Dynamics of large radius polaron in a model polynucleotide chain with random perturbations

N. S. Fialko ; V. D. Lakhno

Matematičeskaâ biologiâ i bioinformatika, Tome 14 (2019) no. 2, pp. 406-419.

Résumé

We consider the dynamics of polaron in a chain using computational experiment. The temperature, which is simulated by random Langevin-type perturbations, and influence of external electric field are taking into account. In a sufficiently long unperturbed chain, the displacement of the center of mass of the polaron and its velocity does not depend on its length. In the semiclassical Holstein model, which is applied for simulations of charge transfer in DNA, the region of polaron existence in the thermodynamic equilibrium state depends not only on temperature, but also on the chain length. Therefore, when modeling dynamics from polaron initial data, the time dependences of the average displacement of the charge mass center at the same temperature are different for chains of different lengths. According to the results of computational experiment, for polaron of large radius the time dependence of the “average polaron displacement”, which takes into account only the polaron peak and its position, for chains of different lengths behaves almost equally at time intervals until the polaron will destroyed. The same slope of the polaron displacement allows us to estimate the average polaron velocity. The results of calculations demonstrate that in Holstein model at zero temperature, the mobility value of the large radius polaron is small but non-zero.

Bibliographie

[1] A. S. Davydov, N. I. Kislukha, “Solitony v odnomernykh molekulyarnykh tsepyakh”, ZhETF, 71:9 (1976), 1090–1098

[2] A. S. Davydov, “Solitons and energy transfer along protein molecules”, J. Theor. Biology, 66:2 (1977), 379–387 | DOI

[3] A. S. Davydov, Solitons in Molecular Systems, Springer, Netherlands, 1985, 319 pp. | DOI | MR

[4] L. V. Yakushevich, Metody teoreticheskoi fiziki v issledovaniyakh svoistv biopolimerov, ed. Klimontovicha Yu. L., ONTI NTsBI AN SSSR, Puschino, 1990, 125 pp.

[5] A. Scott, “Davydov's soliton”, Phys. Rep., 217:1 (1992), 1–67 | DOI

[6] P. T. Henderson, D. Jones, G. Hampikian, Y. Kan, G. B. Schuster, “Long-distance charge transport in duplex DNA: The phonon-assisted polaron-like hopping mechanism”, PNAS USA, 96:15 (1999), 8353–8358 | DOI

[7] A. Offenhausser, R. Rinaldi (eds.), Nanobioelectronics for Electronics, Biology, and Medicine, Springer, New York, 2009, 337 pp. | DOI

[8] G. B. Schuster (ed.), Long-Range Charge Transfer in DNA II, Topics in Current Chemistry, 237, Springer, 2004, 245 pp.

[9] T. Chakraborty (ed.), Charge Migration in DNA. Perspectives from Physics, Chemistry, and Biology, Springer, Berlin, 2007, 288 pp. | DOI

[10] V. D. Lakhno, “DNA nanobioelectronics”, International Journal of Quantum Chemistry, 108:11 (2008), 1970–1981 | DOI

[11] M. Ratner, “A brief history of molecular electronics”, Nature Nanotechnology, 8:6 (2013), 378–381 | DOI

[12] T. Yu. Astakhova, V. A. Kashin, V. N. Likhachev, G. A. Vinogradov, “Polaron dynamics on the nonlinear lattice in the Su-Schrieffer-Heeger approximation. Exact and approximate solutions”, Acta Physica Polonica A, 129:3 (2016), 334–339 | DOI

[13] T. Yu. Astakhova, V. A. Kashin, V. N. Likhachev, G. A. Vinogradov, “Polyarony na odnomernoi reshetke v modeli Su-Shriffera-Khigera”, Perenos zaryada v DNK. Matem. biologiya i bioinform, 8:1 (2013), 316–339 | DOI

[14] V. D. Lakhno, A. N. Korshunova, “Electron motion in a Holstein molecular chain in an electric field”, Eur. Phys. J. B, 79 (2011), 147–151 | DOI

[15] Zh. Huang, L. Chen, N. Zhou, Y. Zhao, “Transient dynamics of a one-dimensional Holstein polaron under the influence of an external electric field”, Ann. Phys. (Berlin), 529 (2017), 1600367 | DOI

[16] A. N. Korshunova, V. D. Lakhno, “Modelirovanie statsionarnykh i nestatsionarnykh rezhimov dvizheniya zaryada v odnorodnoi kholsteinovskoi tsepochke v postoyannom elektricheskom pole”, Zhurnal tekhnicheskoi fiziki, 88:9 (2018), 1312–1319 | DOI

[17] Zh. Huang, M. Hoshina, H. Ishihara, Y. Zhao, “Transient Dynamics of Super Bloch Oscillations of a 1D Holstein Polaron under the Influence of an External AC Electric Field”, Ann. Phys. (Berlin), 531 (2019), 1800303 | DOI

