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Millan E, Lavaud M, Amarouchene Y, Salez T. Numerical simulations of confined Brownian-yet-non-Gaussian motion. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:24. [PMID: 37002415 DOI: 10.1140/epje/s10189-023-00281-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Accepted: 03/20/2023] [Indexed: 06/19/2023]
Abstract
Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of investigation. Essentially, when confined near a wall, a particle moves much slower than in the bulk due to friction at the boundaries. The mobility is therefore locally hindered and space-dependent, which in turn leads to the apparition of so-called multiplicative noises, and associated non-Gaussianities which remain difficult to resolve at all times. Here, we exploit simple, optimized and efficient numerical simulations to address Brownian motion in confinement in a broadrange and quantitative way. To do so, we integrate the overdamped Langevin equation governing the thermal dynamics of a negatively-buoyant single spherical colloid within a viscous fluid confined by two rigid walls, including surface charges. From the produced large set of long random trajectories, we perform a complete statistical analysis and extract all the key quantities, such as the probability distributions in displacements and their main moments. In particular, we propose a novel method to compute high-order cumulants by reducing convergence problems, and employ it to efficiently characterize the inherent non-Gaussianity of the confined process.
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Affiliation(s)
- Elodie Millan
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France
| | - Maxime Lavaud
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France
| | | | - Thomas Salez
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France.
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2
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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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3
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Affiliation(s)
- Jaeoh Shin
- Department
of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Anatoly B. Kolomeisky
- Department
of Chemistry, Rice University, Houston, Texas 77005, United States
- Center
for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
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4
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Wang D, Wu H, Schwartz DK. Three-Dimensional Tracking of Interfacial Hopping Diffusion. PHYSICAL REVIEW LETTERS 2017; 119:268001. [PMID: 29328686 DOI: 10.1103/physrevlett.119.268001] [Citation(s) in RCA: 47] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Indexed: 05/04/2023]
Abstract
Theoretical predictions have suggested that molecular motion at interfaces-which influences processes including heterogeneous catalysis, (bio)chemical sensing, lubrication and adhesion, and nanomaterial self-assembly-may be dominated by hypothetical "hops" through the adjacent liquid phase, where a diffusing molecule readsorbs after a given hop according to a probabilistic "sticking coefficient." Here, we use three-dimensional (3D) single-molecule tracking to explicitly visualize this process for human serum albumin at solid-liquid interfaces that exert varying electrostatic interactions on the biomacromolecule. Following desorption from the interface, a molecule experiences multiple unproductive surface encounters before readsorption. An average of approximately seven surface collisions is required for the repulsive surfaces, decreasing to approximately two and a half for surfaces that are more attractive. The hops themselves are also influenced by long-range interactions, with increased electrostatic repulsion causing hops of longer duration and distance. These findings explicitly demonstrate that interfacial diffusion is dominated by biased 3D Brownian motion involving bulk-surface coupling and that it can be controlled by influencing short- and long-range adsorbate-surface interactions.
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Affiliation(s)
- Dapeng Wang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People's Republic of China
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Haichao Wu
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Daniel K Schwartz
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA
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5
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Gherardi M, Calabrese L, Tamm M, Cosentino Lagomarsino M. Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport. Phys Rev E 2017; 96:042402. [PMID: 29347533 DOI: 10.1103/physreve.96.042402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2017] [Indexed: 06/07/2023]
Abstract
The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E. coli. This analysis yields the characteristic time scales for intermittency. Finally, we discuss the possible shortcomings of this model, and show that an increase in the effective local noise felt by the chromosome associates to the active relocations.
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Affiliation(s)
- Marco Gherardi
- Sorbonne Universités, UPMC Univ Paris 06, 75005 Paris, France
- Physics Department, University of Milan, Via Celoria 16, 20133 Milano, Italy
| | - Ludovico Calabrese
- Physics Department, University of Milan, Via Celoria 16, 20133 Milano, Italy
| | - Mikhail Tamm
- Physics Department, University of Moscow, 119991 Moscow, Russia
- Department of Applied Mathematics, Higher School of Economics, 101000 Moscow, Russia
| | - Marco Cosentino Lagomarsino
- Sorbonne Universités, UPMC Univ Paris 06, 75005 Paris, France
- CNRS, UMR 7238, Paris, France
- IFOM, FIRC Institute of Molecular Oncology, 20139 Milan, Italy
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6
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First capture success in two dimensions: The search for prey by a random walk predator in a comprehensive space of random walks. ECOLOGICAL COMPLEXITY 2016. [DOI: 10.1016/j.ecocom.2016.09.004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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7
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Monserud JH, Schwartz DK. Interfacial Molecular Searching Using Forager Dynamics. PHYSICAL REVIEW LETTERS 2016; 116:098303. [PMID: 26991206 DOI: 10.1103/physrevlett.116.098303] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2015] [Indexed: 06/05/2023]
Abstract
Many biological and technological systems employ efficient non-Brownian intermittent search strategies where localized searches alternate with long flights. Coincidentally, molecular species exhibit intermittent behavior at the solid-liquid interface, where periods of slow motion are punctuated by fast flights through the liquid phase. Single-molecule tracking was used here to observe the interfacial search process of DNA for complementary DNA. Measured search times were qualitatively consistent with an intermittent-flight model, and ∼10 times faster than equivalent Brownian searches, suggesting that molecular searches for reactive sites benefit from similar efficiencies as biological organisms.
