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McDonald MN, Tree DR, Peterson CK. Chemical herding as a multiplicative factor for top-down manipulation of colloids. Phys Rev E 2024; 109:064609. [PMID: 39020876 DOI: 10.1103/physreve.109.064609] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2023] [Accepted: 05/21/2024] [Indexed: 07/20/2024]
Abstract
Colloidal particles can create reconfigurable nanomaterials, with applications such as color-changing, self-repairing, and self-regulating materials and reconfigurable drug delivery systems. However, top-down methods for manipulating colloids are limited in the scale they can control. We consider here a new method for using chemical reactions to multiply the effects of existing top-down colloidal manipulation methods to arrange large numbers of colloids with single-particle precision, which we refer to as chemical herding. Using simulation-based methods, we show that if a set of chemically active colloids (herders) can be steered using external forces (i.e., electrophoretic, dielectrophoretic, magnetic, or optical forces), then a larger set of colloids (followers) that move in response to the chemical gradients produced by the herders can be steered using the control algorithms given in this paper. We also derive bounds that predict the maximum number of particles that can be steered in this way, and we illustrate the effectiveness of this approach using Brownian dynamics simulations. Based on the theoretical results and simulations, we conclude that chemical herding is a viable method for multiplying the effects of existing colloidal manipulation methods to create useful structures and materials.
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2
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Długosz M, Cichocki B, Szymczak P. First coarse grain then scale: How to estimate diffusion coefficients of confined molecules. J Chem Phys 2023; 159:214101. [PMID: 38038202 DOI: 10.1063/5.0175501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2023] [Accepted: 11/09/2023] [Indexed: 12/02/2023] Open
Abstract
An approach for approximating position and orientation dependent translational and rotational diffusion coefficients of rigid molecules of any shape suspended in a viscous fluid under geometric confinement is proposed. It is an extension of the previously developed scheme for evaluating near-wall diffusion of macromolecules, now applied to any geometry of boundaries. The method relies on shape based coarse-graining combined with scaling of mobility matrix components by factors derived based on energy dissipation arguments for Stokes flows. Tests performed for a capsule shaped molecule and its coarse-grained model, a dumbbell, for three different types of boundaries (a sphere, an open cylinder, and two parallel planes) are described. An almost perfect agreement between mobility functions of the detailed and coarse-grained models, even close to boundary surfaces, is obtained. The proposed method can be used to simplify hydrodynamic calculations and reduce errors introduced due to coarse-graining of molecular shapes.
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Affiliation(s)
- Maciej Długosz
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, Pasteura 5, Poland
| | - Bogdan Cichocki
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, Pasteura 5, Poland
| | - Piotr Szymczak
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, Pasteura 5, Poland
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3
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Rusková R, Račko D. Knot Formation on DNA Pushed Inside Chiral Nanochannels. Polymers (Basel) 2023; 15:4185. [PMID: 37896430 PMCID: PMC10611388 DOI: 10.3390/polym15204185] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2023] [Revised: 10/18/2023] [Accepted: 10/19/2023] [Indexed: 10/29/2023] Open
Abstract
We performed coarse-grained molecular dynamics simulations of DNA polymers pushed inside infinite open chiral and achiral channels. We investigated the behavior of the polymer metrics in terms of span, monomer distributions and changes of topological state of the polymer in the channels. We also compared the regime of pushing a polymer inside the infinite channel to the case of polymer compression in finite channels of knot factories investigated in earlier works. We observed that the compression in the open channels affects the polymer metrics to different extents in chiral and achiral channels. We also observed that the chiral channels give rise to the formation of equichiral knots with the same handedness as the handedness of the chiral channels.
