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Koon WS, Owhadi H, Tao M, Yanao T. Can specific THz fields induce collective base-flipping in DNA? A stochastic averaging and resonant enhancement investigation based on a new mesoscopic model. CHAOS (WOODBURY, N.Y.) 2024; 34:083137. [PMID: 39177954 DOI: 10.1063/5.0208609] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Accepted: 08/11/2024] [Indexed: 08/24/2024]
Abstract
We study the metastability, internal frequencies, activation mechanism, energy transfer, and the collective base-flipping in a mesoscopic DNA via resonance with specific electric fields. Our new mesoscopic DNA model takes into account not only the issues of helicity and the coupling of an electric field with the base dipole moments, but also includes environmental effects, such as fluid viscosity and thermal noise. Also, all the parameter values are chosen to best represent the typical values for the opening and closing dynamics of a DNA. Our study shows that while the mesoscopic DNA is metastable and robust to environmental effects, it is vulnerable to certain frequencies that could be targeted by specific THz fields for triggering its collective base-flipping dynamics and causing large amplitude separation of base pairs. Based on applying the Freidlin-Wentzell method of stochastic averaging and the newly developed theory of resonant enhancement to our mesoscopic DNA model, our semi-analytic estimates show that the required fields should be THz fields with frequencies around 0.28 THz and with amplitudes in the order of 450 kV/cm. These estimates compare well with the experimental data of Titova et al., which have demonstrated that they could affect the function of DNA in human skin tissues by THz pulses with frequencies around 0.5 THz and with a peak electric field at 220 kV/cm. Moreover, our estimates also conform to a number of other experimental results, which appeared in the last couple years.
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Affiliation(s)
- Wang Sang Koon
- Control and Dynamical Systems, California Institute of Technology, Pasadena, California 91125, USA
| | - Houman Owhadi
- Applied and Computational Mathematics and Control and Dynamical Systems, California Institute of Technology, Pasadena, California 91125, USA
| | - Molei Tao
- School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Tomohiro Yanao
- Department of Applied Mechanics and Aerospace Engineering, Waseda University, Tokyo 169-8555, Japan
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Yakushevich LV, Krasnobaeva LA. Ideas and methods of nonlinear mathematics and theoretical physics in DNA science: the McLaughlin-Scott equation and its application to study the DNA open state dynamics. Biophys Rev 2021; 13:315-338. [PMID: 34178171 PMCID: PMC8214655 DOI: 10.1007/s12551-021-00801-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Accepted: 04/22/2021] [Indexed: 12/11/2022] Open
Abstract
The review is devoted to a new and rapidly developing area related to the application of ideas and methods of nonlinear mathematics and theoretical physics to study the internal dynamics of DNA and, in particular, the behavior of the open states of DNA. There are two main competing approaches to this research. The first approach is based on the molecular dynamics method, which takes into account the motions of all structural elements of the DNA molecule and all interactions between them. The second approach is based on prior selection of the main (dominant) motions and their mathematical description using a small number of model equations. This review describes the results of the study of the open states of DNA performed within the framework of the second approach using the McLaughlin-Scott equation. We present the results obtained both in the case of homogeneous sequences: poly (A), poly (T), poly (G) and poly (C), and in the inhomogeneous case when the McLaughlin-Scott equation has been used for studying the dynamics of open states activated in the promoters A1, A2 and A3 of the bacteriophage T7 genome, in the genes IFNA17, ADRB2, NOS1 and IL-5, in the pBR322 and pTTQ18 plasmids. Particular attention is paid to the results concerning the effect of various external fields on the behavior of open states. In the concluding part of the review, new possibilities and prospects for the development of the considered approach and especially of the McLaughlin-Scott equation are discussed. SUPPLEMENTARY INFORMATION The online version contains supplementary material available at 10.1007/s12551-021-00801-0.
