qiu
- School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan 430200, People's Republic of China
| | - Tianhai Tian
- School of Mathematics, Monash University, Melbourne 3800, Australia
| | - Tianshou Zhou
- School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
- Key Laboratory of Computational Mathematics, Guangdong Province, and School of Mathematics, Sun Yat-sen University, Guangzhou 510275, People's Republic of China
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23
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Grebenkov DS, Skvortsov AT. Mean first-passage time to a small absorbing target in three-dimensional elongated domains. Phys Rev E 2022; 105:054107. [PMID: 35706289 DOI: 10.1103/physreve.105.054107] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 04/15/2022] [Indexed: 06/15/2023]
Abstract
We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in three dimensions is reduced to an effective one-dimensional problem on an interval with a semipermeable semiabsorbing membrane. The approximate formula captures correctly the dependence of the MFPT on the distance to the target, the radial profile of the domain, and the size and the shape of the target. This approximation is validated by Monte Carlo simulations.
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Affiliation(s)
- Denis S Grebenkov
- Laboratoire de Physique de la Matière Condensée, UMR No. 7643, CNRS, Ecole Polytechnique, IP Paris, 91120 Palaiseau, France
| | - Alexei T Skvortsov
- Maritime Division, Defence Science and Technology Group, 506 Lorimer Street, Fishermans Bend, Victoria 3207, Australia
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24
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Chaigneau A, Grebenkov DS. First-passage times to anisotropic partially reactive targets. Phys Rev E 2022; 105:054146. [PMID: 35706315 DOI: 10.1103/physreve.105.054146] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Accepted: 05/05/2022] [Indexed: 06/15/2023]
Abstract
We investigate restricted diffusion in a bounded domain towards a small partially reactive target in three- and higher-dimensional spaces. We propose a simple explicit approximation for the principal eigenvalue of the Laplace operator with mixed Robin-Neumann boundary conditions. This approximation involves the harmonic capacity and the surface area of the target, the volume of the confining domain, the diffusion coefficient, and the reactivity. The accuracy of the approximation is checked by using a finite-elements method. The proposed approximation determines also the mean first-reaction time, the long-time decay of the survival probability, and the overall reaction rate on that target. We identify the relevant lengthscale of the target, which determines its trapping capacity, and we investigate its relation to the target shape. In particular, we study the effect of target anisotropy on the principal eigenvalue by computing the harmonic capacity of prolate and oblate spheroids in various space dimensions. Some implications of these results in chemical physics and biophysics are briefly discussed.
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Affiliation(s)
- Adrien Chaigneau
- Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, IP Paris, 91120 Palaiseau, France
| | - Denis S Grebenkov
- Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, IP Paris, 91120 Palaiseau, France
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25
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Stana R, Lythe G. Diffusion in a disk with inclusion: Evaluating Green’s functions. PLoS One 2022; 17:e0265935. [PMID: 35421102 PMCID: PMC9009627 DOI: 10.1371/journal.pone.0265935] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 03/07/2022] [Indexed: 11/18/2022] Open
Abstract
We give exact Green’s functions in two space dimensions. We work in a scaled domain that is a circle of unit radius with a smaller circular “inclusion”, of radius a, removed, without restriction on the size or position of the inclusion. We consider the two cases where one of the two boundaries is absorbing and the other is reflecting. Given a particle with diffusivity D, in a circle with radius R, the mean time to reach the absorbing boundary is a function of the initial condition, given by the integral of Green’s function over the domain. We scale to a circle of unit radius, then transform to bipolar coordinates. We show the equivalence of two different series expansions, and obtain closed expressions that are not series expansions.
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Affiliation(s)
- Remus Stana
- Department of Applied Mathematics, University of Leeds, Leeds, United Kingdom
| | - Grant Lythe
- Department of Applied Mathematics, University of Leeds, Leeds, United Kingdom
- * E-mail:
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26
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Gao L, Peng J, Tang C. Mean trapping time for an arbitrary trap site on a class of fractal scale-free trees. Phys Rev E 2022; 105:044201. [PMID: 35590606 DOI: 10.1103/physreve.105.044201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2021] [Accepted: 02/22/2022] [Indexed: 06/15/2023]
Abstract
Fractals are ubiquitous in nature and random walks on fractals have attracted lots of scientific attention in the past several years. In this work, we consider discrete random walks on a class of fractal scale-free trees (FST), whose topologies are controlled by two integer parameters (i.e., u≥2 and v≥1) and exhibit a wide range of topological properties by suitably varying the parameters u and v. The mean trapping time (MTT), referred to as T_{y}, which is the mean time it takes the walker to be absorbed by the trap fixed at site y of the FST, is addressed analytically on the FST, and the effects of the trap location y on the MTT for the FST and for the general trees are also analyzed. First, a method, which is based on the connection between the MTT and the effective resistances, to derive analytically T_{y} for an arbitrary site y of the FST is presented, and some examples are provided to show the effectiveness of the method. Then, we compare T_{y} for all the possible site y of the trees, and find the sites where T_{y} achieves the minimum (or maximum) on the FST. Finally, we analyze the effects of trap location on the MTT in general trees and find that the average path length (APL) from an arbitrary site to the trap is the decisive factor which dominates the difference in the MTTs for different trap locations on general trees. We find, for any tree, the MTT obtains the minimum (or maximum) at sites where the APL achieves the minimum (or maximum).