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Affiliation(s)
- Renáta Rusková
- Polymer Institute of the Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia
| | - Dušan Račko
- Polymer Institute of the Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia
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4
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Jiao Y, Zeng C, Luo Y. Roughness induced current reversal in fractional hydrodynamic memory. CHAOS (WOODBURY, N.Y.) 2023; 33:093140. [PMID: 37748483 DOI: 10.1063/5.0164625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Accepted: 09/07/2023] [Indexed: 09/27/2023]
Abstract
The existence of a corrugated surface is of great importance and ubiquity in biological systems, exhibiting diverse dynamic behaviors. However, it has remained unclear whether such rough surface leads to the current reversal in fractional hydrodynamic memory. We investigate the transport of a particle within a rough potential under external forces in a subdiffusive media with fractional hydrodynamic memory. The results demonstrate that roughness induces current reversal and a transition from no transport to transport. These phenomena are analyzed through the subdiffusion, Peclet number, useful work, input power, and thermodynamic efficiency. The analysis reveals that transport results from energy conversion, wherein time-dependent periodic force is partially converted into mechanical energy to drive transport against load, and partially dissipated through environmental absorption. In addition, the findings indicate that the size and shape of ratchet tune the occurrence and disappearance of the current reversal, and control the number of times of the current reversal occurring. Furthermore, we find that temperature, friction, and load tune transport, resonant-like activity, and enhanced stability of the system, as evidenced by thermodynamic efficiency. These findings may have implications for understanding dynamics in biological systems and may be relevant for applications involving molecular devices for particle separation at the mesoscopic scale.
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Affiliation(s)
- Yuanyuan Jiao
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Chunhua Zeng
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Yuhui Luo
- School of Physics and Information Engineering, Zhaotong University, Zhaotong 657000, China
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5
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Suma A, Carnevale V, Micheletti C. Nonequilibrium Thermodynamics of DNA Nanopore Unzipping. PHYSICAL REVIEW LETTERS 2023; 130:048101. [PMID: 36763417 DOI: 10.1103/physrevlett.130.048101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 09/27/2022] [Accepted: 12/23/2022] [Indexed: 06/18/2023]
Abstract
Using theory and simulations, we carried out a first systematic characterization of DNA unzipping via nanopore translocation. Starting from partially unzipped states, we found three dynamical regimes depending on the applied force f: (i) heterogeneous DNA retraction and rezipping (f<17 pN), (ii) normal (17 pN<f<60 pN), and (iii) anomalous (f>60 pN) drift-diffusive behavior. We show that the normal drift-diffusion regime can be effectively modeled as a one-dimensional stochastic process in a tilted periodic potential. We use the theory of stochastic processes to recover the potential from nonequilibrium unzipping trajectories and show that it corresponds to the free-energy landscape for single-base-pair unzipping. Applying this general approach to other single-molecule systems with periodic potentials ought to yield detailed free-energy landscapes from out-of-equilibrium trajectories.
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Affiliation(s)
- Antonio Suma
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari, I-70126, Italy
- Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Vincenzo Carnevale
- Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Cristian Micheletti
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
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6
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McDonald MN, Peterson CK, Tree DR. Steering particles via micro-actuation of chemical gradients using model predictive control. BIOMICROFLUIDICS 2023; 17:014107. [PMID: 36742353 PMCID: PMC9894658 DOI: 10.1063/5.0126690] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
Biological systems rely on chemical gradients to direct motion through both chemotaxis and signaling, but synthetic approaches for doing the same are still relatively naïve. Consequently, we present a novel method for using chemical gradients to manipulate the position and velocity of colloidal particles in a microfluidic device. Specifically, we show that a set of spatially localized chemical reactions that are sufficiently controllable can be used to steer colloidal particles via diffusiophoresis along an arbitrary trajectory. To accomplish this, we develop a control method for steering colloidal particles with chemical gradients using nonlinear model predictive control with a model based on the unsteady Green's function solution of the diffusion equation. We illustrate the effectiveness of our approach using Brownian dynamics simulations that steer single particles along paths, such as circle, square, and figure-eight. We subsequently compare our results with published techniques for steering colloids using electric fields, and we provide an analysis of the physical parameter space where our approach is useful. Based on these findings, we conclude that it is theoretically possible to explicitly steer particles via chemical gradients in a microfluidics paradigm.