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Affiliation(s)
- Ludmila V. Yakushevich
- Institute of Cell Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region, Russia
| | - Larisa A. Krasnobaeva
- Siberian State Medical University, Tomsk, Russia
- Tomsk State University, Tomsk, Russia
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Chevizovich D, Michieletto D, Mvogo A, Zakiryanov F, Zdravković S. A review on nonlinear DNA physics. ROYAL SOCIETY OPEN SCIENCE 2020; 7:200774. [PMID: 33391787 PMCID: PMC7735367 DOI: 10.1098/rsos.200774] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 10/23/2020] [Indexed: 06/12/2023]
Abstract
The study and the investigation of structural and dynamical properties of complex systems have attracted considerable interest among scientists in general and physicists and biologists in particular. The present review paper represents a broad overview of the research performed over the nonlinear dynamics of DNA, devoted to some different aspects of DNA physics and including analytical, quantum and computational tools to understand nonlinear DNA physics. We review in detail the semi-discrete approximation within helicoidal Peyrard-Bishop model and show that localized modulated solitary waves, usually called breathers, can emerge and move along the DNA. Since living processes occur at submolecular level, we then discuss a quantum treatment to address the problem of how charge and energy are transported on DNA and how they may play an important role for the functioning of living cells. While this problem has attracted the attention of researchers for a long time, it is still poorly understood how charge and energy transport can occur at distances comparable to the size of macromolecules. Here, we review a theory based on the mechanism of 'self-trapping' of electrons due to their interaction with mechanical (thermal) oscillation of the DNA structure. We also describe recent computational models that have been developed to capture nonlinear mechanics of DNA in vitro and in vivo, possibly under topological constraints. Finally, we provide some conjectures on potential future directions for this field.
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Affiliation(s)
- Dalibor Chevizovich
- Institut za nuklearne nauke Vinča, Univerzitet u Beogradu, 11001 Beograd, Serbia
| | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - Alain Mvogo
- Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, PO Box 812, Cameroon
| | - Farit Zakiryanov
- Bashkir State University, 32 Zali Validi Street, 450076 Ufa, Republic of Bashkortostan, Russia
| | - Slobodan Zdravković
- Institut za nuklearne nauke Vinča, Univerzitet u Beogradu, 11001 Beograd, Serbia
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Jeon JH, Sung W. An effective mesoscopic model of double-stranded DNA. J Biol Phys 2014; 40:1-14. [PMID: 24306264 PMCID: PMC3923960 DOI: 10.1007/s10867-013-9333-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2013] [Accepted: 10/11/2013] [Indexed: 11/26/2022] Open
Abstract
Watson and Crick's epochal presentation of the double helix structure in 1953 has paved the way to intense exploration of DNA's vital functions in cells. Also, recent advances of single molecule techniques have made it possible to probe structures and mechanics of constrained DNA at length scales ranging from nanometers to microns. There have been a number of atomistic scale quantum chemical calculations or molecular level simulations, but they are too computationally demanding or analytically unfeasible to describe the DNA conformation and mechanics at mesoscopic levels. At micron scales, on the other hand, the wormlike chain model has been very instrumental in describing analytically the DNA mechanics but lacks certain molecular details that are essential in describing the hybridization, nano-scale confinement, and local denaturation. To fill this fundamental gap, we present a workable and predictive mesoscopic model of double-stranded DNA where the nucleotides beads constitute the basic degrees of freedom. With the inter-strand stacking given by an interaction between diagonally opposed monomers, the model explains with analytical simplicity the helix formation and produces a generalized wormlike chain model with the concomitant large bending modulus given in terms of the helical structure and stiffness. It also explains how the helical conformation undergoes overstretch transition to the ladder-like conformation at a force plateau, in agreement with the experiment.
