1
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Olmeda F, Rulands S. Field theory of enzyme-substrate systems with restricted long-range interactions. Phys Rev E 2024; 110:024404. [PMID: 39294986 DOI: 10.1103/physreve.110.024404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2024] [Accepted: 07/24/2024] [Indexed: 09/21/2024]
Abstract
Enzyme-substrate kinetics form the basis of many biomolecular processes. The interplay between substrate binding and substrate geometry can give rise to long-range interactions between enzyme binding events. Here we study a general model of enzyme-substrate kinetics with restricted long-range interactions described by an exponent -γ. We employ a coherent-state path integral and renormalization group approach to calculate the first moment and two-point correlation function of the enzyme-binding profile. We show that starting from an empty substrate the average occupancy follows a power law with an exponent 1/(1-γ) over time. The correlation function decays algebraically with two distinct spatial regimes characterized by exponents -γ on short distances and -(2/3)(2-γ) on long distances. The crossover between both regimes scales inversely with the average substrate occupancy. Our work allows associating experimental measurements of bound enzyme locations with their binding kinetics and the spatial conformation of the substrate.
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2
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Méndez V, Flaquer-Galmés R, Campos D. First-passage time of a Brownian searcher with stochastic resetting to random positions. Phys Rev E 2024; 109:044134. [PMID: 38755900 DOI: 10.1103/physreve.109.044134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2024] [Accepted: 03/22/2024] [Indexed: 05/18/2024]
Abstract
We study the effect of a resetting point randomly distributed around the origin on the mean first-passage time of a Brownian searcher moving in one dimension. We compare the search efficiency with that corresponding to reset to the origin and find that the mean first-passage time of the latter can be larger or smaller than the distributed case, depending on whether the resetting points are symmetrically or asymmetrically distributed. In particular, we prove the existence of an optimal reset rate that minimizes the mean first-passage time for distributed resetting to a finite interval if the target is located outside this interval. When the target position belongs to the resetting interval or it is infinite then no optimal reset rate exists, but there is an optimal resetting interval width or resetting characteristic scale which minimizes the mean first-passage time. We also show that the first-passage density averaged over the resetting points depends on its first moment only. As a consequence, there is an equivalent point such that the first-passage problem with resetting to that point is statistically equivalent to the case of distributed resetting. We end our study by analyzing the fluctuations of the first-passage times for these cases. All our analytical results are verified through numerical simulations.
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Affiliation(s)
- V Méndez
- Grup de Física Estadística, Departament de Física. Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain
| | - R Flaquer-Galmés
- Grup de Física Estadística, Departament de Física. Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain
| | - D Campos
- Grup de Física Estadística, Departament de Física. Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain
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3
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Go BG, Jeon E, Kim YW. Active search for a reactive target in thermal environments. J Chem Phys 2024; 160:044103. [PMID: 38258927 DOI: 10.1063/5.0179968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2023] [Accepted: 12/15/2023] [Indexed: 01/24/2024] Open
Abstract
We study a stochastic process where an active particle, modeled by a one-dimensional run-and-tumble particle, searches for a target with a finite absorption strength in thermal environments. Solving the Fokker-Planck equation for a uniform initial distribution, we analytically calculate the mean searching time (MST), the time for the active particle to be finally absorbed, and show that there exists an optimal self-propulsion velocity of the active particle at which MST is minimized. As the diffusion constant increases, the optimal velocity changes from a finite value to zero, which implies that a purely diffusive Brownian motion outperforms an active motion in terms of searching time. Depending on the absorption strength of the target, the transition of the optimal velocity becomes either continuous or discontinuous, which can be understood based on the Landau approach. In addition, we obtain the phase diagram indicating the passive-efficient and the active-efficient regions. Finally, the initial condition dependence of MST is presented in limiting cases.
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Affiliation(s)
- Byeong Guk Go
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Euijin Jeon
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Yong Woon Kim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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4
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Fazio N, Mersch KN, Hao L, Lohman TM. E. coli RecBCD Nuclease Domain Regulates Helicase Activity but not Single Stranded DNA Translocase Activity. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.10.13.561901. [PMID: 37905078 PMCID: PMC10614803 DOI: 10.1101/2023.10.13.561901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
Much is still unknown about the mechanisms by which helicases unwind duplex DNA. Whereas structure-based models describe DNA unwinding as a consequence of mechanically pulling the DNA duplex across a wedge domain in the helicase by the single stranded (ss)DNA translocase activity of the ATPase motors, biochemical data indicate that processive DNA unwinding by the E. coli RecBCD helicase can occur in the absence of ssDNA translocation of the canonical RecB and RecD motors. Here, we present evidence that dsDNA unwinding is not a simple consequence of ssDNA translocation by the RecBCD motors. Using stopped-flow fluorescence approaches, we show that a RecB nuclease domain deletion variant (RecB ΔNuc CD) unwinds dsDNA at significantly slower rates than RecBCD, while the rate of ssDNA translocation is unaffected. This effect is primarily due to the absence of the nuclease domain and not the absence of the nuclease activity, since a nuclease-dead mutant (RecB D1080A CD), which retains the nuclease domain, showed no significant change in rates of ssDNA translocation or dsDNA unwinding relative to RecBCD on short DNA substrates (≤ 60 base pairs). This indicates that ssDNA translocation is not rate-limiting for DNA unwinding. RecB ΔNuc CD also initiates unwinding much slower than RecBCD from a blunt-ended DNA, although it binds with higher affinity than RecBCD. RecB ΔNuc CD also unwinds DNA ∼two-fold slower than RecBCD on long DNA (∼20 kilo base pair) in single molecule optical tweezer experiments, although the rates for RecB D1080A CD unwinding are intermediate between RecBCD and RecB ΔNuc CD. Surprisingly, significant pauses occur even in the absence of chi (crossover hotspot instigator) sites. We hypothesize that the nuclease domain influences the rate of DNA base pair melting, rather than DNA translocation, possibly allosterically. Since the rate of DNA unwinding by RecBCD also slows after it recognizes a chi sequence, RecB ΔNuc CD may mimic a post- chi state of RecBCD.
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5
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Briantceva N, Chouhan L, Parsani M, Alouini MS. Impact of Evanescence Process on Three-Dimensional Sub-Diffusion-Based Molecular Communication Channel. IEEE Trans Nanobioscience 2023; 22:923-932. [PMID: 37030875 DOI: 10.1109/tnb.2023.3260107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/10/2023]
Abstract
In most of the existing works of molecular communication (MC), the standard diffusion environment is taken into account where the mean square displacement (MSD) of an information molecule (IM) scales linearly with time. On the contrary, this work considers the sub-diffusion motion that appears in crowded and complex (porous or fractal) environments (movement of the particles in the living cells) where the particle's MSD scales as a fractional order power law in time. Moreover, we examine an additional evanescence process resulting from which the molecules can degrade before hitting the boundary of the receiver (RX). Thus, in this work, we present a 3D MC system with a point transmitter (TX) and the spherical RX with the sub-diffusive behavior of an IM along with its evanescence. Furthermore, an IM's closed-form expressions for the arrival probability and the first passage time density (FPTD) are emulated in the above context. Additionally, we investigate the performance of MC by using the concentration-based modulation technique in a sub-diffusion channel. Finally, the considered MC channel is exploited in terms of the probability of detection, probability of false alarm, and probability of error for different parameters such as the reaction rate, fractional power, and radius of the RX.
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6
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Biroli M, Majumdar SN, Schehr G. Critical number of walkers for diffusive search processes with resetting. Phys Rev E 2023; 107:064141. [PMID: 37464619 DOI: 10.1103/physreve.107.064141] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 05/30/2023] [Indexed: 07/20/2023]
Abstract
We consider N Brownian motions diffusing independently on a line, starting at x_{0}>0, in the presence of an absorbing target at the origin. The walkers undergo stochastic resetting under two protocols: (A) each walker resets independently to x_{0} with rate r and (B) all walkers reset simultaneously to x_{0} with rate r. We derive an explicit analytical expression for the mean first-passage time to the origin in terms of an integral which is evaluated numerically using Mathematica. We show that, as a function of r and for fixed x_{0}, it has a minimum at an optimal value r^{*}>0 as long as N<N_{c}. Thus resetting is beneficial for the search for N<N_{c}. When N>N_{c}, the optimal value occurs at r^{*}=0 indicating that resetting hinders search processes. We obtain different values of N_{c} for protocols A and B; indeed, for N≤7 resetting is beneficial in protocol A, while for N≤6 resetting is beneficial for protocol B. Our theoretical predictions are verified in numerical Langevin simulations.