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Affiliation(s)
- Jon H Monserud
- Department of Chemical and Biological Engineering University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Daniel K Schwartz
- Department of Chemical and Biological Engineering University of Colorado Boulder, Boulder, Colorado 80309, USA
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8
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Brasiliense V, Patel AN, Martinez-Marrades A, Shi J, Chen Y, Combellas C, Tessier G, Kanoufi F. Correlated Electrochemical and Optical Detection Reveals the Chemical Reactivity of Individual Silver Nanoparticles. J Am Chem Soc 2016; 138:3478-83. [PMID: 26900633 DOI: 10.1021/jacs.5b13217] [Citation(s) in RCA: 102] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Electrochemical (EC) impacts of single nanoparticles (NPs) on an ultramicroelectrode are coupled with optics to identify chemical processes at the level of individual NPs. While the EC signals characterize the charge transfer process, the optical monitoring gives a complementary picture of the transport and chemical transformation of the NPs. This is illustrated in the case of electrodissolution of Ag NPs. In the simplest case, the optically monitored dissolution of individual NPs is synchronized with individual EC spikes. Optics then validates in situ the concept of EC nanoimpacts for sizing and counting of NPs. Chemical complexity is introduced by using a precipitating agent, SCN(-), which tunes the overall electrodissolution kinetics. Particularly, the charge transfer and dissolution steps occur sequentially as the synchronicity between the EC and optical signals is lost. This demonstrates the level of complexity that can be revealed from such electrochemistry/optics coupling.
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Affiliation(s)
- Vitor Brasiliense
- Sorbonne Paris Cité, Université Paris Diderot, Interfaces, Traitements, Organisation et Dynamique des Systèmes, CNRS-UMR 7086 , 15 rue J. A. Baif, F-75013 Paris, France
| | - Anisha N Patel
- Sorbonne Paris Cité, Université Paris Diderot, Interfaces, Traitements, Organisation et Dynamique des Systèmes, CNRS-UMR 7086 , 15 rue J. A. Baif, F-75013 Paris, France
| | - Ariadna Martinez-Marrades
- Sorbonne Paris Cité, Université Paris Descartes, Neurophotonics Laboratory, CNRS-UMR 8250 , 45 rue des Saints-Pères, F-75006 Paris, France
| | - Jian Shi
- Chemistry Department, Ecole Normale Supérieure-PSL Research University CNRS-UMR 8640 , 24 Rue Lhomond, F-75005 Paris, France
| | - Yong Chen
- Chemistry Department, Ecole Normale Supérieure-PSL Research University CNRS-UMR 8640 , 24 Rue Lhomond, F-75005 Paris, France
| | - Catherine Combellas
- Sorbonne Paris Cité, Université Paris Diderot, Interfaces, Traitements, Organisation et Dynamique des Systèmes, CNRS-UMR 7086 , 15 rue J. A. Baif, F-75013 Paris, France
| | - Gilles Tessier
- Sorbonne Paris Cité, Université Paris Descartes, Neurophotonics Laboratory, CNRS-UMR 8250 , 45 rue des Saints-Pères, F-75006 Paris, France
| | - Frédéric Kanoufi
- Sorbonne Paris Cité, Université Paris Diderot, Interfaces, Traitements, Organisation et Dynamique des Systèmes, CNRS-UMR 7086 , 15 rue J. A. Baif, F-75013 Paris, France
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9
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Zhang Z, Dong Y, Sheng Y. Mixed random walks with a trap in scale-free networks including nearest-neighbor and next-nearest-neighbor jumps. J Chem Phys 2015; 143:134101. [PMID: 26450286 DOI: 10.1063/1.4931988] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Random walks including non-nearest-neighbor jumps appear in many real situations such as the diffusion of adatoms and have found numerous applications including PageRank search algorithm; however, related theoretical results are much less for this dynamical process. In this paper, we present a study of mixed random walks in a family of fractal scale-free networks, where both nearest-neighbor and next-nearest-neighbor jumps are included. We focus on trapping problem in the network family, which is a particular case of random walks with a perfect trap fixed at the central high-degree node. We derive analytical expressions for the average trapping time (ATT), a quantitative indicator measuring the efficiency of the trapping process, by using two different methods, the results of which are consistent with each other. Furthermore, we analytically determine all the eigenvalues and their multiplicities for the fundamental matrix characterizing the dynamical process. Our results show that although next-nearest-neighbor jumps have no effect on the leading scaling of the trapping efficiency, they can strongly affect the prefactor of ATT, providing insight into better understanding of random-walk process in complex systems.