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Affiliation(s)
- Long Gao
- School of Mathematical and Information Science, Guangzhou University, Guangzhou 510006, China
| | - Junhao Peng
- School of Mathematical and Information Science, Guangzhou University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory co-sponsored by province and city of Information Security Technology, Guangzhou University, Guangzhou 510006, China
| | - Chunming Tang
- School of Mathematical and Information Science, Guangzhou University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory co-sponsored by province and city of Information Security Technology, Guangzhou University, Guangzhou 510006, China
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27
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Le Vot F, Yuste SB, Abad E, Grebenkov DS. First-encounter time of two diffusing particles in two- and three-dimensional confinement. Phys Rev E 2022; 105:044119. [PMID: 35590615 DOI: 10.1103/physreve.105.044119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Accepted: 03/15/2022] [Indexed: 06/15/2023]
Abstract
The statistics of the first-encounter time of diffusing particles changes drastically when they are placed under confinement. In the present work, we make use of Monte Carlo simulations to study the behavior of a two-particle system in two- and three-dimensional domains with reflecting boundaries. Based on the outcome of the simulations, we give a comprehensive overview of the behavior of the survival probability S(t) and the associated first-encounter time probability density H(t) over a broad time range spanning several decades. In addition, we provide numerical estimates and empirical formulas for the mean first-encounter time 〈T〉, as well as for the decay time T characterizing the monoexponential long-time decay of the survival probability. Based on the distance between the boundary and the center of mass of two particles, we obtain an empirical lower bound t_{B} for the time at which S(t) starts to significantly deviate from its counterpart for the no boundary case. Surprisingly, for small-sized particles, the dominant contribution to T depends only on the total diffusivity D=D_{1}+D_{2}, in sharp contrast to the one-dimensional case. This contribution can be related to the Wiener sausage generated by a fictitious Brownian particle with diffusivity D. In two dimensions, the first subleading contribution to T is found to depend weakly on the ratio D_{1}/D_{2}. We also investigate the slow-diffusion limit when D_{2}≪D_{1}, and we discuss the transition to the limit when one particle is a fixed target. Finally, we give some indications to anticipate when T can be expected to be a good approximation for 〈T〉.
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Affiliation(s)
- F Le Vot
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain
| | - S B Yuste
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain
| | - E Abad
- Departamento de Física Aplicada and Instituto de Computación Científica Avanzada (ICCAEx), Centro Universitario de Mérida, Universidad de Extremadura, E-06800 Mérida, Spain
| | - D S Grebenkov
- Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, IP Paris, 91128 Palaiseau, France
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28
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Diffusion control in biochemical specificity. Biophys J 2022; 121:1541-1548. [PMID: 35278424 PMCID: PMC9072584 DOI: 10.1016/j.bpj.2022.03.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Revised: 09/28/2021] [Accepted: 03/04/2022] [Indexed: 11/20/2022] Open
Abstract
Biochemical specificity is critical in enzyme function, evolution, and engineering. Here we employ an established kinetic model to dissect the effects of reactant geometry and diffusion on product formation speed and accuracy in the presence of cognate (correct) and near-cognate (incorrect) substrates. Using this steady-state model for spherical geometries, we find that, for distinct kinetic regimes, the speed and accuracy of the reactions are optimized on different regions of the geometric landscape. From this model we deduce that accuracy can be strongly dependent on reactant geometric properties even for chemically limited reactions. Notably, substrates with a specific geometry and reactivity can be discriminated by the enzyme with higher efficacy than others through purely diffusive effects. For similar cognate and near-cognate substrate geometries (as is the case for polymerases or the ribosome), we observe that speed and accuracy are maximized in opposing regions of the geometric landscape. We also show that, in relevant environments, diffusive effects on accuracy can be substantial even far from extreme kinetic conditions. Finally, we find how reactant chemical discrimination and diffusion can be related to simultaneously optimize steady-state flux and accuracy. These results highlight how diffusion and geometry can be employed to enhance reaction speed and discrimination, and similarly how they impose fundamental restraints on these quantities.
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29
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Grebenkov DS, Kumar A. Reversible target-binding kinetics of multiple impatient particles. J Chem Phys 2022; 156:084107. [DOI: 10.1063/5.0083849] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Certain biochemical reactions can only be triggered after binding a sufficient number of particles to a specific target region such as an enzyme or a protein sensor. We investigate the distribution of the reaction time, i.e., the first instance when all independently diffusing particles are bound to the target. When each particle binds irreversibly, this is equivalent to the first-passage time of the slowest (last) particle. In turn, reversible binding to the target renders the problem much more challenging and drastically changes the distribution of the reaction time. We derive the exact solution of this problem and investigate the short-time and long-time asymptotic behaviors of the reaction time probability density. We also analyze how the mean reaction time depends on the unbinding rate and the number of particles. Our exact and asymptotic solutions are compared to Monte Carlo simulations.