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Affiliation(s)
- Marco Biroli
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Satya N Majumdar
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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7
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Jain S, Boyer D, Pal A, Dagdug L. Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting. J Chem Phys 2023; 158:054113. [PMID: 36754825 DOI: 10.1063/5.0135249] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023] Open
Abstract
The transport of particles through channels is of paramount importance in physics, chemistry, and surface science due to its broad real world applications. Much insight can be gained by observing the transition paths of a particle through a channel and collecting statistics on the lifetimes in the channel or the escape probabilities from the channel. In this paper, we consider the diffusive transport through a narrow conical channel of a Brownian particle subject to intermittent dynamics, namely, stochastic resetting. As such, resetting brings the particle back to a desired location from where it resumes its diffusive phase. To this end, we extend the Fick-Jacobs theory of channel-facilitated diffusive transport to resetting-induced transport. Exact expressions for the conditional mean first passage times, escape probabilities, and the total average lifetime in the channel are obtained, and their behavior as a function of the resetting rate is highlighted. It is shown that resetting can expedite the transport through the channel-rigorous constraints for such conditions are then illustrated. Furthermore, we observe that a carefully chosen resetting rate can render the average lifetime of the particle inside the channel minimal. Interestingly, the optimal rate undergoes continuous and discontinuous transitions as some relevant system parameters are varied. The validity of our one-dimensional analysis and the corresponding theoretical predictions is supported by three-dimensional Brownian dynamics simulations. We thus believe that resetting can be useful to facilitate particle transport across biological membranes-a phenomenon that can spearhead further theoretical and experimental studies.
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Affiliation(s)
- Siddharth Jain
- Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad (Prayagraj), UP, 211019, India
| | - Denis Boyer
- Instituto de Física, Universidad Nacional Autónoma de México, Ciudad de México C.P. 04510, Mexico
| | - Arnab Pal
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
| | - Leonardo Dagdug
- Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de México 09340, Mexico
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8
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Pompa-García I, Castilla R, Metzler R, Dagdug L. First-passage times in conical varying-width channels biased by a transverse gravitational force: Comparison of analytical and numerical results. Phys Rev E 2022; 106:064137. [PMID: 36671151 DOI: 10.1103/physreve.106.064137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Accepted: 12/20/2022] [Indexed: 06/17/2023]
Abstract
We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean first-passage time for such a system is derived under the assumption that the axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as a one-dimensional diffusion in an entropic potential with position-dependent effective diffusivity in terms of the modified Fick-Jacobs equation. We analyze the channel crossing dynamics in terms of the mean first-passage time, combining our analytical results with extensive two-dimensional Brownian dynamics simulations, allowing us to find the range of applicability of the one-dimensional approximation. We find that the effective particle diffusivity decreases with increasing amplitude of the external potential. Remarkably, the mean first-passage time for crossing the channel is shown to assume a minimum at finite values of the potential amplitude.
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Affiliation(s)
- Ivan Pompa-García
- Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de México, 09340, México
| | - Rodrigo Castilla
- Engineering Faculty, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México, 04510, México
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Leonardo Dagdug
- Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de México, 09340, México
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9
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Singh RK, Singh S. Capture of a diffusing lamb by a diffusing lion when both return home. Phys Rev E 2022; 106:064118. [PMID: 36671194 DOI: 10.1103/physreve.106.064118] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Accepted: 12/01/2022] [Indexed: 06/17/2023]
Abstract
A diffusing lion pursues a diffusing lamb when both of them are allowed to get back to their homes intermittently. Identifying the system with a pair of vicious random walkers, we study their dynamics under Poissonian and sharp resetting. In the absence of any resets, the location of intersection of the two walkers follows a Cauchy distribution. In the presence of resetting, the distribution of the location of annihilation is composed of two parts: one in which the trajectories cross without being reset (center) and the other where trajectories are reset at least once before they cross each other (tails). We find that the tail part decays exponentially for both the resetting protocols. The central part of the distribution, on the other hand, depends on the nature of the restart protocol, with Cauchy for Poisson resetting and Gaussian for sharp resetting. We find good agreement of the analytical results with numerical calculations.
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Affiliation(s)
- R K Singh
- Department of Physics, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | - Sadhana Singh
- The Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben-Gurion University of the Negev, Be'er Sheva 84105, Israel
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10
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Zhao W, Du H, Xia Y, Xie S, Huang YP, Xu T, Zhang J, Gao YQ, Wan X. Accelerating supramolecular aggregation by molecular sliding. Phys Chem Chem Phys 2022; 24:23840-23848. [PMID: 36165176 DOI: 10.1039/d2cp04064f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Diffusion-based translocation along DNA or RNA molecules is essential for genome regulatory proteins to execute their biological functions. The reduced dimensionality of the searching process makes the proteins bind specific target sites at a "faster-than-diffusion-controlled rate". We herein report a photoresponsive slider-track diffusion system capable of self-assembly rate acceleration, which consists of (-)-camphorsulfonic acid, 4-(4'-n-octoxylphenylazo)benzenesulfonic acid, and isotactic poly(2-vinylpyridine). The protonated pyridine rings act as the footholds for anionic azo sliders to diffusively bind and slide along polycationic tracks via electrostatic interactions. Ultraviolet light triggers the trans to cis isomerization and aggregation of azo sliders, which can be monitored by multiple spectroscopic methods without labeling. The presence of vinyl polymer track increases the aggregation rate of cis azobenzene up to ∼20 times, depending on the stereoregularity of the polymer chain, the acid/base ratio and the addition of salt. This system has a feature of simplicity, monitorability, controllability, and could find applications in designing molecular machines with desired functionalities.
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Affiliation(s)
- Wenjing Zhao
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
| | - Hongxu Du
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
| | - Yijie Xia
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
| | - Siyu Xie
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
| | - Yu-Peng Huang
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
| | - Tieqi Xu
- State Key Laboratory of Fine Chemicals, College of Chemistry, Dalian University of Technology, Dalian 116024, China
| | - Jie Zhang
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
| | - Yi Qin Gao
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
| | - Xinhua Wan
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
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11
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Luo Y, Zeng C, Huang T, Ai BQ. Anomalous transport tuned through stochastic resetting in the rugged energy landscape of a chaotic system with roughness. Phys Rev E 2022; 106:034208. [PMID: 36266857 DOI: 10.1103/physreve.106.034208] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
Stochastic resetting causes kinetic phase transitions, whereas its underlying physical mechanism remains to be elucidated. We here investigate the anomalous transport of a particle moving in a chaotic system with a stochastic resetting and a rough potential and focus on how the stochastic resetting, roughness, and nonequilibrium noise affect the transports of the particle. We uncover the physical mechanism for stochastic resetting resulting in the anomalous transport in a nonlinear chaotic system: The particle is reset to a new basin of attraction which may be different from the initial basin of attraction from the view of dynamics. From the view of the energy landscape, the particle is reset to a new energy state of the energy landscape which may be different from the initial energy state. This resetting can lead to a kinetic phase transition between no transport and a finite net transport or between negative mobility and positive mobility. The roughness and noise also lead to the transition. Based on the mechanism, the transport of the particle can be tuned by these parameters. For example, the combination of the stochastic resetting, roughness, and noise can enhance the transport and tune negative mobility, the enhanced stability of the system, and the resonant-like activity. We analyze these results through variances (e.g., mean-squared velocity, etc.) and correlation functions (i.e., velocity autocorrelation function, position-velocity correlation function, etc.). Our results can be extensively applied in the biology, physics, and chemistry, even social system.