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Affiliation(s)
- Zhongzhi Zhang
- School of Computer Science, Fudan University, Shanghai 200433, China
| | - Yuze Dong
- School of Computer Science, Fudan University, Shanghai 200433, China
| | - Yibin Sheng
- School of Computer Science, Fudan University, Shanghai 200433, China
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10
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Chabaud M, Heuzé ML, Bretou M, Vargas P, Maiuri P, Solanes P, Maurin M, Terriac E, Le Berre M, Lankar D, Piolot T, Adelstein RS, Zhang Y, Sixt M, Jacobelli J, Bénichou O, Voituriez R, Piel M, Lennon-Duménil AM. Cell migration and antigen capture are antagonistic processes coupled by myosin II in dendritic cells. Nat Commun 2015; 6:7526. [PMID: 26109323 PMCID: PMC4491822 DOI: 10.1038/ncomms8526] [Citation(s) in RCA: 101] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2014] [Accepted: 05/16/2015] [Indexed: 12/23/2022] Open
Abstract
The immune response relies on the migration of leukocytes and on their ability to stop in precise anatomical locations to fulfil their task. How leukocyte migration and function are coordinated is unknown. Here we show that in immature dendritic cells, which patrol their environment by engulfing extracellular material, cell migration and antigen capture are antagonistic. This antagonism results from transient enrichment of myosin IIA at the cell front, which disrupts the back-to-front gradient of the motor protein, slowing down locomotion but promoting antigen capture. We further highlight that myosin IIA enrichment at the cell front requires the MHC class II-associated invariant chain (Ii). Thus, by controlling myosin IIA localization, Ii imposes on dendritic cells an intermittent antigen capture behaviour that might facilitate environment patrolling. We propose that the requirement for myosin II in both cell migration and specific cell functions may provide a general mechanism for their coordination in time and space.
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Affiliation(s)
- Mélanie Chabaud
- Inserm U932, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Mélina L. Heuzé
- Inserm U932, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Marine Bretou
- Inserm U932, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Pablo Vargas
- Inserm U932, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Paolo Maiuri
- CNRS UMR144, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Paola Solanes
- Inserm U932, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Mathieu Maurin
- Inserm U932, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Emmanuel Terriac
- CNRS UMR144, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Maël Le Berre
- CNRS UMR144, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Danielle Lankar
- Inserm U932, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Tristan Piolot
- CNRS UMR3215/Inserm U934, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
| | - Robert S. Adelstein
- Laboratory of Molecular Cardiology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Yingfan Zhang
- Laboratory of Molecular Cardiology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Michael Sixt
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Jordan Jacobelli
- National Jewish Health & University of Colorado, 1250 14th Street, Denver, USA
| | - Olivier Bénichou
- CNRS UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 7600 Paris, France
| | - Raphaël Voituriez
- CNRS UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 7600 Paris, France
- CNRS FRE 3231, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France
| | - Matthieu Piel
- CNRS UMR144, Institut Curie, 26 rue d'Ulm, 75248 Paris cedex 05, France
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11
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Mabry JN, Schwartz DK. Tuning the Flight Length of Molecules Diffusing on a Hydrophobic Surface. J Phys Chem Lett 2015; 6:2065-2069. [PMID: 26266503 DOI: 10.1021/acs.jpclett.5b00799] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Transport at solid-liquid interfaces is critical to self-assembly, biosensing, and heterogeneous catalysis, but surface diffusion remains difficult to characterize and rationally manipulate, due to the inherent heterogeneity of adsorption on solid surfaces. Using single-molecule tracking, we characterized the diffusion of a fluorescent long-chain surfactant on a hydrophobic surface, which involved periods of confinement alternating with bulk-mediated "flights". The concentration of methanol in solution was varied to tune the strength of the hydrophobic surface-molecule interaction. The frequency of confinement had a nonmonotonic dependence on methanol concentration that reflected the relative influence of anomalously strong adsorption sites. By carefully accounting for the effect of this surface heterogeneity, we demonstrated that flight lengths increased monotonically as the hydrophobic attraction decreased, in agreement with theoretical predictions for bulk-mediated surface diffusion. The theory provided an accurate description of surface diffusion, despite the system being heterogeneous, and can be leveraged to optimize molecular search and assembly processes.
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Affiliation(s)
- Joshua N Mabry
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309-0596, United States
| | - Daniel K Schwartz
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309-0596, United States
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12
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Abstract
A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed.
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13
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Calandre T, Bénichou O, Voituriez R. Accelerating search kinetics by following boundaries. PHYSICAL REVIEW LETTERS 2014; 112:230601. [PMID: 24972192 DOI: 10.1103/physrevlett.112.230601] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2014] [Indexed: 06/03/2023]
Abstract
We derive exact expressions of the mean first-passage time to a bulk target for a random searcher that performs boundary-mediated diffusion in a circular domain. Although nonintuitive for bulk targets, it is found that boundary excursions, if fast enough, can minimize the search time. A scaling analysis generalizes these findings to domains of arbitrary shapes and underlines their robustness. Overall, these results provide a generic mechanism of optimization of search kinetics in interfacial systems, which could have important implications in chemical physics. In the context of animal behavior sciences, it shows that following the boundaries of a domain can accelerate a search process, and therefore suggests that thigmotactism could be a kinetically efficient behavior.
