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Chauhan K, Singh A. Delayed collapse transitions in a pinned polymer system. Phys Rev E 2022; 105:064505. [PMID: 35854509 DOI: 10.1103/physreve.105.064505] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2022] [Accepted: 06/05/2022] [Indexed: 11/07/2022]
Abstract
Employing Langevin dynamics simulations, we investigated the kinetics of the collapse transition for a polymer of length N when a particular monomer at a position 1≤X≤N is pinned. The results are compared with the kinetics of a free polymer. The equilibrium θ-point separating the coil from the globule phase is located by a crossover in 〈R_{g}^{2}〉/N plots of different chain lengths. Our simulation supports a three-stage mechanism for free and pinned polymer collapse: the formation of pearls, the coarsening of pearls, and the formation of a compact globule. Pinning the central monomer has negligible effects on the kinetics as it does not break the symmetry. However, pinning a monomer elsewhere causes the process to be delayed by a constant factor ϕ_{X} depending linearly upon X. The total collapse time scales with N as τ_{c}∼ϕ_{X}N^{1.60±0.03}, which implies τ_{c} is maximum when an end monomer is pinned (X=1 or N), while when pinning the central monomer (X=N/2) it is minimum and identical to that of a free polymer. The average cluster size N_{c}(t) grows in time as t^{z}, where z=1.00±0.04 for a free particle, whereas we identify two time regimes separated by a plateau for pinned polymers. At longer times, z=1.00±0.04, while it deviates in early time regimes significantly, depending on the value of X.
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Affiliation(s)
- Keerti Chauhan
- Department of Physics, Banaras Hindu University, Varanasi 221005, India
| | - Ankit Singh
- Department of Physics, Banaras Hindu University, Varanasi 221005, India
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Kapri R. Hysteresis loop area scaling exponents in DNA unzipping by a periodic force: A Langevin dynamics simulation study. Phys Rev E 2021; 104:024401. [PMID: 34525510 DOI: 10.1103/physreve.104.024401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 07/16/2021] [Indexed: 11/07/2022]
Abstract
Using Langevin dynamics simulations, we study the hysteresis in unzipping of longer double-stranded DNA chains whose ends are subjected to a time-dependent periodic force with frequency ω and amplitude G keeping the other end fixed. We find that the area of the hysteresis loop, A_{loop}, scales as 1/ω at higher frequencies, whereas it scales as (G-G_{c})^{α}ω^{β} with exponents α=1 and β=1.25 in the low-frequency regime. These values are same as the exponents obtained in Monte Carlo simulation studies of a directed self-avoiding walk model of a homopolymer DNA [R. Kapri, Phys. Rev. E 90, 062719 (2014)10.1103/PhysRevE.90.062719], and the block copolymer DNA [R. K. Yadav and R. Kapri, Phys. Rev. E 103, 012413 (2021)2470-004510.1103/PhysRevE.103.012413] on a square lattice, and differs from the values reported earlier using Langevin dynamics simulation studies on a much shorter DNA hairpins.
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Affiliation(s)
- Rajeev Kapri
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, Knowledge City, S. A. S. Nagar, Manauli P. O. 140306, India
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Yadav RK, Kapri R. Unzipping of a double-stranded block copolymer DNA by a periodic force. Phys Rev E 2021; 103:012413. [PMID: 33601556 DOI: 10.1103/physreve.103.012413] [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: 10/23/2020] [Accepted: 01/09/2021] [Indexed: 11/07/2022]
Abstract
Using Monte Carlo simulations, we study the hysteresis in unzipping of a double-stranded block copolymer DNA with -A_{n}B_{n}- repeat units. Here A and B represent two different types of base pairs having two and three bonds, respectively, and 2n represents the number of such base pairs in a unit. The end of the DNA are subjected to a time-dependent periodic force with frequency (ω) and amplitude (g_{0}) keeping the other end fixed. We find that the equilibrium force-temperature phase diagram for the static force is independent of the DNA sequence. For a periodic force case, the results are found to be dependent on the block copolymer DNA sequence and on the base pair type on which the periodic force is acting. We observe hysteresis loops of various shapes and sizes and obtain the scaling of loop area both at low- and high-frequency regimes.