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Affiliation(s)
- Yuhui Luo
- Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
- School of Physics and Information Engineering, Zhaotong University, Zhaotong 657000, China
| | - Chunhua Zeng
- Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Tao Huang
- Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, SPTE, South China Normal University, Guangzhou 510006, China
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12
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Alexandre A, Mangeat M, Guérin T, Dean DS. How Stickiness Can Speed Up Diffusion in Confined Systems. PHYSICAL REVIEW LETTERS 2022; 128:210601. [PMID: 35687439 DOI: 10.1103/physrevlett.128.210601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Accepted: 04/15/2022] [Indexed: 06/15/2023]
Abstract
The paradigmatic model for heterogeneous media used in diffusion studies is built from reflecting obstacles and surfaces. It is well known that the crowding effect produced by these reflecting surfaces slows the dispersion of Brownian tracers. Here, using a general adsorption desorption model with surface diffusion, we show analytically that making surfaces or obstacles attractive can accelerate dispersion. In particular, we show that this enhancement of diffusion can exist even when the surface diffusion constant is smaller than that in the bulk. Even more remarkably, this enhancement effect occurs when the effective diffusion constant, when restricted to surfaces only, is lower than the effective diffusivity with purely reflecting boundaries. We give analytical formulas for this intriguing effect in periodic arrays of spheres as well as undulating microchannels. Our results are confirmed by numerical calculations and Monte Carlo simulations.
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Affiliation(s)
- A Alexandre
- Laboratoire Ondes et matière d'Aquitaine, CNRS/University of Bordeaux, F-33400 Talence, France
| | - M Mangeat
- Center for Biophysics and Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany
| | - T Guérin
- Laboratoire Ondes et matière d'Aquitaine, CNRS/University of Bordeaux, F-33400 Talence, France
| | - D S Dean
- Laboratoire Ondes et matière d'Aquitaine, CNRS/University of Bordeaux, F-33400 Talence, France
- Team MONC, INRIA Bordeaux Sud Ouest, CNRS UMR 5251, Bordeaux INP, University Bordeaux, F-33400 Talence, France
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13
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Felipe C, Shin J, Kolomeisky AB. How Pioneer Transcription Factors Search for Target Sites on Nucleosomal DNA. J Phys Chem B 2022; 126:4061-4068. [PMID: 35622093 DOI: 10.1021/acs.jpcb.2c01931] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
All major biological processes start after protein molecules known as transcription factors detect specific regulatory sequences on DNA and initiate genetic expression by associating to them. But in eukaryotic cells, much of the DNA is covered by nucleosomes and other chromatin structures, preventing transcription factors from binding to their targets. At the same time, experimental studies show that there are several classes of proteins, called "pioneer transcription factors", that are able to reach the targets on nucleosomal DNA; however, the underlying microscopic mechanisms remain not well understood. We propose a new theoretical approach that might explain how pioneer transcription factors can find their targets. It is argued that pioneer transcription factors might weaken the interactions between the DNA and nucleosome by substituting them with similar interactions between transcription factors and DNA. Using this idea, we develop a discrete-state stochastic model that allows for exact calculations of target search dynamics on nucleosomal DNA using first-passage probabilities approach. It is found that the target search on nuclesomal DNA for pioneer transcription factors might be significantly accelerated while the search is slower on naked DNA in comparison with normal transcription factors. Our theoretical predictions are supported by Monte Carlo computer simulations, and they also agree with available experimental observations.
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Affiliation(s)
- Cayke Felipe
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
| | - Jaeoh Shin
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.,Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Anatoly B Kolomeisky
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.,Department of Chemistry, Rice University, Houston, Texas 77005, United States.,Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States
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14
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De Bruyne B, Majumdar SN, Schehr G. Optimal Resetting Brownian Bridges via Enhanced Fluctuations. PHYSICAL REVIEW LETTERS 2022; 128:200603. [PMID: 35657896 DOI: 10.1103/physrevlett.128.200603] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2022] [Revised: 04/06/2022] [Accepted: 04/25/2022] [Indexed: 06/15/2023]
Abstract
We introduce a resetting Brownian bridge as a simple model to study search processes where the total search time t_{f} is finite and the searcher returns to its starting point at t_{f}. This is simply a Brownian motion with a Poissonian resetting rate r to the origin which is constrained to start and end at the origin at time t_{f}. We unveil a surprising general mechanism that enhances fluctuations of a Brownian bridge, by introducing a small amount of resetting. This is verified for different observables, such as the mean-square displacement, the hitting probability of a fixed target and the expected maximum. This mechanism, valid for a Brownian bridge in arbitrary dimensions, leads to a finite optimal resetting rate that minimizes the time to search a fixed target. The physical reason behind an optimal resetting rate in this case is entirely different from that of resetting Brownian motions without the bridge constraint. We also derive an exact effective Langevin equation that generates numerically the trajectories of a resetting Brownian bridge in all dimensions via a completely rejection-free algorithm.
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Affiliation(s)
- Benjamin De Bruyne
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Satya N Majumdar
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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15
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Punia B, Chaudhury S. Influence of Nonspecific Interactions between Proteins and In Vivo Cytoplasmic Crowders in Facilitated Diffusion of Proteins: Theoretical Insights. J Phys Chem B 2022; 126:3037-3047. [PMID: 35438996 DOI: 10.1021/acs.jpcb.2c01021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The binding of proteins to their respective specific sites on the DNA through facilitated diffusion serves as the initial step of various important biological processes. While this search process has been thoroughly investigated via in vitro studies, the cellular environment is complex and may interfere with the protein's search dynamics. The cytosol is heavily crowded, which can potentially modify the search by nonspecifically interacting with the protein that has been mostly overlooked. In this work, we probe the target search dynamics in the presence of explicit crowding agents that have an affinity toward the protein. We theoretically investigate the role of such protein-crowder associations in the target search process using a discrete-state stochastic framework that allows for the analytical description of dynamic properties. It is found that stronger nonspecific associations between the crowder and proteins can accelerate the facilitated diffusion of proteins in comparison with a purely inert, rather weakly interacting cellular environment. This effect depends on how strong these associations are, the spatial positions of the target with respect to the crowders, and the size of the crowded region. Our theoretical results are also tested with Monte Carlo computer simulations. Our predictions are in qualitative agreement with existing experimental observations and computational studies.
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Affiliation(s)
- Bhawakshi Punia
- Department of Chemistry, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, Maharashtra, India
| | - Srabanti Chaudhury
- Department of Chemistry, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, Maharashtra, India
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16
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González FH, Riascos AP, Boyer D. Diffusive transport on networks with stochastic resetting to multiple nodes. Phys Rev E 2021; 103:062126. [PMID: 34271672 DOI: 10.1103/physreve.103.062126] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2021] [Accepted: 05/27/2021] [Indexed: 01/30/2023]
Abstract
We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first passage times. This general approach allows us to characterize the effect of resetting on the capacity of random walk strategies to reach a particular target or to explore the network. Our formalism holds for ergodic random walks and can be implemented from the spectral properties of the random walk without resetting, providing a tool to analyze the efficiency of search strategies with resetting to multiple nodes. We apply the methods developed here to the dynamics with two reset nodes and derive analytical results for normal random walks and Lévy flights on rings. We also explore the effect of resetting to multiple nodes on a comb graph, Lévy flights that visit specific locations in a continuous space, and the Google random walk strategy on regular networks.
