1
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Morrison G, Thirumalai D. Scaling regimes for wormlike chains confined to cylindrical surfaces under tension. Eur Phys J E Soft Matter 2024; 47:6. [PMID: 38252375 DOI: 10.1140/epje/s10189-023-00384-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2023] [Accepted: 11/20/2023] [Indexed: 01/23/2024]
Abstract
We compute the free energy of confinement [Formula: see text] for a wormlike chain (WLC), with persistence length [Formula: see text], that is confined to the surface of a cylinder of radius R under an external tension f using a mean field variational approach. For long chains, we analytically determine the behavior of the chain in a variety of regimes, which are demarcated by the interplay of [Formula: see text], the Odijk deflection length ([Formula: see text]), and the Pincus length ([Formula: see text], with [Formula: see text] being the thermal energy). The theory accurately reproduces the Odijk scaling for strongly confined chains at [Formula: see text], with [Formula: see text]. For moderate values of f, the Odijk scaling is discernible only when [Formula: see text] for strongly confined chains. Confinement does not significantly alter the scaling of the mean extension for sufficiently high tension. The theory is used to estimate unwrapping forces for DNA from nucleosomes.
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Affiliation(s)
- Greg Morrison
- Department of Physics, University of Houston, Houston, TX, 77204, USA
- Center for Theoretical Biological Physics, Rice University, Houston, TX, 77005, USA
| | - D Thirumalai
- Departments of Chemistry, The University of Texas at Austin, Austin, TX, 78712, USA.
- Department of Physics, The University of Texas at Austin, Austin, TX, 78712, USA.
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2
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Locatelli E, Bianco V, Valeriani C, Malgaretti P. Nonmonotonous Translocation Time of Polymers across Pores. Phys Rev Lett 2023; 131:048101. [PMID: 37566871 DOI: 10.1103/physrevlett.131.048101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Accepted: 07/06/2023] [Indexed: 08/13/2023]
Abstract
Polymers confined in corrugated channels, i.e., channels of varying amplitude, display multiple local maxima and minima of the diffusion coefficient upon increasing their degree of polymerization N. We propose a theoretical effective free energy for linear polymers based on a Fick-Jacobs approach. We validate the predictions against numerical data, obtaining quantitative agreement for the effective free energy, the diffusion coefficient, and the mean first passage time. Finally, we employ the effective free energy to compute the polymer lengths N_{min} at which the diffusion coefficient presents a minimum: we find a scaling expression that we rationalize with a blob model. Our results could be useful to design porous adsorbers, that separate polymers of different sizes without the action of an external flow.
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Affiliation(s)
- Emanuele Locatelli
- Dipartimento di Fisica e Astronomia, Università di Padova, via Marzolo 8, I-35131 Padova, Italy
- INFN, Sezione di Padova, via Marzolo 8, I-35131 Padova, Italy
| | - Valentino Bianco
- Faculty of Chemistry, Chemical Physics Department, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Chantal Valeriani
- Departamento de Estructura de la Materia, Física Termica y Electronica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Paolo Malgaretti
- Helmholtz Institut Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Cauer Strasse 1, 91058, Erlangen, Germany
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3
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Milchev A, Binder K. Adsorption of Semiflexible Polymers in Cylindrical Tubes. Langmuir 2021; 37:11759-11770. [PMID: 34581575 DOI: 10.1021/acs.langmuir.1c01715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Conformations of wormlike chains in cylindrical pores with attractive walls are explored for varying pore radius and strength of the attractive wall potential by molecular dynamics simulations of a coarse-grained model. Local quantities such as the fraction of monomeric units bound to the surface and the bond-orientational order parameter as well as the radial density distribution are studied, as well as the global chain extensions parallel to the cylinder axis and perpendicular to the cylinder surface. A nonmonotonic convergence of these properties to their counterparts for adsorption on a planar substrate is observed due to the conflict between pore surface curvature and chain stiffness. Also the interpretation of partially adsorbed chains in terms of trains, loops, and tails is discussed.
