1
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Zhang R, Jalali S, Dias CL, Haataja MP. Growth kinetics of amyloid-like fibrils: An integrated atomistic simulation and continuum theory approach. PNAS NEXUS 2024; 3:pgae045. [PMID: 38725528 PMCID: PMC11079572 DOI: 10.1093/pnasnexus/pgae045] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Accepted: 01/19/2024] [Indexed: 05/12/2024]
Abstract
Amyloid fibrils have long been associated with many neurodegenerative diseases. The conventional picture of the formation and proliferation of fibrils from unfolded proteins comprises primary and secondary nucleation of oligomers followed by elongation and fragmentation thereof. In this work, we first employ extensive all-atom molecular dynamics (MD) simulations of short peptides to investigate the governing processes of fibril growth at the molecular scale. We observe that the peptides in the bulk solution can bind onto and subsequently diffuse along the fibril surface, which leads to fibril elongation via either bulk- or surface-mediated docking mechanisms. Then, to guide the quantitative interpretation of these observations and to provide a more comprehensive picture of the growth kinetics of single fibrils, a continuum model which incorporates the key processes observed in the MD simulations is formulated. The model is employed to investigate how relevant physical parameters affect the kinetics of fibril growth and identify distinct growth regimes. In particular, it is shown that fibrils which strongly bind peptides may undergo a transient exponential growth phase in which the entire fibril surface effectively acts as a sink for peptides. We also demonstrate how the relevant model parameters can be estimated from the MD trajectories. Our results provide compelling evidence that the overall fibril growth rates are determined by both bulk and surface peptide fluxes, thereby contributing to a more fundamental understanding of the growth kinetics of amyloid-like fibrils.
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Affiliation(s)
- Ruoyao Zhang
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Sharareh Jalali
- Department of Physics, New Jersey Institute of Technology, Newark, NJ 07102, USA
| | - Cristiano Luis Dias
- Department of Physics, New Jersey Institute of Technology, Newark, NJ 07102, USA
| | - Mikko P Haataja
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
- Princeton Materials Institute, Princeton University, Princeton, NJ 08544, USA
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2
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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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3
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Grebenkov DS. Surface hopping propagator: An alternative approach to diffusion-influenced reactions. Phys Rev E 2020; 102:032125. [PMID: 33075930 DOI: 10.1103/physreve.102.032125] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Accepted: 08/28/2020] [Indexed: 06/11/2023]
Abstract
Dynamics of a particle diffusing in a confinement can be seen a sequence of bulk-diffusion-mediated hops on the confinement surface. Here, we investigate the surface hopping propagator that describes the position of the diffusing particle after a prescribed number of encounters with that surface. This quantity plays the central role in diffusion-influenced reactions and determines their most common characteristics such as the propagator, the first-passage time distribution, and the reaction rate. We derive explicit formulas for the surface hopping propagator and related quantities for several Euclidean domains: half-space, circular annuli, circular cylinders, and spherical shells. These results provide the theoretical ground for studying diffusion-mediated surface phenomena. The behavior of the surface hopping propagator is investigated for both "immortal" and "mortal" particles.
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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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4
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Grebenkov DS. Paradigm Shift in Diffusion-Mediated Surface Phenomena. PHYSICAL REVIEW LETTERS 2020; 125:078102. [PMID: 32857533 DOI: 10.1103/physrevlett.125.078102] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2020] [Accepted: 07/21/2020] [Indexed: 06/11/2023]
Abstract
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation, and filtration processes. Their current description via diffusion equations with mixed boundary conditions is limited to simple surface reactions with infinite or constant reactivity. In this Letter, we propose a probabilistic approach based on the concept of boundary local time to investigate the intricate dynamics of diffusing particles near a reactive surface. Reformulating surface-particle interactions in terms of stopping conditions, we obtain in a unified way major diffusion-reaction characteristics such as the propagator, the survival probability, the first-passage time distribution, and the reaction rate. This general formalism allows us to describe new surface reaction mechanisms such as for instance surface reactivity depending on the number of encounters with the diffusing particle that can model the effects of catalyst fooling or membrane degradation. The disentanglement of the geometric structure of the medium from surface reactivity opens far-reaching perspectives for modeling, optimization, and control of diffusion-mediated surface phenomena.
