1
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Radhakrishnan K, Singh SP. Compression of a confined semiflexible polymer under direct and oscillating fields. Phys Rev E 2023; 108:014501. [PMID: 37583203 DOI: 10.1103/physreve.108.014501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2023] [Accepted: 06/19/2023] [Indexed: 08/17/2023]
Abstract
The folding transition of biopolymers from the coil to compact structures has attracted wide research interest in the past and is well studied in polymer physics. Recent seminal works on DNA in confined devices have shown that these long biopolymers tend to collapse under an external field, which is contrary to the previously reported stretching of the chain. In this work, we capture the compression of a confined semiflexible polymer under direct and oscillating fields using a coarse-grained computer simulation model in the presence of long-range hydrodynamics. In the case of a semiflexible polymer chain, the inhomogeneous hydrodynamic drag from the center to the periphery of the coil couples with the chain bending to cause a swirling movement of the chain segments, leading to structural intertwining and compaction. Contrarily, a flexible chain of the same length lacks such structural deformation and forms a well-established tadpole structure. While bending rigidity profoundly influences the chain's folding favorability, we also found that subject to the direct field, chains in stronger confinements exhibit substantial compaction, contrary to the one in moderate confinements or bulk where such compaction is absent. However, an alternating field within an optimum frequency can effectuate this compression even in moderate or no confinement. This field-induced collapse is a quintessential hydrodynamic phenomenon, resulting in intertwined knotted structures even for shorter chains, unlike other spontaneous knotting experiments where it happens exclusively for longer chains.
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Affiliation(s)
- Keerthi Radhakrishnan
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
| | - Sunil P Singh
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
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2
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Chiarantoni P, Micheletti C. Linear Catenanes in Channel Confinement. Macromolecules 2023. [DOI: 10.1021/acs.macromol.3c00249] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
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3
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Chen J, Sun L, Wang S, Tian F, Zhu H, Zhang R, Dai L. Crowding-induced polymer trapping in a channel. Phys Rev E 2021; 104:054502. [PMID: 34942690 DOI: 10.1103/physreve.104.054502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2021] [Accepted: 10/20/2021] [Indexed: 11/07/2022]
Abstract
In this work, we report an intriguing phenomenon: crowding-induced polymer trapping in a channel. Using Langevin dynamics simulations and analytical calculations, we find that for a polymer confined in a channel, crowding particles can push a polymer into the channel corner through inducing an effective polymer-corner attraction due to the depletion effect. This phenomenon is referred to as polymer trapping. The occurrence of polymer trapping requires a minimum volume fraction of crowders, ϕ^{*}, which scales as ϕ^{*}∼(a_{c}/L_{p})^{1/3} for a_{c}≫a_{m} and ϕ^{*}∼(a_{c}/L_{p})^{1/3}(a_{c}/a_{m})^{1/2} for a_{c}≪a_{m}, where a_{c} is the crowder diameter, a_{m} is the monomer diameter, and L_{p} is the polymer persistence length. For DNA, ϕ^{*} is estimated to be around 0.25 for crowders with a_{c}=2nm. We find that ϕ^{*} also strongly depends on the shape of the channel cross section, and ϕ^{*} is much smaller for a triangle channel than a square channel. The polymer trapping leads to a nearly fully stretched polymer conformation along a channel corner, which may have practical applications, such as full stretching of DNA for the nanochannel-based genome mapping technology.
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Affiliation(s)
- Jialu Chen
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Liang Sun
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Simin Wang
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Fujia Tian
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Haoqi Zhu
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Ruiqin Zhang
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Hong Kong, China
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4
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Chen W, Wei S. Compressive deformations of ring polymers in a confining channel. POLYMER 2021. [DOI: 10.1016/j.polymer.2021.124340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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5
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Bucci G, Gadelrab K, Spakowitz AJ. Free Energy and Dynamics of Annihilation of Topological Defects in Nanoconfined DNA. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Giovanna Bucci
- Robert Bosch LLC, 384 Santa Trinita Ave, Sunnyvale, California 94085, United States
| | - Karim Gadelrab
- Robert Bosch LLC, 1 Kendall Square, Suite 7-101, Cambridge, Massachusetts 02139, United States
| | - Andrew J. Spakowitz
- Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, United States
- Department of Applied Physics, Stanford University, Stanford, California 94305, United States
- Biophysics Program, Stanford University, Stanford, California 94305, United States
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6
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Milchev A, Binder K. Adsorption of Semiflexible Polymers in Cylindrical Tubes. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 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] [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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7
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Teng Y, Andersen NT, Chen JZY. Statistical Properties of a Slit-Confined Wormlike Chain of Finite Length. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00759] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Yue Teng
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Nigel T. Andersen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Jeff Z. Y. Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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8
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Radhakrishnan K, Singh SP. Collapse of a Confined Polyelectrolyte Chain under an AC Electric Field. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00637] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Keerthi Radhakrishnan
- Department of Physics, Indian Institute of Science Education and Research Bhopal, Bhopal 462066, Madhya Pradesh, India
| | - Sunil P. Singh
- Department of Physics, Indian Institute of Science Education and Research Bhopal, Bhopal 462066, Madhya Pradesh, India
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9
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Affiliation(s)
- Peter Cifra
- Polymer Institute Slovak Academy of Sciences Bratislava 84541 Slovakia
| | - Tomáš Bleha
- Polymer Institute Slovak Academy of Sciences Bratislava 84541 Slovakia
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10
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Nikoubashman A. Ordering, phase behavior, and correlations of semiflexible polymers in confinement. J Chem Phys 2021; 154:090901. [DOI: 10.1063/5.0038052] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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11
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Basak R, Rosencrans W, Yadav I, Yan P, Berezhnoy NV, Chen Q, van Kan JA, Nordenskiöld L, Zinchenko A, van der Maarel JRC. Internal Motion of Chromatin Fibers Is Governed by Dynamics of Uncompressed Linker Strands. Biophys J 2020; 119:2326-2334. [PMID: 33121944 PMCID: PMC7732777 DOI: 10.1016/j.bpj.2020.10.018] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2020] [Revised: 09/23/2020] [Accepted: 10/13/2020] [Indexed: 11/25/2022] Open
Abstract
Chromatin compaction and internal motion are fundamental aspects of gene expression regulation. Here, we have investigated chromatin fibers comprising recombinant histone octamers reconstituted with double-stranded bacteriophage T4-DNA. The size of the fibers approaches the typical size of genomic topologically associated domains. Atomic force and fluorescence (correlation) microscopy have been used to assess the structural organization, histone-induced compaction, and internal motion. In particular, the fibers are stretched on arrays of nanochannels, each channel with a diameter of 60 or 125 nm. Major intrafiber segregation and fast internal fluctuations are observed. Full compaction was only achieved by triggering an attractive nucleosome interaction through the addition of magnesium cations. Besides compaction, histone complexation results in a dramatic decrease in the fiber's relaxation time. The relaxation times are similar to those of naked DNA with a comparable stretch, which indicates that internal motion is governed by the dynamics of uncompressed linker strands. Furthermore, the main reorganization process is association-dissociation of individually compacted regions. We surmise that the modulation of chromatin's internal motion by histone complexation might have implications for transcriptional bursting.