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Affiliation(s)
- A Milchev
- Institute of Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
| | - K Binder
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
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4
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Milchev A, Binder K. Cylindrical confinement of solutions containing semiflexible macromolecules: surface-induced nematic order versus phase separation. Soft Matter 2021; 17:3443-3454. [PMID: 33646224 DOI: 10.1039/d1sm00172h] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a phase separated structure with cylindrical symmetry occurs, with the isotropic phase located around the cylinder axis. For melt densities the mixed nematic phase forms at the wall a layer with a screw-like structure of a tilted smectic phase. The observed behavior is tentatively interpreted in terms of the competition of the chain orientational entropy with entropy of mixing and excluded volume due to the wall.
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Affiliation(s)
- Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113, Sofia, Bulgaria.
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5
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Abstract
When compressed in a slit of width D, a Θ-chain that displays the scaling of size R0 (diameter) with respect to the number of monomers N, R0 ∼ aN1/2, expands in the lateral direction as R|| ∼ aNν(a/D)2ν-1. Provided that the Θ condition is strictly maintained throughout the compression, the well-known scaling exponent of Θ-chain in two dimensions, ν = 4/7, is anticipated in a perfect confinement. However, numerics shows that upon increasing compression from R0/D < 1 to R0/D ≫ 1, ν gradually deviates from ν = 1/2 and plateaus at ν = 3/4, the exponent associated with the self-avoiding walk in two dimensions. Using both theoretical considerations and numerics, we argue that it is highly nontrivial to maintain the Θ condition under confinement because of two major effects. First, as the dimension is reduced from three to two dimensions, the contributions of higher order virial terms, which can be ignored in three dimensions at large N, become significant, making the perturbative expansion used in Flory-type approach inherently problematic. Second and more importantly, the geometrical confinement, which is regarded as an applied external field, alters the second virial coefficient (B2) changes from B2 = 0 (Θ condition) in free space to B2 > 0 (good-solvent condition) in confinement. Our study provides practical insight into how confinement affects the conformation of a single polymer chain.
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Affiliation(s)
- Lei Liu
- Korea Institute for Advanced Study , Seoul 02455 , Korea
| | - Philip A Pincus
- Physics and Material Department , University of California , Santa Barbara , California 93106 , United States
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6
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Abstract
In synthetic chemistry and biological or biomimetic systems, polymers are often grown in cavities. Polymerizations in microemulsions, biopolymers grown in cells, or in vesicles containing artificial organelles have an influence on the shape of liquid boundaries. We consider confined grand-canonical polymers to address equilibrium properties of annealed polymers. We calculate the concentration profiles established by annealed (star-) polymers inside a confining cavity. Our emphasis is on the description of pressure fields derived from the contact theorem. We further show how the pressure field exerted by a localized annealed polymer (or pair of polymers) deforms the confining vesicle/ microemulsions droplet.
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Affiliation(s)
- Nam-Kyung Lee
- Department of Physics and Astronomy, Sejong University, Seoul 05006, South Korea
| | - Albert Johner
- Institute Charles Sadron, CNRS, 23 Rue du Loess, 67034 Strasbourg Cedex 2, France
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7
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Haldar S, Tapia-Rojo R, Eckels EC, Valle-Orero J, Fernandez JM. Trigger factor chaperone acts as a mechanical foldase. Nat Commun 2017; 8:668. [PMID: 28939815 DOI: 10.1038/s41467-017-00771-6] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2017] [Accepted: 07/26/2017] [Indexed: 01/28/2023] Open
Abstract
Proteins fold under mechanical forces in a number of biological processes, ranging from muscle contraction to co-translational folding. As force hinders the folding transition, chaperones must play a role in this scenario, although their influence on protein folding under force has not been directly monitored yet. Here, we introduce single-molecule magnetic tweezers to study the folding dynamics of protein L in presence of the prototypical molecular chaperone trigger factor over the range of physiological forces (4–10 pN). Our results show that trigger factor increases prominently the probability of folding against force and accelerates the refolding kinetics. Moreover, we find that trigger factor catalyzes the folding reaction in a force-dependent manner; as the force increases, higher concentrations of trigger factor are needed to rescue folding. We propose that chaperones such as trigger factor can work as foldases under force, a mechanism which could be of relevance for several physiological processes. Proteins fold under mechanical force during co-translational folding at the ribosome. Here, the authors use single molecule magnetic tweezers to study the influence of chaperones on protein folding and show that the ribosomal chaperone trigger factor acts as a mechanical foldase by promoting protein folding under force.