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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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5
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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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6
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Berezhkovskii AM, Dagdug L, Bezrukov SM. Bulk-mediated surface transport in the presence of bias. J Chem Phys 2017; 147:014103. [PMID: 28688439 PMCID: PMC5500123 DOI: 10.1063/1.4991730] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2017] [Accepted: 06/21/2017] [Indexed: 12/22/2022] Open
Abstract
Surface transport, when the particle is allowed to leave the surface, travel in the bulk for some time, and then return to the surface, is referred to as bulk-mediated surface transport. Recently, we proposed a formalism that significantly simplifies analysis of bulk-mediated surface diffusion [A. M. Berezhkovskii, L. Dagdug, and S. M. Bezrukov, J. Chem. Phys. 143, 084103 (2015)]. Here this formalism is extended to bulk-mediated surface transport in the presence of bias, i.e., when the particle has arbitrary drift velocities on the surface and in the bulk. A key advantage of our approach is that the transport problem reduces to that of a two-state problem of the particle transitions between the surface and the bulk. The latter can be solved with relative ease. The formalism is used to find the Laplace transforms of the first two moments of the particle displacement over the surface in time t at arbitrary values of the particle drift velocities and diffusivities on the surface and in the bulk. This allows us to analyze in detail the time dependence of the effective drift velocity of the particle on the surface, which can be highly nontrivial.
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Affiliation(s)
- Alexander M Berezhkovskii
- Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Leonardo Dagdug
- Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Sergey M Bezrukov
- Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
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7
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Ma Y, Chen Y, Yu W, Luo K. How nonspecifically DNA-binding proteins search for the target in crowded environments. J Chem Phys 2016; 144:125102. [PMID: 27036479 DOI: 10.1063/1.4944905] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Abstract
We investigate how a tracer particle searches a target located in DNA modeled by a stiff chain in crowded environments using theoretical analysis and Langevin dynamics simulations. First, we show that the three-dimensional (3D) diffusion coefficient of the tracer only depends on the density of crowders ϕ, while its one-dimensional (1D) diffusion coefficient is affected by not only ϕ but also the nonspecific binding energy ε. With increasing ϕ and ε, no obvious change in the average 3D diffusion time is observed, while the average 1D sliding time apparently increases. We propose theoretically that the 1D sliding of the tracer along the chain could be well captured by the Kramers' law of escaping rather than the Arrhenius law, which is verified directly by the simulations. Finally, the average search time increases monotonously with an increase in ϕ while it has a minimum as a function of ε, which could be understood from the different behaviors of the average number of search rounds with the increasing ϕ or ε. These results provide a deeper understanding of the role of facilitated diffusion in target search of proteins on DNA in vivo.
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Affiliation(s)
- Yiding Ma
- CAS Key Laboratory of Soft Matter Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Yuhao Chen
- CAS Key Laboratory of Soft Matter Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Wancheng Yu
- CAS Key Laboratory of Soft Matter Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Kaifu Luo
- CAS Key Laboratory of Soft Matter Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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8
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Lenzi EK, Novatski A, Farago PV, Almeida MA, Zawadzki SF, Menechini Neto R. Diffusion Processes and Drug Release: Capsaicinoids - Loaded Poly (ε-caprolactone) Microparticles. PLoS One 2016; 11:e0157662. [PMID: 27309358 PMCID: PMC4911155 DOI: 10.1371/journal.pone.0157662] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2016] [Accepted: 06/02/2016] [Indexed: 12/02/2022] Open
Abstract
We present a generalmodel based on fractional diffusion equation coupled with a kinetic equation through the boundary condition. It covers several scenarios that may be characterized by usual or anomalous diffusion or present relaxation processes on the surface with non-Debye characteristics. A particular case of this model is used to investigate the experimental data obtained from the drug release of the capsaicinoids-loaded Poly (ε-caprolactone) microparticles. These considerations lead us to a good agreement with experimental data and to the conjecture that the burst effect, i.e., an initial large bolus of drug is released before the release rate reaches a stable profile, may be related to an anomalous diffusion manifested by the system.