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Affiliation(s)
- Rajib Basak
- Department of Physics, National University of Singapore, Singapore, Republic of Singapore
| | - William Rosencrans
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland
| | - Indresh Yadav
- Department of Physics, National University of Singapore, Singapore, Republic of Singapore
| | - Peiyan Yan
- Department of Physics, National University of Singapore, Singapore, Republic of Singapore
| | - Nikolay V Berezhnoy
- School of Biological Sciences, Nanyang Technological University, Singapore, Republic of Singapore
| | - Qinming Chen
- School of Biological Sciences, Nanyang Technological University, Singapore, Republic of Singapore
| | - Jeroen A van Kan
- Department of Physics, National University of Singapore, Singapore, Republic of Singapore
| | - Lars Nordenskiöld
- School of Biological Sciences, Nanyang Technological University, Singapore, Republic of Singapore
| | - Anatoly Zinchenko
- Graduate School of Environmental Studies, Nagoya University, Nagoya, Japan
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12
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Benková Z, Rišpanová L, Cifra P. Conformation of Flexible and Semiflexible Chains Confined in Nanoposts Array of Various Geometries. Polymers (Basel) 2020; 12:E1064. [PMID: 32384748 PMCID: PMC7284769 DOI: 10.3390/polym12051064] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2020] [Revised: 04/27/2020] [Accepted: 04/29/2020] [Indexed: 01/17/2023] Open
Abstract
The conformation and distribution of a flexible and semiflexible chain confined in an array of nanoposts arranged in parallel way in a square-lattice projection of their cross-section was investigated using coarse-grained molecular dynamics simulations. The geometry of the nanopost array was varied at the constant post diameter dp and the ensuing modifications of the chain conformation were compared with the structural behavior of the chain in the series of nanopost arrays with the constant post separation Sp as well as with the constant distance between two adjacent post walls (passage width) wp. The free energy arguments based on an approximation of the array of nanopost to a composite of quasi-channels of diameter dc and quasi-slits of height wp provide semiqualitative explanations for the observed structural behavior of both chains. At constant post separation and passage width, the occupation number displays a monotonic decrease with the increasing geometry ratio dc/wp or volume fraction of posts, while a maximum is observed at constant post diameter. The latter finding is attributed to a relaxed conformation of the chains at small dc/wp ratio, which results from a combination of wide interstitial volumes and wide passage apertures. This maximum is approximately positioned at the same dc/wp value for both flexible and semiflexible chains. The chain expansion from a single interstitial volume into more interstitial volumes also starts at the same value of dc/wp ratio for both chains. The dependence of the axial chain extension on the dc/wp ratio turns out to be controlled by the diameter of the interstitial space and by the number of monomers in the individual interstitial volumes. If these two factors act in the same way on the axial extension of chain fragments in interstitial volumes the monotonic increase of the axial chain extension with the dc/wp in the nanopost arrays is observed. At constant wp, however, these two factors act in opposite way and the axial chain extension plotted against the dc/wp ratio exhibits a maximum. In the case of constant post diameter, the characteristic hump in the single chain structure factor whose position correlates with the post separation is found only in the structure factor of the flexible chain confined in the nanopost array of certain value of Sp. The structure factor of the flexible chain contains more information on the monomer organization and mutual correlations than the structure factor of the semiflexible chain. The stiffer chain confined in the nanopost array is composed of low number of statistical segments important for the presence of respective hierarchical regimes in the structure factor.
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Affiliation(s)
- Zuzana Benková
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia; (L.R.); (P.C.)
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13
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Wang X, Procházka K, Limpouchová Z. Partitioning of polymers between bulk and porous media: Monte Carlo study of the effect of pore size distribution. J Colloid Interface Sci 2020; 567:103-112. [DOI: 10.1016/j.jcis.2020.01.119] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2019] [Revised: 01/27/2020] [Accepted: 01/28/2020] [Indexed: 02/04/2023]
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14
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Bhandari AB, Dorfman KD. Limitations of the equivalent neutral polymer assumption for theories describing nanochannel-confined DNA. Phys Rev E 2020; 101:012501. [PMID: 32069627 PMCID: PMC7040977 DOI: 10.1103/physreve.101.012501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Indexed: 11/07/2022]
Abstract
The prevailing theories describing DNA confinement in a nanochannel are predicated on the assumption that wall-DNA electrostatic interactions are sufficiently short-ranged such that the problem can be mapped to an equivalent neutral polymer confined by hard walls with an appropriately reduced effective channel size. To determine when this hypothesis is valid, we leveraged a recently reported experimental data set for the fractional extension of DNA molecules in a 250-nm-wide poly(dimethyl siloxane) (PDMS) nanochannel with buffer ionic strengths between 0.075 and 48 mM. Evaluating these data in the context of the weakly correlated telegraph model of DNA confinement reveals that, at ionic strengths greater than 0.3 mM, the average fractional extension of the DNA molecules agree with theoretical predictions with a mean absolute error of 0.04. In contrast, experiments at ionic strengths below 0.3 mM produce average fractional extensions that are systematically smaller than the theoretical predictions with a larger mean absolute error of 0.15. The deviations between experiment and theory display a correlation coefficient of 0.82 with the decay length for the DNA-wall electrostatics, linking the deviations with a breakdown in approximating the DNA with an equivalent neutral polymer.
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Affiliation(s)
- Aditya Bikram Bhandari
- Department of Chemical Engineering and Materials Science, University of Minnesota, Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota, Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
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15
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Li M, Wang J. Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections. Polymers (Basel) 2019; 11:E2050. [PMID: 31835594 PMCID: PMC6960511 DOI: 10.3390/polym11122050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2019] [Accepted: 12/06/2019] [Indexed: 12/03/2022] Open
Abstract
We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. This single formula was generalized to be valid for tube confinements with arbitrary cross-sections. In addition, we extended the generalized bead-rod model for Brownian dynamics simulations of confined polymer chains subjected to force stretching, so that the confinement effects to the chains applied by the tubes with arbitrary cross-sections can be quantitatively taken into account through numerical simulations. Extensive simulation examples on the wormlike chains confined in tubes of various shapes quantitatively justified the theoretically derived generalized formula on the force-confinement-extension relation of the chains.
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Affiliation(s)
| | - Jizeng Wang
- Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China;
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16
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Chuang HM, Reifenberger JG, Bhandari AB, Dorfman KD. Extension distribution for DNA confined in a nanochannel near the Odijk regime. J Chem Phys 2019; 151:114903. [PMID: 31542006 DOI: 10.1063/1.5121305] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
DNA confinement in a nanochannel typically is understood via mapping to the confinement of an equivalent neutral polymer by hard walls. This model has proven to be effective for confinement in relatively large channels where hairpin formation is frequent. An analysis of existing experimental data for Escherichia coli DNA extension in channels smaller than the persistence length, combined with an additional dataset for λ-DNA confined in a 34 nm wide channel, reveals a breakdown in this approach as the channel size approaches the Odijk regime of strong confinement. In particular, the predicted extension distribution obtained from the asymptotic solution to the weakly correlated telegraph model for a confined wormlike chain deviates significantly from the experimental distribution obtained for DNA confinement in the 34 nm channel, and the discrepancy cannot be resolved by treating the alignment fluctuations or the effective channel size as fitting parameters. We posit that the DNA-wall electrostatic interactions, which are sensible throughout a significant fraction of the channel cross section in the Odijk regime, are the source of the disagreement between theory and experiment. Dimensional analysis of the wormlike chain propagator in channel confinement reveals the importance of a dimensionless parameter, reflecting the magnitude of the DNA-wall electrostatic interactions relative to thermal energy, which has not been considered explicitly in the prevailing theories for DNA confinement in a nanochannel.