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Affiliation(s)
- Ramu Kumar Yadav
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, Knowledge City, S. A. S. Nagar, Manauli PO 140306, India
| | - Rajeev Kapri
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, Knowledge City, S. A. S. Nagar, Manauli PO 140306, India
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Kalyan MS, Kapri R. Unzipping DNA by a periodic force: Hysteresis loops, dynamical order parameter, correlations, and equilibrium curves. J Chem Phys 2019; 150:224903. [DOI: 10.1063/1.5081099] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- M. Suman Kalyan
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, Knowledge City, S. A. S. Nagar, Manauli PO, Mohali 140306, India
| | - Rajeev Kapri
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, Knowledge City, S. A. S. Nagar, Manauli PO, Mohali 140306, India
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Wu M, Lu HP. Oscillating Piconewton Force Manipulation on Single-Molecule Enzymatic Conformational and Reaction Dynamics. J Phys Chem B 2018; 122:12312-12321. [PMID: 30481025 DOI: 10.1021/acs.jpcb.8b08980] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Oscillation force has been demonstrated in theoretical studies as a critical role in unraveling the comprehensive enzymatic dynamics and addressing its regulation on enzyme activity. Utilizing the imposed external mechanical oscillation force by our newly developed magnetic tweezers coupled with a single-molecule photon-stamping imaging spectroscopic microscope, we experimentally studied a millisecond-scale oscillation force manipulation on single horseradish peroxidase enzymatic conformational and reaction dynamics. We have studied the enzymatic reaction dynamics and found that the enzyme activity changes under the real-time oscillatory force manipulation. Moreover, the oscillation force shows the capability of manipulating the enzyme active-site conformational state as well as the nascent-formed product's interaction with the active site of the enzyme, which impacts on the product release pathways. Specifically, we have identified that there are two product releasing pathways, the solvation-mediated diffusion releasing pathway and the spilling-out releasing pathway. We have observed that the spilling-out pathway can be significantly perturbed by the oscillatory force manipulation. Our correlated interpretation of enzymatic conformational and reaction dynamics provides a new insight into the comprehensive understanding of the complex conformational dynamics evolved in an enzymatic reaction. Technically, we have also demonstrated a novel approach capable of unfolding an enzyme under an enzymatic reaction condition in real time and, furthermore, by using an oscillatory mechanical weak piconewton force to manipulate enzyme conformations, and the enzyme thermal fluctuation is fully maintained. The real-time in situ fluorescence probe at the enzymatic active site reports the active-site conformational dynamics through each enzymatic reaction turnovers.
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Affiliation(s)
- Meiling Wu
- Department of Chemistry, Center for Photochemical Sciences , Bowling Green State University , Bowling Green , Ohio 43403 , United States
| | - H Peter Lu
- Department of Chemistry, Center for Photochemical Sciences , Bowling Green State University , Bowling Green , Ohio 43403 , United States
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Kumar S, Kumar R, Janke W. Periodically driven DNA: Theory and simulation. Phys Rev E 2016; 93:010402. [PMID: 26871010 DOI: 10.1103/physreve.93.010402] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Indexed: 11/07/2022]
Abstract
We propose a generic model of driven DNA under the influence of an oscillatory force of amplitude F and frequency ν and show the existence of a dynamical transition for a chain of finite length. We find that the area of the hysteresis loop, A_{loop}, scales with the same exponents as observed in a recent study based on a much more detailed model. However, towards the true thermodynamic limit, the high-frequency scaling regime extends to lower frequencies for larger chain length L and the system has only one scaling (A_{loop}≈ν^{-1}F^{2}). Expansion of an analytical expression for A_{loop} obtained for the model system in the low-force regime revealed that there is a new scaling exponent associated with force (A_{loop}≈ν^{-1}F^{2.5}), which has been validated by high-precision numerical calculation. By a combination of analytical and numerical arguments, we also deduce that for large but finite L, the exponents are robust and independent of temperature and friction coefficient.