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Affiliation(s)
- T Calandre
- Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), CNRS / UPMC, 4 Place Jussieu, 75255 Paris Cedex
| | - O Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), CNRS / UPMC, 4 Place Jussieu, 75255 Paris Cedex
| | - R Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), CNRS / UPMC, 4 Place Jussieu, 75255 Paris Cedex and Laboratoire Jean Perrin (FRE 3231) CNRS /UPMC, 4 Place Jussieu, 75255 Paris Cedex
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14
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Chupeau M, Bénichou O, Voituriez R. Mean cover time of one-dimensional persistent random walks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062129. [PMID: 25019746 DOI: 10.1103/physreve.89.062129] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2014] [Indexed: 06/03/2023]
Abstract
The cover time is defined as the time needed for a random walker to visit every site of a confined domain. Here, we focus on persistent random walks, which provide a minimal model of random walks with short-range memory. We derive the exact expression of the mean cover time of a one-dimensional lattice by such a persistent random walk, both for periodic and reflecting boundary conditions.
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Affiliation(s)
- Marie Chupeau
- Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex France
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex France
| | - Raphaël Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex France and Laboratoire Jean Perrin, FRE 3231 CNRS /UPMC, 4 Place Jussieu, 75255 Paris Cedex
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15
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Monserud JH, Schwartz DK. Mechanisms of surface-mediated DNA hybridization. ACS NANO 2014; 8:4488-4499. [PMID: 24708278 PMCID: PMC4046783 DOI: 10.1021/nn4064874] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/18/2013] [Accepted: 04/07/2014] [Indexed: 06/03/2023]
Abstract
Single-molecule total internal reflection fluorescence microscopy was employed in conjunction with resonance energy transfer (RET) to observe the dynamic behavior of donor-labeled ssDNA at the interface between aqueous solution and a solid surface decorated with complementary acceptor-labeled ssDNA. At least 100,000 molecular trajectories were determined for both complementary strands and negative control ssDNA. RET was used to identify trajectory segments corresponding to the hybridized state. The vast majority of molecules from solution adsorbed nonspecifically to the surface, where a brief two-dimensional search was performed with a 7% chance of hybridization. Successful hybridization events occurred with a characteristic search time of ∼0.1 s, and unsuccessful searches resulted in desorption from the surface, ultimately repeating the adsorption and search process. Hybridization was reversible, and two distinct modes of melting (i.e., dehybridization) were observed, corresponding to long-lived (∼15 s) and short-lived (∼1.4 s) hybridized time intervals. A strand that melted back onto the surface could rehybridize after a brief search or desorb from the interface. These mechanistic observations provide guidance for technologies that involve DNA interactions in the near-surface region, suggesting a need to design surfaces that both enhance the complex multidimensional search process and stabilize the hybridized state.
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16
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Skaug MJ, Lacasta AM, Ramirez-Piscina L, Sancho JM, Lindenberg K, Schwartz DK. Single-molecule diffusion in a periodic potential at a solid-liquid interface. SOFT MATTER 2014; 10:753-759. [PMID: 24837682 DOI: 10.1039/c3sm52160e] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We used single-molecule tracking experiments to observe the motion of small hydrophobic fluorescent molecules at the interface between water and a solid surface that exhibited periodic chemical patterns. The dynamics were characterized by non-ergodic, continuous time random walk statistics. The step-size distributions displayed enhanced probability of steps to periodic distances, consistent with theoretical predictions for diffusion in an atomic/molecular scale periodic potential. Surprisingly, this general behavior was observed here for surfaces exhibiting characteristic length scales three orders of magnitude larger than atomic/molecular dimensions, and may provide a new way to understand and control solid-liquid interfacial diffusion for molecular targeting applications.
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Affiliation(s)
- Michael J Skaug
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, CO 80309, USA.
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17
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Ezer D, Zabet NR, Adryan B. Physical constraints determine the logic of bacterial promoter architectures. Nucleic Acids Res 2014; 42:4196-207. [PMID: 24476912 PMCID: PMC3985651 DOI: 10.1093/nar/gku078] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
Site-specific transcription factors (TFs) bind to their target sites on the DNA, where they regulate the rate at which genes are transcribed. Bacterial TFs undergo facilitated diffusion (a combination of 3D diffusion around and 1D random walk on the DNA) when searching for their target sites. Using computer simulations of this search process, we show that the organization of the binding sites, in conjunction with TF copy number and binding site affinity, plays an important role in determining not only the steady state of promoter occupancy, but also the order at which TFs bind. These effects can be captured by facilitated diffusion-based models, but not by standard thermodynamics. We show that the spacing of binding sites encodes complex logic, which can be derived from combinations of three basic building blocks: switches, barriers and clusters, whose response alone and in higher orders of organization we characterize in detail. Effective promoter organizations are commonly found in the E. coli genome and are highly conserved between strains. This will allow studies of gene regulation at a previously unprecedented level of detail, where our framework can create testable hypothesis of promoter logic.