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Affiliation(s)
- Hui-Min Chuang
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Jeffrey G Reifenberger
- Bionano Genomics, Inc., 9640 Towne Centre Drive, Suite 100, San Diego, California 92121, USA
| | - Aditya Bikram Bhandari
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
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17
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Bhandari AB, Dorfman KD. Simulations corroborate telegraph model predictions for the extension distributions of nanochannel confined DNA. BIOMICROFLUIDICS 2019; 13:044110. [PMID: 31406555 PMCID: PMC6687496 DOI: 10.1063/1.5109566] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Accepted: 07/21/2019] [Indexed: 05/15/2023]
Abstract
Hairpins in the conformation of DNA confined in nanochannels close to their persistence length cause the distribution of their fractional extensions to be heavily left skewed. A recent theory rationalizes these skewed distributions using a correlated telegraph process, which can be solved exactly in the asymptotic limit of small but frequent hairpin formation. Pruned-enriched Rosenbluth method simulations of the fractional extension distribution for a channel-confined wormlike chain confirm the predictions of the telegraph model. Remarkably, the asymptotic result of the telegraph model remains robust well outside the asymptotic limit. As a result, the approximations in the theory required to map it to the polymer model and solve it in the asymptotic limit are not the source of discrepancies between the predictions of the telegraph model and experimental distributions of the extensions of DNA during genome mapping. The agreement between theory and simulations motivates future work to determine the source of the remaining discrepancies between the predictions of the telegraph model and experimental distributions of the extensions of DNA in nanochannels used for genome mapping.
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Affiliation(s)
- Aditya Bikram Bhandari
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
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18
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Krog J, Alizadehheidari M, Werner E, Bikkarolla SK, Tegenfeldt JO, Mehlig B, Lomholt MA, Westerlund F, Ambjörnsson T. Stochastic unfolding of nanoconfined DNA: Experiments, model and Bayesian analysis. J Chem Phys 2019; 149:215101. [PMID: 30525714 DOI: 10.1063/1.5051319] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Nanochannels provide a means for detailed experiments on the effect of confinement on biomacromolecules, such as DNA. Here we introduce a model for the complete unfolding of DNA from the circular to linear configuration. Two main ingredients are the entropic unfolding force and the friction coefficient for the unfolding process, and we describe the associated dynamics by a non-linear Langevin equation. By analyzing experimental data where DNA molecules are photo-cut and unfolded inside a nanochannel, our model allows us to extract values for the unfolding force as well as the friction coefficient for the first time. In order to extract numerical values for these physical quantities, we employ a recently introduced Bayesian inference framework. We find that the determined unfolding force is in agreement with estimates from a simple Flory-type argument. The estimated friction coefficient is in agreement with theoretical estimates for motion of a cylinder in a channel. We further validate the estimated friction constant by extracting this parameter from DNA's center-of-mass motion before and after unfolding, yielding decent agreement. We provide publically available software for performing the required image and Bayesian analysis.
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Affiliation(s)
- Jens Krog
- MEMPHYS-Center for Biomembrane Physics, Department of Physics, Chemistry, and Pharmacy, University of Southern Denmark, Odense, Denmark
| | | | - Erik Werner
- Department of Physics, Gothenburg University, Gothenburg, Sweden
| | - Santosh Kumar Bikkarolla
- Department of Biology and Biological Engineering, Chalmers University of Technology, Gothenburg, Sweden
| | | | - Bernhard Mehlig
- Department of Physics, Gothenburg University, Gothenburg, Sweden
| | - Michael A Lomholt
- MEMPHYS-Center for Biomembrane Physics, Department of Physics, Chemistry, and Pharmacy, University of Southern Denmark, Odense, Denmark
| | - Fredrik Westerlund
- Department of Biology and Biological Engineering, Chalmers University of Technology, Gothenburg, Sweden
| | - Tobias Ambjörnsson
- Department of Astronomy and Theoretical Physics, Lund University, Lund, Sweden
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19
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Dangi S, Riehn R. Nanoplumbing with 2D Metamaterials. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2019; 15:e1803478. [PMID: 30537130 PMCID: PMC6785347 DOI: 10.1002/smll.201803478] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2018] [Revised: 11/09/2018] [Indexed: 06/09/2023]
Abstract
Complex manipulations of DNA in a nanofluidic device require channels with branches and junctions. However, the dynamic response of DNA in such nanofluidic networks is relatively unexplored. Here, the transport of DNA in a 2D metamaterial made by arrays of nanochannel junctions is investigated. The mechanism of transport is explained as Brownian motion through an energy landscape formed by the combination of the confinement free energy of DNA and the effective potential of hydrodynamic flow, which both can be tuned independently within the device. For the quantitative understanding of DNA transport, a dynamic mean-field model of DNA at a nanochannel junction is proposed. It is shown that the dynamics of DNA in a nanofluidic device with branched channels and junctions is well described by the model.
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20
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Lee S, Lee Y, Kim Y, Wang C, Park J, Jung GY, Chen Y, Chang R, Ikeda S, Sugiyama H, Jo K. Nanochannel-Confined TAMRA-Polypyrrole Stained DNA Stretching by Varying the Ionic Strength from Micromolar to Millimolar Concentrations. Polymers (Basel) 2018; 11:E15. [PMID: 30959999 PMCID: PMC6401831 DOI: 10.3390/polym11010015] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2018] [Revised: 12/17/2018] [Accepted: 12/17/2018] [Indexed: 12/19/2022] Open
Abstract
Large DNA molecules have been utilized as a model system to investigate polymer physics. However, DNA visualization via intercalating dyes has generated equivocal results due to dye-induced structural deformation, particularly unwanted unwinding of the double helix. Thus, the contour length increases and the persistence length changes so unpredictably that there has been a controversy. In this paper, we used TAMRA-polypyrrole to stain single DNA molecules. Since this staining did not change the contour length of B-form DNA, we utilized TAMRA-polypyrrole stained DNA as a tool to measure the persistence length by changing the ionic strength. Then, we investigated DNA stretching in nanochannels by varying the ionic strength from 0.06 mM to 47 mM to evaluate several polymer physics theories proposed by Odijk, de Gennes and recent papers to deal with these regimes.
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Affiliation(s)
- Seonghyun Lee
- Department of Chemistry and Integrated Biotechnology, Sogang University, Seoul 04107, Korea.
| | - Yelin Lee
- Department of Chemistry and Integrated Biotechnology, Sogang University, Seoul 04107, Korea.
| | - Yongkyun Kim
- Department of Chemistry and Integrated Biotechnology, Sogang University, Seoul 04107, Korea.
| | - Cong Wang
- Department of Mechanical Engineering, Sogang University, Seoul 04107, Korea.
| | - Jungyul Park
- Department of Mechanical Engineering, Sogang University, Seoul 04107, Korea.
| | - Gun Young Jung
- School of Material Science and Engineering, GIST, Gwangju 61005, Korea.
| | - Yenglong Chen
- Institute of Physics, Academia Sinica and Department of Chemical Engineering, National Tsing-Hua University and Department of Physics, National Taiwan University, Taipei 10617, Taiwan.
| | - Rakwoo Chang
- Department of Chemistry, Kwangwoon University, Seoul 01897, Korea.
| | - Shuji Ikeda
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyo-Ku, Kyoto 606-8501, Japan.
| | - Hiroshi Sugiyama
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyo-Ku, Kyoto 606-8501, Japan.
| | - Kyubong Jo
- Department of Chemistry and Integrated Biotechnology, Sogang University, Seoul 04107, Korea.
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21
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Milchev A, Egorov SA, Binder K, Nikoubashman A. Nematic order in solutions of semiflexible polymers: Hairpins, elastic constants, and the nematic-smectic transition. J Chem Phys 2018; 149:174909. [PMID: 30408984 DOI: 10.1063/1.5049630] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Coarse-grained models of lyotropic solutions of semiflexible polymers are studied by both molecular dynamics simulations and density functional theory calculations, using an implicit solvent bead-spring model with a bond-angle potential. We systematically vary the monomer density, persistence length, and contour length over a wide range and explore the full range from the isotropic-nematic transition to the nematic-smectic transition. In the nematic regime, we span the entire regime from rigid-rod like polymers to thin wormlike chains, confined in effective straight tubes caused by the collective nematic effective ordering field. We show that the distribution of bond angles relative to the director is well described by a Gaussian, irrespective of whether the chains are rod-like or rather flexible. However, the related concept of "deflection length" is shown to make sense only in the latter case for rather dilute solutions since otherwise the deflection length is of the order of about two bond lengths only. When the solution is semi-dilute, a substantial renormalization of the persistence length occurs, while this effect is absent in the isotropic phase even at rather high monomer densities. The effective radii of the "tubes" confining the chains in the related description of orientational ordering are significantly larger than the distances between neighboring chains, providing evidence for a pronounced collective character of orientational fluctuations. Hairpins can be identified close to the isotropic-nematic transition, and their probability of occurrence agrees qualitatively with the Vroege-Odijk theory. The corresponding theoretical predictions for the elastic constants, however, are not in good agreement with the simulations. We attribute the shortcomings of the theories to their neglect of the coupling between local density and orientational fluctuations. Finally, we detected for this model a transition to a smectic phase for reduced monomer densities near 0.7.