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Affiliation(s)
- Mark N. McDonald
- Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, USA
| | - Cameron K. Peterson
- Department of Electrical and Computer Engineering, Brigham Young University, Provo, Utah 84602, USA
| | - Douglas R. Tree
- Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, USA
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7
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Długosz M, Cichocki B, Szymczak P. Estimating near-wall diffusion coefficients of arbitrarily shaped rigid macromolecules. Phys Rev E 2022; 106:014407. [PMID: 35974550 DOI: 10.1103/physreve.106.014407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 07/10/2022] [Indexed: 06/15/2023]
Abstract
We developed a computationally efficient approach to approximate near-wall diffusion coefficients of arbitrarily shaped rigid macromolecules. The proposed method relies on extremum principles for Stokes flows produced by the motion of rigid bodies. In the presence of the wall, the rate of energy dissipation is decreased relative to the unbounded fluid. In our approach, the position- and orientation-dependent mobility matrix of a body suspended near a no-slip plane is calculated numerically using a coarse-grained molecular model and the Rotne-Prager-Yamakawa description of hydrodynamics. Effects of the boundary are accounted for via Blake's image construction. The matrix components are scaled using ratios of the corresponding bulk values evaluated for the detailed representation of the molecule and its coarse-grained model, leading to accurate values of the near-wall diffusion coefficients. We assess the performance of the approach for two biomolecules at different levels of coarse-graining.
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Affiliation(s)
- Maciej Długosz
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, Pasteura 5, Poland
| | - Bogdan Cichocki
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, Pasteura 5, Poland
| | - Piotr Szymczak
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, Pasteura 5, Poland
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8
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Rothörl J, Wettermann S, Virnau P, Bhattacharya A. Knot formation of dsDNA pushed inside a nanochannel. Sci Rep 2022; 12:5342. [PMID: 35351953 PMCID: PMC8964721 DOI: 10.1038/s41598-022-09242-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 03/17/2022] [Indexed: 12/23/2022] Open
Abstract
Recent experiments demonstrated that knots in single molecule dsDNA can be formed by compression in a nanochannel. In this manuscript, we further elucidate the underlying molecular mechanisms by carrying out a compression experiment in silico, where an equilibrated coarse-grained double-stranded DNA confined in a square channel is pushed by a piston. The probability of forming knots is a non-monotonic function of the persistence length and can be enhanced significantly by increasing the piston speed. Under compression knots are abundant and delocalized due to a backfolding mechanism from which chain-spanning loops emerge, while knots are less frequent and only weakly localized in equilibrium. Our in silico study thus provides insights into the formation, origin and control of DNA knots in nanopores.
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9
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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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10
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Nowicki W. Electrostatic/entropic macromolecule manipulation in nanochannel. Swapping of macromolecule locations. J Mol Model 2019; 25:269. [DOI: 10.1007/s00894-019-4155-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2019] [Accepted: 08/14/2019] [Indexed: 11/24/2022]
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11
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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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12
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Gupta D, Bhandari AB, Dorfman KD. Evaluation of Blob Theory for the Diffusion of DNA in Nanochannels. Macromolecules 2018; 51:1748-1755. [PMID: 29599567 DOI: 10.1021/acs.macromol.7b02270] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
We have measured the diffusivity of λ-DNA molecules in approximately square nanochannels with effective sizes ranging from 117 nm to 260 nm at moderate ionic strength. The experimental results do not agree with the non-draining scaling predicted by blob theory. Rather, the data are consistent with the predictions of previous simulations of the Kirkwood diffusivity of a discrete wormlike chain model, without the need for any fitting parameters.