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Affiliation(s)
- E. K. Lenzi
- Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, 84030–900, Brazil
- * E-mail:
| | - A. Novatski
- Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, 84030–900, Brazil
| | - P. V. Farago
- Departamento de Ciências Farmacêuticas, Universidade Estadual de Ponta Grossa,Ponta Grossa, 84030–900, Brazil
| | - M. A. Almeida
- Departamento Química, Universidade Federal de Curitiba, Curitiba, 81531–980, Brazil
| | - S. F. Zawadzki
- Departamento Química, Universidade Federal de Curitiba, Curitiba, 81531–980, Brazil
| | - R. Menechini Neto
- Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, 84030–900, Brazil
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9
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Wang D, Chin HY, He C, Stoykovich MP, Schwartz DK. Polymer Surface Transport Is a Combination of in-Plane Diffusion and Desorption-Mediated Flights. ACS Macro Lett 2016; 5:509-514. [PMID: 35607234 DOI: 10.1021/acsmacrolett.6b00183] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Previous studies of polymer motion at solid/liquid interfaces described the transport in the context of a continuous time random walk (CTRW) process, in which diffusion switches between desorption-mediated "flights" (i.e., hopping) and surface-adsorbed waiting-time intervals. However, it has been unclear whether the waiting times represented periods of complete immobility or times during which molecules engaged in a different (e.g., slower or confined) mode of interfacial transport. Here we designed high-throughput, single-molecule tracking measurements to address this question. Specifically, we studied polymer dynamics on either chemically homogeneous or nanopatterned surfaces (hexagonal diblock copolymer films) with chemically distinct domains, where polymers were essentially excluded from the low-affinity domains, eliminating the possibility of significant continuous diffusion in the absence of desorption-mediated flights. Indeed, the step-size distributions on homogeneous surfaces exhibited an additional diffusive mode that was missing on the chemically heterogeneous nanopatterned surfaces, confirming the presence of a slow continuous mode due to 2D in-plane diffusion. Kinetic Monte Carlo simulations were performed to test this model and, with the theoretical in-plane diffusion coefficient of D2D = 0.20 μm2/s, we found a good agreement between simulations and experimental data on both chemically homogeneous and nanopatterned surfaces.
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Affiliation(s)
- Dapeng Wang
- Department of Chemical and
Biological Engineering, University of Colorado, Boulder, Colorado 80309, United States
| | - Huai-Ying Chin
- Department of Chemical and
Biological Engineering, University of Colorado, Boulder, Colorado 80309, United States
| | - Chunlin He
- Department of Chemical and
Biological Engineering, University of Colorado, Boulder, Colorado 80309, United States
| | - Mark P. Stoykovich
- Department of Chemical and
Biological Engineering, University of Colorado, Boulder, Colorado 80309, United States
| | - Daniel K. Schwartz
- Department of Chemical and
Biological Engineering, University of Colorado, Boulder, Colorado 80309, United States
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10
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Berezhkovskii AM, Dagdug L, Bezrukov SM. A new approach to the problem of bulk-mediated surface diffusion. J Chem Phys 2015; 143:084103. [PMID: 26328814 DOI: 10.1063/1.4928741] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper is devoted to bulk-mediated surface diffusion of a particle which can diffuse both on a flat surface and in the bulk layer above the surface. It is assumed that the particle is on the surface initially (at t = 0) and at time t, while in between it may escape from the surface and come back any number of times. We propose a new approach to the problem, which reduces its solution to that of a two-state problem of the particle transitions between the surface and the bulk layer, focusing on the cumulative residence times spent by the particle in the two states. These times are random variables, the sum of which is equal to the total observation time t. The advantage of the proposed approach is that it allows for a simple exact analytical solution for the double Laplace transform of the conditional probability density of the cumulative residence time spent on the surface by the particle observed for time t. This solution is used to find the Laplace transform of the particle mean square displacement and to analyze the peculiarities of its time behavior over the entire range of time. We also establish a relation between the double Laplace transform of the conditional probability density and the Fourier-Laplace transform of the particle propagator over the surface. The proposed approach treats the cases of both finite and infinite bulk layer thicknesses (where bulk-mediated surface diffusion is normal and anomalous at asymptotically long times, respectively) on equal footing.