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Affiliation(s)
- Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113 Sofia, Bulgaria
| | - Sergei A Egorov
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Kurt Binder
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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22
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Bhandari AB, Reifenberger JG, Chuang HM, Cao H, Dorfman KD. Measuring the wall depletion length of nanoconfined DNA. J Chem Phys 2018; 149:104901. [PMID: 30219022 PMCID: PMC6135644 DOI: 10.1063/1.5040458] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2018] [Accepted: 08/20/2018] [Indexed: 12/14/2022] Open
Abstract
Efforts to study the polymer physics of DNA confined in nanochannels have been stymied by a lack of consensus regarding its wall depletion length. We have measured this quantity in 38 nm wide, square silicon dioxide nanochannels for five different ionic strengths between 15 mM and 75 mM. Experiments used the Bionano Genomics Irys platform for massively parallel data acquisition, attenuating the effect of the sequence-dependent persistence length and finite-length effects by using nick-labeled E. coli genomic DNA with contour length separations of at least 30 µm (88 325 base pairs) between nick pairs. Over 5 × 106 measurements of the fractional extension were obtained from 39 291 labeled DNA molecules. Analyzing the stretching via Odijk's theory for a strongly confined wormlike chain yielded a linear relationship between the depletion length and the Debye length. This simple linear fit to the experimental data exhibits the same qualitative trend as previously defined analytical models for the depletion length but now quantitatively captures the experimental data.
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Affiliation(s)
- Aditya Bikram Bhandari
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Jeffrey G Reifenberger
- Bionano Genomics, Inc., 9640 Towne Centre Drive, Suite 100, San Diego, California 92121, USA
| | - Hui-Min Chuang
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Han Cao
- Bionano Genomics, Inc., 9640 Towne Centre Drive, Suite 100, San Diego, California 92121, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
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23
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Polson JM. Free Energy of a Folded Semiflexible Polymer Confined to a Nanochannel of Various Geometries. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01148] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Affiliation(s)
- James M. Polson
- Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island C1A 4P3, Canada
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24
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Chen JZY. Self-Avoiding Wormlike Chain Confined in a Cylindrical Tube: Scaling Behavior. PHYSICAL REVIEW LETTERS 2018; 121:037801. [PMID: 30085819 DOI: 10.1103/physrevlett.121.037801] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Revised: 04/27/2018] [Indexed: 05/27/2023]
Abstract
Within a confining tube section, the multithreads of a strongly confined, backfolding polymer exert the excluded-volume repulsions on each other and produce physical properties that are very different from those of a confined ideal chain. The conformational properties of a such confined wormlike chain are of fundamental interest and are also practically useful in understanding the DNA confinement problems. Here, the excluded-volume effects are added to the standard wormlike-chain model by a self-consistent field theory. The numerical solutions are examined in light of their scaling properties.
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Affiliation(s)
- Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3GI, Canada
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25
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Saleem I, Masood S, Smith D, Chu WK. Adhesion of gram-negative rod-shaped bacteria on 1D nano-ripple glass pattern in weak magnetic fields. Microbiologyopen 2018; 8:e00640. [PMID: 29799166 PMCID: PMC6391264 DOI: 10.1002/mbo3.640] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2017] [Revised: 02/16/2018] [Accepted: 03/06/2018] [Indexed: 02/06/2023] Open
Abstract
This research project has major applications in the healthcare and biomedical industries. Bacteria reside in human bodies and play an integral role in the mechanism of life. However, their excessive growth or the invasion of similar agents can be dangerous and may cause fatal or incurable diseases. On the other hand, increased exposure to electromagnetic radiation and its impact on health and safety is a common concern to medical science. Some nanostructure materials have interesting properties regarding facilitating or impeding cell growth. An understanding of these phenomena can be utilized to establish the optimum benefit of these structures in healthcare and medical research. We focus on the commonly found rod‐shaped, gram‐negative bacteria and their orientation and community development on the cellular level in the presence of weak magnetic fields on one dimensional nano‐ripple glass patterns to investigate the impact of nanostructures on the growth pattern of bacteria. The change in bacterial behavior on nanostructures and the impact of magnetic fields will open up new venues in the utilization of nanostructures. It is noticed that bacterial entrapment in nano‐grooves leads to the growth of larger colonies on the nanostructures, whereas magnetic fields reduce the size of colonies and suppress their growth.
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Affiliation(s)
- Iram Saleem
- Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, Texas
| | - Samina Masood
- Department of Physical and Applied Sciences, University of Houston-Clear Lake, Houston, Texas
| | - Derek Smith
- Department of Physical and Applied Sciences, University of Houston-Clear Lake, Houston, Texas
| | - Wei-Kan Chu
- Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, Texas
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26
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Bernier S, Huang A, Reisner W, Bhattacharya A. Evolution of Nested Folding States in Compression of a Strongly Confined Semiflexible Chain. Macromolecules 2018. [DOI: 10.1021/acs.macromol.7b02748] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Simon Bernier
- Department of Physics, McGill University, 3600 rue university, Montreal, Quebec H3A 2T8, Canada
| | - Aiqun Huang
- Department of Physics, University of Central Florida, 4111 Libra Drive, Orlando, Florida 32816, United States
| | - Walter Reisner
- Department of Physics, McGill University, 3600 rue university, Montreal, Quebec H3A 2T8, Canada
| | - Aniket Bhattacharya
- Department of Physics, University of Central Florida, 4111 Libra Drive, Orlando, Florida 32816, United States
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27
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Ödman D, Werner E, Dorfman KD, Doering CR, Mehlig B. Distribution of label spacings for genome mapping in nanochannels. BIOMICROFLUIDICS 2018; 12:034115. [PMID: 30018694 PMCID: PMC6019347 DOI: 10.1063/1.5038417] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2018] [Accepted: 06/06/2018] [Indexed: 05/27/2023]
Abstract
In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice, its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here, we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.
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Affiliation(s)
- D Ödman
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
| | - E Werner
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
| | - K D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - C R Doering
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109-1042, USA
| | - B Mehlig
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
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28
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Yu M, Hou Y, Song R, Xu X, Yao S. Tunable Confinement for Bridging Single-Cell Manipulation and Single-Molecule DNA Linearization. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2018; 14:e1800229. [PMID: 29575689 DOI: 10.1002/smll.201800229] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Revised: 02/07/2018] [Indexed: 06/08/2023]
Abstract
DNA linearization by nanoconfinement has offered a new avenue toward large-scale genome mapping. The ability to smoothly interface the widely different length scales from cell manipulation to DNA linearization is critical to the development of single-cell genomic mapping or sequencing technologies. Conventional nanochannel technologies for DNA analysis suffer from complex fabrication procedures, DNA stacking at the nanochannel entrance, and inefficient solution exchange. In this work, a dynamic and tunable confinement strategy is developed to manipulate and linearize genomic-length DNA molecules from a single cell. By leveraging pneumatic microvalve control and elastomeric collapse, an array of nanochannels with confining dimension down to 20 nm and length up to sub-millimeter is created and can be dynamically tuned in size. The curved edges of the microvalve form gradual transitions from microscale to nanoscale confinement, smoothly facilitating DNA entry into the nanochannels. A unified micro/nanofluidic device that integrates single-cell trapping and lysis, DNA extraction, purification, labeling, and linearization is developed based on dynamically controllable nanochannels. Mbp-long DNA molecules are extracted directly from a single cell and in situ linearized in the nanochannels. The device provides a facile and promising platform to achieve the ultimate goal of single-cell, single-genome analysis.
