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Yeboah IO, Young RT, Mosioma M, Sensale S. A mean-field theory for characterizing the closing rates of DNA origami hinges. J Chem Phys 2024; 161:074901. [PMID: 39145564 DOI: 10.1063/5.0222446] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2024] [Accepted: 08/01/2024] [Indexed: 08/16/2024] Open
Abstract
The evolution of dynamic DNA nanostructures has propelled DNA nanotechnology into a robust and versatile field, offering groundbreaking applications in nanoscale communication, drug delivery, and molecular computing. Yet, the full potential of this technology awaits further enhancement through optimization of kinetic properties governing conformational changes. In this work, we introduce a mean-field theory to characterize the kinetic behavior of a dynamic DNA origami hinge where each arm bears complementary single-stranded DNA overhangs of different lengths, which can latch the hinge at a closed conformation. This device is currently being investigated for multiple applications, being of particular interest the development of DNA-based rapid diagnostic tests for coronavirus. Drawing from classical statistical mechanics theories, we derive analytical expressions for the mean binding time of these overhangs within a constant hinge. This analysis is then extended to flexible hinges, where the angle diffuses within a predetermined energy landscape. We validate our model by comparing it with experimental measurements of the closing rates of DNA nanocalipers with different energy landscapes and overhang lengths, demonstrating excellent agreement and suggesting fast angular relaxation relative to binding. These findings offer insights that can guide the optimization of devices for specific state lifetimes. Moreover, the framework introduced here lays the groundwork for further advancements in modeling the kinetics of dynamic DNA nanostructures.
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Affiliation(s)
- Isaac O Yeboah
- Department of Physics, Cleveland State University, Cleveland, Ohio 44115, USA
| | - Robert T Young
- Department of Physics, Cleveland State University, Cleveland, Ohio 44115, USA
| | - Mark Mosioma
- Department of Physics, Cleveland State University, Cleveland, Ohio 44115, USA
| | - Sebastian Sensale
- Department of Physics, Cleveland State University, Cleveland, Ohio 44115, USA
- Department of Physics, Indiana University Indianapolis, Indianapolis, Indiana 46202, USA
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Kumar S, Chauhan K, Singh S, Foster D. Polymer in wedge-shaped confinement: Effect on the θ temperature. Phys Rev E 2020; 101:030502. [PMID: 32290024 DOI: 10.1103/physreve.101.030502] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Accepted: 01/29/2020] [Indexed: 11/07/2022]
Abstract
The equilibrium properties of a finite-length linear polymer chain confined in an infinite wedge composed of two perfectly reflecting hard walls meeting at a variable apex angle (α) are presented. One end of the polymer is anchored a distance y from the apex on the conical axis of symmetry, while the other end is free. We report here, the nonmonotonic behavior of θ temperature as a function of y for a finite-length chain. Data collapse for different chain lengths indicates that such behavior will exist for all finite lengths. We delineate the origin of such nonmonotonic behavior, which may have potential applications in understanding the cellular process occurring in nanoconfined geometries.
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Affiliation(s)
- Sanjay Kumar
- Department of Physics, Banaras Hindu University, Varanasi 221005, India
| | - Keerti Chauhan
- Department of Physics, Banaras Hindu University, Varanasi 221005, India
| | - Sadhana Singh
- Department of Physics, Banaras Hindu University, Varanasi 221005, India
| | - Damien Foster
- Centre for Data Science, Coventry University, Coventry CV1 5FB, United Kingdom
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Levi RH, Kantor Y, Kardar M. Localization of random walks to competing manifolds of distinct dimensions. Phys Rev E 2018; 98:022108. [PMID: 30253483 DOI: 10.1103/physreve.98.022108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2018] [Indexed: 11/07/2022]
Abstract
We consider localization of a random walk (RW) when attracted or repelled by multiple extended manifolds of different dimensionalities. In particular, we consider a RW near a rectangular wedge in two dimensions, where the (zero-dimensional) corner and the (one-dimensional) wall have competing localization properties. This model applies also (as cross section) to an ideal polymer attracted to the surface or edge of a rectangular wedge in three dimensions. More generally, we consider (d-1)- and (d-2)-dimensional manifolds in d-dimensional space, where attractive interactions are (fully or marginally) relevant. The RW can then be in one of four phases where it is localized to neither, one, or both manifolds. The four phases merge at a special multicritical point where (away from the manifolds) the RW spreads diffusively. Extensive numerical analyses on two-dimensional RWs confined inside or outside a rectangular wedge confirm general features expected from a continuum theory, but also exhibit unexpected attributes, such as a reentrant localization to the corner while repelled by it.
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Affiliation(s)
- Raz Halifa Levi
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - Yacov Kantor
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - Mehran Kardar
- Massachusetts Institute of Technology, Department of Physics, Cambridge, Massachusetts 02139, USA
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Levi RH, Kantor Y, Kardar M. Pinning and unbinding of ideal polymers from a wedge corner. Phys Rev E 2018; 96:062132. [PMID: 29347457 DOI: 10.1103/physreve.96.062132] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2017] [Indexed: 11/07/2022]
Abstract
A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a repulsive wedge. The well-known mapping between the statistical mechanics of an ideal polymer and the quantum problem of a particle in a potential is then used to analyze the singular behavior of the unbinding transition of the polymer. The divergence of the localization length is found to be governed by an exponent that varies continuously with the angle (when reflex). Numerical treatment of the discrete (lattice) version of such an adsorption problem confirms this behavior.