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Affiliation(s)
- Jae-Hyung Jeon
- />Department of Physics and PCTP, Pohang University of Science and Technology, Pohang, 790-784 Republic of Korea
| | - Wokyung Sung
- />Department of Physics and PCTP, Pohang University of Science and Technology, Pohang, 790-784 Republic of Korea
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Zoli M. Anharmonic stacking in supercoiled DNA. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:195103. [PMID: 22495298 DOI: 10.1088/0953-8984/24/19/195103] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Multistep denaturation in a short circular DNA molecule is analyzed by a mesoscopic Hamiltonian model which accounts for the helicoidal geometry. Computation of melting profiles by the path integral method suggests that stacking anharmonicity stabilizes the double helix against thermal disruption of the hydrogen bonds. Twisting is essential in the model to capture the importance of nonlinear effects on the thermodynamical properties. In a ladder model with zero twist, anharmonic stacking scarcely affects the thermodynamics. Moderately untwisted helices, with respect to the equilibrium conformation, show an energetic advantage against the overtwisted ones. Accordingly moderately untwisted helices better sustain local fluctuational openings and make more unlikely the thermally driven complete strand separation.
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Affiliation(s)
- Marco Zoli
- School of Science and Technology-CNISM, University of Camerino, Camerino, Italy.
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Daniel M, Vanitha M. Bubble solitons in an inhomogeneous, helical DNA molecular chain with flexible strands. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:031928. [PMID: 22060424 DOI: 10.1103/physreve.84.031928] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2011] [Revised: 07/13/2011] [Indexed: 05/31/2023]
Abstract
Base pair opening in an inhomogeneous, DNA double helical molecular chain with flexible strands is investigated by studying its internal dynamics. For the study, a generalized model which takes into account the energies involved in stacking and hydrogen bonds along with inhomogeneity, helicity, and phonons coupled to the stacking and hydrogen bonds is proposed. The internal dynamics of the proposed DNA model is governed by a perturbed nonlinear Schrödinger equation. The unperturbed, completely integrable nonlinear Schrödinger equation which admits soliton solutions and forming a bubble corresponds to DNA dynamics with homogeneous and rigid strands. The results of the soliton perturbation analysis show that the inhomogeneity in stacking and hydrogen bonds in localized and periodic forms and the helicity do not alter the amplitude under perturbation. However, the flexibility of the strands diminishes the perturbed amplitude. On the other hand, the velocity of the soliton and bubble are unaltered due to all the above effects. However, the position and phase of the soliton and the bubble vary linearly in time. While the position of the soliton depends on the initial velocity, the phase depends on both the initial velocity and the initial amplitude of the soliton. The above effects introduce small fluctuation in the tail of the soliton, without affecting the robust nature of the soliton and the bubble during propagation. The soliton and the bubble obtained as solutions of the internal dynamics of the DNA molecule represent an opening of the base pairs which is essential for the transcription process.
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Affiliation(s)
- M Daniel
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024, India.
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Savin AV, Mazo MA, Kikot IP, Manevitch LI, Onufriev AV. Heat conductivity of DNA double helix. PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS 2011; 83:245406. [PMID: 26207085 PMCID: PMC4508875 DOI: 10.1103/physrevb.83.245406] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Thermal conductivity of isolated single molecule DNA fragments is of importance for nanotechnology, but has not yet been measured experimentally. Theoretical estimates based on simplified (1D) models predict anomalously high thermal conductivity. To investigate thermal properties of single molecule DNA we have developed a 3D coarse-grained (CG) model that retains the realism of the full all-atom description, but is significantly more efficient. Within the proposed model each nucleotide is represented by 6 particles or grains; the grains interact via effective potentials inferred from classical molecular dynamics (MD) trajectories based on a well-established all-atom potential function. Comparisons of 10 ns long MD trajectories between the CG and the corresponding all-atom model show similar root-mean-square deviations from the canonical B-form DNA, and similar structural fluctuations. At the same time, the CG model is 10 to 100 times faster depending on the length of the DNA fragment in the simulation. Analysis of dispersion curves derived from the CG model yields longitudinal sound velocity and torsional stiffness in close agreement with existing experiments. The computational efficiency of the CG model makes it possible to calculate thermal conductivity of a single DNA molecule not yet available experimentally. For a uniform (polyG-polyC) DNA, the estimated conductivity coefficient is 0.3 W/mK which is half the value of thermal conductivity for water. This result is in stark contrast with estimates of thermal conductivity for simplified, effectively 1D chains ("beads on a spring") that predict anomalous (infinite) thermal conductivity. Thus, full 3D character of DNA double-helix retained in the proposed model appears to be essential for describing its thermal properties at a single molecule level.