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Affiliation(s)
- Miao Yu
- Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Kowloon, 999077, Hong Kong, China
| | - Youmin Hou
- Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Kowloon, 999077, Hong Kong, China
| | - Ruyuan Song
- Department of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Kowloon, 999077, Hong Kong, China
| | - Xiaonan Xu
- Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Kowloon, 999077, Hong Kong, China
| | - Shuhuai Yao
- Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Kowloon, 999077, Hong Kong, China
- Department of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Kowloon, 999077, Hong Kong, China
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29
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Werner E, Jain A, Muralidhar A, Frykholm K, St Clere Smithe T, Fritzsche J, Westerlund F, Dorfman KD, Mehlig B. Hairpins in the conformations of a confined polymer. BIOMICROFLUIDICS 2018; 12:024105. [PMID: 29576836 PMCID: PMC5844772 DOI: 10.1063/1.5018787] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2017] [Accepted: 02/21/2018] [Indexed: 06/01/2023]
Abstract
If a semiflexible polymer confined to a narrow channel bends around by 180°, the polymer is said to exhibit a hairpin. The equilibrium extension statistics of the confined polymer are well understood when hairpins are vanishingly rare or when they are plentiful. Here, we analyze the extension statistics in the intermediate situation via experiments with DNA coated by the protein RecA, which enhances the stiffness of the DNA molecule by approximately one order of magnitude. We find that the extension distribution is highly non-Gaussian, in good agreement with Monte-Carlo simulations of confined discrete wormlike chains. We develop a simple model that qualitatively explains the form of the extension distribution. The model shows that the tail of the distribution at short extensions is determined by conformations with one hairpin.
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Affiliation(s)
- E Werner
- Department of Physics, University of Gothenburg, Origovägen 6B, 412 96 Göteborg, Sweden
| | - A Jain
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - A Muralidhar
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - K Frykholm
- Department of Biology and Biological Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - T St Clere Smithe
- Department of Physics, University of Gothenburg, Origovägen 6B, 412 96 Göteborg, Sweden
| | - J Fritzsche
- Department of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - F Westerlund
- Department of Biology and Biological Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - K D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - B Mehlig
- Department of Physics, University of Gothenburg, Origovägen 6B, 412 96 Göteborg, Sweden
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30
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Reifenberger JG, Cao H, Dorfman KD. Odijk excluded volume interactions during the unfolding of DNA confined in a nanochannel. Macromolecules 2018; 51:1172-1180. [PMID: 29479117 PMCID: PMC5823525 DOI: 10.1021/acs.macromol.7b02466] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We report experimental data on the unfolding of human and E. coli genomic DNA molecules shortly after injection into a 45 nm nanochannel. The unfolding dynamics are deterministic, consistent with previous experiments and modeling in larger channels, and do not depend on the biological origin of the DNA. The measured entropic unfolding force per friction per unit contour length agrees with that predicted by combining the Odijk excluded volume with numerical calculations of the Kirkwood diffusivity of confined DNA. The time scale emerging from our analysis has implications for genome mapping in nanochannels, especially as the technology moves towards longer DNA, by setting a lower bound for the delay time before making a measurement.
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Affiliation(s)
| | - Han Cao
- BioNano Genomics Inc., 9640 Towne Centre Drive, Suite 100, San Diego, CA 92121
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota – Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, USA
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31
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Cheong GK, Li X, Dorfman KD. Evidence for the extended de Gennes regime of a semiflexible polymer in slit confinement. Phys Rev E 2018; 97:022502. [PMID: 29479576 PMCID: PMC5823612 DOI: 10.1103/physreve.97.022502] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
We use off-lattice, pruned-enriched Rosenbluth method (PERM) simulations to compute the confinement free energy of a real wormlike chain of effective width w and persistence length lp in a slit of height H. For slit heights much larger than the persistence length of the polymer and much smaller than the thermal blob size, the excess free energy of the confined chain is consistent with a modified version of the scaling theory for the extended de Gennes regime in a channel that reflects the blob statistics in slit confinement. Explicitly, for channel sizes [Formula: see text], the difference between the confinement free energy of the real chain and that of an ideal chain scales like w/H.
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Affiliation(s)
- Guo Kang Cheong
- Department of Chemical Engineering and Materials Science, University of Minnesota – Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - Xiaolan Li
- Department of Chemical Engineering and Materials Science, University of Minnesota – Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota – Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
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32
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Dorfman KD. The Statistical Segment Length of DNA: Opportunities for Biomechanical Modeling in Polymer Physics and Next-Generation Genomics. J Biomech Eng 2018; 140:2653367. [PMID: 28857114 PMCID: PMC5816256 DOI: 10.1115/1.4037790] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2017] [Revised: 08/16/2017] [Indexed: 12/28/2022]
Abstract
The development of bright bisintercalating dyes for deoxyribonucleic acid (DNA) in the 1990s, most notably YOYO-1, revolutionized the field of polymer physics in the ensuing years. These dyes, in conjunction with modern molecular biology techniques, permit the facile observation of polymer dynamics via fluorescence microscopy and thus direct tests of different theories of polymer dynamics. At the same time, they have played a key role in advancing an emerging next-generation method known as genome mapping in nanochannels. The effect of intercalation on the bending energy of DNA as embodied by a change in its statistical segment length (or, alternatively, its persistence length) has been the subject of significant controversy. The precise value of the statistical segment length is critical for the proper interpretation of polymer physics experiments and controls the phenomena underlying the aforementioned genomics technology. In this perspective, we briefly review the model of DNA as a wormlike chain and a trio of methods (light scattering, optical or magnetic tweezers, and atomic force microscopy (AFM)) that have been used to determine the statistical segment length of DNA. We then outline the disagreement in the literature over the role of bisintercalation on the bending energy of DNA, and how a multiscale biomechanical approach could provide an important model for this scientifically and technologically relevant problem.
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Affiliation(s)
- Kevin D. Dorfman
- Department of Chemical Engineering and
Materials Science,
University of Minnesota—Twin Cities,
421 Washington Ave SE,
Minneapolis, MN 55455
e-mail:
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33
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Werner E, Cheong GK, Gupta D, Dorfman KD, Mehlig B. One-Parameter Scaling Theory for DNA Extension in a Nanochannel. PHYSICAL REVIEW LETTERS 2017; 119:268102. [PMID: 29328690 PMCID: PMC5769985 DOI: 10.1103/physrevlett.119.268102] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2017] [Indexed: 05/27/2023]
Abstract
Experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA. We show that a theory based on a weakly self-avoiding, one-dimensional "telegraph" process collapses experimental data and simulation results onto a single master curve throughout the experimentally relevant region of parameter space and explains the mechanisms at play.