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8
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Irianto J, Xia Y, Pfeifer CR, Greenberg RA, Discher DE. As a Nucleus Enters a Small Pore, Chromatin Stretches and Maintains Integrity, Even with DNA Breaks. Biophys J 2016; 112:446-449. [PMID: 28341535 DOI: 10.1016/j.bpj.2016.09.047] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2016] [Revised: 09/17/2016] [Accepted: 09/30/2016] [Indexed: 10/20/2022] Open
Abstract
As a cell pushes or pulls its nucleus through a small constriction, the chromatin must distort and somehow maintain genomic stability despite ever-present double-strand breaks in the DNA. Here we visualize within a living cell the pore-size dependent deformation of a specific locus engineered into chromosome-1 and cleaved. An mCherry-tagged nuclease targets the submicron locus, causing DNA cleavage and recruiting repair factors such as GFP-53BP1 to a large region around the locus. Aspiration of a cell and its nucleus into a micropipette shows that chromatin aligns and stretches parallel to the pore. Extension is largest in small pores, increasing >10-fold but remaining 30-fold shorter than the DNA contour length in the locus. Brochard and de Gennes' blob model for tube geometry fits the data, with a simple modification for chromatin crowding. Continuity of the highly extended, cleaved chromatin is also maintained, consistent with folding and cross bridging of the DNA. Surprisingly, extensional integrity is unaffected by an inhibitor of the DNA repair scaffold.
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Affiliation(s)
- Jerome Irianto
- Physical Sciences Oncology Center at Penn, University of Pennsylvania, Philadelphia, Pennsylvania; Molecular & Cell Biophysics Lab, University of Pennsylvania, Philadelphia, Pennsylvania
| | - Yuntao Xia
- Physical Sciences Oncology Center at Penn, University of Pennsylvania, Philadelphia, Pennsylvania; Molecular & Cell Biophysics Lab, University of Pennsylvania, Philadelphia, Pennsylvania
| | - Charlotte R Pfeifer
- Physical Sciences Oncology Center at Penn, University of Pennsylvania, Philadelphia, Pennsylvania; Molecular & Cell Biophysics Lab, University of Pennsylvania, Philadelphia, Pennsylvania; Graduate Group/Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania
| | - Roger A Greenberg
- Physical Sciences Oncology Center at Penn, University of Pennsylvania, Philadelphia, Pennsylvania; Cancer Biology, Abramson Family Cancer Research Institute, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania
| | - Dennis E Discher
- Physical Sciences Oncology Center at Penn, University of Pennsylvania, Philadelphia, Pennsylvania; Molecular & Cell Biophysics Lab, University of Pennsylvania, Philadelphia, Pennsylvania; Graduate Group/Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania.
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9
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Huang A, Hsu HP, Bhattacharya A, Binder K. Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles. J Chem Phys 2016; 143:243102. [PMID: 26723587 DOI: 10.1063/1.4929600] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymers, while the second model (roughly) describes synthetic polymers like alkane chains. It is first demonstrated that in the bulk the crossover from rods to self-avoiding walks for both models is very similar, when one studies average chain linear dimensions, transverse fluctuations, etc., despite their differences in local conformations. However, in quasi-one-dimensional confinement two significant differences between both models occur: (i) The persistence length (extracted from the average cosine of the bond angle) gets renormalized for the lattice model when D gets less than the bulk persistence length, while in the continuum model it stays unchanged. (ii) The monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model in the case of the bead-spring model, while for the lattice case it tends to a nonzero constant across the strip. However, for the density of chain ends, such a constant behavior seems to occur for both models, unlike the power law observed for flexible polymers. In the regime where the bulk persistence length ℓp is comparable to D, hairpin conformations are detected, and the chain linear dimensions are discussed in terms of a crossover from the Daoud/De Gennes "string of blobs"-picture to the flexible rod picture when D decreases and/or the chain stiffness increases. Introducing a suitable further coarse-graining of the chain contours of the continuum model, direct estimates for the deflection length and its distribution could be obtained.