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Affiliation(s)
- Alexander V Savin
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia
| | - Mikhail A Mazo
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia
| | - Irina P Kikot
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia
| | - Leonid I Manevitch
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia
| | - Alexey V Onufriev
- Departments of Computer Science and Physics, 2160C Torgersen Hall, Virginia Tech, Blacksburg, VA 24061, USA
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Bin-Bin LÜ, Qiang T. Different Kinds of Discrete Breathers in Three Types of One-Dimensional Models. COMMUNICATIONS IN THEORETICAL PHYSICS 2010; 54:728-734. [DOI: 10.1088/0253-6102/54/4/27] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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Daniel M, Vasumathi V. Solitonlike base pair opening in a helicoidal DNA: an analogy with a helimagnet and a cholesteric liquid crystal. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:012901. [PMID: 19257092 DOI: 10.1103/physreve.79.012901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2008] [Indexed: 05/27/2023]
Abstract
We propose a model for DNA dynamics by introducing the helical structure through twist deformation in analogy with the structure of a helimagnet and a cholesteric liquid-crystal system. The dynamics in this case is found to be governed by the completely integrable sine Gordon equation, which admits kink-antikink solitons with increased width, representing a wide base-pair opening configuration in DNA. The results show that the helicity introduces a length-scale variation and thus provides a better representation of the base-pair opening in DNA.
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Affiliation(s)
- M Daniel
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India.
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Gaeta G, Venier L. Solitary waves in twist-opening models of DNA dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:011901. [PMID: 18763976 DOI: 10.1103/physreve.78.011901] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2008] [Revised: 05/30/2008] [Indexed: 05/26/2023]
Abstract
We analyze traveling solitary wave solutions in the Barbi-Cocco-Peyrard twist-opening model of nonlinear DNA dynamics. We identify conditions, involving an interplay of physical parameters and asymptotic behavior, for such solutions to exist, and provide first-order ordinary differential equations whose solutions give the required solitary waves; these are not solvable in analytical terms, but are easily integrated numerically. The conditions for existence of solitary waves are not satisfied for trivial asymptotic behavior and physical values of the parameters, i.e., the Barbi-Cocco-Peyrard model admits only solitary wave solutions that entail a global modification of the molecule; this is compared with the situation met in another recently formulated class of DNA models with two degrees of freedom per site.
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Affiliation(s)
- Giuseppe Gaeta
- Dipartimento di Matematica, Università di Milano, via Saldini 50, Milano, Italy.
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Hien DL, Nhan NT, Ngo VT, Viet NA. Simple combined model for nonlinear excitations in DNA. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021921. [PMID: 17930079 DOI: 10.1103/physreve.76.021921] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2007] [Revised: 04/30/2007] [Indexed: 05/25/2023]
Abstract
We propose a simple model for DNA denaturation bases on the pendulum model of Englander [Proc. Natl. Acad. Sci. U.S.A. 77, 7222 (1980)] and the microscopic model of Peyrard and Bishop [Phys. Rev. Lett. 62, 2755 (1989)], so-called "combined model." The main parameters of our model are the coupling constant k along each strand, the mean stretching y* of the hydrogen bonds, the ratio of the damping constant and driven force gamma/F. We show that both the length L of unpaired bases and the velocity v of kinks depend on not only the coupling constant k but also the temperature T. Our results are in good agreement with previous works.
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Affiliation(s)
- D L Hien
- Institute of Physics and Electronics, P. O. Box 429, Boho, Hanoi 10000, Vietnam
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