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Affiliation(s)
- Fernanda H González
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, México
| | - Alejandro P Riascos
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, México
| | - Denis Boyer
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, México
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17
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Felipe C, Shin J, Kolomeisky AB. DNA Looping and DNA Conformational Fluctuations Can Accelerate Protein Target Search. J Phys Chem B 2021; 125:1727-1734. [PMID: 33570939 DOI: 10.1021/acs.jpcb.0c09599] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Protein searching and binding to specific sites on DNA is a fundamentally important process that marks the beginning of all major cellular transformations. While the dynamics of protein-DNA interactions in in vitro settings is well investigated, the situation is much more complex for in vivo conditions because the DNA molecules in live cells are packed into chromosomal structures where they are undergoing strong dynamic and conformational fluctuations. In this work, we present a theoretical investigation on the role of DNA looping and DNA conformational fluctuations in the protein target search. It is based on a discrete-state stochastic analysis that allows for explicit calculations of dynamic properties, which is also supplemented by Monte Carlo computer simulations. It is found that for stronger nonspecific interactions between DNA and proteins the search occurs faster on the DNA looped conformation in comparison with the unlooped conformation, and the fastest search is observed when the loop is formed near the target site. It is also shown that DNA fluctuations between the looped and unlooped conformations influence the search dynamics, and this depends on the magnitude of conformational transition rates and on which conformation is more energetically stable. Physical-chemical arguments explaining these observations are presented. Our theoretical study suggests that the geometry and conformational changes in DNA are additional factors that might efficiently control the gene regulation processes.
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Affiliation(s)
- Cayke Felipe
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
| | - Jaeoh Shin
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.,Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Anatoly B Kolomeisky
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.,Department of Chemistry, Rice University, Houston, Texas 77005, United States.,Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States
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18
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Bressloff PC. First-passage processes and the target-based accumulation of resources. Phys Rev E 2021; 103:012101. [PMID: 33601498 DOI: 10.1103/physreve.103.012101] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Accepted: 12/16/2020] [Indexed: 12/26/2022]
Abstract
A random search for one or more targets in a bounded domain occurs widely in nature, with examples ranging from animal foraging to the transport of vesicles within cells. Most theoretical studies take a searcher-centric viewpoint, focusing on the first passage time (FTP) problem to find a target. This single search-and-capture event then triggers a downstream process or provides the searcher with some resource such as food. In this paper we take a target-centric viewpoint by considering the accumulation of resources in one or more targets due to multiple rounds of search-and-capture events combined with resource degradation; whenever a searcher finds a target it delivers a resource packet to the target, after which it escapes and returns to its initial position. The searcher is then resupplied with cargo and a new search process is initiated after a random delay. It has previously been shown how queuing theory can be used to derive general expressions for the steady-state mean and variance of the resulting resource distributions. Here we apply the theory to some classical FPT problems involving diffusion in simple geometries with absorbing boundaries, including concentric spheres, wedge domains, and branching networks. In each case, we determine how the resulting Fano factor depends on the degradation rate, the delay distribution, and various geometric parameters. We thus establish that the Fano factor can deviate significantly from Poisson statistics and exhibits a nontrivial dependence on model parameters, including nonmonotonicity and crossover behavior. This indicates the nontrivial nature of the higher-order statistics of resource accumulation.
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Affiliation(s)
- Paul C Bressloff
- Department of Mathematics, University of Utah 155 South 1400 East, Salt Lake City, Utah 84112, USA
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19
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Jana T, Brodsky S, Barkai N. Speed-Specificity Trade-Offs in the Transcription Factors Search for Their Genomic Binding Sites. Trends Genet 2021; 37:421-432. [PMID: 33414013 DOI: 10.1016/j.tig.2020.12.001] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2020] [Revised: 12/04/2020] [Accepted: 12/07/2020] [Indexed: 12/17/2022]
Abstract
Transcription factors (TFs) regulate gene expression by binding DNA sequences recognized by their DNA-binding domains (DBDs). DBD-recognized motifs are short and highly abundant in genomes. The ability of TFs to bind a specific subset of motif-containing sites, and to do so rapidly upon activation, is fundamental for gene expression in all eukaryotes. Despite extensive interest, our understanding of the TF-target search process is fragmented; although binding specificity and detection speed are two facets of this same process, trade-offs between them are rarely addressed. In this opinion article, we discuss potential speed-specificity trade-offs in the context of existing models. We further discuss the recently described 'distributed specificity' paradigm, suggesting that intrinsically disordered regions (IDRs) promote specificity while reducing the TF-target search time.
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Affiliation(s)
- Tamar Jana
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Sagie Brodsky
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Naama Barkai
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot 76100, Israel.
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20
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Lost in the Crowd: How Does Human 8-Oxoguanine DNA Glycosylase 1 (OGG1) Find 8-Oxoguanine in the Genome? Int J Mol Sci 2020; 21:ijms21218360. [PMID: 33171795 PMCID: PMC7664663 DOI: 10.3390/ijms21218360] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Revised: 11/03/2020] [Accepted: 11/04/2020] [Indexed: 12/11/2022] Open
Abstract
The most frequent DNA lesion resulting from an oxidative stress is 7,8-dihydro-8-oxoguanine (8-oxoG). 8-oxoG is a premutagenic base modification due to its capacity to pair with adenine. Thus, the repair of 8-oxoG is critical for the preservation of the genetic information. Nowadays, 8-oxoG is also considered as an oxidative stress-sensor with a putative role in transcription regulation. In mammalian cells, the modified base is excised by the 8-oxoguanine DNA glycosylase (OGG1), initiating the base excision repair (BER) pathway. OGG1 confronts the massive challenge that is finding rare occurrences of 8-oxoG among a million-fold excess of normal guanines. Here, we review the current knowledge on the search and discrimination mechanisms employed by OGG1 to find its substrate in the genome. While there is considerable data from in vitro experiments, much less is known on how OGG1 is recruited to chromatin and scans the genome within the cellular nucleus. Based on what is known of the strategies used by proteins searching for rare genomic targets, we discuss the possible scenarios allowing the efficient detection of 8-oxoG by OGG1.
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21
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Bressloff PC. Target competition for resources under multiple search-and-capture events with stochastic resetting. Proc Math Phys Eng Sci 2020; 476:20200475. [PMID: 33223946 PMCID: PMC7655747 DOI: 10.1098/rspa.2020.0475] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Accepted: 09/15/2020] [Indexed: 12/19/2022] Open
Abstract
We develop a general framework for analysing the distribution of resources in a population of targets under multiple independent search-and-capture events. Each event involves a single particle executing a stochastic search that resets to a fixed location x r at a random sequence of times. Whenever the particle is captured by a target, it delivers a packet of resources and then returns to x r , where it is reloaded with cargo and a new round of search and capture begins. Using renewal theory, we determine the mean number of resources in each target as a function of the splitting probabilities and unconditional mean first passage times of the corresponding search process without resetting. We then use asymptotic PDE methods to determine the effects of resetting on the distribution of resources generated by diffusive search in a bounded two-dimensional domain with N small interior targets. We show that slow resetting increases the total number of resources M tot across all targets provided that ∑ j = 1 N G ( x r , x j ) < 0 , where G is the Neumann Green's function and x j is the location of the j-th target. This implies that M tot can be optimized by varying r. We also show that the k-th target has a competitive advantage if ∑ j = 1 N G ( x r , x j ) > N G ( x r , x k ) .
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Affiliation(s)
- P. C. Bressloff
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA
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22
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Felipe C, Shin J, Loginova Y, Kolomeisky AB. The effect of obstacles in multi-site protein target search with DNA looping. J Chem Phys 2020; 152:025101. [PMID: 31941320 DOI: 10.1063/1.5135917] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Many fundamental biological processes are regulated by protein-DNA complexes called synaptosomes, which possess multiple interaction sites. Despite the critical importance of synaptosomes, the mechanisms of their formation are not well understood. Because of the multisite nature of participating proteins, it is widely believed that their search for specific sites on DNA involves the formation and breaking of DNA loops and sliding in the looped configurations. In reality, DNA in live cells is densely covered by other biological molecules that might interfere with the formation of synaptosomes. In this work, we developed a theoretical approach to evaluate the role of obstacles in the target search of multisite proteins when the formation of DNA loops and the sliding in looped configurations are possible. Our theoretical method is based on analysis of a discrete-state stochastic model that uses a master equations approach and extensive computer simulations. It is found that the obstacle slows down the search dynamics in the system when DNA loops are long-lived, but the effect is minimal for short-lived DNA loops. In addition, the relative positions of the target and the obstacle strongly influence the target search kinetics. Furthermore, the presence of the obstacle might increase the noise in the system. These observations are discussed using physical-chemical arguments. Our theoretical approach clarifies the molecular mechanisms of formation of protein-DNA complexes with multiple interactions sites.