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Affiliation(s)
- Aiqun Huang
- Department of Physics, University of Central Florida, Orlando, Florida 32816-2385, USA
| | - Hsiao-Ping Hsu
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
| | - Aniket Bhattacharya
- Department of Physics, University of Central Florida, Orlando, Florida 32816-2385, USA
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
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10
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Abstract
We present a numerical study of polyelectrolytes electrophoresing in free solution while squeezed by an axisymmetric confinement force transverse to their net displacement. Hybrid multiparticle collision dynamics and molecular dynamics simulations with mean-field finite Debye layers show that even though the polyelectrolyte chains remain "free-draining" their electrophoretic mobility increases with confinement in nanoconfining potential wells. The primary mechanism leading to the increase in mobility above the free-solution value, despite long-range hydrodynamic screening by counterion layers, is the orientation of polymer segments within Debye layers. The observed length dependence of the electrophoretic mobility arises due to secondary effects of counterion condensation related to confinement compactification.
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Affiliation(s)
- Tyler N. Shendruk
- The
Rudolf Peierls Centre for Theoretical Physics, Department of Physics,
Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
| | - Martin Bertrand
- Department
of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario K1N 6N5, Canada
| | - Gary W. Slater
- Department
of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario K1N 6N5, Canada
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11
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Abstract
How confinement or a physical constraint modifies polymer chains is not only a classical problem in polymer physics but also relevant in a variety of contexts such as single-molecule manipulations, nanofabrication in narrow pores, and modelling of chromosome organization. Here, we review recent progress in our understanding of polymers in a confined (and crowded) space. To this end, we highlight converging views of these systems from computational, experimental, and theoretical approaches, and then clarify what remains to be clarified. In particular, we focus on exploring how cylindrical confinement reshapes individual chains and induces segregation forces between them - by pointing to the relationships between intra-chain organization and chain segregation. In the presence of crowders, chain molecules can be entropically phase-separated into a condensed state. We include a kernel of discussions on the nature of chain compaction by crowders, especially in a confined space. Finally, we discuss the relevance of confined polymers for the nucleoid, an intracellular space in which the bacterial chromosome is tightly packed, in part by cytoplasmic crowders.
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Affiliation(s)
- Bae-Yeun Ha
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
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12
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Abstract
We show that the problem of describing the conformations of a semiflexible polymer confined to a channel can be mapped onto an exactly solvable model in the so-called extended de Gennes regime. This regime (where the polymer is neither weakly nor strongly confined) has recently been intensively studied experimentally and by means of computer simulations. The exact solution predicts precisely how the conformational fluctuations depend upon the channel width and upon the microscopic parameters characterizing the physical properties of the polymer.
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Affiliation(s)
- E Werner
- Department of Physics, University of Gothenburg, SE-40530 Gothenburg, Sweden
| | - B Mehlig
- Department of Physics, University of Gothenburg, SE-40530 Gothenburg, Sweden
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13
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Benková Z, Cifra P. Comparison of linear and ring DNA macromolecules moderately and strongly confined in nanochannels. Biochem Soc Trans 2013; 41:625-9. [DOI: 10.1042/bst20120279] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Understanding the mechanism of DNA extension in nanochannels is necessary for interpretation of experiments in nanofluidic channel devices that have been conducted recently with both linear and ring chains. The present article reviews the situation with linear chains and analyses the experimental results and simulations for channel-induced extension (linearization) of ring chains. Results for confined rings indicate a transition between moderate and strong confinement similar to that of linear chains. Owing to stronger self-avoidance in confined rings, the transition and chain extension is shifted relative to linear DNA. We suggest that a relationship similar to that used for the extension of linear chains may also be used for circular DNA.
