1
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Jeon E, Go BG, Kim YW. Searching for a partially absorbing target by a run-and-tumble particle in a confined space. Phys Rev E 2024; 109:014103. [PMID: 38366428 DOI: 10.1103/physreve.109.014103] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2023] [Accepted: 11/30/2023] [Indexed: 02/18/2024]
Abstract
A random search of a partially absorbing target by a run-and-tumble particle in a confined one-dimensional space is investigated. We analytically obtain the mean searching time, which shows a nonmonotonic behavior as a function of the self-propulsion speed of the active particle, indicating the existence of an optimal speed, when the absorption strength of the target is finite. In the limit of large and small absorption strengths, respectively, asymptotes of the mean searching time and the optimal speed are found. We also demonstrate that the first-passage problem of a diffusive run-and-tumble particle in high dimensions can be mapped into a one-dimensional problem with a partially absorbing target. Finally, as a practical application exploiting the existence of the optimal speed, we propose a filtering device to extract active particles with a desired speed and evaluate how the resolution of the filtering device depends on the absorption strength.
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Affiliation(s)
- Euijin Jeon
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Byeong Guk Go
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Yong Woon Kim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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2
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Grebenkov DS. Diffusion-Controlled Reactions: An Overview. Molecules 2023; 28:7570. [PMID: 38005291 PMCID: PMC10674959 DOI: 10.3390/molecules28227570] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2023] [Revised: 10/20/2023] [Accepted: 10/21/2023] [Indexed: 11/26/2023] Open
Abstract
We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski, who recognized the importance of diffusion in chemical reactions, we discuss perfect and imperfect surface reactions, their microscopic origins, and the underlying mathematical framework. Single-molecule reaction schemes, anomalous bulk diffusions, reversible binding/unbinding kinetics, and many other extensions are presented. An alternative encounter-based approach to diffusion-controlled reactions is introduced, with emphasis on its advantages and potential applications. Some open problems and future perspectives are outlined.
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Affiliation(s)
- Denis S Grebenkov
- Laboratoire de Physique de la Matière Condensée, CNRS-Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
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3
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Kumar Mishra S, Bhattacherjee A. Understanding the Target Search by Multiple Transcription Factors on Nucleosomal DNA. Chemphyschem 2023; 24:e202200644. [PMID: 36602094 DOI: 10.1002/cphc.202200644] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Revised: 01/04/2023] [Accepted: 01/05/2023] [Indexed: 01/06/2023]
Abstract
The association of multiple Transcription Factors (TFs) in the cis-regulatory region is imperative for developmental changes in eukaryotes. The underlying process is exceedingly complex, and it is not at all clear what orchestrates the overall search process by multiple TFs. In this study, by developing a theoretical model based on a discrete-state stochastic approach, we investigated the target search mechanism of multiple TFs on nucleosomal DNA. Experimental kinetic rate constants of different TFs are taken as input to estimate the Mean-First-Passage time to recognize the binding motifs by two TFs on a dynamic nucleosome model. The theory systematically analyzes when the TFs search their binding motifs hierarchically and when simultaneously by proceeding via the formation of a protein-protein complex. Our results, validated by extensive Monte Carlo simulations, elucidate the molecular basis of the complex target search phenomenon of multiple TFs on nucleosomal DNA.
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Affiliation(s)
- Sujeet Kumar Mishra
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, India
| | - Arnab Bhattacherjee
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, India
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4
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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: 6] [Impact Index Per Article: 3.0] [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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5
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Mondal A, Mishra SK, Bhattacherjee A. Kinetic origin of nucleosome invasion by pioneer transcription factors. Biophys J 2021; 120:5219-5230. [PMID: 34757077 DOI: 10.1016/j.bpj.2021.10.039] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2020] [Revised: 05/14/2021] [Accepted: 10/27/2021] [Indexed: 01/25/2023] Open
Abstract
Recently, a cryo-electron microscopy study has captured different stages of nucleosome breathing dynamics that show partial unwrapping of DNA from histone core to permit transient access to the DNA sites by transcription factors. In practice, however, only a subset of transcription factors named pioneer factors can invade nucleosomes and bind to specific DNA sites to trigger essential DNA metabolic processes. We propose a discrete-state stochastic model that considers the interplay of nucleosome breathing and protein dynamics explicitly and estimate the mean time to search the target DNA sites. It is found that the molecular principle governing the search process on nucleosome is very different compared to that on naked DNA. The pioneer factors minimize their search times on nucleosomal DNA by compensating their nucleosome association rates by dissociation rates. A fine balance between the two presents a tradeoff between their nuclear mobility and error associated with the search process.
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Affiliation(s)
- Anupam Mondal
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, India
| | - Sujeet Kumar Mishra
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, India; Institute for Theoretical Physics, Heidelberg University, Heidelberg, Germany
| | - Arnab Bhattacherjee
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, India.
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6
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Misiura MM, Berezhkovskii AM, Bezrukov SM, Kolomeisky AB. Surface-facilitated trapping by active sites: From catalysts to viruses. J Chem Phys 2021; 155:184106. [PMID: 34773956 PMCID: PMC8730370 DOI: 10.1063/5.0069917] [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: 09/02/2021] [Accepted: 10/20/2021] [Indexed: 11/14/2022] Open
Abstract
Trapping by active sites on surfaces plays important roles in various chemical and biological processes, including catalysis, enzymatic reactions, and viral entry into host cells. However, the mechanisms of these processes remain not well understood, mostly because the existing theoretical descriptions are not fully accounting for the role of the surfaces. Here, we present a theoretical investigation on the dynamics of surface-assisted trapping by specific active sites. In our model, a diffusing particle can occasionally reversibly bind to the surface and diffuse on it before reaching the final target site. An approximate theoretical framework is developed, and its predictions are tested by Brownian dynamics computer simulations. It is found that the surface diffusion can be crucial in mediating trapping by active sites. Our theoretical predictions work reasonably well as long as the area of the active site is much smaller than the overall surface area. Potential applications of our approach are discussed.
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Affiliation(s)
- Mikita M. Misiura
- Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Alexander M. Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Office of Intramural Research, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Sergey M. Bezrukov
- Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
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7
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Dahlenburg M, Chechkin AV, Schumer R, Metzler R. Stochastic resetting by a random amplitude. Phys Rev E 2021; 103:052123. [PMID: 34134286 DOI: 10.1103/physreve.103.052123] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2020] [Accepted: 04/29/2021] [Indexed: 11/07/2022]
Abstract
Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting step by introducing a random resetting amplitude such that the diffusing particle may be only partially reset towards the trajectory origin or even overshoot the origin in a resetting step. We introduce different scenarios for the random-amplitude stochastic resetting process and discuss the resulting dynamics. Direct applications are geophysical layering (stratigraphy) and population dynamics or financial markets, as well as generic search processes.