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Affiliation(s)
- Daphne Ezer
- Cambridge Systems Biology Centre, University of Cambridge, Tennis Court Road, Cambridge CB2 1QR, UK and Department of Genetics, University of Cambridge, Downing Street, Cambridge CB2 3EH, UK
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Calandre T, Bénichou O, Grebenkov DS, Voituriez R. Splitting probabilities and interfacial territory covered by two-dimensional and three-dimensional surface-mediated diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012149. [PMID: 24580214 DOI: 10.1103/physreve.89.012149] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2013] [Indexed: 06/03/2023]
Abstract
We consider the mean territory covered by a particle that performs surface-mediated diffusion inside a spherical confining domain (in two and three dimensions) before exit through an opening on the surface. This quantity can be expressed in terms of the splitting probability between two targets on the surface. We derive a general formula that relates this splitting probability to the mean first passage time to a single target that has been recently calculated for such a surface-mediated diffusion process. This formula is exact for pointlike targets and is shown to be accurate for extended targets. The mean covered territory is then found and analyzed for an arbitrary extension of the exit region in both two- and three-dimensional spherical domains.
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Affiliation(s)
- T Calandre
- Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), 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
| | - D S Grebenkov
- Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS, Ecole Polytechnique, F-91128 Palaiseau 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 (FRE 3231) CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
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19
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Skaug MJ, Mabry JN, Schwartz DK. Single-Molecule Tracking of Polymer Surface Diffusion. J Am Chem Soc 2013; 136:1327-32. [DOI: 10.1021/ja407396v] [Citation(s) in RCA: 86] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Michael J. Skaug
- Department of Chemical and
Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, United States
| | - Joshua N. Mabry
- Department of Chemical and
Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, United States
| | - Daniel K. Schwartz
- Department of Chemical and
Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, United States
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20
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Abstract
A mathematical model is devised to study the diffusion of mRNA in the nucleus from the site of synthesis to a nuclear pore where it is exported to the cytoplasm. This study examines the role that nuclear structure can play in determining the kinetics of export by considering models in which elements of the nuclear skeleton and confinement by chromatin direct the mRNA movement. As a rule, a dense chromatin layer favours rapid export by reducing the effective volume for diffusion. However, it may also result in a heavy tail in the export time distribution because of the low mobility of molecules that accidentally find their way deep into the dense layer. An anisotropic solid-state transport system can also assist export. There exist both an optimal ratio of the anisotropy and an optimal depth of the solid-state transport layer that favour rapid export.
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Affiliation(s)
- M R Roussel
- Department of Chemistry and Biochemistry, University of Lethbridge, Lethbridge, Canada.
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21
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Zabet NR, Adryan B. Computational models for large-scale simulations of facilitated diffusion. MOLECULAR BIOSYSTEMS 2012; 8:2815-27. [PMID: 22892851 PMCID: PMC4007627 DOI: 10.1039/c2mb25201e] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
The binding of site-specific transcription factors to their genomic target sites is a key step in gene regulation. While the genome is huge, transcription factors belong to the least abundant protein classes in the cell. It is therefore fascinating how short the time frame is that they require to home in on their target sites. The underlying search mechanism is called facilitated diffusion and assumes a combination of three-dimensional diffusion in the space around the DNA combined with one-dimensional random walk on it. In this review, we present the current understanding of the facilitated diffusion mechanism and identify questions that lack a clear or detailed answer. One way to investigate these questions is through stochastic simulation and, in this manuscript, we support the idea that such simulations are able to address them. Finally, we review which biological parameters need to be included in such computational models in order to obtain a detailed representation of the actual process.
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Affiliation(s)
- Nicolae Radu Zabet
- Cambridge Systems Biology Centre, University of Cambridge, Tennis Court Road, Cambridge CB2 1QR, UK
- Department of Genetics, University of Cambridge, Downing Street, Cambridge CB2 3EH, UK
| | - Boris Adryan
- Cambridge Systems Biology Centre, University of Cambridge, Tennis Court Road, Cambridge CB2 1QR, UK
- Department of Genetics, University of Cambridge, Downing Street, Cambridge CB2 3EH, UK
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22
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Meyer B, Bénichou O, Kafri Y, Voituriez R. Geometry-induced bursting dynamics in gene expression. Biophys J 2012; 102:2186-91. [PMID: 22824283 PMCID: PMC3341560 DOI: 10.1016/j.bpj.2012.03.060] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2012] [Revised: 03/21/2012] [Accepted: 03/26/2012] [Indexed: 11/17/2022] Open
Abstract
In prokaryotes and eukaryotes, genes are transcribed stochastically according to various temporal patterns that range from simple first-order kinetics to marked bursts, resulting in temporal and cell-to-cell variations of mRNA and protein levels. Here, we consider the effect of the transport of regulatory molecules on the noise in gene expression by taking into account explicitly the dynamics of a finite number of transcription factors confined in the cell. We calculate analytically time-dependent correlation functions of mRNA levels for a wide range of transport mechanisms and find that in the limit of small-transcription-factor copy number, the results differ significantly from standard approaches, which ignore confinement. It is shown how such dynamical quantities, which can now be obtained experimentally, can be used to identify the underlying mechanisms of transcription. Of particular importance, it is demonstrated that the geometry of transcription-factor trajectories in the cellular environment plays a key role in transcription kinetics, and can intrinsically generate the observed various transcription patterns ranging from simple first-order kinetics to bursts.