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15
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Fu CL, Sun ZY, An LJ. The properties of a single polymer chain in solvent confined in a slit: A molecular dynamics simulation. Chin J Polym Sci 2012. [DOI: 10.1007/s10118-013-1231-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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16
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Abstract
DNA is the central storage molecule of genetic information in the cell, and reading that information is a central problem in biology. While sequencing technology has made enormous advances over the past decade, there is growing interest in platforms that can readout genetic information directly from long single DNA molecules, with the ultimate goal of single-cell, single-genome analysis. Such a capability would obviate the need for ensemble averaging over heterogeneous cellular populations and eliminate uncertainties introduced by cloning and molecular amplification steps (thus enabling direct assessment of the genome in its native state). In this review, we will discuss how the information contained in genomic-length single DNA molecules can be accessed via physical confinement in nanochannels. Due to self-avoidance interactions, DNA molecules will stretch out when confined in nanochannels, creating a linear unscrolling of the genome along the channel for analysis. We will first review the fundamental physics of DNA nanochannel confinement--including the effect of varying ionic strength--and then discuss recent applications of these systems to genomic mapping. Apart from the intense biological interest in extracting linear sequence information from elongated DNA molecules, from a physics view these systems are fascinating as they enable probing of single-molecule conformation in environments with dimensions that intersect key physical length-scales in the 1 nm to 100 µm range.
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Affiliation(s)
- Walter Reisner
- Physics Department, McGill University, Montreal QC, Canada.
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17
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Abstract
The confinement of a polymer into a small space is thermodynamically unfavorable because of the reduction in the number of conformational states. The entropic penalty affects a variety of biological processes, and it plays an important role in polymer transport properties and in microfluidic devices. We determine the entropic penalty for the confinement of elastic polymer of persistence length P in the long-chain limit. We examine three geometries: (1) parallel planes separated by a distance d (a slit); (2) a circular tube of diameter d; and (3) a sphere of diameter d. We first consider infinitely thin (ideal) chains. As d/P drops from 100 to 0.01, TΔS rises from ∼5 × 10(-4) kT to ∼30 kT per persistence length for cases (1) and (2), with the entropic penalty for case (2) being consistently about twice that for case (1). TΔS is ∼5 kT per persistence length for confinement to a sphere when d = P, about twice the value predicted by mean field theory. For all three geometries, in the limit d/P ≫ 1, the asymptotic behavior of ΔS vs d is consistent with the d(-2) behavior predicted by theory. In the limit d/P ≪ 1, the scaling of ΔS for slits and tubes is also consistent with earlier predictions (d(-2/3)). Finally, we treat volume exclusion effects, examining chains of diameter D > 0. Confinement to a narrow slit or tube (d/P ≪ 1) has the same entropic penalty as that for an ideal chain in a slit or tube with d' = d - D; in the weak confinement regime (d/P ≫ 1), the entropic penalties are significantly larger than those for infinitely thin chains. When a chain of finite diameter is forced into a sphere or other closed cavity, the entropic confinement penalty rises without limit because there are no configurations available to the chain once its volume exceeds that of the cavity.
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Affiliation(s)
- Mark R Smyda
- School of Biology, Georgia Institute of Technology, Atlanta Georgia 30332, United States
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18
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19
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Affiliation(s)
- Rong Wang
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger
Weg 7, D-55099 Mainz, Germany
- Department of Polymer Science
and Engineering, State Key Laboratory of Coordination Chemistry, Nanjing
National Laboratory of Microstructures, School of Chemistry and Chemical
Engineering, Nanjing University, Nanjing
210093, China
| | - Sergei A. Egorov
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger
Weg 7, D-55099 Mainz, Germany
- Department
of Chemistry, University of Virginia, Charlottesville,
Virginia 22901,
United States
| | - Andrey Milchev
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger
Weg 7, D-55099 Mainz, Germany
- Institute
of Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger
Weg 7, D-55099 Mainz, Germany
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20
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Chaudhuri D, Mulder B. Size and shape of excluded volume polymers confined between parallel plates. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 83:031803. [PMID: 21517518 DOI: 10.1103/physreve.83.031803] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2010] [Revised: 11/01/2010] [Indexed: 05/30/2023]
Abstract
A number of recent experiments have provided detailed observations of the configurations of long DNA strands under nano-to-micrometer-sized confinement. We therefore revisit the problem of an excluded volume polymer chain confined between two parallel plates with varying plate separation. We show that the nonmonotonic behavior of the overall size of the chain as a function of plate separation, seen in computer simulations and reproduced by earlier theories, can already be predicted on the basis of scaling arguments. However, the behavior of the size in a plane parallel to the plates, a quantity observed in recent experiments, is predicted to be monotonic, in contrast to the experimental findings. We analyze this problem in depth with a mean-field approach that maps the confined polymer onto an anisotropic Gaussian chain, which allows the size of the polymer to be determined separately in the confined and unconfined directions. The theory allows the analytical construction of a smooth crossover between the small-plate-separation de Gennes regime and the large-plate-separation Flory regime. The results show good agreement with molecular dynamics simulations in the presence of a Langevin heat bath and confirm the scaling predictions.