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Affiliation(s)
- Cayke Felipe
- Department of Physics, Rice University, Houston, Texas 77005, USA
| | - Jaeoh Shin
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Yulia Loginova
- Department of Chemistry, Moscow State University, Moscow, Russia
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23
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Shin J, Kolomeisky AB. Target search on DNA by interacting molecules: First-passage approach. J Chem Phys 2019; 151:125101. [PMID: 31575173 DOI: 10.1063/1.5123988] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Gene regulation is one of the most important fundamental biological processes in living cells. It involves multiple protein molecules that locate specific sites on DNA and assemble gene initiation or gene repression multimolecular complexes. While the protein search dynamics for DNA targets has been intensively investigated, the role of intermolecular interactions during the genetic activation or repression remains not well quantified. Here, we present a simple one-dimensional model of target search for two interacting molecules that can reversibly form a dimer molecular complex, which also participates in the search process. In addition, the proteins have finite residence times on specific target sites, and the gene is activated or repressed when both proteins are simultaneously present at the target. The model is analyzed using first-passage analytical calculations and Monte Carlo computer simulations. It is shown that the search dynamics exhibit a complex behavior depending on the strength of intermolecular interactions and on the target residence times. We also found that the search time shows a nonmonotonic behavior as a function of the dissociation rate for the molecular complex. Physical-chemical arguments to explain these observations are presented. Our theoretical approach highlights the importance of molecular interactions in the complex process of gene activation/repression by multiple transcription factor proteins.
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Affiliation(s)
- Jaeoh Shin
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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24
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Pal A, Castillo IP, Kundu A. Motion of a Brownian particle in the presence of reactive boundaries. Phys Rev E 2019; 100:042128. [PMID: 31770986 DOI: 10.1103/physreve.100.042128] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2019] [Indexed: 06/10/2023]
Abstract
We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understanding the effects of such boundaries is important in physics, chemistry, and biology. We compute the probability density of the particle displacement exactly, from which we derive expressions for the survival probability and the mean absorption time as a function of the reactive coefficients. Furthermore, using the Feynman-Kac formalism, we investigate the local time profile, which is the fluctuating time spent by the particle at a given location, both till a fixed observation time and till the absorption time. Our analytical results are compared to numerical simulations, showing perfect agreement.
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Affiliation(s)
- Arnab Pal
- School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel; Center for the Physics and Chemistry of Living Systems, Tel Aviv University, 6997801, Tel Aviv, Israel; and Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 6997801, Tel Aviv, Israel
| | - Isaac Pérez Castillo
- Department of Quantum Physics and Photonics, Institute of Physics, UNAM, P.O. Box 20-364, 01000 Mexico City, Mexico and London Mathematical Laboratory, 8 Margravine Gardens, London, W6 8RH, United Kingdom
| | - Anupam Kundu
- International Centre for Theoretical Sciences, TIFR, Bangalore 560089, India
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25
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Shin J, Kolomeisky AB. Facilitation of DNA loop formation by protein-DNA non-specific interactions. SOFT MATTER 2019; 15:5255-5263. [PMID: 31204761 DOI: 10.1039/c9sm00671k] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Complex DNA topological structures, including polymer loops, are frequently observed in biological processes when protein molecules simultaneously bind to several distant sites on DNA. However, the molecular mechanisms of formation of these systems remain not well understood. Existing theoretical studies focus only on specific interactions between protein and DNA molecules at target sequences. However, the electrostatic origin of primary protein-DNA interactions suggests that interactions of proteins with all DNA segments should be considered. Here we theoretically investigate the role of non-specific interactions between protein and DNA molecules on the dynamics of loop formation. Our approach is based on analyzing a discrete-state stochastic model via a method of first-passage probabilities supplemented by Monte Carlo computer simulations. It is found that depending on a protein sliding length during the non-specific binding event three different dynamic regimes of the DNA loop formation might be observed. In addition, the loop formation time might be optimized by varying the protein sliding length, the size of the DNA molecule, and the position of the specific target sequences on DNA. Our results demonstrate the importance of non-specific protein-DNA interactions in the dynamics of DNA loop formations.
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Affiliation(s)
- Jaeoh Shin
- Department of Chemistry, Rice University, Houston, Texas 77005, USA.
| | - Anatoly B Kolomeisky
- Department of Chemistry, Rice University, Houston, Texas 77005, USA. and Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
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26
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Wang X, Chen Y, Deng W. Aging two-state process with Lévy walk and Brownian motion. Phys Rev E 2019; 100:012136. [PMID: 31499767 DOI: 10.1103/physreve.100.012136] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2019] [Indexed: 06/10/2023]
Abstract
With the rich dynamics studies of single-state processes, the two-state processes are attracting more interest, since they are widely observed in complex system and have effective applications in diverse fields, such as foraging behavior of animals. This paper builds the theoretical foundation of the process with two states: Lévy walk and Brownian motion, having been proved to be an efficient intermittent search process. The sojourn time distributions in two states are both assumed to be heavy-tailed with exponents α_{±}∈(0,2). The dynamical behaviors of this two-state process are obtained through analyzing the ensemble-averaged and time-averaged mean-squared displacements (MSDs) in weak and strong aging cases. It is discovered that the magnitude relationship of α_{±} decides the fraction of two states for long times, playing a crucial role in these MSDs. According to the generic expressions of MSDs, some inherent characteristics of the two-state process are detected. The effects of the fraction on these observables are presented in detail for six different cases. The key of getting these results is to calculate the velocity correlation function of the two-state process, the techniques of which can be generalized to other multistate processes.
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Affiliation(s)
- Xudong Wang
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China
| | - Yao Chen
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China
| | - Weihua Deng
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China
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27
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Fractional Prabhakar Derivative in Diffusion Equation with Non-Static Stochastic Resetting. PHYSICS 2019. [DOI: 10.3390/physics1010005] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this work, we investigate a series of mathematical aspects for the fractional diffusion equation with stochastic resetting. The stochastic resetting process in Evans–Majumdar sense has several applications in science, with a particular emphasis on non-equilibrium physics and biological systems. We propose a version of the stochastic resetting theory for systems in which the reset point is in motion, so the walker does not return to the initial position as in the standard model, but returns to a point that moves in space. In addition, we investigate the proposed stochastic resetting model for diffusion with the fractional operator of Prabhakar. The derivative of Prabhakar consists of an integro-differential operator that has a Mittag–Leffler function with three parameters in the integration kernel, so it generalizes a series of fractional operators such as Riemann–Liouville–Caputo. We present how the generalized model of stochastic resetting for fractional diffusion implies a rich class of anomalous diffusive processes, i.e., ⟨ ( Δ x ) 2 ⟩ ∝ t α , which includes sub-super-hyper-diffusive regimes. In the sequence, we generalize these ideas to the fractional Fokker–Planck equation for quadratic potential U ( x ) = a x 2 + b x + c . This work aims to present the generalized model of Evans–Majumdar’s theory for stochastic resetting under a new perspective of non-static restart points.
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28
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Shin J, Kolomeisky AB. Molecular search with conformational change: One-dimensional discrete-state stochastic model. J Chem Phys 2018; 149:174104. [PMID: 30409016 DOI: 10.1063/1.5051035] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Molecular search phenomena are observed in a variety of chemical and biological systems. During the search, the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic modes. To understand the mechanisms of molecular search with alternating dynamics, we investigate the search dynamics with stochastic transitions between two conformations in a one-dimensional discrete-state stochastic model. It is explicitly analyzed using the first-passage time probability method to obtain a full dynamic description of the search process. A general dynamic phase diagram is developed. It is found that there are several dynamic regimes in the molecular search with conformational transitions, and they are determined by the relative values of the relevant length scales in the system. Theoretical predictions are fully supported by Monte Carlo computer simulations.