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Affiliation(s)
- B. Meyer
- UMR 7600, Université Pierre et Marie Curie/CNRS, Paris, France
| | - O. Bénichou
- UMR 7600, Université Pierre et Marie Curie/CNRS, Paris, France
| | - Y. Kafri
- Department of Physics, Technion, Haifa, Israel
| | - R. Voituriez
- UMR 7600, Université Pierre et Marie Curie/CNRS, Paris, France
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23
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Calandre T, Bénichou O, Grebenkov DS, Voituriez R. Interfacial territory covered by surface-mediated diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051111. [PMID: 23004707 DOI: 10.1103/physreve.85.051111] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2012] [Indexed: 06/01/2023]
Abstract
We consider a minimal model of heterogeneous catalysis in which a molecule performs surface-mediated diffusion inside a confining domain whose boundary contains catalytic sites. We explicitly take into account the combination of surface and bulk diffusion, and we obtain exact results for the mean and variance of the territory covered on the boundary by the particle before its exit in the case of a two-dimensional spherical domain. Depending on the relative positions of the entrance and exit points, very different behaviors with respect to the mean adsorption time of the molecule on the surface are found. We also determine both exact lower and upper bounds and an approximate expression of the probability of reacting with catalytic sites before exiting the domain. These results provide a quantitative measure of the efficiency of an idealized catalyst.
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Affiliation(s)
- T Calandre
- Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), CNRS/UPMC, 4 Place Jussieu, F-75255 Paris Cedex, France
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24
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Nunige S, Cornut R, Hazimeh H, Hauquier F, Lefrou C, Combellas C, Kanoufi F. Reactivity of Surfaces Determined by Local Electrochemical Triggering: A Bromo-Terminated Self-Assembled Monolayer. Angew Chem Int Ed Engl 2012. [DOI: 10.1002/ange.201201083] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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25
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Nunige S, Cornut R, Hazimeh H, Hauquier F, Lefrou C, Combellas C, Kanoufi F. Reactivity of Surfaces Determined by Local Electrochemical Triggering: A Bromo-Terminated Self-Assembled Monolayer. Angew Chem Int Ed Engl 2012; 51:5208-12. [DOI: 10.1002/anie.201201083] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2012] [Indexed: 11/06/2022]
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26
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Tejedor V, Voituriez R, Bénichou O. Optimizing persistent random searches. PHYSICAL REVIEW LETTERS 2012; 108:088103. [PMID: 22463578 DOI: 10.1103/physrevlett.108.088103] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2011] [Indexed: 05/31/2023]
Abstract
We consider a minimal model of persistent random searcher with a short range memory. We calculate exactly for such a searcher the mean first-passage time to a target in a bounded domain and find that it admits a nontrivial minimum as function of the persistence length. This reveals an optimal search strategy which differs markedly from the simple ballistic motion obtained in the case of Poisson distributed targets. Our results show that the distribution of targets plays a crucial role in the random search problem. In particular, in the biologically relevant cases of either a single target or regular patterns of targets, we find that, in strong contrast to repeated statements in the literature, persistent random walks with exponential distribution of excursion lengths can minimize the search time, and in that sense perform better than any Levy walk.
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Affiliation(s)
- Vincent Tejedor
- Physics Department, Technical University of Munich, Garching, Germany
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27
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Meyer B, Agliari E, Bénichou O, Voituriez R. Exact calculations of first-passage quantities on recursive networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:026113. [PMID: 22463285 DOI: 10.1103/physreve.85.026113] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2011] [Indexed: 05/31/2023]
Abstract
We present general methods to exactly calculate mean first-passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and one or several targets; averaged quantities over a given set of sources (e.g., same-connectivity nodes) are also derived. The exact estimate of such quantities highlights the dependency of first-passage processes with respect to the source-target distance, which has recently revealed to be a key parameter in characterizing transport in complex media. We explicitly perform calculations for different classes of recursive networks [finitely ramified fractals, scale-free (trans)fractals, nonfractals, mixtures between fractals and nonfractals, nondecimable hierarchical graphs] of arbitrary size. Our approach unifies and significantly extends the available results in the field.
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Affiliation(s)
- B Meyer
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Case Courrier 121, Université Paris 6, 4 Place Jussieu, FR-75255 Paris Cedex, France
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28
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Sheinman M, Bénichou O, Kafri Y, Voituriez R. Classes of fast and specific search mechanisms for proteins on DNA. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:026601. [PMID: 22790348 DOI: 10.1088/0034-4885/75/2/026601] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Problems of search and recognition appear over different scales in biological systems. In this review we focus on the challenges posed by interactions between proteins, in particular transcription factors, and DNA and possible mechanisms which allow for fast and selective target location. Initially we argue that DNA-binding proteins can be classified, broadly, into three distinct classes which we illustrate using experimental data. Each class calls for a different search process and we discuss the possible application of different search mechanisms proposed over the years to each class. The main thrust of this review is a new mechanism which is based on barrier discrimination. We introduce the model and analyze in detail its consequences. It is shown that this mechanism applies to all classes of transcription factors and can lead to a fast and specific search. Moreover, it is shown that the mechanism has interesting transient features which allow for stability at the target despite rapid binding and unbinding of the transcription factor from the target.