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Affiliation(s)
- Debasish Chaudhuri
- FOM Institute AMOLF, Science Park 104, NL-1098XG Amsterdam, The Netherlands.
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22
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Abstract
The effect of confinement on the stability and dynamics of peptides and proteins is relevant in the context of a number of problems in biology and biotechnology. We have examined the stability of different helix-forming sequences upon confinement to a carbon nanotube using Langevin dynamics simulations of a coarse-grained representation of the polypeptide chain. We show that the interplay of several factors that include sequence, solvent conditions, strength (lambda) of nanotube-peptide interactions, and the nanotube diameter (D) determines confinement-induced stability of helicies. In agreement with predictions based on polymer theory, the helical state is entropically stabilized for all sequences when the interaction between the peptide and the nanotube is weakly hydrophobic and D is small. However, there is a strong sequence dependence as the strength of the lambda increases. For an amphiphilic sequence, the helical stability increases with lambda, whereas for polyalanine the diagram of states is a complex function of lambda and D. In addition, decreasing the size of the "hydrophobic patch" lining the nanotube, which mimics the chemical heterogeneity of the ribosome tunnel, increases the helical stability of the polyalanine sequence. Our results provide a framework for interpreting a number of experiments involving the structure formation of peptides in the ribosome tunnel as well as transport of biopolymers through nanotubes.
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Affiliation(s)
- Edward P. O’Brien
- Biophysics Program, Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742
- Laboratory of Computational Biology, National Heart Lung and Blood Institute, National Institutes of Health, Bethesda, MD 20892
| | - George Stan
- Department of Chemistry, University of Cincinnati, Cincinnati, OH 45221
| | - D. Thirumalai
- Biophysics Program, Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742
| | - Bernard R. Brooks
- Laboratory of Computational Biology, National Heart Lung and Blood Institute, National Institutes of Health, Bethesda, MD 20892
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23
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Abstract
Force-induced deformations of a self-avoiding chain confined inside a cylindrical cavity, with diameter D, are probed using molecular dynamics simulations, scaling analysis, and analytical calculations. We obtain and confirm a simple scaling relation -fD approximately R(-9/4) in the strong-compression regime, while for weak deformations, we find fD = -A(R/R0) + B(R/R0)(-2), where A and B are constants, f the external force, and R the chain extension (with R0 its unperturbed value). For a strong stretch, we present a universal, analytical force-extension relation. Our results can be used to analyze the behavior of biomolecules in confinement.
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Affiliation(s)
- Suckjoon Jun
- FAS Center for Systems Biology, Harvard University, 7 Divinity Avenue, Cambridge, Massachusetts 02138, USA
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24
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Abstract
Biological macromolecules, living in the confines of a cell, often adopt conformations that are unlikely to occur in free space. In this paper, we investigate the effects of confinement on the shape of a semiflexible chain. Results of Monte Carlo simulations show the existence of a shape transition when the persistence length of the polymer becomes comparable to the dimensions of the box. An order parameter is introduced to quantify this behavior. A simple model is constructed to study the effect of the shape transition on the effective persistence length of the polymer.