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Affiliation(s)
- Jaeoh Shin
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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29
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Woringer M, Darzacq X. Protein motion in the nucleus: from anomalous diffusion to weak interactions. Biochem Soc Trans 2018; 46:945-956. [PMID: 30065106 PMCID: PMC6103463 DOI: 10.1042/bst20170310] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2018] [Revised: 05/02/2018] [Accepted: 05/14/2018] [Indexed: 12/12/2022]
Abstract
Understanding how transcription factors (TFs) regulate mammalian gene expression in space and time is a central topic in biology. To activate a gene, a TF has first to diffuse in the available space of the nucleus until it reaches a target DNA sequence or protein (target site). This eventually results in the recruitment of the whole transcriptional machinery. All these processes take place in the mammalian nucleoplasm, a highly organized and dynamic environment, in which some complexes transiently assemble and break apart, whereas others appear more stable. This diversity of dynamic behaviors arises from the number of biomolecules that make up the nucleoplasm and their pairwise interactions. Indeed, interactions energies that span several orders of magnitude, from covalent bounds to transient and dynamic interactions, can shape nuclear landscapes. Thus, the nuclear environment determines how frequently and how fast a TF contacts its target site, and it indirectly regulates gene expression. How exactly transient interactions are involved in the regulation of TF diffusion is unclear, but are reflected by live cell imaging techniques, including single-particle tracking (SPT). Overall, the macroscopic result of these microscopic interactions is almost always anomalous diffusion, a phenomenon widely studied and modeled. Here, we review the connections between the anomalous diffusion of a TF observed by SPT and the microscopic organization of the nucleus, including recently described topologically associated domains and dynamic phase-separated compartments. We propose that anomalous diffusion found in SPT data result from weak and transient interactions with dynamic nuclear substructures, and that SPT data analysis would benefit from a better description of such structures.
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Affiliation(s)
- Maxime Woringer
- Department of Molecular and Cell Biology, Li Ka Shing Center for Biomedical and Health Sciences, CIRM Center of Excellence, University of California, Berkeley, CA 94720, U.S.A.
- Unité Imagerie et Modélisation, Institut Pasteur, 25 rue du Docteur Roux, 75015 Paris, France
- Sorbonne Universités, CNRS, F-75005 Paris, France
| | - Xavier Darzacq
- Department of Molecular and Cell Biology, Li Ka Shing Center for Biomedical and Health Sciences, CIRM Center of Excellence, University of California, Berkeley, CA 94720, U.S.A.
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30
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Wilson DB, Baker RE, Woodhouse FG. Topology-dependent density optima for efficient simultaneous network exploration. Phys Rev E 2018; 97:062301. [PMID: 30011429 DOI: 10.1103/physreve.97.062301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2017] [Indexed: 11/07/2022]
Abstract
A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimize this process: How many concurrent searchers can a topology support before the benefits of parallelism are outweighed by competition for space? Here, we introduce the searcher-averaged parallel cover time (APCT) to quantify these economies of scale. We show that the APCT of the networked symmetric exclusion process is optimized at a searcher density that is well predicted by the spectral gap. Furthermore, we find that nonequilibrium processes, realized through the addition of bias, can support significantly increased density optima. Our results suggest alternative hybrid strategies of serial and parallel search for efficient information gathering in social interaction and biological transport networks.
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Affiliation(s)
- Daniel B Wilson
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford OX2 6GG, United Kingdom
| | - Ruth E Baker
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford OX2 6GG, United Kingdom
| | - Francis G Woodhouse
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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31
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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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32
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Kar P, Cherstvy AG, Metzler R. Acceleration of bursty multiprotein target search kinetics on DNA by colocalisation. Phys Chem Chem Phys 2018; 20:7931-7946. [DOI: 10.1039/c7cp06922g] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Proteins are capable of locating specific targets on DNA by employing a facilitated diffusion process with intermittent 1D and 3D search steps. We here uncover the implications of colocalisation of protein production and DNA binding sites via computer simulations.
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Affiliation(s)
- Prathitha Kar
- Dept of Inorganic and Physical Chemistry
- Indian Institute of Science
- Bengaluru
- India
- Institute for Physics & Astronomy
| | - Andrey G. Cherstvy
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
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33
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Liu L, Cherstvy AG, Metzler R. Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion. J Phys Chem B 2017; 121:1284-1289. [DOI: 10.1021/acs.jpcb.6b12413] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Lin Liu
- CAS
Key Laboratory of Soft Matter Chemistry, Dept. of Polymer Science
and Engineering, University of Science and Technology of China, Hefei, Anhui Province 230026, China
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Andrey G. Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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34
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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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35
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Rad4 recognition-at-a-distance: Physical basis of conformation-specific anomalous diffusion of DNA repair proteins. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2016; 127:93-104. [PMID: 27939760 DOI: 10.1016/j.pbiomolbio.2016.12.004] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Accepted: 12/06/2016] [Indexed: 11/20/2022]
Abstract
Since Robert Brown's first observations of random walks by pollen particles suspended in solution, the concept of diffusion has been subject to countless theoretical and experimental studies in diverse fields from finance and social sciences, to physics and biology. Diffusive transport of macromolecules in cells is intimately linked to essential cellular functions including nutrient uptake, signal transduction, gene expression, as well as DNA replication and repair. Advancement in experimental techniques has allowed precise measurements of these diffusion processes. Mathematical and physical descriptions and computer simulations have been applied to model complicated biological systems in which anomalous diffusion, in addition to simple Brownian motion, was observed. The purpose of this review is to provide an overview of the major physical models of anomalous diffusion and corresponding experimental evidence on the target search problem faced by DNA-binding proteins, with an emphasis on DNA repair proteins and the role of anomalous diffusion in DNA target recognition.
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36
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Lange M, Kochugaeva M, Kolomeisky AB. Protein search for multiple targets on DNA. J Chem Phys 2016; 143:105102. [PMID: 26374061 DOI: 10.1063/1.4930113] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Protein-DNA interactions are crucial for all biological processes. One of the most important fundamental aspects of these interactions is the process of protein searching and recognizing specific binding sites on DNA. A large number of experimental and theoretical investigations have been devoted to uncovering the molecular description of these phenomena, but many aspects of the mechanisms of protein search for the targets on DNA remain not well understood. One of the most intriguing problems is the role of multiple targets in protein search dynamics. Using a recently developed theoretical framework we analyze this question in detail. Our method is based on a discrete-state stochastic approach that takes into account most relevant physical-chemical processes and leads to fully analytical description of all dynamic properties. Specifically, systems with two and three targets have been explicitly investigated. It is found that multiple targets in most cases accelerate the search in comparison with a single target situation. However, the acceleration is not always proportional to the number of targets. Surprisingly, there are even situations when it takes longer to find one of the multiple targets in comparison with the single target. It depends on the spatial position of the targets, distances between them, average scanning lengths of protein molecules on DNA, and the total DNA lengths. Physical-chemical explanations of observed results are presented. Our predictions are compared with experimental observations as well as with results from a continuum theory for the protein search. Extensive Monte Carlo computer simulations fully support our theoretical calculations.
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Affiliation(s)
- Martin Lange
- Johannes Gutenberg University, Mainz 55122, Germany
| | - Maria Kochugaeva
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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37
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Klein M, Chandradoss SD, Depken M, Joo C. Why Argonaute is needed to make microRNA target search fast and reliable. Semin Cell Dev Biol 2016; 65:20-28. [PMID: 27235676 DOI: 10.1016/j.semcdb.2016.05.017] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2016] [Revised: 05/19/2016] [Accepted: 05/21/2016] [Indexed: 10/21/2022]
Abstract
MicroRNA (miRNA) interferes with the translation of cognate messenger RNA (mRNA) by finding, preferentially binding, and marking it for degradation. To facilitate the search process, Argonaute (Ago) proteins come together with miRNA, forming a dynamic search complex. In this review we use the language of free-energy landscapes to discuss recent single-molecule and high-resolution structural data in the light of theoretical work appropriated from the study of transcription-factor search. We suggest that experimentally observed internal states of the Ago-miRNA search complex may have the explicit biological function of speeding up search while maintaining specificity.