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Affiliation(s)
- Denis S. Grebenkov
- Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS–Ecole Polytechnique, IP Paris, 91120 Palaiseau, France
| | - Aanjaneya Kumar
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India
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30
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Zunke C, Bewerunge J, Platten F, Egelhaaf SU, Godec A. First-passage statistics of colloids on fractals: Theory and experimental realization. SCIENCE ADVANCES 2022; 8:eabk0627. [PMID: 35061533 PMCID: PMC8782457 DOI: 10.1126/sciadv.abk0627] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2021] [Accepted: 11/29/2021] [Indexed: 05/30/2023]
Abstract
In nature and technology, particle dynamics frequently occur in complex environments, for example in restricted geometries or crowded media. These dynamics have often been modeled invoking a fractal structure of the medium although the fractal structure was only indirectly inferred through the dynamics. Moreover, systematic studies have not yet been performed. Here, colloidal particles moving in a laser speckle pattern are used as a model system. In this case, the experimental observations can be reliably traced to the fractal structure of the underlying medium with an adjustable fractal dimension. First-passage time statistics reveal that the particles explore the speckle in a self-similar, fractal manner at least over four decades in time and on length scales up to 20 times the particle radius. The requirements for fractal diffusion to be applicable are laid out, and methods to extract the fractal dimension are established.
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Affiliation(s)
- Christoph Zunke
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Jörg Bewerunge
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Florian Platten
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstrasse 1, 40225 Düsseldorf, Germany
- Institute of Biological Information Processing, Biomacromolecular Systems and Processes (IBI-4), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Stefan U. Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
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31
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Abstract
Transport of intracellular components relies on a variety of active and passive mechanisms, ranging from the diffusive spreading of small molecules over short distances to motor-driven motion across long distances. The cell-scale behavior of these mechanisms is fundamentally dependent on the morphology of the underlying cellular structures. Diffusion-limited reaction times can be qualitatively altered by the presence of occluding barriers or by confinement in complex architectures, such as those of reticulated organelles. Motor-driven transport is modulated by the architecture of cytoskeletal filaments that serve as transport highways. In this review, we discuss the impact of geometry on intracellular transport processes that fulfill a broad range of functional objectives, including delivery, distribution, and sorting of cellular components. By unraveling the interplay between morphology and transport efficiency, we aim to elucidate key structure-function relationships that govern the architecture of transport systems at the cellular scale. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Anamika Agrawal
- Department of Physics, University of California, San Diego, La Jolla, California, USA;
| | - Zubenelgenubi C Scott
- Department of Physics, University of California, San Diego, La Jolla, California, USA;
| | - Elena F Koslover
- Department of Physics, University of California, San Diego, La Jolla, California, USA;
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32
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Darzacq X, Tjian R. Weak multivalent biomolecular interactions: a strength versus numbers tug of war with implications for phase partitioning. RNA (NEW YORK, N.Y.) 2022; 28:48-51. [PMID: 34772790 PMCID: PMC8675282 DOI: 10.1261/rna.079004.121] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
In this short Perspective, we discuss how recent dynamic live-cell imaging experiments have challenged our understanding of mechanisms driving functional molecular interactions in vivo. While we have generally considered the formation of functional biomolecular complexes as resulting from the stable assembly of two or more partner molecules, here we entertain the possibility that function may actually be maintained while molecules are rapidly exchanged within a complex. We postulate that at high effective concentrations, even very weak interactions can lead to strong binding site occupancy and thereby mediate function in a highly dynamic fashion. This new perspective in our definition of what represents a functional complex in living cells and in vivo could significantly alter how we define the nature of molecular transactions critical for mediating regulation in the cellular context. These less conventional principles also allow a broadening of the mechanistic options we should explore when interpreting essential biological processes such as gene regulation.
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Affiliation(s)
- Xavier Darzacq
- Molecular and Cell Biology, University of California, Berkeley, California 94707, USA
| | - Robert Tjian
- Molecular and Cell Biology, University of California, Berkeley, California 94707, USA
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33
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Karr JP, Ferrie JJ, Tjian R, Darzacq X. The transcription factor activity gradient (TAG) model: contemplating a contact-independent mechanism for enhancer-promoter communication. Genes Dev 2022; 36:7-16. [PMID: 34969825 PMCID: PMC8763055 DOI: 10.1101/gad.349160.121] [Citation(s) in RCA: 67] [Impact Index Per Article: 33.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
How distal cis-regulatory elements (e.g., enhancers) communicate with promoters remains an unresolved question of fundamental importance. Although transcription factors and cofactors are known to mediate this communication, the mechanism by which diffusible molecules relay regulatory information from one position to another along the chromosome is a biophysical puzzle-one that needs to be revisited in light of recent data that cannot easily fit into previous solutions. Here we propose a new model that diverges from the textbook enhancer-promoter looping paradigm and offer a synthesis of the literature to make a case for its plausibility, focusing on the coactivator p300.
