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Janissen R, Eslami-Mossallam B, Artsimovitch I, Depken M, Dekker NH. High-throughput single-molecule experiments reveal heterogeneity, state switching, and three interconnected pause states in transcription. Cell Rep 2022; 39:110749. [PMID: 35476989 DOI: 10.1016/j.celrep.2022.110749] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2021] [Revised: 02/17/2022] [Accepted: 04/07/2022] [Indexed: 11/19/2022] Open
Abstract
Pausing by bacterial RNA polymerase (RNAp) is vital in the recruitment of regulatory factors, RNA folding, and coupled translation. While backtracking and intra-structural isomerization have been proposed to trigger pausing, our mechanistic understanding of backtrack-associated pauses and catalytic recovery remains incomplete. Using high-throughput magnetic tweezers, we examine the Escherichia coli RNAp transcription dynamics over a wide range of forces and NTP concentrations. Dwell-time analysis and stochastic modeling identify, in addition to a short-lived elemental pause, two distinct long-lived backtrack pause states differing in recovery rates. We identify two stochastic sources of transcription heterogeneity: alterations in short-pause frequency that underlies elongation-rate switching, and variations in RNA cleavage rates in long-lived backtrack states. Together with effects of force and Gre factors, we demonstrate that recovery from deep backtracks is governed by intrinsic RNA cleavage rather than diffusional Brownian dynamics. We introduce a consensus mechanistic model that unifies our findings with prior models.
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Affiliation(s)
- Richard Janissen
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Behrouz Eslami-Mossallam
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Irina Artsimovitch
- Department of Microbiology, Ohio State University, Columbus, OH 43210, USA.
| | - Martin Depken
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2629 HZ Delft, The Netherlands.
| | - Nynke H Dekker
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2629 HZ Delft, The Netherlands.
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Eslami-Mossallam B, Klein M, Smagt CVD, Sanden KVD, Jones SK, Hawkins JA, Finkelstein IJ, Depken M. A kinetic model predicts SpCas9 activity, improves off-target classification, and reveals the physical basis of targeting fidelity. Nat Commun 2022; 13:1367. [PMID: 35292641 PMCID: PMC8924176 DOI: 10.1038/s41467-022-28994-2] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 02/11/2022] [Indexed: 12/26/2022] Open
Abstract
The S. pyogenes (Sp) Cas9 endonuclease is an important gene-editing tool. SpCas9 is directed to target sites based on complementarity to a complexed single-guide RNA (sgRNA). However, SpCas9-sgRNA also binds and cleaves genomic off-targets with only partial complementarity. To date, we lack the ability to predict cleavage and binding activity quantitatively, and rely on binary classification schemes to identify strong off-targets. We report a quantitative kinetic model that captures the SpCas9-mediated strand-replacement reaction in free-energy terms. The model predicts binding and cleavage activity as a function of time, target, and experimental conditions. Trained and validated on high-throughput bulk-biochemical data, our model predicts the intermediate R-loop state recently observed in single-molecule experiments, as well as the associated conversion rates. Finally, we show that our quantitative activity predictor can be reduced to a binary off-target classifier that outperforms the established state-of-the-art. Our approach is extensible, and can characterize any CRISPR-Cas nuclease - benchmarking natural and future high-fidelity variants against SpCas9; elucidating determinants of CRISPR fidelity; and revealing pathways to increased specificity and efficiency in engineered systems.