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Affiliation(s)
- Misha Klein
- Kavli Institute of NanoScience and Department of BioNanoScience, Delft University of Technology, Delft, 2629HZ, The Netherlands
| | - Stanley D Chandradoss
- Kavli Institute of NanoScience and Department of BioNanoScience, Delft University of Technology, Delft, 2629HZ, The Netherlands
| | - Martin Depken
- Kavli Institute of NanoScience and Department of BioNanoScience, Delft University of Technology, Delft, 2629HZ, The Netherlands.
| | - Chirlmin Joo
- Kavli Institute of NanoScience and Department of BioNanoScience, Delft University of Technology, Delft, 2629HZ, The Netherlands.
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38
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Carter AR, Seaberg MH, Fan HF, Sun G, Wilds CJ, Li HW, Perkins TT. Sequence-dependent nanometer-scale conformational dynamics of individual RecBCD-DNA complexes. Nucleic Acids Res 2016; 44:5849-60. [PMID: 27220465 PMCID: PMC4937329 DOI: 10.1093/nar/gkw445] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Accepted: 05/09/2016] [Indexed: 01/02/2023] Open
Abstract
RecBCD is a multifunctional enzyme that possesses both helicase and nuclease activities. To gain insight into the mechanism of its helicase function, RecBCD unwinding at low adenosine triphosphate (ATP) (2-4 μM) was measured using an optical-trapping assay featuring 1 base-pair (bp) precision. Instead of uniformly sized steps, we observed forward motion convolved with rapid, large-scale (∼4 bp) variations in DNA length. We interpret this motion as conformational dynamics of the RecBCD-DNA complex in an unwinding-competent state, arising, in part, by an enzyme-induced, back-and-forth motion relative to the dsDNA that opens and closes the duplex. Five observations support this interpretation. First, these dynamics were present in the absence of ATP. Second, the onset of the dynamics was coupled to RecBCD entering into an unwinding-competent state that required a sufficiently long 5' strand to engage the RecD helicase. Third, the dynamics were modulated by the GC-content of the dsDNA. Fourth, the dynamics were suppressed by an engineered interstrand cross-link in the dsDNA that prevented unwinding. Finally, these dynamics were suppressed by binding of a specific non-hydrolyzable ATP analog. Collectively, these observations show that during unwinding, RecBCD binds to DNA in a dynamic mode that is modulated by the nucleotide state of the ATP-binding pocket.
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Affiliation(s)
- Ashley R Carter
- Department of Physics, Amherst College, Amherst, MA 01002, USA
| | - Maasa H Seaberg
- Department of Physics, University of Colorado, Boulder, CO 80309, USA JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, USA
| | - Hsiu-Fang Fan
- Department of Life Sciences and Institute of Genome Sciences, National Yang-Ming University, Taipei 11221, Taiwan Department of Chemistry and Biochemistry, Concordia University, Montreal, Quebec H4B1R6, Canada
| | - Gang Sun
- Department of Chemistry, National Taiwan University, Taipei 10617, Taiwan
| | | | - Hung-Wen Li
- Department of Chemistry and Biochemistry, Concordia University, Montreal, Quebec H4B1R6, Canada
| | - Thomas T Perkins
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, CO 80309, USA Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO 80309, USA
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39
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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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40
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Mak CH, Pham P, Afif SA, Goodman MF. Random-walk enzymes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032717. [PMID: 26465508 PMCID: PMC4672870 DOI: 10.1103/physreve.92.032717] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2015] [Indexed: 05/26/2023]
Abstract
Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C→U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.
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Affiliation(s)
- Chi H Mak
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
- Center for Applied Mathematical Sciences, University of Southern California, Los Angeles, California 90089, USA
| | - Phuong Pham
- Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA
| | - Samir A Afif
- Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA
| | - Myron F Goodman
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
- Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA
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41
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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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42
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Tabaka M, Burdzy K, Hołyst R. Method for the analysis of contribution of sliding and hopping to a facilitated diffusion of DNA-binding protein: Application to in vivo data. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022721. [PMID: 26382446 DOI: 10.1103/physreve.92.022721] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2015] [Indexed: 06/05/2023]
Abstract
DNA-binding protein searches for its target, a specific site on DNA, by means of diffusion. The search process consists of many recurrent steps of one-dimensional diffusion (sliding) along the DNA chain and three-dimensional diffusion (hopping) after dissociation of a protein from the DNA chain. Here we propose a computational method that allows extracting the contribution of sliding and hopping to the search process in vivo from the measurements of the kinetics of the target search by the lac repressor in Escherichia coli [P. Hammar et al., Science 336, 1595 (2012)]. The method combines lattice Monte Carlo simulations with the Brownian excursion theory and includes explicitly steric constraints for hopping due to the helical structure of DNA. The simulation results including all experimental data reveal that the in vivo target search is dominated by sliding. The short-range hopping to the same base pair interrupts one-dimensional sliding while long-range hopping does not contribute significantly to the kinetics of the search of the target in vivo.
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Affiliation(s)
- Marcin Tabaka
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Krzysztof Burdzy
- Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195, USA
| | - Robert Hołyst
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
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43
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Akimoto T, Seki K. Transition from distributional to ergodic behavior in an inhomogeneous diffusion process: Method revealing an unknown surface diffusivity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022114. [PMID: 26382351 DOI: 10.1103/physreve.92.022114] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Indexed: 06/05/2023]
Abstract
Diffusion of molecules in cells plays an important role in providing a biological reaction on the surface by finding a target on the membrane surface. The water retardation (slow diffusion) near the target assists the searching molecules to recognize the target. Here, we consider effects of the surface diffusivity on the effective diffusivity, where diffusion on the surface is slower than that in bulk. We show that the ensemble-averaged mean-square displacements increase linearly with time when the desorption rate from the surface is finite, which is valid even when the diffusion on the surface is anomalous (subdiffusion). Moreover, this slow diffusion on the surface affects the fluctuations of the time-averaged mean-square displacements (TAMSDs). We find that fluctuations of the TAMSDs remain large when the measurement time is smaller than a characteristic time, and decays according to an increase of the measurement time for a relatively large measurement time. Therefore, we find a transition from nonergodic (distributional) to ergodic diffusivity in a target search process. Moreover, this fluctuation analysis provides a method to estimate an unknown surface diffusivity.
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Affiliation(s)
- Takuma Akimoto
- Department of Mechanical Engineering, Keio University, Yokohama, 223-8522, Japan
| | - Kazuhiko Seki
- Nanosystem Research Institute, AIST, Tsukuba, 305-8565, Japan
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44
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Cartailler J, Reingruber J. Facilitated diffusion framework for transcription factor search with conformational changes. Phys Biol 2015. [PMID: 26200216 DOI: 10.1088/1478-3975/12/4/046012] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Cellular responses often require the fast activation or repression of specific genes, which depends on transcription factors (TFs) that have to quickly find the promoters of these genes within a large genome. TFs search for their DNA promoter target by alternating between bulk diffusion and sliding along the DNA, a mechanism known as facilitated diffusion. We study a facilitated diffusion framework with switching between three search modes: a bulk mode and two sliding modes triggered by conformational changes between two protein conformations. In one conformation (search mode) the TF interacts unspecifically with the DNA backbone resulting in fast sliding. In the other conformation (recognition mode) it interacts specifically and strongly with DNA base pairs leading to slow displacement. From the bulk, a TF associates with the DNA at a random position that is correlated with the previous dissociation point, which implicitly is a function of the DNA structure. The target affinity depends on the conformation. We derive exact expressions for the mean first passage time (MFPT) to bind to the promoter and the conditional probability to bind before detaching when arriving at the promoter site. We systematically explore the parameter space and compare various search scenarios. We compare our results with experimental data for the dimeric Lac repressor search in E. coli bacteria. We find that a coiled DNA conformation is absolutely necessary for a fast MFPT. With frequent spontaneous conformational changes, a fast search time is achieved even when a TF becomes immobilized in the recognition state due to the specific bindings. We find a MFPT compatible with experimental data in presence of a specific TF-DNA interaction energy that has a Gaussian distribution with a large variance.