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Affiliation(s)
- M Sheinman
- Department of Physics and Astronomy, Vrije Universiteit, Amsterdam, The Netherlands
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29
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Meyer B, Chevalier C, Voituriez R, Bénichou O. Universality classes of first-passage-time distribution in confined media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:051116. [PMID: 21728499 DOI: 10.1103/physreve.83.051116] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2010] [Indexed: 05/31/2023]
Abstract
We study the first-passage time (FPT) distribution to a target site for a random walker evolving in a bounded domain. We show that in the limit of large volume of the confining domain, this distribution falls into universality classes indexed by the walk dimension d(w) and the fractal dimension d(f) of the medium, which have been recently identified previously [Bénichou et al., Nat. Chem. 2, 472 (2010)]. We present in this paper a complete derivation of these universal distributions, discuss extensively the range of applicability of the results, and extend the method to continuous-time random walks. This analysis puts forward the importance of the geometry, and in particular the position of the starting point, in first-passage statistics. Analytical results are validated by numerical simulations, applied to various models of transport in disordered media, which illustrate the universality classes of the FPT distribution.
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Affiliation(s)
- B Meyer
- Laboratoire de Physique Théorique de la matière Condensée (UMR 7600), Université Paris 6, Paris, France
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30
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Bénichou O, Chevalier C, Meyer B, Voituriez R. Facilitated diffusion of proteins on chromatin. PHYSICAL REVIEW LETTERS 2011; 106:038102. [PMID: 21405302 DOI: 10.1103/physrevlett.106.038102] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2010] [Indexed: 05/30/2023]
Abstract
We present a theoretical model of facilitated diffusion of proteins in the cell nucleus. This model, which takes into account the successive binding and unbinding events of proteins to DNA, relies on a fractal description of the chromatin which has been recently evidenced experimentally. Facilitated diffusion is shown quantitatively to be favorable for a fast localization of a target locus by a transcription factor and even to enable the minimization of the search time by tuning the affinity of the transcription factor with DNA. This study shows the robustness of the facilitated diffusion mechanism, invoked so far only for linear conformations of DNA.
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Affiliation(s)
- O Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée CNRS-UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
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31
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Tejedor V, Bénichou O, Voituriez R, Moreau M. Response to targeted perturbations for random walks on networks. Phys Rev E 2011; 82:056106. [PMID: 21230544 DOI: 10.1103/physreve.82.056106] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2010] [Indexed: 11/07/2022]
Abstract
We introduce a general framework, applicable to a broad class of random walks on networks, that quantifies the response of the mean first-passage time to a target node to a local perturbation of the network, both in the context of attacks (damaged link) or strategies of transport enhancement (added link). This approach enables to determine explicitly the dependence of this response on geometric parameters (such as the network size and the localization of the perturbation) and on the intensity of the perturbation. In particular, it is showed that the relative variation of the mean first-passage time is independent of the network size, and remains significant in the large size limit. Furthermore, in the case of noncompact exploration of the network, it is found that a targeted perturbation keeps a substantial impact on transport properties for any localization of the damaged link.
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Affiliation(s)
- Vincent Tejedor
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie-CNRS, Paris, France
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32
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Bénichou O, Grebenkov D, Levitz P, Loverdo C, Voituriez R. Optimal reaction time for surface-mediated diffusion. PHYSICAL REVIEW LETTERS 2010; 105:150606. [PMID: 21230885 DOI: 10.1103/physrevlett.105.150606] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2010] [Revised: 09/14/2010] [Indexed: 05/30/2023]
Abstract
We present an exact calculation of the mean first-passage time to a small target on the surface of a 2D or 3D spherical domain, for a molecule performing surface-mediated diffusion. This minimal model of interfacial reactions, which explicitly takes into account the combination of surface and bulk diffusion, shows the importance of correlations induced by the coupling of the switching dynamics to the geometry of the confinement, ignored so far. Our results show that, in the context of interfacial systems in confinement, the reaction time can be minimized as a function of the desorption rate from the surface, which puts forward a general mechanism of enhancement and regulation of chemical and biological reactivity.
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Affiliation(s)
- O Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), case courrier 121, Université Paris 6, 4 Place Jussieu, 75255 Paris Cedex, France
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33
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Abstract
It has long been appreciated that the transport properties of molecules can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target-the first-passage time (FPT). Determining the FPT distribution in realistic confined geometries has until now, however, seemed intractable. Here, we calculate this FPT distribution analytically and show that transport processes as varied as regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, fall into the same universality classes. Beyond the theoretical aspect, this result changes our views on standard reaction kinetics and we introduce the concept of 'geometry-controlled kinetics'. More precisely, we argue that geometry-and in particular the initial distance between reactants in 'compact' systems-can become a key parameter. These findings could help explain the crucial role that the spatial organization of genes has in transcription kinetics, and more generally the impact of geometry on diffusion-limited reactions.