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Affiliation(s)
- Behrouz Eslami-Mossallam
- Kavli Institute of NanoScience and Department of BionanoScience, Delft University of Technology, Delft, 2629HZ, the Netherlands
- Dept. Building Physics and Systems, TNO Building and Construction Research, Leeghwaterstraat 44, Delft, The Netherlands
| | - Misha Klein
- Kavli Institute of NanoScience and Department of BionanoScience, Delft University of Technology, Delft, 2629HZ, the Netherlands
- Department of Physics and Astronomy, and LaserLaB Amsterdam, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, the Netherlands
| | - Constantijn V D Smagt
- Kavli Institute of NanoScience and Department of BionanoScience, Delft University of Technology, Delft, 2629HZ, the Netherlands
- Department of Physics and Astronomy, and LaserLaB Amsterdam, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, the Netherlands
| | - Koen V D Sanden
- Kavli Institute of NanoScience and Department of BionanoScience, Delft University of Technology, Delft, 2629HZ, the Netherlands
| | - Stephen K Jones
- Department of Molecular Biosciences, University of Texas at Austin, Austin, TX, 78712, USA
- Institute for Cellular and Molecular Biology, University of Texas at Austin, Austin, TX, 78712, USA
- Center for Systems and Synthetic Biology, University of Texas at Austin, Austin, TX, 78712, USA
- VU LSC-EMBL Partnership for Genome Editing Technologies, Life Sciences Center, Vilnius University, Vilnius, Lithuania
| | - John A Hawkins
- Department of Molecular Biosciences, University of Texas at Austin, Austin, TX, 78712, USA
- Institute for Cellular and Molecular Biology, University of Texas at Austin, Austin, TX, 78712, USA
- Center for Systems and Synthetic Biology, University of Texas at Austin, Austin, TX, 78712, USA
- Oden Institute for Computational Engineering and Science, University of Texas at Austin, Austin, TX, 78712, USA
- European Molecular Biology Laboratory, Genome Biology Department, Heidelberg, Germany
| | - Ilya J Finkelstein
- Department of Molecular Biosciences, University of Texas at Austin, Austin, TX, 78712, USA
- Institute for Cellular and Molecular Biology, University of Texas at Austin, Austin, TX, 78712, USA
- Center for Systems and Synthetic Biology, University of Texas at Austin, Austin, TX, 78712, USA
| | - Martin Depken
- Kavli Institute of NanoScience and Department of BionanoScience, Delft University of Technology, Delft, 2629HZ, the Netherlands.
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Klein M, Eslami-Mossallam B, Arroyo DG, Depken M. Hybridization Kinetics Explains CRISPR-Cas Off-Targeting Rules. Cell Rep 2019; 22:1413-1423. [PMID: 29425498 DOI: 10.1016/j.celrep.2018.01.045] [Citation(s) in RCA: 72] [Impact Index Per Article: 14.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Revised: 12/07/2017] [Accepted: 01/17/2018] [Indexed: 12/26/2022] Open
Abstract
Due to their specificity, efficiency, and ease of programming, CRISPR-associated nucleases are popular tools for genome editing. On the genomic scale, these nucleases still show considerable off-target activity though, posing a serious obstacle to the development of therapies. Off targeting is often minimized by choosing especially high-specificity guide sequences, based on algorithms that codify empirically determined off-targeting rules. A lack of mechanistic understanding of these rules has so far necessitated their ad hoc implementation, likely contributing to the limited precision of present algorithms. To understand the targeting rules, we kinetically model the physics of guide-target hybrid formation. Using only four parameters, our model elucidates the kinetic origin of the experimentally observed off-targeting rules, thereby rationalizing the results from both binding and cleavage assays. We favorably compare our model to published data from CRISPR-Cas9, CRISPR-Cpf1, CRISPR-Cascade, as well as the human Argonaute 2 system.
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Affiliation(s)
- Misha Klein
- Kavli Institute of NanoScience and Department of BioNanoScience, Delft University of Technology, Delft 2629HZ, the Netherlands
| | - Behrouz Eslami-Mossallam
- Kavli Institute of NanoScience and Department of BioNanoScience, Delft University of Technology, Delft 2629HZ, the Netherlands
| | - Dylan Gonzalez Arroyo
- Kavli Institute of NanoScience and Department of BioNanoScience, Delft University of Technology, Delft 2629HZ, the Netherlands
| | - Martin Depken
- Kavli Institute of NanoScience and Department of BioNanoScience, Delft University of Technology, Delft 2629HZ, the Netherlands.