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45
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Real sequence effects on the search dynamics of transcription factors on DNA. Sci Rep 2015; 5:10072. [PMID: 26154484 PMCID: PMC5507490 DOI: 10.1038/srep10072] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2015] [Accepted: 03/30/2015] [Indexed: 11/15/2022] Open
Abstract
Recent experiments show that transcription factors (TFs) indeed use the facilitated diffusion mechanism to locate their target sequences on DNA in living bacteria cells: TFs alternate between sliding motion along DNA and relocation events through the cytoplasm. From simulations and theoretical analysis we study the TF-sliding motion for a large section of the DNA-sequence of a common E. coli strain, based on the two-state TF-model with a fast-sliding search state and a recognition state enabling target detection. For the probability to detect the target before dissociating from DNA the TF-search times self-consistently depend heavily on whether or not an auxiliary operator (an accessible sequence similar to the main operator) is present in the genome section. Importantly, within our model the extent to which the interconversion rates between search and recognition states depend on the underlying nucleotide sequence is varied. A moderate dependence maximises the capability to distinguish between the main operator and similar sequences. Moreover, these auxiliary operators serve as starting points for DNA looping with the main operator, yielding a spectrum of target detection times spanning several orders of magnitude. Auxiliary operators are shown to act as funnels facilitating target detection by TFs.
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46
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Smrek J, Grosberg AY. Facilitated diffusion of proteins through crumpled fractal DNA globules. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012702. [PMID: 26274198 DOI: 10.1103/physreve.92.012702] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2015] [Indexed: 06/04/2023]
Abstract
We explore how the specific fractal globule conformation, found for the chromatin fiber of higher eukaryotes and topologically constrained dense polymers, affects the facilitated diffusion of proteins in this environment. Using scaling arguments and supporting Monte Carlo simulations, we relate DNA looping probability distribution, fractal dimension, and protein nonspecific affinity for the DNA to the effective diffusion parameters of the proteins. We explicitly consider correlations between subsequent readsorption events of the proteins, and we find that facilitated diffusion is faster for the crumpled globule conformation with high intersegmental surface dimension than in the case of dense fractal conformations with smooth surfaces. As a byproduct, we obtain an expression for the macroscopic conductivity of a hypothetic material consisting of conducting fractal nanowires immersed in a weakly conducting medium.
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Affiliation(s)
- Jan Smrek
- Center for Soft Matter Research and Department of Physics, New York University, New York, New York 10003, USA
| | - Alexander Y Grosberg
- Center for Soft Matter Research and Department of Physics, New York University, New York, New York 10003, USA
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47
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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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48
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Unbiased Diffusion through a Linear Porous Media with Periodic Entropy Barriers: A Tube Formed by Contacting Ellipses. J CHEM-NY 2015. [DOI: 10.1155/2015/986402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
This work is devoted to the study of unbiased diffusion of point-like Brownian particles through channels with radial symmetry of varying cross-section and elliptic shape. The effective one-dimensional reduction is used with distinct forms of a position-dependent diffusion coefficient,D(x), found in literature, to obtain expressions for (I) narrow escape times from a single open-ended tube, (II) its correspondent effective diffusion coefficient, both as functions of the eccentricity of the tube,ε, whereε= 0 returns the system to a spherical vesicle with two open opposite sides, and (III) finally, Lifson-Jackson formula that is used to compute expressions to assess the mean effective diffusion coefficient for a periodic elliptic channel formed by contacting ellipses, also as a function of the eccentricity. Mathematical expressions are presented and contrasted against computational simulations to validate them.
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49
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Kusmierz L, Majumdar SN, Sabhapandit S, Schehr G. First Order Transition for the Optimal Search Time of Lévy Flights with Resetting. PHYSICAL REVIEW LETTERS 2014; 113:220602. [PMID: 25494063 DOI: 10.1103/physrevlett.113.220602] [Citation(s) in RCA: 110] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 05/27/2023]
Abstract
We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at x_{0}≥0, where successive jumps are drawn independently from an arbitrary jump distribution f(η). In addition, with a probability 0≤r<1, the position of the searcher is reset to its initial position x_{0}. The efficiency of the search strategy is characterized by the mean time to find the target, i.e., the mean first passage time (MFPT) to the origin. For arbitrary jump distribution f(η), initial position x_{0} and resetting probability r, we compute analytically the MFPT. For the heavy-tailed Lévy stable jump distribution characterized by the Lévy index 0<μ<2, we show that, for any given x_{0}, the MFPT has a global minimum in the (μ,r) plane at (μ^{*}(x_{0}),r^{*}(x_{0})). We find a remarkable first-order phase transition as x_{0} crosses a critical value x_{0}^{*} at which the optimal parameters change discontinuously. Our analytical results are in good agreement with numerical simulations.
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Affiliation(s)
- Lukasz Kusmierz
- Institute of Physics, UJ, Reymonta 4, 30-059 Krakow, Poland and Department of Automatics and Biomedical Engineering, AGH, Aleja Mickiewicza 30, 30-059 Krakow, Poland
| | - Satya N Majumdar
- Université Paris-Sud, CNRS, LPTMS, UMR 8626, Orsay F-91405, France
| | | | - Grégory Schehr
- Université Paris-Sud, CNRS, LPTMS, UMR 8626, Orsay F-91405, France
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50
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Schmidt HG, Sewitz S, Andrews SS, Lipkow K. An integrated model of transcription factor diffusion shows the importance of intersegmental transfer and quaternary protein structure for target site finding. PLoS One 2014; 9:e108575. [PMID: 25333780 PMCID: PMC4204827 DOI: 10.1371/journal.pone.0108575] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2014] [Accepted: 08/30/2014] [Indexed: 11/30/2022] Open
Abstract
We present a computational model of transcription factor motion that explains both the observed rapid target finding of transcription factors, and how this motion influences protein and genome structure. Using the Smoldyn software, we modelled transcription factor motion arising from a combination of unrestricted 3D diffusion in the nucleoplasm, sliding along the DNA filament, and transferring directly between filament sections by intersegmental transfer. This presents a fine-grain picture of the way in which transcription factors find their targets two orders of magnitude faster than 3D diffusion alone allows. Eukaryotic genomes contain sections of nucleosome free regions (NFRs) around the promoters; our model shows that the presence and size of these NFRs can be explained as their acting as antennas on which transcription factors slide to reach their targets. Additionally, our model shows that intersegmental transfer may have shaped the quaternary structure of transcription factors: sequence specific DNA binding proteins are unusually enriched in dimers and tetramers, perhaps because these allow intersegmental transfer, which accelerates target site finding. Finally, our model shows that a ‘hopping’ motion can emerge from 3D diffusion on small scales. This explains the apparently long sliding lengths that have been observed for some DNA binding proteins observed in vitro. Together, these results suggest that transcription factor diffusion dynamics help drive the evolution of protein and genome structure.
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Affiliation(s)
- Hugo G. Schmidt
- Department of Biochemistry & Cambridge Systems Biology Centre, University of Cambridge, Cambridge, United Kingdom
- * E-mail: (HS); (KL)
| | - Sven Sewitz
- Department of Biochemistry & Cambridge Systems Biology Centre, University of Cambridge, Cambridge, United Kingdom
- Nuclear Dynamics Programme, The Babraham Institute, Cambridge, United Kingdom
| | - Steven S. Andrews
- Fred Hutchinson Cancer Research Center, Seattle, Washington, United States of America
| | - Karen Lipkow
- Department of Biochemistry & Cambridge Systems Biology Centre, University of Cambridge, Cambridge, United Kingdom
- Nuclear Dynamics Programme, The Babraham Institute, Cambridge, United Kingdom
- * E-mail: (HS); (KL)
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