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Affiliation(s)
- Marcus Dahlenburg
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam, Germany.,Basque Center for Applied Mathematics, 48009 Bilbao, Basque Country, Spain
| | - Aleksei V Chechkin
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam, Germany.,Akhiezer Institute for Theoretical Physics, 61108 Kharkov, Ukraine
| | - Rina Schumer
- Desert Research Institute, Reno, Nevada 89512, USA
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam, Germany
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8
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Frutiger A, Tanno A, Hwu S, Tiefenauer RF, Vörös J, Nakatsuka N. Nonspecific Binding-Fundamental Concepts and Consequences for Biosensing Applications. Chem Rev 2021; 121:8095-8160. [PMID: 34105942 DOI: 10.1021/acs.chemrev.1c00044] [Citation(s) in RCA: 91] [Impact Index Per Article: 30.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Nature achieves differentiation of specific and nonspecific binding in molecular interactions through precise control of biomolecules in space and time. Artificial systems such as biosensors that rely on distinguishing specific molecular binding events in a sea of nonspecific interactions have struggled to overcome this issue. Despite the numerous technological advancements in biosensor technologies, nonspecific binding has remained a critical bottleneck due to the lack of a fundamental understanding of the phenomenon. To date, the identity, cause, and influence of nonspecific binding remain topics of debate within the scientific community. In this review, we discuss the evolution of the concept of nonspecific binding over the past five decades based upon the thermodynamic, intermolecular, and structural perspectives to provide classification frameworks for biomolecular interactions. Further, we introduce various theoretical models that predict the expected behavior of biosensors in physiologically relevant environments to calculate the theoretical detection limit and to optimize sensor performance. We conclude by discussing existing practical approaches to tackle the nonspecific binding challenge in vitro for biosensing platforms and how we can both address and harness nonspecific interactions for in vivo systems.
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Affiliation(s)
- Andreas Frutiger
- Laboratory of Biosensors and Bioelectronics, Institute for Biomedical Engineering, ETH Zürich, Zürich CH-8092, Switzerland
| | - Alexander Tanno
- Laboratory of Biosensors and Bioelectronics, Institute for Biomedical Engineering, ETH Zürich, Zürich CH-8092, Switzerland
| | - Stephanie Hwu
- Laboratory of Biosensors and Bioelectronics, Institute for Biomedical Engineering, ETH Zürich, Zürich CH-8092, Switzerland
| | - Raphael F Tiefenauer
- Laboratory of Biosensors and Bioelectronics, Institute for Biomedical Engineering, ETH Zürich, Zürich CH-8092, Switzerland
| | - János Vörös
- Laboratory of Biosensors and Bioelectronics, Institute for Biomedical Engineering, ETH Zürich, Zürich CH-8092, Switzerland
| | - Nako Nakatsuka
- Laboratory of Biosensors and Bioelectronics, Institute for Biomedical Engineering, ETH Zürich, Zürich CH-8092, Switzerland
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9
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Bigman LS, Greenblatt HM, Levy Y. What Are the Molecular Requirements for Protein Sliding along DNA? J Phys Chem B 2021; 125:3119-3131. [PMID: 33754737 PMCID: PMC8041311 DOI: 10.1021/acs.jpcb.1c00757] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
![]()
DNA-binding proteins rely on linear
diffusion along the longitudinal
DNA axis, supported by their nonspecific electrostatic affinity for
DNA, to search for their target recognition sites. One may therefore
expect that the ability to engage in linear diffusion along DNA is
universal to all DNA-binding proteins, with the detailed biophysical
characteristics of that diffusion differing between proteins depending
on their structures and functions. One key question is whether the
linear diffusion mechanism is defined by translation coupled with
rotation, a mechanism that is often termed sliding. We conduct coarse-grained
and atomistic molecular dynamics simulations to investigate the minimal
requirements for protein sliding along DNA. We show that coupling,
while widespread, is not universal. DNA-binding proteins that slide
along DNA transition to uncoupled translation–rotation (i.e.,
hopping) at higher salt concentrations. Furthermore, and consistently
with experimental reports, we find that the sliding mechanism is the
less dominant mechanism for some DNA-binding proteins, even at low
salt concentrations. In particular, the toroidal PCNA protein is shown
to follow the hopping rather than the sliding mechanism.
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Affiliation(s)
- Lavi S Bigman
- Department of Chemical and Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Harry M Greenblatt
- Department of Chemical and Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yaakov Levy
- Department of Chemical and Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel
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10
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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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11
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Iwahara J, Kolomeisky AB. Discrete-state stochastic kinetic models for target DNA search by proteins: Theory and experimental applications. Biophys Chem 2021; 269:106521. [PMID: 33338872 PMCID: PMC7855466 DOI: 10.1016/j.bpc.2020.106521] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Revised: 12/03/2020] [Accepted: 12/03/2020] [Indexed: 12/15/2022]
Abstract
To perform their functions, transcription factors and DNA-repair/modifying enzymes randomly search DNA in order to locate their specific targets on DNA. Discrete-state stochastic kinetic models have been developed to explain how the efficiency of the search process is influenced by the molecular properties of proteins and DNA as well as by other factors such as molecular crowding. These theoretical models not only offer explanations on the relation of microscopic processes to macroscopic behavior of proteins, but also facilitate the analysis and interpretation of experimental data. In this review article, we provide an overview on discrete-state stochastic kinetic models and explain how these models can be applied to experimental investigations using stopped-flow, single-molecule, nuclear magnetic resonance (NMR), and other biophysical and biochemical methods.
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Affiliation(s)
- Junji Iwahara
- Department of Biochemistry and Molecular Biology, Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, Galveston, TX 77555, USA.
| | - Anatoly B Kolomeisky
- Department of Chemistry, Department of Chemical and Biomolecular Engineering, Department of Physics and Astronomy and Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
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12
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Cagnetta F, Michieletto D, Marenduzzo D. Nonequilibrium Strategy for Fast Target Search on the Genome. PHYSICAL REVIEW LETTERS 2020; 124:198101. [PMID: 32469558 DOI: 10.1103/physrevlett.124.198101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2019] [Accepted: 04/21/2020] [Indexed: 06/11/2023]
Abstract
Vital biological processes such as genome repair require fast and efficient binding of selected proteins to specific target sites on DNA. Here we propose an active target search mechanism based on "chromophoresis," the dynamics of DNA-binding proteins up or down gradients in the density of epigenetic marks, or colors (biochemical tags on the genome). We focus on a set of proteins that deposit marks from which they are repelled-a case which is only encountered away from thermodynamic equilibrium. For suitable ranges of kinetic parameter values, chromophoretic proteins can perform undirectional motion and are optimally redistributed along the genome. Importantly, they can also locally unravel a region of the genome which is collapsed due to self-interactions and "dive" deep into its core, for a striking enhancement of the efficiency of target search on such an inaccessible substrate. We discuss the potential relevance of chromophoresis for DNA repair.