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4
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Janissen R, Arens MMA, Vtyurina NN, Rivai Z, Sunday ND, Eslami-Mossallam B, Gritsenko AA, Laan L, de Ridder D, Artsimovitch I, Dekker NH, Abbondanzieri EA, Meyer AS. Global DNA Compaction in Stationary-Phase Bacteria Does Not Affect Transcription. Cell 2018; 174:1188-1199.e14. [PMID: 30057118 DOI: 10.1016/j.cell.2018.06.049] [Citation(s) in RCA: 61] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2017] [Revised: 03/14/2018] [Accepted: 06/26/2018] [Indexed: 11/18/2022]
Abstract
In stationary-phase Escherichia coli, Dps (DNA-binding protein from starved cells) is the most abundant protein component of the nucleoid. Dps compacts DNA into a dense complex and protects it from damage. Dps has also been proposed to act as a global regulator of transcription. Here, we directly examine the impact of Dps-induced compaction of DNA on the activity of RNA polymerase (RNAP). Strikingly, deleting the dps gene decompacted the nucleoid but did not significantly alter the transcriptome and only mildly altered the proteome during stationary phase. Complementary in vitro assays demonstrated that Dps blocks restriction endonucleases but not RNAP from binding DNA. Single-molecule assays demonstrated that Dps dynamically condenses DNA around elongating RNAP without impeding its progress. We conclude that Dps forms a dynamic structure that excludes some DNA-binding proteins yet allows RNAP free access to the buried genes, a behavior characteristic of phase-separated organelles.
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Affiliation(s)
- Richard Janissen
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft, South-Holland 2629HZ, the Netherlands
| | - Mathia M A Arens
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft, South-Holland 2629HZ, the Netherlands
| | - Natalia N Vtyurina
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft, South-Holland 2629HZ, the Netherlands
| | - Zaïda Rivai
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft, South-Holland 2629HZ, the Netherlands
| | - Nicholas D Sunday
- Department of Microbiology and the Center for RNA Biology, The Ohio State University, Columbus, OH 43210, USA
| | - Behrouz Eslami-Mossallam
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft, South-Holland 2629HZ, the Netherlands
| | - Alexey A Gritsenko
- Department of Intelligent Systems, Delft University of Technology, Delft, South-Holland 2628CD, the Netherlands
| | - Liedewij Laan
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft, South-Holland 2629HZ, the Netherlands
| | - Dick de Ridder
- Department of Intelligent Systems, Delft University of Technology, Delft, South-Holland 2628CD, the Netherlands; Bioinformatics Group, Wageningen University, Wageningen, Gelderland 6700AP, the Netherlands
| | - Irina Artsimovitch
- Department of Microbiology and the Center for RNA Biology, The Ohio State University, Columbus, OH 43210, USA
| | - Nynke H Dekker
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft, South-Holland 2629HZ, the Netherlands.
| | - Elio A Abbondanzieri
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft, South-Holland 2629HZ, the Netherlands.
| | - Anne S Meyer
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft, South-Holland 2629HZ, the Netherlands.
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Abstract
About three quarters of our DNA is wrapped into nucleosomes: DNA spools with a protein core. It is well known that the affinity of a given DNA stretch to be incorporated into a nucleosome depends on the geometry and elasticity of the basepair sequence involved, causing the positioning of nucleosomes. Here we show that DNA elasticity can have a much deeper effect on nucleosomes than just their positioning: it affects their "identities". Employing a recently developed computational algorithm, the mutation Monte Carlo method, we design nucleosomes with surprising physical characteristics. Unlike any other nucleosomes studied so far, these nucleosomes are short-lived when put under mechanical tension whereas other physical properties are largely unaffected. This suggests that the nucleosome, the most abundant DNA-protein complex in our cells, might more properly be considered a class of complexes with a wide array of physical properties, and raises the possibility that evolution has shaped various nucleosome species according to their genomic context.
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Affiliation(s)
- M Tompitak
- Instituut-Lorentz for Theoretical Physics, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| | - L de Bruin
- Section de Mathématiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - B Eslami-Mossallam
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands
| | - H Schiessel
- Instituut-Lorentz for Theoretical Physics, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
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Salari H, Eslami-Mossallam B, Ranjbar HF, Ejtehadi MR. Stiffer double-stranded DNA in two-dimensional confinement due to bending anisotropy. Phys Rev E 2017; 94:062407. [PMID: 28085439 DOI: 10.1103/physreve.94.062407] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2016] [Indexed: 11/07/2022]
Abstract
Using analytical approach and Monte Carlo (MC) simulations, we study the elastic behavior of the intrinsically twisted elastic ribbons with bending anisotropy, such as double-stranded DNA (dsDNA), in two-dimensional (2D) confinement. We show that, due to the bending anisotropy, the persistence length of dsDNA in 2D conformations is always greater than three-dimensional (3D) conformations. This result is in consistence with the measured values for DNA persistence length in 2D and 3D in equal biological conditions. We also show that in two dimensions, an anisotropic, intrinsically twisted polymer exhibits an implicit twist-bend coupling, which leads to the transient curvature increasing with a half helical turn periodicity along the bent polymer.