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Affiliation(s)
- Jonathan P Karr
- University of California at Berkeley, Berkeley, California 94720, USA
| | - John J Ferrie
- University of California at Berkeley, Berkeley, California 94720, USA
- Howard Hughes Medical Institute, Berkeley, California 94720, USA
| | - Robert Tjian
- University of California at Berkeley, Berkeley, California 94720, USA
- Howard Hughes Medical Institute, Berkeley, California 94720, USA
| | - Xavier Darzacq
- University of California at Berkeley, Berkeley, California 94720, USA
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34
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Casiulis M, Hexner D, Levine D. Self-propulsion and self-navigation: Activity is a precursor to jamming. Phys Rev E 2021; 104:064614. [PMID: 35030902 DOI: 10.1103/physreve.104.064614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 12/02/2021] [Indexed: 06/14/2023]
Abstract
Traffic jams are an everyday hindrance to transport and typically arise when many vehicles have the same or a similar destination. We show, however, that even when uniformly distributed in space and uncorrelated, targets have a crucial effect on transport. At modest densities an instability arises leading to jams with emergent correlations between the targets. By considering limiting cases of the dynamics which map onto active Brownian particles, we argue that motility induced phase separation is the precursor to jams. That is, jams are MIPS seeds that undergo an extra instability due to target accumulation. This provides a quantitative prediction of the onset density for jamming, and suggests how jamming might be delayed or prevented. We study the transition between jammed and flowing phase, and find that transport is most efficient on the cusp of jamming.
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Affiliation(s)
| | - Daniel Hexner
- Department of Mechanical Engineering, Technion-IIT, 32000 Haifa, Israel
| | - Dov Levine
- Department of Physics, Technion-IIT, 32000 Haifa, Israel
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35
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Guérin T, Dolgushev M, Bénichou O, Voituriez R. Universal kinetics of imperfect reactions in confinement. Commun Chem 2021; 4:157. [PMID: 36697538 PMCID: PMC9814865 DOI: 10.1038/s42004-021-00591-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2021] [Accepted: 10/14/2021] [Indexed: 01/28/2023] Open
Abstract
Chemical reactions generically require that particles come into contact. In practice, reaction is often imperfect and can necessitate multiple random encounters between reactants. In confined geometries, despite notable recent advances, there is to date no general analytical treatment of such imperfect transport-limited reaction kinetics. Here, we determine the kinetics of imperfect reactions in confining domains for any diffusive or anomalously diffusive Markovian transport process, and for different models of imperfect reactivity. We show that the full distribution of reaction times is obtained in the large confining volume limit from the knowledge of the mean reaction time only, which we determine explicitly. This distribution for imperfect reactions is found to be identical to that of perfect reactions upon an appropriate rescaling of parameters, which highlights the robustness of our results. Strikingly, this holds true even in the regime of low reactivity where the mean reaction time is independent of the transport process, and can lead to large fluctuations of the reaction time - even in simple reaction schemes. We illustrate our results for normal diffusion in domains of generic shape, and for anomalous diffusion in complex environments, where our predictions are confirmed by numerical simulations.
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Affiliation(s)
- Thomas Guérin
- grid.412041.20000 0001 2106 639XLaboratoire Ondes et Matière d’Aquitaine, CNRS/University of Bordeaux, F-33400 Talence, France
| | - Maxim Dolgushev
- grid.462844.80000 0001 2308 1657Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne University, 4 Place Jussieu, 75005 Paris, France
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne University, 4 Place Jussieu, 75005, Paris, France.
| | - Raphaël Voituriez
- grid.462844.80000 0001 2308 1657Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne University, 4 Place Jussieu, 75005 Paris, France ,grid.462844.80000 0001 2308 1657Laboratoire Jean Perrin, CNRS/Sorbonne University, 4 Place Jussieu, 75005 Paris, France
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36
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Optimizing the First-Passage Process on a Class of Fractal Scale-Free Trees. FRACTAL AND FRACTIONAL 2021. [DOI: 10.3390/fractalfract5040184] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
First-passage processes on fractals are of particular importance since fractals are ubiquitous in nature, and first-passage processes are fundamental dynamic processes that have wide applications. The global mean first-passage time (GMFPT), which is the expected time for a walker (or a particle) to first reach the given target site while the probability distribution for the position of target site is uniform, is a useful indicator for the transport efficiency of the whole network. The smaller the GMFPT, the faster the mass is transported on the network. In this work, we consider the first-passage process on a class of fractal scale-free trees (FSTs), aiming at speeding up the first-passage process on the FSTs. Firstly, we analyze the global mean first-passage time (GMFPT) for unbiased random walks on the FSTs. Then we introduce proper weight, dominated by a parameter w (w > 0), to each edge of the FSTs and construct a biased random walks strategy based on these weights. Next, we analytically evaluated the GMFPT for biased random walks on the FSTs. The exact results of the GMFPT for unbiased and biased random walks on the FSTs are both obtained. Finally, we view the GMFPT as a function of parameter w and find the point where the GMFPT achieves its minimum. The exact result is obtained and a way to optimize and speed up the first-passage process on the FSTs is presented.