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34
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Bénichou O, Voituriez R. Optimization of the residence time of a Brownian particle in a spherical subdomain. J Chem Phys 2010; 131:181104. [PMID: 19916589 DOI: 10.1063/1.3264122] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this communication, we show that the residence time of a Brownian particle, defined as the cumulative time spent in a given region of space, can be optimized as a function of the diffusion coefficient. We discuss the relevance of this effect to several schematic experimental situations classified in nature--random or deterministic--both of the observation time and of the starting position of the Brownian particle.
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Affiliation(s)
- O Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), Case Courrier 121, UniversitéParis 6, 4 Place Jussieu, 75255 Paris Cedex, France.
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35
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Licata NA, Grill SW. The first-passage problem for diffusion through a cylindrical pore with sticky walls. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2009; 30:439-447. [PMID: 19856004 DOI: 10.1140/epje/i2009-10529-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2009] [Revised: 08/10/2009] [Accepted: 10/01/2009] [Indexed: 05/28/2023]
Abstract
We calculate the first-passage time distribution for diffusion through a cylindrical pore with sticky walls. A particle diffusively explores the interior of the pore through a series of binding and unbinding events with the cylinder wall. Through a diagrammatic expansion we obtain first-passage time statistics for the particle's exit from the pore. Connections between the model and nucleocytoplasmic transport in cells are discussed.
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Affiliation(s)
- N A Licata
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187, Dresden, Germany.
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36
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Bénichou O, Kafri Y, Sheinman M, Voituriez R. Searching fast for a target on DNA without falling to traps. PHYSICAL REVIEW LETTERS 2009; 103:138102. [PMID: 19905543 DOI: 10.1103/physrevlett.103.138102] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2009] [Indexed: 05/28/2023]
Abstract
Genomic expression depends critically on both the ability of regulatory proteins to locate specific target sites on DNA within seconds and on the formation of long-lived (many minutes) complexes between these proteins and the DNA. Equilibrium experiments show that indeed regulatory proteins bind tightly to their target site. However, they also find strong binding to other nonspecific sites which act as traps that can dramatically increase the time needed to locate the target. This gives rise to a conflict between the speed and stability requirements. Here we suggest a simple mechanism which can resolve this long-standing paradox.
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Affiliation(s)
- O Bénichou
- UMR 7600, Université Pierre et Marie Curie/CNRS, 75255 Paris Cedex 05, France
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37
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Loverdo C, Bénichou O, Moreau M, Voituriez R. Robustness of optimal intermittent search strategies in one, two, and three dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:031146. [PMID: 19905101 DOI: 10.1103/physreve.80.031146] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2009] [Indexed: 05/28/2023]
Abstract
Search problems at various scales involve a searcher, be it a molecule before reaction or a foraging animal, which performs an intermittent motion. Here we analyze a generic model based on such type of intermittent motion, in which the searcher alternates phases of slow motion allowing detection and phases of fast motion without detection. We present full and systematic results for different modeling hypotheses of the detection mechanism in space in one, two, and three dimensions. Our study completes and extends the results of our recent letter [Loverdo, Nat. Phys. 4, 134 (2008)] and gives the necessary calculation details. In addition, another modeling of the detection case is presented. We show that the mean target detection time can be minimized as a function of the mean duration of each phase in one, two, and three dimensions. Importantly, this optimal strategy does not depend on the details of the modeling of the slow detection phase, which shows the robustness of our results. We believe that this systematic analysis can be used as a basis to study quantitatively various real search problems involving intermittent behaviors.
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Affiliation(s)
- C Loverdo
- Laboratoire de Physique Théorique de la Matière Condensée, UMR CNRS 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris, France
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38
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Abstract
When DNA-binding proteins search for their specific binding site on a DNA molecule they alternate between linear 1-dimensional diffusion along the DNA molecule, mediated by nonspecific binding, and 3-dimensional volume excursion events between successive dissociation from and rebinding to DNA. If the DNA molecule is kept in a straight configuration, for instance, by optical tweezers, these 3-dimensional excursions may be divided into long volume excursions and short hops along the DNA. These short hops correspond to immediate rebindings after dissociation such that a rebinding event to the DNA occurs at a site that is close to the site of the preceding dissociation. When the DNA molecule is allowed to coil up, immediate rebinding may also lead to so-called intersegmental jumps, i.e., immediate rebindings to a DNA segment that is far away from the unbinding site when measured in the chemical distance along the DNA, but close by in the embedding 3-dimensional space. This effect is made possible by DNA looping. The significance of intersegmental jumps was recently demonstrated in a single DNA optical tweezers setup. Here we present a theoretical approach in which we explicitly take the effect of DNA coiling into account. By including the spatial correlations of the short hops we demonstrate how the facilitated diffusion model can be extended to account for intersegmental jumping at varying DNA densities. It is also shown that our approach provides a quantitative interpretation of the experimentally measured enhancement of the target location by DNA-binding proteins.
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