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Affiliation(s)
- H Salari
- Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
| | - B Eslami-Mossallam
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, the Netherlands
| | - H F Ranjbar
- Institute of Complex Systems (ICS-2), Forschungszentrum Jülich, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
| | - M R Ejtehadi
- Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran and School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
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7
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Abstract
Experimental data of the DNA cyclization (J-factor) at short length scales exceed the theoretical expectation based on the wormlike chain (WLC) model by several orders of magnitude. Here, we propose that asymmetric bending rigidity of the double helix in the groove direction can be responsible for extreme bendability of DNA at short length scales and it also facilitates DNA loop formation at these lengths. To account for the bending asymmetry, we consider the asymmetric elastic rod (AER) model which has been introduced and parametrized in an earlier study [B. Eslami-Mossallam and M. R. Ejtehadi, Phys. Rev. E 80, 011919 (2009)]. Exploiting a coarse grained representation of the DNA molecule at base pair (bp) level and using the Monte Carlo simulation method in combination with the umbrella sampling technique, we calculate the loop formation probability of DNA in the AER model. We show that the DNA molecule has a larger J-factor compared to the WLC model which is in excellent agreement with recent experimental data.
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Affiliation(s)
- H Salari
- Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
| | - B Eslami-Mossallam
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands
| | - S Naderi
- Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
| | - M R Ejtehadi
- Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
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8
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Eslami-Mossallam B, Schiessel H, van Noort J. Nucleosome dynamics: Sequence matters. Adv Colloid Interface Sci 2016; 232:101-113. [PMID: 26896338 DOI: 10.1016/j.cis.2016.01.007] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2015] [Revised: 01/22/2016] [Accepted: 01/25/2016] [Indexed: 02/06/2023]
Abstract
About three quarter of all eukaryotic DNA is wrapped around protein cylinders, forming nucleosomes. Even though the histone proteins that make up the core of nucleosomes are highly conserved in evolution, nucleosomes can be very different from each other due to posttranslational modifications of the histones. Another crucial factor in making nucleosomes unique has so far been underappreciated: the sequence of their DNA. This review provides an overview of the experimental and theoretical progress that increasingly points to the importance of the nucleosomal base pair sequence. Specifically, we discuss the role of the underlying base pair sequence in nucleosome positioning, sliding, breathing, force-induced unwrapping, dissociation and partial assembly and also how the sequence can influence higher-order structures. A new view emerges: the physical properties of nucleosomes, especially their dynamical properties, are determined to a large extent by the mechanical properties of their DNA, which in turn depends on DNA sequence.
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9
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Abstract
Nucleosomes, DNA spools with a protein core, engage about three-quarters of eukaryotic DNA and play a critical role in chromosomal processes, ranging from gene regulation, recombination, and replication to chromosome condensation. For more than a decade, micromanipulation experiments where nucleosomes are put under tension, as well as the theoretical interpretations of these experiments, have deepened our understanding of the stability and dynamics of nucleosomes. Here we give a theoretical explanation for a surprising new experimental finding: nucleosomes wrapped onto the 601 positioning sequence (the sequence used in most laboratories) respond highly asymmetrically to external forces by always unwrapping from the same end. Using a computational nucleosome model, we show that this asymmetry can be explained by differences in the DNA mechanics of two very short stretches on the wrapped DNA portion. Our finding suggests that the physical properties of nucleosomes, here the response to forces, can be tuned locally by the choice of the underlying base-pair sequence. This leads to a new view of nucleosomes: a physically highly varied set of DNA-protein complexes whose properties can be tuned on evolutionary time scales to their specific function in the genomic context.