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Affiliation(s)
- F Cagnetta
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - D Michieletto
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
- MRC Human Genetics Unit, Institute of Genetics and Molecular Medicine, University of Edinburgh, Edinburgh EH4 2XU, United Kingdom
- Department of Mathematical Sciences, University of Bath, North Road, Bath BA2 7AY, United Kingdom
| | - D Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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13
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Saxton MJ. Diffusion of DNA-Binding Species in the Nucleus: A Transient Anomalous Subdiffusion Model. Biophys J 2020; 118:2151-2167. [PMID: 32294478 PMCID: PMC7203007 DOI: 10.1016/j.bpj.2020.03.015] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2019] [Revised: 02/28/2020] [Accepted: 03/16/2020] [Indexed: 12/21/2022] Open
Abstract
Single-particle tracking experiments have measured escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution is a truncated power law. Working backward from the experimental results, the observed distribution appears inconsistent with a Gaussian distribution of binding energies. Working forward, the observed distribution leads to transient anomalous subdiffusion, in which diffusion is anomalous at short times and normal at long times, here only mildly anomalous. Monte Carlo simulations are used to characterize the time-dependent diffusion coefficient D(t) in terms of the anomalous exponent α, the crossover time tcross, and the limits D(0) and D(∞) and to relate these quantities to the escape time distribution. The simplest interpretations identify the escape time as the actual binding time to DNA or the period of one-dimensional diffusion on DNA in the standard model combining one-dimensional and three-dimensional search, but a more complicated interpretation may be required. The model has several implications for cell biophysics. 1) The initial anomalous regime represents the search of the DNA-binding species for its target DNA sequence. 2) Non-target DNA sites have a significant effect on search kinetics. False positives in bioinformatic searches of the genome are potentially rate-determining in vivo. For simple binding, the search would be speeded if false-positive sequences were eliminated from the genome. 3) Both binding and obstruction affect diffusion. Obstruction ought to be measured directly, using as the primary probe the DNA-binding species with the binding site inactivated and eGFP as a calibration standard among laboratories and cell types. 4) Overexpression of the DNA-binding species reduces anomalous subdiffusion because the deepest binding sites are occupied and unavailable. 5) The model provides a coarse-grained phenomenological description of diffusion of a DNA-binding species, useful in larger-scale modeling of kinetics, FCS, and FRAP.
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Affiliation(s)
- Michael J Saxton
- Department of Biochemistry and Molecular Medicine, University of California, Davis, California.
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14
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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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15
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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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16
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Cencini M, Pigolotti S. Energetic funnel facilitates facilitated diffusion. Nucleic Acids Res 2019; 46:558-567. [PMID: 29216364 PMCID: PMC5778461 DOI: 10.1093/nar/gkx1220] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2017] [Accepted: 11/24/2017] [Indexed: 01/25/2023] Open
Abstract
Transcription factors (TFs) are able to associate to their binding sites on DNA faster than the physical limit posed by diffusion. Such high association rates can be achieved by alternating between three-dimensional diffusion and one-dimensional sliding along the DNA chain, a mechanism-dubbed facilitated diffusion. By studying a collection of TF binding sites of Escherichia coli from the RegulonDB database and of Bacillus subtilis from DBTBS, we reveal a funnel in the binding energy landscape around the target sequences. We show that such a funnel is linked to the presence of gradients of AT in the base composition of the DNA region around the binding sites. An extensive computational study of the stochastic sliding process along the energetic landscapes obtained from the database shows that the funnel can significantly enhance the probability of TFs to find their target sequences when sliding in their proximity. We demonstrate that this enhancement leads to a speed-up of the association process.
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Affiliation(s)
- Massimo Cencini
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via dei Taurini 19, 00185 Rome, Italy
| | - Simone Pigolotti
- Biological Complexity Unit, Okinawa Institute of Science and Technology and Graduate University, Onna, Okinawa 904-0495, Japan.,Max Planck Institute for the Physics of Complex Systems, Nöthnitzerstraße 38, 01187 Dresden, Germany.,Departament de Fisica, Universitat Politecnica de Catalunya Edif. GAIA, Rambla Sant Nebridi 22, 08222 Terrassa, Barcelona, Spain
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17
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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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18
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Rudnizky S, Khamis H, Malik O, Squires AH, Meller A, Melamed P, Kaplan A. Single-molecule DNA unzipping reveals asymmetric modulation of a transcription factor by its binding site sequence and context. Nucleic Acids Res 2019; 46:1513-1524. [PMID: 29253225 PMCID: PMC5815098 DOI: 10.1093/nar/gkx1252] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Accepted: 12/11/2017] [Indexed: 12/31/2022] Open
Abstract
Most functional transcription factor (TF) binding sites deviate from their ‘consensus’ recognition motif, although their sites and flanking sequences are often conserved across species. Here, we used single-molecule DNA unzipping with optical tweezers to study how Egr-1, a TF harboring three zinc fingers (ZF1, ZF2 and ZF3), is modulated by the sequence and context of its functional sites in the Lhb gene promoter. We find that both the core 9 bp bound to Egr-1 in each of the sites, and the base pairs flanking them, modulate the affinity and structure of the protein–DNA complex. The effect of the flanking sequences is asymmetric, with a stronger effect for the sequence flanking ZF3. Characterization of the dissociation time of Egr-1 revealed that a local, mechanical perturbation of the interactions of ZF3 destabilizes the complex more effectively than a perturbation of the ZF1 interactions. Our results reveal a novel role for ZF3 in the interaction of Egr-1 with other proteins and the DNA, providing insight on the regulation of Lhb and other genes by Egr-1. Moreover, our findings reveal the potential of small changes in DNA sequence to alter transcriptional regulation, and may shed light on the organization of regulatory elements at promoters.