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37
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Balanikas E, Banyasz A, Baldacchino G, Markovitsi D. Deprotonation Dynamics of Guanine Radical Cations †. Photochem Photobiol 2021; 98:523-531. [PMID: 34653259 DOI: 10.1111/php.13540] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 10/08/2021] [Indexed: 01/25/2023]
Abstract
This review is dedicated to guanine radical cations (G+ )· that are precursors to oxidatively generated damage to DNA. (G+ )· are unstable in neutral aqueous solution and tend to lose a proton. The deprotonation process has been studied by time-resolved absorption experiments in which (G+ )· radicals are produced either by an electron abstraction reaction, using an external oxidant, or by low-energy/low-intensity photoionization of DNA. Both the position of the released proton and the dynamics of the process depend on the secondary DNA structure. While deprotonation in duplex DNA leads to (G-H1)· radicals, in guanine quadruplexes the (G-H2)· analogs are observed. Deprotonation in monomeric guanosine proceeds with a time constant of ˜60 ns; in genomic DNA, it is completed within 2 µs; and in guanine quadruplexes, it spans from at least 30 ns to over 50 µs. Such a deprotonation dynamics in four-stranded structures, extended over more than three decades of times, is correlated with the anisotropic structure of DNA and the mobility of its hydration shell. In this case, commonly used second-order reaction models are inappropriate for its description.
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Affiliation(s)
| | - Akos Banyasz
- Université Paris-Saclay, CEA, CNRS, LIDYL, Gif-sur-Yvette, F-91191, France.,Univ Lyon, ENS de Lyon, CNRS, UMR 5182, Université Claude Bernard Lyon 1, Laboratoire de Chimie, Lyon, F-69342, France
| | - Gérard Baldacchino
- Université Paris-Saclay, CEA, CNRS, LIDYL, Gif-sur-Yvette, F-91191, France
| | - Dimitra Markovitsi
- Université Paris-Saclay, CEA, CNRS, LIDYL, Gif-sur-Yvette, F-91191, France
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38
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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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39
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Mazzocca M, Fillot T, Loffreda A, Gnani D, Mazza D. The needle and the haystack: single molecule tracking to probe the transcription factor search in eukaryotes. Biochem Soc Trans 2021; 49:1121-1132. [PMID: 34003257 PMCID: PMC8286828 DOI: 10.1042/bst20200709] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Revised: 04/18/2021] [Accepted: 04/19/2021] [Indexed: 12/13/2022]
Abstract
Transcription factors (TFs) regulate transcription of their target genes by identifying and binding to regulatory regions of the genome among billions of potential non-specific decoy sites, a task that is often presented as a 'needle in the haystack' challenge. The TF search process is now well understood in bacteria, but its characterization in eukaryotes needs to account for the complex organization of the nuclear environment. Here we review how live-cell single molecule tracking is starting to shed light on the TF search mechanism in the eukaryotic cell and we outline the future challenges to tackle in order to understand how nuclear organization modulates the TF search process in physiological and pathological conditions.
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Affiliation(s)
- Matteo Mazzocca
- Experimental Imaging Center, IRCCS San Raffaele Scientific Institute, Milan 20132, Italy
| | - Tom Fillot
- Experimental Imaging Center, IRCCS San Raffaele Scientific Institute, Milan 20132, Italy
| | - Alessia Loffreda
- Experimental Imaging Center, IRCCS San Raffaele Scientific Institute, Milan 20132, Italy
| | - Daniela Gnani
- Experimental Imaging Center, IRCCS San Raffaele Scientific Institute, Milan 20132, Italy
| | - Davide Mazza
- Experimental Imaging Center, IRCCS San Raffaele Scientific Institute, Milan 20132, Italy
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40
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Scott ZC, Brown AI, Mogre SS, Westrate LM, Koslover EF. Diffusive search and trajectories on tubular networks: a propagator approach. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:80. [PMID: 34143351 PMCID: PMC8213674 DOI: 10.1140/epje/s10189-021-00083-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 05/25/2021] [Indexed: 05/11/2023]
Abstract
Several organelles in eukaryotic cells, including mitochondria and the endoplasmic reticulum, form interconnected tubule networks extending throughout the cell. These tubular networks host many biochemical pathways that rely on proteins diffusively searching through the network to encounter binding partners or localized target regions. Predicting the behavior of such pathways requires a quantitative understanding of how confinement to a reticulated structure modulates reaction kinetics. In this work, we develop both exact analytical methods to compute mean first passage times and efficient kinetic Monte Carlo algorithms to simulate trajectories of particles diffusing in a tubular network. Our approach leverages exact propagator functions for the distribution of transition times between network nodes and allows large simulation time steps determined by the network structure. The methodology is applied to both synthetic planar networks and organelle network structures, demonstrating key general features such as the heterogeneity of search times in different network regions and the functional advantage of broadly distributing target sites throughout the network. The proposed algorithms pave the way for future exploration of the interrelationship between tubular network structure and biomolecular reaction kinetics.