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Affiliation(s)
- Raz Halifa Levi
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - Yacov Kantor
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Kantor Y, Kardar M. Attractive and repulsive polymer-mediated forces between scale-free surfaces. Phys Rev E 2017; 96:022148. [PMID: 28950594 DOI: 10.1103/physreve.96.022148] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2017] [Indexed: 11/07/2022]
Abstract
We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone) when the polymer is repelled by the obstacles or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation h between obstacles is the only relevant macroscopic length scale, and the polymer-mediated force equals Ak_{B}T/h, where T is temperature. The amplitude A is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of A, which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find A=0 for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e., at this special point there is no polymer-mediated force between obstacles (scale free or not).
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Affiliation(s)
- Yacov Kantor
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - Mehran Kardar
- Massachusetts Institute of Technology, Department of Physics, Cambridge, Massachusetts 02139, USA
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Hammer Y, Kantor Y. Long polymers near wedges and cones. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062602. [PMID: 26764719 DOI: 10.1103/physreve.92.062602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2015] [Indexed: 06/05/2023]
Abstract
We perform a Monte Carlo study of N-step self-avoiding walks, attached to the corner of an impenetrable wedge in two dimensions (d=2), or the tip of an impenetrable cone in d=3, of sizes ranging up to N=10(6) steps. We find that the critical exponent γ(α), which determines the dependence of the number of available conformations on N for a cone or wedge with opening angle α, is in good agreement with the theory for d=2. We study the end-point distribution of the walks in the allowed space and find similarities to the known behavior of random walks (ideal polymers) in the same geometry. For example, the ratio between the mean square end-to-end distances of a polymer near the cone or wedge and a polymer in free space depends linearly on γ(α), as is known for ideal polymers. We show that the end-point distribution of polymers attached to a wedge does not separate into a product of angular and radial functions, as it does for ideal polymers in the same geometry. The angular dependence of the end position of polymers near the wedge differs from theoretical predictions.
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Affiliation(s)
- Yosi Hammer
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - Yacov Kantor
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
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Waters JT, Kim HD. Calculation of a fluctuating entropic force by phase space sampling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:013308. [PMID: 26274308 DOI: 10.1103/physreve.92.013308] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2015] [Indexed: 06/04/2023]
Abstract
A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.
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Affiliation(s)
- James T Waters
- School of Physics, Georgia Institute of Technology and 832 State Street, Atlanta, Georgia 30332-0430
| | - Harold D Kim
- School of Physics, Georgia Institute of Technology and 832 State Street, Atlanta, Georgia 30332-0430
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Nikoofard N, Fazli H. A flexible polymer confined inside a cone-shaped nano-channel. SOFT MATTER 2015; 11:4879-4887. [PMID: 25994794 DOI: 10.1039/c5sm00818b] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The nano-scale confinement of polymers in cone-shaped geometries occurs in many experimental situations. A flexible polymer confined in a cone-shaped nano-channel is studied theoretically and by using molecular dynamics simulations. Distribution of the monomers inside the channel, configuration of the confined polymer, the entropic force acting on the polymer, and their dependence on the channel and the polymer parameters are investigated. The theory and the simulation results are in very good agreement. The entropic force on the polymer that results from the asymmetric shape of the channel is measured in the simulations and its magnitude is found to be significant relative to thermal energy. The obtained dependence of the force on the channel parameters may be useful in the design of cone-shaped nano-channels.
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Affiliation(s)
- Narges Nikoofard
- Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan 51167-87317, Iran.
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Alfasi N, Kantor Y. Diffusion in the presence of scale-free absorbing boundaries. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042126. [PMID: 25974457 DOI: 10.1103/physreve.91.042126] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Indexed: 06/04/2023]
Abstract
Scale-free surfaces, such as cones, remain unchanged under a simultaneous expansion of all coordinates by the same factor. Probability density of a particle diffusing near such absorbing surface at large time approaches a simple form that incorporates power-law dependencies on time and distance from a special point, such as apex of the cone, which are characterized by a single exponent η. The same exponent is used to describe the number of spatial conformations of long ideal polymer attached to the special point of a repulsive surface of the same geometry and can be used in calculation of entropic forces between such polymers and surfaces. We use the solution of diffusion equation near such surfaces to find the numerical values of η, as well as to provide some insight into the behavior of ideal polymers near such surfaces.
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Affiliation(s)
- Nir Alfasi
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
- Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Yacov Kantor
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
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Foteinopoulou K, Karayiannis NC, Laso M. Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement. Chem Eng Sci 2015. [DOI: 10.1016/j.ces.2014.08.021] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Hammer Y, Kantor Y. Entropic pressure in lattice models for polymers. J Chem Phys 2014; 141:204905. [DOI: 10.1063/1.4902231] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yosi Hammer
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - Yacov Kantor
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
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12
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Benetatos P. Crosslink-induced shrinkage of grafted Gaussian chains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042602. [PMID: 24827269 DOI: 10.1103/physreve.89.042602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2014] [Indexed: 06/03/2023]
Abstract
The statistical mechanics of polymers grafted on surfaces has been the subject of intense research activity because of many potential applications. In this paper, we analytically investigate the conformational changes caused by a single crosslink on two ideal (Gaussian) chains grafted onto a rigid planar surface. Both the crosslink and the surface reduce the number of allowed configurations. In the absence of the hard substrate, the sole effect of the crosslink is a reduction in the effective Kuhn length of a tethered chain. The crosslink-induced shrinkage (collapse) of the grafted chains (mushrooms) turns out to be a reduction in the variance of the distribution of the height of the chain rather than a reduction of the height itself.
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Affiliation(s)
- Panayotis Benetatos
- Department of Physics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 702-701, Korea
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