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Affiliation(s)
- Sergei Rudnizky
- Faculty of Biology, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Hadeel Khamis
- Faculty of Biology, Technion-Israel Institute of Technology, Haifa 32000, Israel.,Faculty of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Omri Malik
- Faculty of Biology, Technion-Israel Institute of Technology, Haifa 32000, Israel.,Russell Berrie Nanotechnology Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Allison H Squires
- Department of Biomedical Engineering, Boston University, Boston, MA 02215, USA
| | - Amit Meller
- Russell Berrie Nanotechnology Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel.,Department of Biomedical Engineering, Boston University, Boston, MA 02215, USA.,Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Philippa Melamed
- Faculty of Biology, Technion-Israel Institute of Technology, Haifa 32000, Israel.,Russell Berrie Nanotechnology Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Ariel Kaplan
- Faculty of Biology, Technion-Israel Institute of Technology, Haifa 32000, Israel.,Russell Berrie Nanotechnology Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel
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19
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Barel I, Reich NO, Brown FLH. Integrated rate laws for processive and distributive enzymatic turnover. J Chem Phys 2019; 150:244120. [PMID: 31255081 DOI: 10.1063/1.5097576] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Recently derived steady-state differential rate laws for the catalytic turnover of molecules containing two substrate sites are reformulated as integrated rate laws. The analysis applies to a broad class of Markovian dynamic models, motivated by the varied and often complex mechanisms associated with DNA modifying enzymes. Analysis of experimental data for the methylation kinetics of DNA by Dam (DNA adenine methyltransferase) is drastically improved through the use of integrated rate laws. Data that are too noisy for fitting to differential predictions are reliably interpreted through the integrated rate laws.
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Affiliation(s)
- Itay Barel
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
| | - Norbert O Reich
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
| | - Frank L H Brown
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
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20
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Chowdhury D. Laying Tracks for Poison Delivery to "Kiss of Death": Search for Immune Synapse by Microtubules. Biophys J 2019; 116:2057-2059. [PMID: 31084901 DOI: 10.1016/j.bpj.2019.05.001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2019] [Revised: 04/29/2019] [Accepted: 05/01/2019] [Indexed: 01/21/2023] Open
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21
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Le Treut G, Képès F, Orland H. A Polymer Model for the Quantitative Reconstruction of Chromosome Architecture from HiC and GAM Data. Biophys J 2018; 115:2286-2294. [PMID: 30527448 DOI: 10.1016/j.bpj.2018.10.032] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2018] [Revised: 10/03/2018] [Accepted: 10/26/2018] [Indexed: 01/03/2023] Open
Abstract
It is widely believed that the folding of the chromosome in the nucleus has a major effect on genetic expression. For example, coregulated genes in several species have been shown to colocalize in space despite being far away on the DNA sequence. In this manuscript, we present a new, to our knowledge, method to model the three-dimensional structure of the chromosome in live cells based on DNA-DNA interactions measured in high-throughput chromosome conformation capture experiments and genome architecture mapping. Our approach incorporates a polymer model and directly uses the contact probabilities measured in high-throughput chromosome conformation capture experiments and genome architecture mapping experiments rather than estimates of average distances between genomic loci. Specifically, we model the chromosome as a Gaussian polymer with harmonic interactions and extract the coupling coefficients best reproducing the experimental contact probabilities. In contrast to existing methods, we give an exact expression of the contact probabilities at thermodynamic equilibrium. The Gaussian effective model reconstructed with our method reproduces experimental contacts with high accuracy. We also show how Brownian dynamics simulations of our reconstructed Gaussian effective model can be used to study chromatin organization and possibly give some clue about its dynamics.
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Affiliation(s)
- Guillaume Le Treut
- Department of Physics, University of California San Diego, La Jolla, California.
| | - François Képès
- institute of Systems and Synthetic Biology, Genopole, CNRS, UEVE, Université Paris-Saclay, Évry, France
| | - Henri Orland
- Institut de Physique Théorique, CEA, CNRS-URA 2306, Gif-sur-Yvette, France; Beijing Computational Science Research Center, Beijing, China
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22
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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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23
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Esadze A, Stivers JT. Facilitated Diffusion Mechanisms in DNA Base Excision Repair and Transcriptional Activation. Chem Rev 2018; 118:11298-11323. [PMID: 30379068 DOI: 10.1021/acs.chemrev.8b00513] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Preservation of the coding potential of the genome and highly regulated gene expression over the life span of a human are two fundamental requirements of life. These processes require the action of repair enzymes or transcription factors that efficiently recognize specific sites of DNA damage or transcriptional regulation within a restricted time frame of the cell cycle or metabolism. A failure of these systems to act results in accumulated mutations, metabolic dysfunction, and disease. Despite the multifactorial complexity of cellular DNA repair and transcriptional regulation, both processes share a fundamental physical requirement that the proteins must rapidly diffuse to their specific DNA-binding sites that are embedded within the context of a vastly greater number of nonspecific DNA-binding sites. Superimposed on the needle-in-the-haystack problem is the complex nature of the cellular environment, which contains such high concentrations of macromolecules that the time frame for diffusion is expected to be severely extended as compared to dilute solution. Here we critically review the mechanisms for how these proteins solve the needle-in-the-haystack problem and how the effects of cellular macromolecular crowding can enhance facilitated diffusion processes. We restrict the review to human proteins that use stochastic, thermally driven site-recognition mechanisms, and we specifically exclude systems involving energy cofactors or circular DNA clamps. Our scope includes ensemble and single-molecule studies of the past decade or so, with an emphasis on connecting experimental observations to biological function.
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Affiliation(s)
- Alexandre Esadze
- Department of Pharmacology and Molecular Sciences , Johns Hopkins University School of Medicine , 725 North Wolfe Street , WBSB 314, Baltimore , Maryland 21205 , United States
| | - James T Stivers
- Department of Pharmacology and Molecular Sciences , Johns Hopkins University School of Medicine , 725 North Wolfe Street , WBSB 314, Baltimore , Maryland 21205 , United States
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24
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Mechanisms of Protein Search for Targets on DNA: Theoretical Insights. Molecules 2018; 23:molecules23092106. [PMID: 30131459 PMCID: PMC6225296 DOI: 10.3390/molecules23092106] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2018] [Revised: 08/13/2018] [Accepted: 08/17/2018] [Indexed: 11/17/2022] Open
Abstract
Protein-DNA interactions are critical for the successful functioning of all natural systems. The key role in these interactions is played by processes of protein search for specific sites on DNA. Although it has been studied for many years, only recently microscopic aspects of these processes became more clear. In this work, we present a review on current theoretical understanding of the molecular mechanisms of the protein target search. A comprehensive discrete-state stochastic method to explain the dynamics of the protein search phenomena is introduced and explained. Our theoretical approach utilizes a first-passage analysis and it takes into account the most relevant physical-chemical processes. It is able to describe many fascinating features of the protein search, including unusually high effective association rates, high selectivity and specificity, and the robustness in the presence of crowders and sequence heterogeneity.