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Affiliation(s)
- E Werner
- Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
| | - G K Cheong
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - D Gupta
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - K D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - B Mehlig
- Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
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34
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Chuang HM, Reifenberger JG, Cao H, Dorfman KD. Sequence-Dependent Persistence Length of Long DNA. PHYSICAL REVIEW LETTERS 2017; 119:227802. [PMID: 29286779 PMCID: PMC5839665 DOI: 10.1103/physrevlett.119.227802] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2017] [Indexed: 05/04/2023]
Abstract
Using a high-throughput genome-mapping approach, we obtained circa 50 million measurements of the extension of internal human DNA segments in a 41 nm×41 nm nanochannel. The underlying DNA sequences, obtained by mapping to the reference human genome, are 2.5-393 kilobase pairs long and contain percent GC contents between 32.5% and 60%. Using Odijk's theory for a channel-confined wormlike chain, these data reveal that the DNA persistence length increases by almost 20% as the percent GC content increases. The increased persistence length is rationalized by a model, containing no adjustable parameters, that treats the DNA as a statistical terpolymer with a sequence-dependent intrinsic persistence length and a sequence-independent electrostatic persistence length.
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Affiliation(s)
- Hui-Min Chuang
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | | | - Han Cao
- BioNano Genomics, 9640 Towne Centre Drive, Suite 100, San Diego, California 92121, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
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35
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Polson JM, Tremblett AF, McLure ZRN. Free Energy of a Folded Polymer under Cylindrical Confinement. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b02114] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- James M. Polson
- Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island C1A 4P3, Canada
| | - Aidan F. Tremblett
- Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island C1A 4P3, Canada
| | - Zakary R. N. McLure
- Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island C1A 4P3, Canada
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36
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Benková Z, Rišpanová L, Cifra P. Effect of chain stiffness for semiflexible macromolecules in array of cylindrical nanoposts. J Chem Phys 2017; 147:134907. [DOI: 10.1063/1.4991649] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Affiliation(s)
- Zuzana Benková
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia
- LAQV@REQUIMTE, Department of Chemistry and Biochemistry, Faculty of Sciences, University of Porto, Rua do Campo Alegre 687, 4168-007 Porto, Portugal
| | - Lucia Rišpanová
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia
| | - Peter Cifra
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia
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37
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Benková Z, Rišpanová L, Cifra P. Structural Behavior of a Semiflexible Polymer Chain in an Array of Nanoposts. Polymers (Basel) 2017; 9:E313. [PMID: 30970991 PMCID: PMC6418663 DOI: 10.3390/polym9080313] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2017] [Revised: 07/24/2017] [Accepted: 07/25/2017] [Indexed: 11/27/2022] Open
Abstract
The structural properties of a flexible and semiflexible circular chain confined in an array of parallel nanoposts with a square lattice cross-sectional projection were studied using coarse-grained molecular dynamics simulations. To address the effect of the circular topology, a comparison with linear analogs was also carried out. In the interpretation of the chain structural properties, the geometry of the post array is considered as a combination of a channel approximating the interstitial volume with the diameter dc and a slit approximating the passage aperture with the width wp. The number of interstitial volumes occupied by a chain monotonically increases with the decreasing ratio dc/wp regardless of the way the geometry of the post array is varied. However, depending on how the array geometry is modified, the chain span along the posts displays a monotonic (constant post separation) or a non-monotonic behavior (constant passage width) when plotted as a function of the post diameter. In the case of monotonic trend, the width of interstitial spaces increases with the increasing chain occupation number, while, in the case of non-monotonic trend, the width of interstitial spaces decreases with the increasing chain occupation number. In comparison with linear topology, for circular topology, the stiffness affects more significantly the relative chain extension along the posts and less significantly the occupation number. The geometrical parameters of the post arrays are stored in the single-chain structure factors. The characteristic humps are recognized in the structure factor which ensue from the local increase in the density of segments in the circular chains presented in an interstitial volume or from the correlation of parallel chain fragments separated by a row of posts. Although the orientation correlations provide qualitative information about the chain topology and the character of confinement within a single interstitial volume, information about the array periodicity is missing.
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Affiliation(s)
- Zuzana Benková
- Polymer Institute, Slovak Academy of Sciences, Dúbravská Cesta 9, 845 41 Bratislava, Slovakia.
- LAQV@REQUIMTE, Department of Chemistry and Biochemistry, Faculty of Sciences, University of Porto, Rua do Campo Alegre 687, 4168-007 Porto, Portugal.
| | - Lucia Rišpanová
- Polymer Institute, Slovak Academy of Sciences, Dúbravská Cesta 9, 845 41 Bratislava, Slovakia.
| | - Peter Cifra
- Polymer Institute, Slovak Academy of Sciences, Dúbravská Cesta 9, 845 41 Bratislava, Slovakia.
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Chen JZY. Conformational Properties of a Back-Folding Wormlike Chain Confined in a Cylindrical Tube. PHYSICAL REVIEW LETTERS 2017; 118:247802. [PMID: 28665664 DOI: 10.1103/physrevlett.118.247802] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2017] [Indexed: 06/07/2023]
Abstract
When a semiflexible chain is confined in a narrow cylindrical tube, the formation of a polymer hairpin is a geometrical conformation that accompanies an exponentially large local free energy and, hence, is a relatively rare event. Numerical solutions of the hairpin distribution functions for persistence-length-to-tube-radius ratios over a wide range are obtained in high precision, by using the Green's function approach for the wormlike-chain model. The crossover region between the narrow and moderately narrow tubes is critically investigated in terms of the hairpin free energy, global persistence length, mean hairpin-tip distance from the tube axis, and hairpin-plane orientational properties. Accurate representations of the solutions by simple interpolation formulae are suggested.
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Affiliation(s)
- Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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39
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Jain A, Dorfman KD. Simulations of knotting of DNA during genome mapping. BIOMICROFLUIDICS 2017; 11:024117. [PMID: 28798853 PMCID: PMC5533507 DOI: 10.1063/1.4979605] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2017] [Accepted: 03/21/2017] [Indexed: 05/28/2023]
Abstract
Genome mapping involves the confinement of long DNA molecules, in excess of 150 kilobase pairs, in nanochannels near the circa 50 nm persistence length of DNA. The fidelity of the map relies on the assumption that the DNA is linearized by channel confinement, which assumes the absence of knots. We have computed the probability of forming different knot types and the size of these knots for long chains (approximately 164 kilobase pairs) via pruned-enriched Rosenbluth method simulations of a discrete wormlike chain model of DNA in channel sizes ranging from 35 nm to 60 nm. Compared to prior simulations of short DNA in similar confinement, these long molecules exhibit both complex knots, with up to seven crossings, and multiple knots per chain. The knotting probability is a very strong function of channel size, ranging from 0.3% to 60%, and rationalized in the context of Odijk's theory for confined semiflexible chains. Overall, the knotting probability and knot size obtained from these equilibrium measurements are not consistent with experimental measurements of the properties of anomalously bright regions along the DNA backbone during genome mapping experiments. This result suggests that these events in experiments are either knots formed during the processing of the DNA prior to injection into the nanochannel or regions of locally high DNA concentration without a topological constraint. If so, knots during genome mapping are not an intrinsic problem for genome mapping technology.
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Affiliation(s)
- Aashish Jain
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
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40
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Cheong GK, Li X, Dorfman KD. Wall depletion length of a channel-confined polymer. Phys Rev E 2017; 95:022501. [PMID: 28297899 DOI: 10.1103/physreve.95.022501] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2016] [Indexed: 11/07/2022]
Abstract
Numerous experiments have taken advantage of DNA as a model system to test theories for a channel-confined polymer. A tacit assumption in analyzing these data is the existence of a well-defined depletion length characterizing DNA-wall interactions such that the experimental system (a polyelectrolyte in a channel with charged walls) can be mapped to the theoretical model (a neutral polymer with hard walls). We test this assumption using pruned-enriched Rosenbluth method (PERM) simulations of a DNA-like semiflexible polymer confined in a tube. The polymer-wall interactions are modeled by augmenting a hard wall interaction with an exponentially decaying, repulsive soft potential. The free energy, mean span, and variance in the mean span obtained in the presence of a soft wall potential are compared to equivalent simulations in the absence of the soft wall potential to determine the depletion length. We find that the mean span and variance about the mean span have the same depletion length for all soft potentials we tested. In contrast, the depletion length for the confinement free energy approaches that for the mean span only when depletion length no longer depends on channel size. The results have implications for the interpretation of DNA confinement experiments under low ionic strengths.