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Affiliation(s)
- Zubenelgenubi C Scott
- Department of Physics, University of California, San Diego, La Jolla, CA, 92093, USA
| | - Aidan I Brown
- Department of Physics, Ryerson University, Toronto, Canada
| | - Saurabh S Mogre
- Department of Physics, University of California, San Diego, La Jolla, CA, 92093, USA
| | - Laura M Westrate
- Department of Chemistry and Biochemistry, Calvin University, Grand Rapids, MI, 49546, USA
| | - Elena F Koslover
- Department of Physics, University of California, San Diego, La Jolla, CA, 92093, USA.
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41
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Mishra B, Johnson ME. Speed limits of protein assembly with reversible membrane localization. J Chem Phys 2021; 154:194101. [PMID: 34240891 PMCID: PMC8131109 DOI: 10.1063/5.0045867] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 04/26/2021] [Indexed: 12/15/2022] Open
Abstract
Protein assembly is often studied in a three-dimensional solution, but a significant fraction of binding events involve proteins that can reversibly bind and diffuse along a two-dimensional surface. In a recent study, we quantified how proteins can exploit the reduced dimensionality of the membrane to trigger complex formation. Here, we derive a single expression for the characteristic timescale of this multi-step assembly process, where the change in dimensionality renders rates and concentrations effectively time-dependent. We find that proteins can accelerate dimer formation due to an increase in relative concentration, driving more frequent collisions, which often win out over slow-downs due to diffusion. Our model contains two protein populations that dimerize with one another and use a distinct site to bind membrane lipids, creating a complex reaction network. However, by identifying two major rate-limiting pathways to reach an equilibrium steady-state, we derive an excellent approximation for the mean first passage time when lipids are in abundant supply. Our theory highlights how the "sticking rate" or effective adsorption coefficient of the membrane is central in controlling timescales. We also derive a corrected localization rate to quantify how the geometry of the system and diffusion can reduce rates of membrane localization. We validate and test our results using kinetic and particle-based reaction-diffusion simulations. Our results establish how the speed of key assembly steps can shift by orders-of-magnitude when membrane localization is possible, which is critical to understanding mechanisms used in cells.
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Affiliation(s)
- Bhavya Mishra
- TC Jenkins Department of Biophysics, Johns Hopkins University, 3400 N Charles St., Baltimore, Maryland 21218, USA
| | - Margaret E. Johnson
- TC Jenkins Department of Biophysics, Johns Hopkins University, 3400 N Charles St., Baltimore, Maryland 21218, USA
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42
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Klinger J, Voituriez R, Bénichou O. Distribution of the span of one-dimensional confined random processes before hitting a target. Phys Rev E 2021; 103:032107. [PMID: 33862775 DOI: 10.1103/physreve.103.032107] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Accepted: 02/16/2021] [Indexed: 11/07/2022]
Abstract
We derive the distribution of the number of distinct sites visited by a random walker before hitting a target site of a finite one-dimensional (1D) domain. Our approach holds for the general class of Markovian processes with connected span-i.e., whose trajectories have no "holes." We show that the distribution can be simply expressed in terms of splitting probabilities only. We provide explicit results for classical examples of random processes with relevance to target search problems, such as simple symmetric random walks, biased random walks, persistent random walks, and resetting random walks. As a by-product, explicit expressions for the splitting probabilities of all these processes are given. Extensions to reflecting boundary conditions, continuous processes, and an example of a random process with a nonconnected span are discussed.