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25
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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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26
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Azimzade Y, Mashaghi A. Search efficiency of biased migration towards stationary or moving targets in heterogeneously structured environments. Phys Rev E 2018; 96:062415. [PMID: 29347391 DOI: 10.1103/physreve.96.062415] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Indexed: 01/27/2023]
Abstract
Efficient search acts as a strong selective force in biological systems ranging from cellular populations to predator-prey systems. The search processes commonly involve finding a stationary or mobile target within a heterogeneously structured environment where obstacles limit migration. An open generic question is whether random or directionally biased motions or a combination of both provide an optimal search efficiency and how that depends on the motility and density of targets and obstacles. To address this question, we develop a simple model that involves a random walker searching for its targets in a heterogeneous medium of bond percolation square lattice and used mean first passage time (〈T〉) as an indication of average search time. Our analysis reveals a dual effect of directional bias on the minimum value of 〈T〉. For a homogeneous medium, directionality always decreases 〈T〉 and a pure directional migration (a ballistic motion) serves as the optimized strategy, while for a heterogeneous environment, we find that the optimized strategy involves a combination of directed and random migrations. The relative contribution of these modes is determined by the density of obstacles and motility of targets. Existence of randomness and motility of targets add to the efficiency of search. Our study reveals generic and simple rules that govern search efficiency. Our findings might find application in a number of areas including immunology, cell biology, ecology, and robotics.
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Affiliation(s)
- Youness Azimzade
- Department of Physics, University of Tehran, Tehran 14395-547, Iran.,Leiden Academic Centre for Drug Research, Faculty of Mathematics and Natural Sciences, Leiden University, Leiden 2300 RA, The Netherlands
| | - Alireza Mashaghi
- Leiden Academic Centre for Drug Research, Faculty of Mathematics and Natural Sciences, Leiden University, Leiden 2300 RA, The Netherlands
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27
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Barel I, Naughton B, Reich NO, Brown FLH. Specificity versus Processivity in the Sequential Modification of DNA: A Study of DNA Adenine Methyltransferase. J Phys Chem B 2018; 122:1112-1120. [DOI: 10.1021/acs.jpcb.7b10349] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Itay Barel
- Department
of Chemistry and Biochemistry, University of California, Santa
Barbara, California 93106, United States
- Department
of Physics, University of California, Santa Barbara, California 93106, United States
| | - Brigitte Naughton
- Department
of Chemistry and Biochemistry, University of California, Santa
Barbara, California 93106, United States
| | - Norbert O. Reich
- Department
of Chemistry and Biochemistry, University of California, Santa
Barbara, California 93106, United States
| | - Frank L. H. Brown
- Department
of Chemistry and Biochemistry, University of California, Santa
Barbara, California 93106, United States
- Department
of Physics, University of California, Santa Barbara, California 93106, United States
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28
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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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29
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Kochugaeva MP, Berezhkovskii AM, Kolomeisky AB. Optimal Length of Conformational Transition Region in Protein Search for Targets on DNA. J Phys Chem Lett 2017; 8:4049-4054. [PMID: 28796515 PMCID: PMC5589516 DOI: 10.1021/acs.jpclett.7b01750] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The starting point of many fundamental biological processes is associated with protein molecules finding and recognizing specific sites on DNA. However, despite a large number of experimental and theoretical studies on protein search for targets on DNA, many molecular aspects of underlying mechanisms are still not well understood. Experiments show that proteins bound to DNA can switch between slow recognition and fast search conformations. However, from a theoretical point of view, such conformational transitions should slow down the protein search for specific sites on DNA, in contrast to available experimental observations. In addition, experiments indicate that the nucleotide composition near the target site is more symmetrically homogeneous, leading to stronger effective interactions between proteins and DNA at these locations. However, as has been shown theoretically, this should also make the search less efficient, which is not observed. We propose a possible resolution of these problems by suggesting that conformational transitions occur only within a segment around the target where stronger interactions between proteins and DNA are observed. Two theoretical methods, based on continuum and discrete-state stochastic calculations, are developed, allowing us to obtain a comprehensive dynamic description for the protein search process in this system. The existence of an optimal length of the conformational transition zone with the shortest mean search time is predicted.
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Affiliation(s)
- Maria P. Kochugaeva
- Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
| | - Alexander M. Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, United States
| | - Anatoly B. Kolomeisky
- Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
- Corresponding Author.
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30
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Ephemeral Protein Binding to DNA Shapes Stable Nuclear Bodies and Chromatin Domains. Biophys J 2017; 112:1085-1093. [PMID: 28355537 DOI: 10.1016/j.bpj.2017.01.025] [Citation(s) in RCA: 51] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2016] [Revised: 12/20/2016] [Accepted: 01/06/2017] [Indexed: 12/18/2022] Open
Abstract
Fluorescence microscopy reveals that the contents of many (membrane-free) nuclear bodies exchange rapidly with the soluble pool while the underlying structure persists; such observations await a satisfactory biophysical explanation. To shed light on this, we perform large-scale Brownian dynamics simulations of a chromatin fiber interacting with an ensemble of (multivalent) DNA-binding proteins able to switch between an "on" (binding) and an "off" (nonbinding) state. This system provides a model for any DNA-binding protein that can be posttranslationally modified to change its affinity for DNA (e.g., through phosphorylation). Protein switching is a nonequilibrium process, and it leads to the formation of clusters of self-limiting size, where individual proteins in a cluster exchange with the soluble pool with kinetics similar to those seen in photobleaching experiments. This behavior contrasts sharply with that exhibited by nonswitching proteins, which are permanently in the on-state; when these bind to DNA nonspecifically, they form clusters that grow indefinitely in size. To explain these findings, we propose a mean-field theory from which we obtain a scaling relation between the typical cluster size and the protein switching rate. Protein switching also reshapes intrachromatin contacts to give networks resembling those seen in topologically associating domains, as switching markedly favors local (short-range) contacts over distant ones. Our results point to posttranslational modification of chromatin-bridging proteins as a generic mechanism driving the self-assembly of highly dynamic, nonequilibrium, protein clusters with the properties of nuclear bodies.