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Affiliation(s)
- Guo Kang Cheong
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - Xiaolan Li
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
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41
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Abstract
More than 20 coarse-grained (CG) DNA models have been developed for simulating the behavior of this molecule under various conditions, including those required for nanotechnology. However, none of these models reproduces the DNA polymorphism associated with conformational changes in the ribose rings of the DNA backbone. These changes make an essential contribution to the DNA local deformability and provide the possibility of the transition of the DNA double helix from the B-form to the A-form during interactions with biological molecules. We propose a CG representation of the ribose conformational flexibility. We substantiate the choice of the CG sites (six per nucleotide) needed for the "sugar" GC DNA model, and obtain the potentials of the CG interactions between the sites by the "bottom-up" approach using the all-atom AMBER force field. We show that the representation of the ribose flexibility requires one non-harmonic and one three-particle potential, the forms of both the potentials being different from the ones generally used. The model also includes (i) explicit representation of ions (in an implicit solvent) and (ii) sequence dependence. With these features, the sugar CG DNA model reproduces (with the same parameters) both the B- and A- stable forms under corresponding conditions and demonstrates both the A to B and the B to A phase transitions. Graphical Abstract The proposed coarse-grained DNA model allows to reproduce both the B- and A- DNA forms and the transitions between them under corresponding conditions.
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42
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Ye Y, Du Z, Tian M, Zhang L, Mi J. Diffusive dynamics of polymer chains in an array of nanoposts. Phys Chem Chem Phys 2017; 19:380-387. [DOI: 10.1039/c6cp07217h] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The diffusion of the head, side, and middle segments in confined polymer chains displays different dynamics in different directions.
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Affiliation(s)
- Yi Ye
- State Key Laboratory of Organic-Inorganic Composites
- Beijing University of Chemical Technology
- Beijing 100029
- China
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials
| | - Zhongjie Du
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials
- Beijing University of Chemical Technology
- Beijing
- China
| | - Ming Tian
- State Key Laboratory of Organic-Inorganic Composites
- Beijing University of Chemical Technology
- Beijing 100029
- China
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials
| | - Liqun Zhang
- State Key Laboratory of Organic-Inorganic Composites
- Beijing University of Chemical Technology
- Beijing 100029
- China
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials
| | - Jianguo Mi
- State Key Laboratory of Organic-Inorganic Composites
- Beijing University of Chemical Technology
- Beijing 100029
- China
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43
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Jeffet J, Kobo A, Su T, Grunwald A, Green O, Nilsson AN, Eisenberg E, Ambjörnsson T, Westerlund F, Weinhold E, Shabat D, Purohit PK, Ebenstein Y. Super-Resolution Genome Mapping in Silicon Nanochannels. ACS NANO 2016; 10:9823-9830. [PMID: 27646634 DOI: 10.1021/acsnano.6b05398] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Optical genome mapping in nanochannels is a powerful genetic analysis method, complementary to deoxyribonucleic acid (DNA) sequencing. The method is based on detecting a pattern of fluorescent labels attached along individual DNA molecules. When such molecules are extended in nanochannels, the labels create a fluorescent genetic barcode that is used for mapping the DNA molecule to its genomic locus and identifying large-scale variation from the genome reference. Mapping resolution is currently limited by two main factors: the optical diffraction limit and the thermal fluctuations of DNA molecules suspended in the nanochannels. Here, we utilize single-molecule tracking and super-resolution localization in order to improve the mapping accuracy and resolving power of this genome mapping technique and achieve a 15-fold increase in resolving power compared to currently practiced methods. We took advantage of a naturally occurring genetic repeat array and labeled each repeat with custom-designed Trolox conjugated fluorophores for enhanced photostability. This model system allowed us to acquire extremely long image sequences of the equally spaced fluorescent markers along DNA molecules, enabling detailed characterization of nanoconfined DNA dynamics and quantitative comparison to the Odijk theory for confined polymer chains. We present a simple method to overcome the thermal fluctuations in the nanochannels and exploit single-step photobleaching to resolve subdiffraction spaced fluorescent markers along fluctuating DNA molecules with ∼100 bp resolution. In addition, we show how time-averaging over just ∼50 frames of 40 ms enhances mapping accuracy, improves mapping P-value scores by 3 orders of magnitude compared to nonaveraged alignment, and provides a significant advantage for analyzing structural variations between DNA molecules with similar sequence composition.
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Affiliation(s)
- Jonathan Jeffet
- Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University , Tel Aviv 6997801, Israel
| | - Asaf Kobo
- Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University , Tel Aviv 6997801, Israel
| | - Tianxiang Su
- School of Engineering and Applied Sciences, Harvard University , Cambridge, Massachusetts 02138, United States
| | - Assaf Grunwald
- Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University , Tel Aviv 6997801, Israel
| | - Ori Green
- Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University , Tel Aviv 6997801, Israel
| | - Adam N Nilsson
- Department of Astronomy and Theoretical Physics, Lund University , SE-221 00 Lund, Sweden
| | - Eli Eisenberg
- Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University , Tel Aviv 6997801, Israel
| | - Tobias Ambjörnsson
- Department of Astronomy and Theoretical Physics, Lund University , SE-221 00 Lund, Sweden
| | - Fredrik Westerlund
- Department of Biology and Biological Engineering, Chalmers University of Technology , SE-412 96 Gothenburg, Sweden
| | - Elmar Weinhold
- Institute of Organic Chemistry, RWTH Aachen University , Aachen D-52056, Germany
| | - Doron Shabat
- Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University , Tel Aviv 6997801, Israel
| | - Prashant K Purohit
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania , Philadelphia, Pennsylvania 19104, United States
| | - Yuval Ebenstein
- Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University , Tel Aviv 6997801, Israel
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44
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Benková Z, Námer P, Cifra P. Comparison of a stripe and slab confinement for ring and linear macromolecules in nanochannel. SOFT MATTER 2016; 12:8425-8439. [PMID: 27722460 DOI: 10.1039/c6sm01507g] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The combined effects of the channel asymmetry and the closed chain topology on the chain extension, structure factor, and the orientation correlations were studied using coarse-grained molecular dynamics simulations for moderate chain lengths. These effects are related to applications in linearization experiments with a DNA molecule in nanofluidic devices. According to the aspect ratio, the channels are classified as a stripe or slabs. The chain segments do not have any freedom to move in the direction of the narrowest stripe size, being approximately the same size as the segment size. The chains of both ring and linear topologies are extended more in a stripe than in a slab; this effect is strengthened for a ring. For a ring in a stripe, the extension-confinement strength dependence leads to effective Flory exponents even larger than 3/4, which is characteristic for a self-avoiding two-dimensional chain. While the chain extension-confinement strength dependence for both topologies conforms to the de Gennes regime in a stripe, a linear chain undergoes gradual transition to the pseudoideal regime as the slab height increases in the slab-like confinement. For a confined circle, the onset of the pseudoideal regime is shifted to larger slab heights. The structure factor confirms the absence of the pseudoideal and extended de Gennes regime in a stripe and the transition from the extended to the pseudoideal regime of a circular and linear chain upon increasing the slab heights.
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Affiliation(s)
- Zuzana Benková
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia. and LAQV@REQUIMTE, Department of Chemistry and Biochemistry, Faculty of Sciences, University of Porto, Rua do Campo Alegre 687, 4168-007 Porto, Portugal
| | - Pavol Námer
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia.
| | - Peter Cifra
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia.