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Affiliation(s)
- J Klinger
- Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France, and Laboratoire Jean Perrin, UMR 8237 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
| | - R Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France, and Laboratoire Jean Perrin, UMR 8237 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
| | - O Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
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43
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44
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Abstract
The intrinsic fluorescence of nucleic acids is extremely weak compared to that of the fluorescent labels used to probe their structural and functional behavior. Thus, for technical reasons, the investigation of the intrinsic DNA fluorescence was limited for a long time. But with the improvement in spectroscopic techniques, the situation started to change around the turn of the century. During the past two decades, various factors modulating the static and dynamic properties of the DNA fluorescence have been determined; it was shown that, under certain conditions, quantum yields may be up 100 times higher than what was known so far. The ensemble of these studies opened up new paths for the development of label-free DNA fluorescence for biochemical applications. In parallel, these studies have shed new light on the primary processes leading to photoreactions that damage DNA when it absorbs UV radiation.We have been studying a variety of DNA systems, ranging from the monomeric nucleobases to double-stranded and four-stranded structures using fluorescence spectroscopy. The specificity of our work resides in the quantitative association of the steady-state fluorescence spectra with time-resolved data recorded from the femtosecond to the nanosecond timescales, made possible by the development of specific methodologies.Among others, our fluorescence studies provide information on the energy and the polarization of electronic transitions. These are valuable indicators for the evolution of electronic excitations in complex systems, where the electronic coupling between chromophores plays a key role. Highlighting collective effects that originate from electronic interactions in DNA multimers is the objective of the present Account.In contrast to the monomeric chromophores, whose fluorescence decays within a few picoseconds, that of DNA multimers persists on the nanosecond timescale. Even if long-lived states represent only a small fraction of electronic excitations, they may be crucial to the DNA photoreactivity because the probability to reach reactive conformations increases over time, owing to the incessant structural dynamics of nucleic acids.Our femtosecond studies have revealed that an ultrafast excitation energy transfer takes place among the nucleobases within duplexes and G-quadruplexes. Such an ultrafast process is possible when collective states are populated directly upon photon absorption. At much longer times, we discovered an unexpected long-lived high-energy emission stemming from what was coined "HELM excitons". These collective states, whose emission increases with the duplex size, could be responsible for the delayed fluorescence of ππ* states observed for genomic DNA.Most studies dealing with excited-state relaxation in DNA were carried out with excitation in the absorption band peaking at around 260 nm. We went beyond this and also performed the first time-resolved study with excitation in the UVA spectral range, where a very weak absorption tail is present. The resulting fluorescence decays are much slower and the fluorescence quantum yields are much higher than for UVC excitation. We showed that the base pairing of DNA strands enhances the UVA fluorescence and, in parallel, increases the photoreactivity because it modifies the nature of the involved collective excited states.
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Affiliation(s)
- Thomas Gustavsson
- Université Paris-Saclay, CEA, CNRS, LIDYL, F-91191 Gif-sur-Yvette, France
| | - Dimitra Markovitsi
- Université Paris-Saclay, CEA, CNRS, LIDYL, F-91191 Gif-sur-Yvette, France
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45
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Stracy M, Schweizer J, Sherratt DJ, Kapanidis AN, Uphoff S, Lesterlin C. Transient non-specific DNA binding dominates the target search of bacterial DNA-binding proteins. Mol Cell 2021; 81:1499-1514.e6. [PMID: 33621478 PMCID: PMC8022225 DOI: 10.1016/j.molcel.2021.01.039] [Citation(s) in RCA: 35] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Key Words] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Revised: 11/24/2020] [Accepted: 01/27/2021] [Indexed: 12/18/2022]
Abstract
Despite their diverse biochemical characteristics and functions, all DNA-binding proteins share the ability to accurately locate their target sites among the vast excess of non-target DNA. Toward identifying universal mechanisms of the target search, we used single-molecule tracking of 11 diverse DNA-binding proteins in living Escherichia coli. The mobility of these proteins during the target search was dictated by DNA interactions rather than by their molecular weights. By generating cells devoid of all chromosomal DNA, we discovered that the nucleoid is not a physical barrier for protein diffusion but significantly slows the motion of DNA-binding proteins through frequent short-lived DNA interactions. The representative DNA-binding proteins (irrespective of their size, concentration, or function) spend the majority (58%–99%) of their search time bound to DNA and occupy as much as ∼30% of the chromosomal DNA at any time. Chromosome crowding likely has important implications for the function of all DNA-binding proteins. Protein motion was compared between unperturbed cells and DNA-free cells Protein mobility was dictated by DNA interactions rather than molecular weight The nucleoid is not a physical barrier for protein diffusion The proteins studied spend most (58%–99%) of their search time bound to DNA
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Affiliation(s)
- Mathew Stracy
- Department of Biochemistry, University of Oxford, Oxford OX1 3QU, UK.
| | - Jakob Schweizer
- Max Planck Institute for Dynamics of Complex Technical Systems, 39106 Magdeburg, Germany
| | - David J Sherratt
- Department of Biochemistry, University of Oxford, Oxford OX1 3QU, UK
| | - Achillefs N Kapanidis
- Biological Physics Research Group, Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, UK
| | - Stephan Uphoff
- Department of Biochemistry, University of Oxford, Oxford OX1 3QU, UK.
| | - Christian Lesterlin
- Molecular Microbiology and Structural Biochemistry (MMSB), Université Lyon 1, CNRS, INSERM, UMR5086, 69007 Lyon, France.