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31
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Bitran A, Chiang WY, Levine E, Prentiss M. Mechanisms of fast and stringent search in homologous pairing of double-stranded DNA. PLoS Comput Biol 2017; 13:e1005421. [PMID: 28257444 PMCID: PMC5360337 DOI: 10.1371/journal.pcbi.1005421] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2016] [Revised: 03/21/2017] [Accepted: 02/21/2017] [Indexed: 12/03/2022] Open
Abstract
Self-organization in the cell relies on the rapid and specific binding of molecules to their cognate targets. Correct bindings must be stable enough to promote the desired function even in the crowded and fluctuating cellular environment. In systems with many nearly matched targets, rapid and stringent formation of stable products is challenging. Mechanisms that overcome this challenge have been previously proposed, including separating the process into multiple stages; however, how particular in vivo systems overcome the challenge remains unclear. Here we consider a kinetic system, inspired by homology dependent pairing between double stranded DNA in bacteria. By considering a simplified tractable model, we identify different homology testing stages that naturally occur in the system. In particular, we first model dsDNA molecules as short rigid rods containing periodically spaced binding sites. The interaction begins when the centers of two rods collide at a random angle. For most collision angles, the interaction energy is weak because only a few binding sites near the collision point contribute significantly to the binding energy. We show that most incorrect pairings are rapidly rejected at this stage. In rare cases, the two rods enter a second stage by rotating into parallel alignment. While rotation increases the stability of matched and nearly matched pairings, subsequent rotational fluctuations reduce kinetic trapping. Finally, in vivo chromosome are much longer than the persistence length of dsDNA, so we extended the model to include multiple parallel collisions between long dsDNA molecules, and find that those additional interactions can greatly accelerate the searching. Protein folding and the binding of sequence dependent proteins to DNA are examples of self-assembling systems in which the binding energy varies continuously throughout the interaction. Previous theoretical work has highlighted the importance of dividing the interaction into separate stages characterized by interaction times and binding energies that vary by orders of magnitude. Insight into how such a division might naturally arise and promote accurate and efficient self-assembly is provided by our study of a simple tractable model inspired by the homology dependent pairing of double stranded DNA molecules in vivo. In the model, the binding energy is controlled by one single continuously tunable variable whose natural evolution creates stages that efficiently and accurately form stable products.
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Affiliation(s)
- Amir Bitran
- Department of Physics, Harvard University, Cambridge, Massachusetts, United States of America
| | - Wei-Yin Chiang
- Department of Physics, Harvard University, Cambridge, Massachusetts, United States of America
- FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts, United States of America
| | - Erel Levine
- Department of Physics, Harvard University, Cambridge, Massachusetts, United States of America
- FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts, United States of America
- * E-mail:
| | - Mara Prentiss
- Department of Physics, Harvard University, Cambridge, Massachusetts, United States of America
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32
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Shvets AA, Kolomeisky AB. The Role of DNA Looping in the Search for Specific Targets on DNA by Multisite Proteins. J Phys Chem Lett 2016; 7:5022-5027. [PMID: 27973894 DOI: 10.1021/acs.jpclett.6b02371] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Many cellular processes involve simultaneous interactions between DNA and protein molecules at several locations. They are regulated and controlled by special protein-DNA complexes, which are known as synaptic complexes or synaptosomes. Because of the multisite nature of involved proteins, it was suggested that during the formation of synaptic complexes DNA loops might appear, but their role is unclear. We developed a theoretical model that allowed us to evaluate the effect of transient DNA loop formation. It is based on a discrete-state stochastic method that explicitly takes into account the free-energy contributions due to the appearance of DNA loops. The formation of the synaptic complexes is viewed as a search for a specific binding site on DNA by the protein molecule already bound to DNA at another location. It was found that the search might be optimized by varying the position of the target and the total length of DNA. Furthermore, the formation of transient DNA loops leads to faster dynamics if it is associated with favorable enthalpic contributions to nonspecific protein-DNA interactions. It is also shown that DNA looping might reduce stochastic noise in the system.
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Affiliation(s)
- Alexey A Shvets
- Department of Chemistry and Center for Theoretical Biological Physics, Rice University , Houston, Texas 77005, United States
| | - Anatoly B Kolomeisky
- Department of Chemistry and Center for Theoretical Biological Physics, Rice University , Houston, Texas 77005, United States
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33
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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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34
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Krepel D, Gomez D, Klumpp S, Levy Y. Mechanism of Facilitated Diffusion during a DNA Search in Crowded Environments. J Phys Chem B 2016; 120:11113-11122. [DOI: 10.1021/acs.jpcb.6b07813] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Dana Krepel
- Department
of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - David Gomez
- Max Planck Institute of Colloids and Interfaces, Science Park Golm, 14424 Potsdam, Germany
| | - Stefan Klumpp
- Max Planck Institute of Colloids and Interfaces, Science Park Golm, 14424 Potsdam, Germany
- Institute
for Nonlinear Dynamics, Georg-August University Göttingen, Friedrich-Hund-Platz
1, 37077 Göttingen, Germany
| | - Yaakov Levy
- Department
of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel
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35
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Shvets AA, Kolomeisky AB. Sequence heterogeneity accelerates protein search for targets on DNA. J Chem Phys 2016; 143:245101. [PMID: 26723711 DOI: 10.1063/1.4937938] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
The process of protein search for specific binding sites on DNA is fundamentally important since it marks the beginning of all major biological processes. We present a theoretical investigation that probes the role of DNA sequence symmetry, heterogeneity, and chemical composition in the protein search dynamics. Using a discrete-state stochastic approach with a first-passage events analysis, which takes into account the most relevant physical-chemical processes, a full analytical description of the search dynamics is obtained. It is found that, contrary to existing views, the protein search is generally faster on DNA with more heterogeneous sequences. In addition, the search dynamics might be affected by the chemical composition near the target site. The physical origins of these phenomena are discussed. Our results suggest that biological processes might be effectively regulated by modifying chemical composition, symmetry, and heterogeneity of a genome.
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Affiliation(s)
- Alexey A Shvets
- Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Anatoly B Kolomeisky
- Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
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36
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Reithmann E, Reese L, Frey E. Nonequilibrium Diffusion and Capture Mechanism Ensures Tip Localization of Regulating Proteins on Dynamic Filaments. PHYSICAL REVIEW LETTERS 2016; 117:078102. [PMID: 27564001 DOI: 10.1103/physrevlett.117.078102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2015] [Indexed: 06/06/2023]
Abstract
Diffusive motion of regulatory enzymes on biopolymers with eventual capture at a reaction site is a common feature in cell biology. Using a lattice gas model we study the impact of diffusion and capture for a microtubule polymerase and a depolymerase. Our results show that the capture mechanism localizes the proteins and creates large-scale spatial correlations. We develop an analytic approximation that globally accounts for relevant correlations and yields results that are in excellent agreement with experimental data. Our results show that diffusion and capture operates most efficiently at cellular enzyme concentrations which points to in vivo relevance.