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Affiliation(s)
- Alexander M Berezhkovskii
- Program in Physical Biology, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Leonardo Dagdug
- Program in Physical Biology, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Sergey M Bezrukov
- Program in Physical Biology, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
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11
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Liu L, Luo K. Molecular crowding effect on dynamics of DNA-binding proteins search for their targets. J Chem Phys 2015; 141:225102. [PMID: 25494769 DOI: 10.1063/1.4903505] [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
DNA-binding proteins locate and bind their target sequences positioned on DNA in crowded environments, but the molecular crowding effect on this search process is not clear. Using analytical techniques and Langevin dynamics simulations in two dimensions (2D), we find that the essential physics for facilitated diffusion in 2D search and 3D search is the same. We observe that the average search times have minima at the same optimal nonspecific binding energy for the cases with and without the crowding particle. Moreover, the molecular crowding increases the search time by increasing the average search rounds and the one-dimensional (1D) sliding time of a round, but almost not changing the average 2D diffusion time of a round. In addition, the fraction of 1D sliding time out of the total search time increases with increasing the concentration of crowders. For 2D diffusion, the molecular crowding decreases the jumping length and narrows its distribution due to the cage effect from crowders. These results shed light on the role of facilitated diffusion in DNA targeting kinetics in living cells.
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Affiliation(s)
- Lin Liu
- CAS Key Laboratory of Soft Matter Chemistry, Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, Anhui Province 230026, People's Republic of China
| | - Kaifu Luo
- CAS Key Laboratory of Soft Matter Chemistry, Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, Anhui Province 230026, People's Republic of China
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12
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Liu L, Luo K. DNA-binding protein searches for its target: Non-monotonic dependence of the search time on the density of roadblocks bound on the DNA chain. J Chem Phys 2015; 142:125101. [DOI: 10.1063/1.4916056] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Affiliation(s)
- Lin Liu
- CAS Key Laboratory of Soft Matter Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, Anhui Province 230026, People’s Republic of China
| | - Kaifu Luo
- CAS Key Laboratory of Soft Matter Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, Anhui Province 230026, People’s Republic of China
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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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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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15
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Levesque M, Bénichou O, Rotenberg B. Molecular diffusion between walls with adsorption and desorption. J Chem Phys 2013; 138:034107. [DOI: 10.1063/1.4775742] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Chechkin AV, Zaid IM, Lomholt MA, Sokolov IM, Metzler R. Bulk-mediated diffusion on a planar surface: full solution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041101. [PMID: 23214523 DOI: 10.1103/physreve.86.041101] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2012] [Indexed: 06/01/2023]
Abstract
We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random-walk approach, we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations, we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover, we study the long-time dynamics for the surface motion.
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Affiliation(s)
- Aleksei V Chechkin
- Institute for Theoretical Physics NSC KIPT, Akademicheskaya st. 1, 61108 Kharkov, Ukraine
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17
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Bauer M, Metzler R. Generalized facilitated diffusion model for DNA-binding proteins with search and recognition states. Biophys J 2012; 102:2321-30. [PMID: 22677385 DOI: 10.1016/j.bpj.2012.04.008] [Citation(s) in RCA: 77] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2012] [Revised: 04/04/2012] [Accepted: 04/05/2012] [Indexed: 11/30/2022] Open
Abstract
Transcription factors (TFs) such as the lac repressor find their target sequence on DNA at remarkably high rates. In the established Berg-von Hippel model for this search process, the TF alternates between three-dimensional diffusion in the bulk solution and one-dimensional sliding along the DNA chain. To overcome the so-called speed-stability paradox, in similar models the TF was considered as being present in two conformations (search state and recognition state) between which it switches stochastically. Combining both the facilitated diffusion model and alternating states, we obtain a generalized model. We explicitly treat bulk excursions for rodlike chains arranged in parallel and consider a simplified model for coiled DNA. Compared to previously considered facilitated diffusion models, corresponding to limiting cases of our generalized model, we surprisingly find a reduced target search rate. Moreover, at optimal conditions there is no longer an equipartition between the time spent by the protein on and off the DNA chain.
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Affiliation(s)
- Maximilian Bauer
- Physics Department, Technical University of Munich, Garching, Germany
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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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