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45
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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] [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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46
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Jain A, Sheats J, Reifenberger JG, Cao H, Dorfman KD. Modeling the relaxation of internal DNA segments during genome mapping in nanochannels. BIOMICROFLUIDICS 2016; 10:054117. [PMID: 27795749 PMCID: PMC5065570 DOI: 10.1063/1.4964927] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2016] [Accepted: 10/04/2016] [Indexed: 06/01/2023]
Abstract
We have developed a multi-scale model describing the dynamics of internal segments of DNA in nanochannels used for genome mapping. In addition to the channel geometry, the model takes as its inputs the DNA properties in free solution (persistence length, effective width, molecular weight, and segmental hydrodynamic radius) and buffer properties (temperature and viscosity). Using pruned-enriched Rosenbluth simulations of a discrete wormlike chain model with circa 10 base pair resolution and a numerical solution for the hydrodynamic interactions in confinement, we convert these experimentally available inputs into the necessary parameters for a one-dimensional, Rouse-like model of the confined chain. The resulting coarse-grained model resolves the DNA at a length scale of approximately 6 kilobase pairs in the absence of any global hairpin folds, and is readily studied using a normal-mode analysis or Brownian dynamics simulations. The Rouse-like model successfully reproduces both the trends and order of magnitude of the relaxation time of the distance between labeled segments of DNA obtained in experiments. The model also provides insights that are not readily accessible from experiments, such as the role of the molecular weight of the DNA and location of the labeled segments that impact the statistical models used to construct genome maps from data acquired in nanochannels. The multi-scale approach used here, while focused towards a technologically relevant scenario, is readily adapted to other channel sizes and polymers.
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Affiliation(s)
- Aashish Jain
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities , 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Julian Sheats
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities , 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | | | - Han Cao
- BioNano Genomics , 9640 Towne Centre Drive, Suite 100, San Diego, California 92121, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities , 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
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47
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Egorov SA, Milchev A, Binder K. Semiflexible Polymers in the Bulk and Confined by Planar Walls. Polymers (Basel) 2016; 8:E296. [PMID: 30974573 PMCID: PMC6432127 DOI: 10.3390/polym8080296] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2016] [Revised: 07/27/2016] [Accepted: 07/29/2016] [Indexed: 11/21/2022] Open
Abstract
Semiflexible polymers in solution under good solvent conditions can undergo an isotropic-nematic transition. This transition is reminiscent of the well-known entropically-driven transition of hard rods described by Onsager's theory, but the flexibility of the macromolecules causes specific differences in behavior, such as anomalous long wavelength fluctuations in the ordered phase, which can be understood by the concept of the deflection length. A brief review of the recent progress in the understanding of these problems is given, summarizing results obtained by large-scale molecular dynamics simulations and density functional theory. These results include also the interaction of semiflexible polymers with hard walls and the wall-induced nematic order, which can give rise to capillary nematization in thin film geometry. Various earlier theoretical approaches to these problems are briefly mentioned, and an outlook on the status of experiments is given. It is argued that in many cases of interest, it is not possible to describe the scaled densities at the isotropic-nematic transition as functions of the ratio of the contour length and the persistence length alone, but the dependence on the ratio of chain diameter and persistence length also needs to be considered.
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Affiliation(s)
- Sergei A Egorov
- Department of Chemistry, University of Virginia, Charlottesville, VA 22901, USA.
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany.
| | - Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113 Sofia, Bulgaria.
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany.
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48
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Egorov SA, Milchev A, Virnau P, Binder K. A new insight into the isotropic-nematic phase transition in lyotropic solutions of semiflexible polymers: density-functional theory tested by molecular dynamics. SOFT MATTER 2016; 12:4944-59. [PMID: 27249320 DOI: 10.1039/c6sm00778c] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Semiflexible polymers in solution are studied for a wide range of both contour length L and persistence length lp as a function of monomer concentration under good solvent conditions. Both density-functional theory (DFT) and molecular dynamics (MD) simulation methods are used, and a very good agreement between both techniques is observed for rather stiff polymers. Evidence for a new mechanism of order parameter fluctuations in the nematic phase is presented, namely collective deformations of bundles of wormlike chains twisted around each other, and the typical wavelengths and amplitudes of these modes are estimated. These long wavelength fluctuations cause a reduction of the order parameter in comparison with the DFT prediction. It is also found that DFT becomes unreliable for rather flexible polymers in predicting that the transition from the isotropic (I)-phase to the nematic (N)-phase still exists at very high monomer concentrations (which in reality does not occur). However, under conditions when DFT is accurate, it provides reliable predictions also for the width of the I-N two-phase coexistence region, which are difficult to obtain from MD in spite of the use of very large systems (up to 500 000 monomers) by means of graphics processing units (GPU). For short and not very stiff chains, a pre-transitional chain stretching is found in the isotropic phase near the I-N-transition, not predicted by theories. A comparison with theoretical predictions by Khokhlov-Semenov, Odijk, and Chen reveals that the scaled transition densities are not simply functions of L/lp only, as these theories predict, but depend on d/lp (where d is the chain diameter) as well. Chain properties in the nematically ordered phase are compared to those of chains confined in tubes, and the deflection length concept is tested. Eventually, some consequences for the interpretation of experiments are spelled out.
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Affiliation(s)
- Sergei A Egorov
- Department of Chemistry, University of Virginia, Charlottesville, VA 22901, USA.
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49
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Dai L, Renner CB, Doyle PS. The polymer physics of single DNA confined in nanochannels. Adv Colloid Interface Sci 2016; 232:80-100. [PMID: 26782150 DOI: 10.1016/j.cis.2015.12.002] [Citation(s) in RCA: 73] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2015] [Revised: 12/01/2015] [Accepted: 12/01/2015] [Indexed: 11/17/2022]
Abstract
In recent years, applications and experimental studies of DNA in nanochannels have stimulated the investigation of the polymer physics of DNA in confinement. Recent advances in the physics of confined polymers, using DNA as a model polymer, have moved beyond the classic Odijk theory for the strong confinement, and the classic blob theory for the weak confinement. In this review, we present the current understanding of the behaviors of confined polymers while briefly reviewing classic theories. Three aspects of confined DNA are presented: static, dynamic, and topological properties. The relevant simulation methods are also summarized. In addition, comparisons of confined DNA with DNA under tension and DNA in semidilute solution are made to emphasize universal behaviors. Finally, an outlook of the possible future research for confined DNA is given.
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602, Singapore
| | - C Benjamin Renner
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, United States
| | - Patrick S Doyle
- BioSystems and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602, Singapore; Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, United States.
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50
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Muralidhar A, Quevillon MJ, Dorfman KD. The Backfolded Odijk Regime for Wormlike Chains Confined in Rectangular Nanochannels. Polymers (Basel) 2016; 8:polym8030079. [PMID: 30979173 PMCID: PMC6432538 DOI: 10.3390/polym8030079] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2016] [Revised: 02/05/2016] [Accepted: 03/07/2016] [Indexed: 11/16/2022] Open
Abstract
We confirm Odijk's scaling laws for (i) the average chain extension; (ii) the variance about the average extension; and (iii) the confinement free energy of a wormlike chain confined in a rectangular nanochannel smaller than its chain persistence length through pruned-enriched Rosenbluth method (PERM) simulations of asymptotically long, discrete wormlike chains. In the course of this analysis, we also computed the global persistence length of ideal wormlike chains for the modestly rectangular channels that are used in many experimental systems. The results are relevant to genomic mapping systems that confine DNA in channel sizes around 50 nm, since fabrication constraints generally lead to rectangular cross-sections.
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Affiliation(s)
- Abhiram Muralidhar
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave. SE, Minneapolis, MN 55455, USA.
| | - Michael J Quevillon
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave. SE, Minneapolis, MN 55455, USA.
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave. SE, Minneapolis, MN 55455, USA.
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