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Affiliation(s)
- Emanuel Reithmann
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany
| | - Louis Reese
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany
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37
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Abstract
Proteins searching and recognizing specific sites on DNA is required for initiating all major biological processes. While the details of the protein search for targets on DNA in purified in vitro systems are reasonably well understood, the situation in real cells is much less clear. The presence of other types of molecules on DNA should prevent reaching the targets, but experiments show that, surprisingly, the molecular crowding on DNA influences the search dynamics much less than expected. We develop a theoretical method that allowed us to clarify the mechanisms of the protein search on DNA in the presence of crowding. It is found that the dimensionality of the search trajectories specifies whether the crowding will affect the target finding. For 3D search pathways it is minimal, while the strongest effect is for 1D search pathways when the crowding particle can block the search. In addition, for 1D search we determined that the critical parameter is a mobility of crowding agents: highly mobile molecules do not affect the search dynamics, while the slow particles can significantly slow down the process. Physical-chemical explanations of the observed phenomena are presented. Our theoretical predictions thus explain the experimental observations, and they are also supported by extensive numerical simulations.
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Affiliation(s)
- Alexey A Shvets
- Department of Chemistry and Center for Theoretical Biological Physics, Rice University , Houston, Texas 77005, United States
| | - Anatoly B Kolomeisky
- Department of Chemistry and Center for Theoretical Biological Physics, Rice University , Houston, Texas 77005, United States
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38
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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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39
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Metzler R, Jeon JH, Cherstvy AG. Non-Brownian diffusion in lipid membranes: Experiments and simulations. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2016; 1858:2451-2467. [PMID: 26826272 DOI: 10.1016/j.bbamem.2016.01.022] [Citation(s) in RCA: 126] [Impact Index Per Article: 15.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2015] [Revised: 01/21/2016] [Accepted: 01/23/2016] [Indexed: 12/14/2022]
Abstract
The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.
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Affiliation(s)
- R Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany; Department of Physics, Tampere University of Technology, 33101 Tampere, Finland.
| | - J-H Jeon
- Korea Institute for Advanced Study (KIAS), Seoul, Republic of Korea
| | - A G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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40
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Le Treut G, Képès F, Orland H. Phase Behavior of DNA in the Presence of DNA-Binding Proteins. Biophys J 2016; 110:51-62. [PMID: 26745409 PMCID: PMC4805876 DOI: 10.1016/j.bpj.2015.10.027] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2015] [Revised: 09/28/2015] [Accepted: 10/15/2015] [Indexed: 10/22/2022] Open
Abstract
To characterize the thermodynamical equilibrium of DNA chains interacting with a solution of nonspecific binding proteins, we implemented a Flory-Huggins free energy model. We explored the dependence on DNA and protein concentrations of the DNA collapse. For physiologically relevant values of the DNA-protein affinity, this collapse gives rise to a biphasic regime with a dense and a dilute phase; the corresponding phase diagram was computed. Using an approach based on Hamiltonian paths, we show that the dense phase has either a molten globule or a crystalline structure, depending on the DNA bending rigidity, which is influenced by the ionic strength. These results are valid at the thermodynamical equilibrium and therefore should be consistent with many biological processes, whose characteristic timescales range typically from 1 ms to 10 s. Our model may thus be applied to biological phenomena that involve DNA-binding proteins, such as DNA condensation with crystalline order, which occurs in some bacteria to protect their chromosome from detrimental factors; or transcription initiation, which occurs in clusters called transcription factories that are reminiscent of the dense phase characterized in this study.
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Affiliation(s)
- Guillaume Le Treut
- Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, Gif-sur-Yvette, France; Institute of Systems and Synthetic Biology, University of Evry-Val-d'Essonne, CNRS, Genopole Campus 1, Evry, France.
| | - François Képès
- Institute of Systems and Synthetic Biology, University of Evry-Val-d'Essonne, CNRS, Genopole Campus 1, Evry, France
| | - Henri Orland
- Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, Gif-sur-Yvette, France
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41
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Demidov GM, Samsonova MG, Gursky VV. A stochastic model of the formation of the molecular configuration of an enhancer site. Biophysics (Nagoya-shi) 2016. [DOI: 10.1134/s0006350916010073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
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42
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Kozlov K, Gursky VV, Kulakovskiy IV, Dymova A, Samsonova M. Analysis of functional importance of binding sites in the Drosophila gap gene network model. BMC Genomics 2015; 16 Suppl 13:S7. [PMID: 26694511 PMCID: PMC4686791 DOI: 10.1186/1471-2164-16-s13-s7] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
BACKGROUND The statistical thermodynamics based approach provides a promising framework for construction of the genotype-phenotype map in many biological systems. Among important aspects of a good model connecting the DNA sequence information with that of a molecular phenotype (gene expression) is the selection of regulatory interactions and relevant transcription factor bindings sites. As the model may predict different levels of the functional importance of specific binding sites in different genomic and regulatory contexts, it is essential to formulate and study such models under different modeling assumptions. RESULTS We elaborate a two-layer model for the Drosophila gap gene network and include in the model a combined set of transcription factor binding sites and concentration dependent regulatory interaction between gap genes hunchback and Kruppel. We show that the new variants of the model are more consistent in terms of gene expression predictions for various genetic constructs in comparison to previous work. We quantify the functional importance of binding sites by calculating their impact on gene expression in the model and calculate how these impacts correlate across all sites under different modeling assumptions. CONCLUSIONS The assumption about the dual interaction between hb and Kr leads to the most consistent modeling results, but, on the other hand, may obscure existence of indirect interactions between binding sites in regulatory regions of distinct genes. The analysis confirms the previously formulated regulation concept of many weak binding sites working in concert. The model predicts a more or less uniform distribution of functionally important binding sites over the sets of experimentally characterized regulatory modules and other open chromatin domains.
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Affiliation(s)
- Konstantin Kozlov
- Peter the Great St. Petersburg Polytechnic University, 29 Polytechnicheskaya, 195251 St.Petersburg, Russia
| | - Vitaly V Gursky
- Peter the Great St. Petersburg Polytechnic University, 29 Polytechnicheskaya, 195251 St.Petersburg, Russia
- Ioffe Institute, 26 Polytechnicheskaya, 194021 St.Petersburg, Russia
| | - Ivan V Kulakovskiy
- Engelhardt Institute of Molecular Biology, 32 Vavilova, 119991 Moscow, Russia
| | - Arina Dymova
- Peter the Great St. Petersburg Polytechnic University, 29 Polytechnicheskaya, 195251 St.Petersburg, Russia
| | - Maria Samsonova
- Peter the Great St. Petersburg Polytechnic University, 29 Polytechnicheskaya, 195251 St.Petersburg, Russia
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43
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Barel I, Reich NO, Brown FLH. Extracting enzyme processivity from kinetic assays. J Chem Phys 2015; 143:224115. [DOI: 10.1063/1.4937155] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Itay Barel
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Norbert O. Reich
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
| | - Frank L. H. Brown
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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44
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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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45
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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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46
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Sheinman M, Chung HR. Conditions for positioning of nucleosomes on DNA. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022704. [PMID: 26382429 DOI: 10.1103/physreve.92.022704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2015] [Indexed: 06/05/2023]
Abstract
Positioning of nucleosomes along a eukaryotic genome plays an important role in its organization and regulation. There are many different factors affecting the location of nucleosomes. Some can be viewed as preferential binding of a single nucleosome to different locations along the DNA and some as interactions between neighboring nucleosomes. In this study, we analyze positioning of nucleosomes and derive conditions for their good positioning. Using analytic and numerical approaches we find that, if the binding preferences are very weak, an interplay between the interactions and the binding preferences is essential for a good positioning of nucleosomes, especially on correlated energy landscapes. Analyzing the empirical energy landscape, we conclude that good positioning of nucleosomes in vivo is possible only if they strongly interact. In this case, our model, predicting long-length-scale fluctuations of nucleosomes' occupancy along the DNA, accounts well for the empirical observations.