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46
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Bressloff PC. First-passage processes and the target-based accumulation of resources. Phys Rev E 2021; 103:012101. [PMID: 33601498 DOI: 10.1103/physreve.103.012101] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Accepted: 12/16/2020] [Indexed: 12/26/2022]
Abstract
A random search for one or more targets in a bounded domain occurs widely in nature, with examples ranging from animal foraging to the transport of vesicles within cells. Most theoretical studies take a searcher-centric viewpoint, focusing on the first passage time (FTP) problem to find a target. This single search-and-capture event then triggers a downstream process or provides the searcher with some resource such as food. In this paper we take a target-centric viewpoint by considering the accumulation of resources in one or more targets due to multiple rounds of search-and-capture events combined with resource degradation; whenever a searcher finds a target it delivers a resource packet to the target, after which it escapes and returns to its initial position. The searcher is then resupplied with cargo and a new search process is initiated after a random delay. It has previously been shown how queuing theory can be used to derive general expressions for the steady-state mean and variance of the resulting resource distributions. Here we apply the theory to some classical FPT problems involving diffusion in simple geometries with absorbing boundaries, including concentric spheres, wedge domains, and branching networks. In each case, we determine how the resulting Fano factor depends on the degradation rate, the delay distribution, and various geometric parameters. We thus establish that the Fano factor can deviate significantly from Poisson statistics and exhibits a nontrivial dependence on model parameters, including nonmonotonicity and crossover behavior. This indicates the nontrivial nature of the higher-order statistics of resource accumulation.
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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
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47
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Bressloff PC. Asymptotic analysis of extended two-dimensional narrow capture problems. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2020.0771] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In this paper, we extend our recent work on two-dimensional diffusive search-and-capture processes with multiple small targets (narrow capture problems) by considering an asymptotic expansion of the Laplace transformed probability flux into each target. The latter determines the distribution of arrival or capture times into an individual target, conditioned on the set of events that result in capture by that target. A characteristic feature of strongly localized perturbations in two dimensions is that matched asymptotics generates a series expansion in
ν
= −1/ln
ϵ
rather than
ϵ
, 0 <
ϵ
≪ 1, where
ϵ
specifies the size of each target relative to the size of the search domain. Moreover, it is possible to sum over all logarithmic terms non-perturbatively. We exploit this fact to show how a Taylor expansion in the Laplace variable
s
for fixed
ν
provides an efficient method for obtaining corresponding asymptotic expansions of the splitting probabilities and moments of the conditional first-passage-time densities. We then use our asymptotic analysis to derive new results for two major extensions of the classical narrow capture problem: optimal search strategies under stochastic resetting and the accumulation of target resources under multiple rounds of search-and-capture.
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Affiliation(s)
- P. C. Bressloff
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA
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48
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Nayak I, Nandi A, Das D. Capture of a diffusive prey by multiple predators in confined space. Phys Rev E 2021; 102:062109. [PMID: 33466016 DOI: 10.1103/physreve.102.062109] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2020] [Accepted: 11/12/2020] [Indexed: 11/07/2022]
Abstract
The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some detail, a systematic study in confined space is still lacking. In this paper, we study the first passage times for this problem in one, two, and three dimensions. Due to confinement, the survival probability of the target takes a form ∼e^{-t/τ} at large times t. The characteristic capture timescale τ associated with the rare capture events are rather challenging to measure. We use a computational algorithm that allows us to estimate τ with high accuracy. We study in detail the behavior of τ as a function of the system parameters, namely, the number of searchers N, the relative diffusivity r of the target with respect to the searcher, and the system size. We find that τ deviates from the ∼1/N scaling seen in the case of a static target, and this deviation varies continuously with r and the spatial dimensions.
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Affiliation(s)
- Indrani Nayak
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Amitabha Nandi
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Dibyendu Das
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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49
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Ray A, Pal A, Ghosh D, Dana SK, Hens C. Mitigating long transient time in deterministic systems by resetting. CHAOS (WOODBURY, N.Y.) 2021; 31:011103. [PMID: 33754784 DOI: 10.1063/5.0038374] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Accepted: 12/24/2020] [Indexed: 06/12/2023]
Abstract
How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest and has stimulated a lot of activities in dynamical and stochastic systems where the metric of this estimation is often known as the transient or first passage time. In nonlinear systems, one often experiences long transients due to their underlying dynamics. We apply resetting or restart, an emerging concept in statistical physics and stochastic process, to mitigate the detrimental effects of prolonged transients in deterministic dynamical systems. We show that resetting the intrinsic dynamics intermittently to a spatial control line that passes through the equilibrium point can dramatically expedite its completion, resulting in a huge reduction in mean transient time and fluctuations around it. Moreover, our study reveals the emergence of an optimal restart time that globally minimizes the mean transient time. We corroborate the results with detailed numerical studies on two canonical setups in deterministic dynamical systems, namely, the Stuart-Landau oscillator and the Lorenz system. The key features-expedition of transient time-are found to be very generic under different resetting strategies. Our analysis opens up a door to control the mean and fluctuations in transient time by unifying the original dynamics with an external stochastic or periodic timer and poses open questions on the optimal way to harness transients in dynamical systems.
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Affiliation(s)
- Arnob Ray
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Arnab Pal
- School of Chemistry, Faculty of Exact Sciences and The Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Syamal K Dana
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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