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Affiliation(s)
- Damini Gupta
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, 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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13
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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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14
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Saadat A, Khomami B. A new bead-spring model for simulation of semi-flexible macromolecules. J Chem Phys 2016; 145:204902. [DOI: 10.1063/1.4968020] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Amir Saadat
- Material Research and Innovation Laboratory, Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996-2200, USA
| | - Bamin Khomami
- Material Research and Innovation Laboratory, Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996-2200, USA
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15
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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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16
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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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17
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Muralidhar A, Dorfman KD. Kirkwood diffusivity of long semiflexible chains in nanochannel confinement. Macromolecules 2015; 48:2829-2839. [PMID: 26166846 PMCID: PMC4494130 DOI: 10.1021/acs.macromol.5b00377] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We compute the axial diffusivity of asymptotically long semiflexible polymers confined in square channels. Our calculations employ the Kirkwood approximation of the mobility tensor by combining computational fluid dynamics (CFD) calculations of the hydrodynamic tensor in channel confinement with pruned-enriched Rosenbluth method (PERM) simulations of a discrete wormlike chain model. Three key results emerge from our study. First, for the classic de Gennes regime, we confirm that Brochard and de Gennes' blob theory correctly predicts the scaling of the axial diffusivity, contrary to the conclusions of previous analyses. Second, for the extended de Gennes regime, we show that a modified blob theory, which has been used to incorporate the effect of local stiffness on DNA diffusion in nanoslits, explains the deviation from the prediction of classic blob theory for diffusion in nanochannels. Third, we provide a calculation similar to the modified blob theory to explain the relative insensitivity of the diffusivity to channel size for channels between the extended de Gennes regime and the Odijk regime, which is the most relevant regime for experiments and technological applications of DNA confinement in nanochannels. Our results are not only relevant to the dynamics of confined semiflexible polymers such as DNA, but also reveal interesting analogies between confinement in channels and slits.
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Affiliation(s)
- Abhiram Muralidhar
- 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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18
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Jain A, Dorfman KD. Evaluation of the Kirkwood approximation for the diffusivity of channel-confined DNA chains in the de Gennes regime. BIOMICROFLUIDICS 2015; 9:024112. [PMID: 25945138 PMCID: PMC4393413 DOI: 10.1063/1.4917269] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2015] [Accepted: 03/30/2015] [Indexed: 05/30/2023]
Abstract
We use Brownian dynamics with hydrodynamic interactions to calculate both the Kirkwood (short-time) diffusivity and the long-time diffusivity of DNA chains from free solution down to channel confinement in the de Gennes regime. The Kirkwood diffusivity in confinement is always higher than the diffusivity obtained from the mean-squared displacement of the center-of-mass, as is the case in free solution. Moreover, the divergence of the local diffusion tensor, which is non-zero in confinement, makes a negligible contribution to the latter diffusivity in confinement. The maximum error in the Kirkwood approximation in our simulations is about 2% for experimentally relevant simulation times. The error decreases with increasing confinement, consistent with arguments from blob theory and the molecular-weight dependence of the error in free solution. In light of the typical experimental errors in measuring the properties of channel-confined DNA, our results suggest that the Kirkwood approximation is sufficiently accurate to model experimental data.
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Affiliation(s)
- Aashish Jain
- Department of Chemical Engineering and Material Science, University of Minnesota-Twin Cities , 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Material Science, University of Minnesota-Twin Cities , 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
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19
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Bezrukov SM, Schimansky-Geier L, Schmid G. Brownian motion in confined geometries. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2014; 223:3021-3025. [PMID: 29034062 PMCID: PMC5635657 DOI: 10.1140/epjst/e2014-02316-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In a great number of technologically and biologically relevant cases, transport of micro- or nanosized objects is governed by both omnipresent thermal fluctuations and confining walls or constrictions limiting the available phase space. The present Topical Issue covers the most recent applications and theoretical findings devoted to studies of Brownian motion under confinement of channel-like geometries.
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Affiliation(s)
- S M Bezrukov
- Program in Physical Biology, NICHD, National Institutes of Health, Bethesda, MD 20892-0924, USA
| | - L Schimansky-Geier
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - G Schmid
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, 86159 Augsburg, Germany
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