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Affiliation(s)
- Ya Liu
- Martin Fisher School of Physics, Brandeis University, Mailstop 057, Waltham, MA 02454-9110, USA
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25
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Affiliation(s)
- Peter Cifra
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 842 36 Bratislava, Slovakia
| | - Zuzana Benková
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 842 36 Bratislava, Slovakia
| | - Tomáš Bleha
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 842 36 Bratislava, Slovakia
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Arnold A, Bozorgui B, Frenkel D, Ha BY, Jun S. Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical confinement. J Chem Phys 2007; 127:164903. [DOI: 10.1063/1.2799513] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Affiliation(s)
- Greg Morrison
- Department of Physics, University of Maryland at College Park, College Park, Maryland 20742; Biophysics Program, IPST, University of Maryland at College Park, College Park, Maryland 20742; Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, California 92093; Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; and Department of Chemistry and Biochemistry, University of Maryland at College Park, College Park, Maryland 20742
| | - Changbong Hyeon
- Department of Physics, University of Maryland at College Park, College Park, Maryland 20742; Biophysics Program, IPST, University of Maryland at College Park, College Park, Maryland 20742; Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, California 92093; Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; and Department of Chemistry and Biochemistry, University of Maryland at College Park, College Park, Maryland 20742
| | - N. M. Toan
- Department of Physics, University of Maryland at College Park, College Park, Maryland 20742; Biophysics Program, IPST, University of Maryland at College Park, College Park, Maryland 20742; Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, California 92093; Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; and Department of Chemistry and Biochemistry, University of Maryland at College Park, College Park, Maryland 20742
| | - Bae-Yeun Ha
- Department of Physics, University of Maryland at College Park, College Park, Maryland 20742; Biophysics Program, IPST, University of Maryland at College Park, College Park, Maryland 20742; Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, California 92093; Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; and Department of Chemistry and Biochemistry, University of Maryland at College Park, College Park, Maryland 20742
| | - D. Thirumalai
- Department of Physics, University of Maryland at College Park, College Park, Maryland 20742; Biophysics Program, IPST, University of Maryland at College Park, College Park, Maryland 20742; Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, California 92093; Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; and Department of Chemistry and Biochemistry, University of Maryland at College Park, College Park, Maryland 20742
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Abstract
Understanding the behavior of a polyelectrolyte in confined spaces has direct relevance in design and manipulation of microfluidic devices, as well as transport in living organisms. In this paper, a coarse-grained model of anionic semiflexible polyelectrolyte is applied, and its structure and dynamics are fully examined with Brownian dynamics (BD) simulations both in bulk solution and under confinement between two negatively charged parallel plates. The modeling is based on the nonlinear bead-spring discretization of a continuous chain with additional long-range electrostatic, Lennard-Jones, and hydrodynamic interactions between pairs of beads. The authors also consider the steric and electrostatic interactions between the bead and the confining wall. Relevant model parameters are determined from experimental rheology data on the anionic polysaccharide xanthan reported previously. For comparison, both flexible and semiflexible models are developed accompanying zero and finite intrinsic persistence lengths, respectively. The conformational changes of the polyelectrolyte chain induced by confinements and their dependence on the screening effect of the electrolyte solution are faithfully characterized with BD simulations. Depending on the intrinsic rigidity and the medium ionic strength, the polyelectrolyte can be classified as flexible, semiflexible, or rigid. Confined flexible and semiflexible chains exhibit a nonmonotonic variation in size, as measured by the radius of gyration and end-to-end distance, with changing slit width. For the semiflexible chain, this is coupled to the variations in long-range bond vector correlation. The rigid chain, realized at low ionic strength, does not have minima in size but exhibits a sigmoidal transition. The size of confined semiflexible and rigid polyelectrolytes can be well described by the wormlike chain model once the electrostatic effects are taken into account by the persistence length measured at long length scale.
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Affiliation(s)
- Jonggu Jeon
- Complex Fluids Research Laboratory, Korea Institute of Science and Technology (KIST), Seoul 136-791, Republic of Korea
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Abstract
We study the link between three seeming-disparate cases of self-avoiding polymers: strongly overlapping multiple chains in dilute solution, chains under spherical confinement, and the onset of semidilute solutions. Our main result is that the free energy for overlapping n chains is independent of chain length and scales as n9/4, slowly crossing over to n3, as n increases. For strongly confined polymers inside a spherical cavity, we show that rearranging the chains does not cost an additional free energy. Our results imply that, during cell cycle, global reorganization of eukaryotic chromosomes in a large cell nucleus could be readily achieved.
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Affiliation(s)
- Suckjoon Jun
- FOM-Institute AMOLF, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands.
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