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Affiliation(s)
- Michael Sheinman
- Max Planck Institute for Molecular Genetics, 14195 Berlin, Germany
| | - Ho-Ryun Chung
- Max Planck Institute for Molecular Genetics, 14195 Berlin, Germany
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47
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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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48
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Normanno D, Boudarène L, Dugast-Darzacq C, Chen J, Richter C, Proux F, Bénichou O, Voituriez R, Darzacq X, Dahan M. Probing the target search of DNA-binding proteins in mammalian cells using TetR as model searcher. Nat Commun 2015; 6:7357. [PMID: 26151127 PMCID: PMC4507003 DOI: 10.1038/ncomms8357] [Citation(s) in RCA: 125] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2014] [Accepted: 04/30/2015] [Indexed: 12/17/2022] Open
Abstract
Many cellular functions rely on DNA-binding proteins finding and associating to specific sites in the genome. Yet the mechanisms underlying the target search remain poorly understood, especially in the case of the highly organized mammalian cell nucleus. Using as a model Tet repressors (TetRs) searching for a multi-array locus, we quantitatively analyse the search process in human cells with single-molecule tracking and single-cell protein–DNA association measurements. We find that TetRs explore the nucleus and reach their target by 3D diffusion interspersed with transient interactions with non-cognate sites, consistent with the facilitated diffusion model. Remarkably, nonspecific binding times are broadly distributed, underlining a lack of clear delimitation between specific and nonspecific interactions. However, the search kinetics is not determined by diffusive transport but by the low association rate to nonspecific sites. Altogether, our results provide a comprehensive view of the recruitment dynamics of proteins at specific loci in mammalian cells. During transcription, replication and repair, DNA-binding proteins must find specific interaction sites hidden within a vast excess of genomic DNA. Here the authors use single-molecule tracking to quantitatively determine the contributions of the different processes that underlie target search in human cells.
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Affiliation(s)
- Davide Normanno
- Laboratoire Kastler Brossel, CNRS UMR 8552, École normale supérieure, Université Pierre et Marie Curie, Paris 6, 46 rue d'Ulm, 75005 Paris, France.,Functional Imaging of Transcription, CNRS UMR 8197, École normale supérieure, Institut de Biologie de l'ENS, IBENS, 46 rue d'Ulm, 75005 Paris, France.,Transcription Imaging Consortium, Janelia Research Campus, Howard Hughes Medical Institute, 19700 Helix Drive, Ashburn, Virginia 20147, USA.,Physico-Chimie Curie, Institut Curie, CNRS UMR 168, Université Pierre et Marie Curie, Paris 6, 26 rue d'Ulm, 75005 Paris, France
| | - Lydia Boudarène
- Laboratoire Kastler Brossel, CNRS UMR 8552, École normale supérieure, Université Pierre et Marie Curie, Paris 6, 46 rue d'Ulm, 75005 Paris, France.,Functional Imaging of Transcription, CNRS UMR 8197, École normale supérieure, Institut de Biologie de l'ENS, IBENS, 46 rue d'Ulm, 75005 Paris, France
| | - Claire Dugast-Darzacq
- Functional Imaging of Transcription, CNRS UMR 8197, École normale supérieure, Institut de Biologie de l'ENS, IBENS, 46 rue d'Ulm, 75005 Paris, France.,Université Paris-Diderot, Paris 7, 5 rue Thomas Mann, 75013 Paris, France
| | - Jiji Chen
- Transcription Imaging Consortium, Janelia Research Campus, Howard Hughes Medical Institute, 19700 Helix Drive, Ashburn, Virginia 20147, USA
| | - Christian Richter
- Laboratoire Kastler Brossel, CNRS UMR 8552, École normale supérieure, Université Pierre et Marie Curie, Paris 6, 46 rue d'Ulm, 75005 Paris, France
| | - Florence Proux
- Functional Imaging of Transcription, CNRS UMR 8197, École normale supérieure, Institut de Biologie de l'ENS, IBENS, 46 rue d'Ulm, 75005 Paris, France
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, Paris 6, 4 place Jussieu, 75005 Paris, France
| | - Raphaël Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, Paris 6, 4 place Jussieu, 75005 Paris, France
| | - Xavier Darzacq
- Functional Imaging of Transcription, CNRS UMR 8197, École normale supérieure, Institut de Biologie de l'ENS, IBENS, 46 rue d'Ulm, 75005 Paris, France.,Transcription Imaging Consortium, Janelia Research Campus, Howard Hughes Medical Institute, 19700 Helix Drive, Ashburn, Virginia 20147, USA
| | - Maxime Dahan
- Laboratoire Kastler Brossel, CNRS UMR 8552, École normale supérieure, Université Pierre et Marie Curie, Paris 6, 46 rue d'Ulm, 75005 Paris, France.,Transcription Imaging Consortium, Janelia Research Campus, Howard Hughes Medical Institute, 19700 Helix Drive, Ashburn, Virginia 20147, USA.,Physico-Chimie Curie, Institut Curie, CNRS UMR 168, Université Pierre et Marie Curie, Paris 6, 26 rue d'Ulm, 75005 Paris, France
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49
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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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50
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Godec A, Metzler R. Optimization and universality of Brownian search in a basic model of quenched heterogeneous media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052134. [PMID: 26066146 DOI: 10.1103/physreve.91.052134] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2015] [Indexed: 06/04/2023]
Abstract
The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time (MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.
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Affiliation(s)
- Aljaž Godec
- Institute of Physics & Astronomy, University of Potsdam, 14776 Potsdam-Golm, Germany
- National Institute of Chemistry, 1000 Ljubljana, Slovenia
| | - Ralf Metzler
- Institute of Physics & Astronomy, University of Potsdam, 14776 Potsdam-Golm, Germany
- Department of Physics, Tampere University of Technology, 33101 Tampere, Finland
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