[18] P. Maniadis, G. Kalosakas, K. O. Rasmussen, A. R. Bishop, “AC conductivity in a DNA charge transport model”, Physical Review E, 72 (2005), 021912 | DOI

[19] M. G. Velarde, W. Ebeling, A. P. Chetverikov, “On the possibility of electric conduction mediated by dissipative solitons”, International Journal of Bifurcation and Chaos, 15:1 (2005), 245–251 | DOI | MR | Zbl

[20] E. Diaz, R. P. A. Lima, F. Dominguez-Adame, “Bloch-like oscillations in the Peyrard-Bishop-Holstein model”, Physical Review B, 78:13 (2008), 134303 | DOI

[21] J. A. Berashevich, A. D. Bookatz, T. Chakraborty, “The electric field effect and conduction in the Peyrard-Bishop-Holstein model”, J. Phys.: Condens. Matter, 20:3 (2008), 035207 | DOI

[22] O. G. Cantu Ros, L. Cruzeiro, M. G. Velarde, W. Ebeling, “On the possibility of electric transport mediated by long living intrinsic localized solectron modes”, Eur. Phys. J. B, 80 (2011), 545–554 | DOI

[23] V. D. Lakhno, “Davydov's solitons in homogeneous nucleotide chain”, International Journal of Quantum Chemistry, 110 (2010), 127–137 | DOI

[24] P. S. Lomdahl, W. C. Kerr, Do Davydov solitons exost at 300K?, Phys. Rev. Lett., 55:11 (1985), 1235–1238 | DOI

[25] D. Vitali, P. Allegrini, P. Grigolini, Nonlinear quantum mechanical effects: real or artefact of inaccurate approximations, Chemical Physics, 180:2-3 (1994), 297–318 | DOI

[26] M. I. Salkola, A. R. Bishop, V. M. Kenkre, S. Raghavan, “Coupled quasiparticle-boson systems: The semiclassical approximation and discrete nonlinear Schrodinger equation”, Physical Review B, 52:6 (1995), R3824 | DOI

[27] A. V. Savin, A. V. Zolotaryuk, “Dynamics of the amide-I excitation in a molecular chain with thermalized acoustic and optical modes”, Physica D: Nonlinear Phenomena, 68:1 (1993), 59–64 | DOI

[28] L. Cruzeiro-Hansson, S. Takeno, “Davydov model: The quantum, mixed quantumclassical, and full classical systems”, Physical Review E, 56:1 (1997), 894–906 | DOI

[29] W. Ebeling, M. G. Velarde, A. P. Chetverikov, “Bound states of electrons with soliton-like excitations in thermal systems. Adiabatic approximations”, Condensed Matter Physics, 12:4 (2009), 633–645 | DOI

[30] V. D. Lakhno, N. S. Fialko, “Podvizhnost dyrok v odnorodnoi nukleotidnoi tsepochke”, Pisma v ZhETF, 78:5 (2003), 786–788 | DOI

[31] V. D. Lakhno, N. S. Fialko, “Blokhovskie ostsillyatsii v odnorodnykh nukleotidnykh fragmentakh”, Pisma v ZhETF, 79:10 (2004), 575–578 | DOI

[32] V. D. Lakhno, N. S. Fialko, “O dinamike polyarona v klassicheskoi tsepochke s konechnoi temperaturoi”, ZhETF, 147 (2015), 142–148 | DOI

[33] N. S. Fialko, E. V. Sobolev, V. D. Lakhno, “O raschetakh termodinamicheskikh velichin v modeli Kholsteina dlya odnorodnykh polinukleotidov”, ZhETF, 151:4 (2017), 744–751 | DOI

[34] T. Holstein, “Studies of polaron motion: Part I. The molecular-crystal model”, Annals of Physics, 8:3 (1959), 325–342 | DOI | Zbl

[35] V. D. Lakhno, N. S. Fialko, “Modelirovanie polyarona malogo radiusa v tsepochke so sluchainymi vozmuscheniyami”, Matem. biologiya i bioinform., 14:1 (2019), 126–136 | DOI

[36] A. A. Voityuk, N. Rosch, M. Bixon, J. Jortner, “Electronic Coupling for Charge Transfer and Transport in DNA”, J. Phys. Chem. B, 104:41 (2000), 9740–9745 | DOI

[37] F. D. Lewis, Ya. Wu, “Dynamics of superexchange photoinduced electron transfer in duplex DNA”, J. Photochem. Photobiol., 2:1 (2001), 1–16 | DOI

[38] J. Jortner, M. Bixon, A. A. Voityuk, N. Roesh, “Superexchange Mediated Charge Hopping in DNA”, J. Phys. Chem. A, 106:33 (2002), 7599–7606 | DOI

[39] H. S. Greenside, E. Helfand, “Numerical integration of stochastic differential equations-II”, Bell System Technical Journal, 60 (1981), 1927–1940 | DOI | MR | Zbl