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Affiliation(s)
- Sanjay Kumar
- Department of Physics, Banaras Hindu University, Varanasi 221 005, India
| | - Ravinder Kumar
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
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Xu TT. Energy dissipation of a two-relaxation-time material. E-POLYMERS 2015. [DOI: 10.1515/epoly-2015-0123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
AbstractEnergy dissipation in polymeric materials was studied using a two-relaxation-time model. A differential form of a constitutive relation was constructed with the viscoelasticity theory. Through the simulation of a cyclic loading and unloading test, the dependence of the dissipated energy on the model parameters and external loading variables was determined and analyzed. In particular, the characteristics of the hysteresis phenomenon of a material with more than one relaxation time were studied in detail.
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Affiliation(s)
- Tao-Tao Xu
- 1Electric and Electronic Engineering College, Wuhan Polytechnic University, Wuhan, China
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Kapri R. Unzipping DNA by a periodic force: hysteresis loop area and its scaling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062719. [PMID: 25615141 DOI: 10.1103/physreve.90.062719] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2014] [Indexed: 06/04/2023]
Abstract
Using Monte Carlo simulations, we study the hysteresis in the unzipping of double-stranded DNA whose ends are subjected to a time-dependent periodic force with frequency (ω) and amplitude (G). For the static force, i.e., ω→0, the DNA is in equilibrium with no hysteresis. On increasing ω, the area of the hysteresis loop initially increases and becomes maximum at frequency ω*(G), which depends on the force amplitude G. If the frequency is increased further, we find that for lower amplitudes the loop area decreases monotonically to zero, but for higher amplitudes it has an oscillatory component. The height of subsequent peaks decreases, and finally the loop area becomes zero at very high frequencies. The number of peaks depends on the length of the DNA. We give a simple analysis to estimate the frequencies at which maxima and minima occur in the loop area. We find that the area of the hysteresis loop scales as 1/ω in the high-frequency regime, whereas it scales as G(α)ω(β) with exponents α=1 and β=5/4 at low frequencies. The values of the exponents α and β are different from the exponents reported earlier based on the hysteresis of small hairpins.
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Affiliation(s)
- Rajeev Kapri
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, Knowledge City, S. A. S. Nagar, Manauli PO 140306, India
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Bandopadhyay A, Hossain SS, Chakraborty S. Ionic size dependent electroviscous effects in ion-selective nanopores. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2014; 30:7251-7258. [PMID: 24853329 DOI: 10.1021/la5014957] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Pressure-driven flows of aqueous ionic liquids are characterized by electroviscosity-an increase in the effective (apparent) viscosity because of an induced back electric field termed streaming potential. In this work, we investigate the electrokinetic phenomenon of streaming potential mediated flows in ion-selective nanopores. We report a dramatic augmentation in the effective viscosity as attributable to the finite size effect of the ionic species in counterion-only systems. The underlying physics involves complex interaction between the concerned electrochemical phenomena and hydrodynamic transport in a confined fluidic environment, which we capture through a modified continuum based approach and validate using molecular dynamics simulations. We obtain an expression for the ionic-size dependent streaming potential pertinent to the physical situation being addressed. The corresponding estimations of effective viscosity implicate that the classical paradigm of point sized ions can give rise to gross underestimations of the flow resistance in counterion-only systems especially for negligible surface (Stern layer) conductivity and large fluidic slip at the surface.
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Affiliation(s)
- Aditya Bandopadhyay
- Advanced Technology Development Center and ‡Department of Mechanical Engineering, Indian Institute of Technology Kharagpur , Kharagpur 721302, India
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