How to Cite
Abstract
Objectives. Analyze the DNA dynamics in Peyrard-Bishop-Dauxois model (PBD) with different control parameters using its energy center of the mobile “breather”. Materials and methods. We used the Peyrard-Bishop-Dauxois mathematical model and the MATLAB software for studying the DNA dynamic using Morse potential, Symmetric Morse and the “hump” potential for simulating the interactions which arise the pile up. Results. It has been observed that the analytical and computational methods allow to detect the influence of the potentials of the PBD model in the behavior of the energy center in the presence of a couple of base A(adenine) or T(thymine) using the control of parameter α=-0.30 and velocity of mobile breather: v0=0.1. In the case of Morse potential, the center of energy respect to the mobile breather undergoes a change in its trajectory and produce a DNA breathing. Conclusions. Analytical and computational approaches can be used for obtaining differences respect to the DNA dynamics using different control parameters: velocity of BM and inhomogeneity. The potential “hump” may decrease the reflective effect with the indicated parameters to the effect on the energy center to the mobile breather.
References
Micklos. D., DNA Science. Laboratory Press. 2003.
James, G., Continuation of discrete breathers from infinity in a nonlinear model for DNA breathing. Applicable Analysis, 2009.
Peyrard, M., Bishop, A. R., Statistical Mechanics of a nonlinear model for DNA, Physica Review Letters 62 (1989) 2755-2758. https://doi.org/10.1103/PhysRevLett.62.2755
Cuevas, J., Localización y Transferencia de Energia en Redes Anarmónicas No Homogéneas, Ph. D. Thesis, Universidad de Sevilla, Sevilla, España, 2003.
Mackay, R. S., Aubry, S., Proof of existence of breathers for time-reversible for Hamiltonian networks of weakly coupled oscillators, Nonlinearity 7 (1994) 1623-1643.
Jefferson, J., Structural dynamics in DNA damage signaling and repair, Curr. Opin. Struct. Biol. 20(3) (2010) 283-294. https://doi.org/10.1016/j.sbi.2010.03.012
Hoppensteadt, F. C., Analysis and Simulation of Chaotic Systems, Spring-Verlag, New York, 2000.
Chen, D., Aubry, S., Tsironis, G. P., Breather mobility in discrete lattices, Physical Review Letters 77 (1996) 4776-4779. https://doi.org/10.1103/PhysRevLett.77.4776
Cuevas, J., Palmero, F., Archilla, J. F. R., Romero, F. R., Moving discrete breather in a Klein-Gordon chain with an impurity, J. Phys. A, 35 (2002) 10519-10530.
Aubry, S., Cretegny, T., Mobility and Reactivity of Discrete Breathers, Physica D, 119 (1998) 34-46. https://doi.org/10.1016/S0167-2789(98)00062-1
Howard, J., Linear stability of natural sympletic maps, Physics Letters A 246 (1998) 273-283. https://doi.org/10.1016/S0375-9601(98)00507-6
Cortez, H., Drigo Filho, E., Ruggiero, J. R., Breather stability in one dimensional Lattices with a symmetric Morse Potential, TEMA. Tend. Mat. Appl. Comput. 9(2) (2008) 205-212. https://doi.org/10.5540/tema.2008.09.02.0205
Cortez, H., Tese de doutorado. Modelo Dinâmico e estatístico aplicado à transição de fase. UNESP. 2009
Gutiérrez, H.C., Drigo Filho, E., Ruggiero, J.R., Gutierrez, M.C., Fuentes Rivera, L.V., Thermodynamics of DNA with “ hump” Morse potential, Eclética Quimica 41 (2016) 60-65. https://doi.org/10.26850/1678-4618eqj.v41.1.2016.p60-65
Peyrard, M., Nonlinear dynamics and statistical physics of DNA, Nonlinearity 17(2) (2004) R1-R40.
Flach, S. Gorbach, A. V., Discrete breathers-Advance in theory and applications, Physics Reports 467 (1-3) (2008) 1-116. https://doi.org/10.1016/j.physrep.2008.05.002
Forinash, K., Peyrard M., Interaction of discrete with impurity modes, Physical Review E 49 (4) (1994) 3400-3411. PMID:9961608
Cuevas, J., Palmero, F., Archilla, J. F. R., Moving discrete breathers in a Klein-Gordon chain with an impurity, Journal of Physics 35(49) (2002) 10519-10530.
Alvarez, A., Romero, F., Breather trapping and breather transmission in a DNA model with an interface, Eur. Phys. J. B51 (2006) 119-130. https://doi.org/10.1140/epjb/e2006-00191-0
Alvarez. A., Moving Breathers collisions in the Peyrard Bishop DNA model. International Conference on Complex Science, 2009.
Thing, J., Peyrard, M., Effective breather trapping mechanism for DNA transcription, Physics Rev. 53(1) (1996) 1011-1020. PMID: 9964336
Bang, O., Peyrard, M., High order breather solutions to a discrete nonlinear Klein-Gordon model, Physica D 81(1-2) (1995) 9-22. https://doi.org/10.1016/0167-2789(94)00202-2
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright (c) 2017 Eclética Química Journal