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Affiliation(s)
- Lennart de Bruin
- Institute Lorentz for Theoretical Physics, Leiden University , Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
| | - Marco Tompitak
- Institute Lorentz for Theoretical Physics, Leiden University , Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
| | - Behrouz Eslami-Mossallam
- Institute Lorentz for Theoretical Physics, Leiden University , Niels Bohrweg 2, 2333 CA Leiden, The Netherlands.,Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology , Lorentzweg 1, 2628 CJ Delft, The Netherlands
| | - Helmut Schiessel
- Institute Lorentz for Theoretical Physics, Leiden University , Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
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10
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Abstract
We study the conformations of a semiflexible chain, confined in nano-scaled spherical cavities, under two distinct processes of confinement. Radial contraction and packaging are employed as two confining procedures. The former method is performed by gradually decreasing the diameter of a spherical shell which envelopes a confined chain. The latter procedure is carried out by injecting the chain inside a spherical shell through a hole on the shell surface. The chain is modeled with a rigid body molecular dynamics simulation and its parameters are adjusted to DNA base-pair elasticity. Directional order parameter is employed to analyze and compare the confined chain and the conformations of the chain for two different sizes of the spheres are studied in both procedures. It is shown that for the confined chains in the sphere sizes of our study, they appear in spiral or tennis-ball structures, and the tennis-ball structure is more likely to be observed in more compact confinements. Our results also show that the dynamical procedure of confinement and the rate of the confinement are influential parameters of the structure of the chain inside spherical cavities.
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Affiliation(s)
- A Fathizadeh
- Sharif University of Technology, Institute for Nanoscience and Nanotechnology, P.O. Box 14588-89694, Tehran, Iran
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Fathizadeh A, Eslami-Mossallam B, Ejtehadi MR. Definition of the persistence length in the coarse-grained models of DNA elasticity. Phys Rev E Stat Nonlin Soft Matter Phys 2012; 86:051907. [PMID: 23214814 DOI: 10.1103/physreve.86.051907] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2012] [Revised: 09/16/2012] [Indexed: 06/01/2023]
Abstract
By considering the detailed structure of DNA in the base pair level, two possible definitions of the persistence length are compared. One definition is related to the orientation of the terminal base pairs, and the other is based on the vectors which connect two adjacent base pairs at each end of the molecule. It is shown that although these definitions approach each other for long DNA molecules, they are dramatically different on short length scales. We show analytically that the difference mostly comes from the shear flexibility of the molecule and can be used to measure the shear modulus of DNA.
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Affiliation(s)
- A Fathizadeh
- Sharif University of Technology, Institue for Nanoscience and Nanotechnology, Post Office Box 14588-89694, Tehran, Iran
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12
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Abstract
A nonlocal harmonic elastic rod model is proposed to describe the elastic behavior of short DNA molecules. We show that the nonlocal interactions contribute to effective bending energy of the molecule and affect its apparent persistence length. It is also shown that the anomalous behavior which has been observed in all-atom molecular dynamic simulations [A. K. Mazur, Biophys. J. 134, 4507 (2006)] can be a consequence of both nonlocal interactions between DNA base pairs and the intrinsic curvature of DNA.
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Affiliation(s)
- B Eslami-Mossallam
- Department of Physics, Sharif University of Technology, P.O. Box 11365-8639, Tehran, Iran
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Eslami-Mossallam B, Ejtehadi MR. Asymmetric elastic rod model for DNA. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 80:011919. [PMID: 19658741 DOI: 10.1103/physreve.80.011919] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2008] [Revised: 06/02/2009] [Indexed: 05/28/2023]
Abstract
In this paper we consider the anharmonic corrections to the anisotropic elastic rod model for DNA. Our model accounts for the difference between the bending energies of positive and negative rolls, which comes from the asymmetric structure of the DNA molecule. We will show that the model can explain the high flexibility of DNA at small length scales, as well as kink formation at high deformation limit.
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Affiliation(s)
- B Eslami-Mossallam
- Department of Physics, Sharif University of Technology, P.O. Box 11365-8639, 14588-89694 Tehran, Iran
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