Equilibrium charge distribution in a finite chain with a trapping site

N. S. Fialko ; M. M. Olshevets ; V. D. Lakhno

Matematičeskaâ biologiâ i bioinformatika, Tome 16 (2021) no. 1, pp. 152-168.

Résumé

The paper considers the problem of the distribution of a quantum particle in a classical one-dimensional lattice with a potential well. The cases of a rigid chain, a Holstein polaron model, and a polaron in a chain with temperature are investigated by direct modeling at fixed parameters. As is known, in the one-dimensional case, a particle is captured by an arbitrarily shallow potential well with an increase of the box size. In the case of a finite chain and finite temperatures, we have quite the opposite result, when a particle, being captured in a well in a short chain, turns into delocalized state with an increase in the chain length. These results may be helpful for further understanding of charge transfer in DNA, where oxoguanine can be considered as a potential well in the case of hole transfer when for excess electron transfer it is thymine dimer.

Bibliographie

[1] Starikov E., Tanaka S., Lewis J. (eds.), Modern Methods for Theoretical Physical Chemistry of Biopolymers, Elsevier Scientific, Amsterdam, 2006, 604 pp. | DOI

[2] Alexandrov A. (ed.), Polarons in Advanced Materials, Springer Series in Materials Science, 103, Springer, 2007, 672 pp. | DOI

[3] Offenhäusser A., Rinaldi R., Nanobioelectronics — for Electronics, Biology, and Medicine, Springer, New York, 2009, 337 pp. | DOI

[4] Seeman N.C., “Nanotechnology and the double helix”, Sci. Am., 290:6 (2004), 64-9–72-5 | DOI

[5] Chakraborty T. (ed.), Charge migration in DNA. Perspectives from physics, chemistry, and biology, Springer, Berlin, 2007, 288 pp. | DOI

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

[7] Conwell E.M., “Charge transport in DNA in solution: The role of polarons”, PNAS USA, 102:25 (2005), 8795–8799 | DOI

[8] Davydov A.S., “The theory of contraction of proteins under their excitation”, J. Theor. Biology, 38 (1973), 559–569 | DOI

[9] Su W.P., Schrieffer J.R., “Soliton dynamics in polyacetylene”, PNAS USA, 77:10 (1980), 5626–5629 | DOI

[10] Landau L.D., Lifshits E.M., Kvantovaya mekhanika, Nauka, M., 1974, 752 pp. | MR

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

[12] Kalosakas G., Rasmussen K., Bishop A., “Charge trapping in DNA due to intrinsic vibrational hot spots”, J. Chem. Phys., 118:8 (2003), 3731–3735 | DOI

[13] Qu Z., Kang D., Jiang H., Xie S., “Temperature effect on polaron dynamics in DNA molecule: The role of electron-base interaction”, Physica B, 405 (2010), S123-S125 | DOI

[14] Patwardhan S., Tonzani S., Lewis F., Siebbeles L., Schatz G., Grozema F., “Effect of structural dynamics and base pair sequence on the nature of excited states in DNA hairpins”, J. Phys. Chem. B, 116 (2012), 11447–11458 | DOI

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

[16] Helfand E., “Brownian dynamics study of transitions in a polymer chain of bistable oscillators”, J. Chem. Phys., 69:3 (1978), 1010–1018 | DOI

[17] Lakhno V.D., Fialko N.S., “O dinamike polyarona v klassicheskoi tsepochke s konechnoi temperaturoi”, ZhETF, 147:1 (2015), 142–148 | DOI

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

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

[20] Holstein T., “Studies of polaron motion: Part II. The “small” polaron”, Annals of Physics, 8:3 (1959), 343–389 | DOI | Zbl

[21] Voityuk A.A., Rösch N., Bixon M., Jortner J., “Electronic coupling for charge transfer and transport in DNA”, J. Phys. Chem. B, 104:41 (2000), 9740–9745 | DOI

[22] Jortner J., Bixon M., Voityuk A.A., Röcsh N., “Superexchange mediated charge hopping in DNA”, J. Phys. Chem. A, 106:33 (2002), 7599–7606 | DOI

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

[24] Chandrasekkhar S., Stokhasticheskie problemy v fizike i astronomii, Izd-vo inostr. lit-ry, M., 1947

[25] Yakushevich L.V., Nonlinear Physics of DNA, Wiley, 1998 | Zbl

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

[27] Cheng K.C., Cahill D.S., Kasai H., Nishimura S., Loeb L.A., “8-Hydroxyguanine, an abundant form of oxidative DNA damage, causes G$\to$T and A$\to$C substitutions”, J. Biol. Chem., 267:1 (1992), 166–172 jbc.org/-abstract | DOI

[28] Fialko N., Pyatkov M., Lakhno V., “On the thermodynamic equilibrium distribution of a charge in a homogeneous chain with a defect”, EPJ Web of Conferences, 173 (2018), 06004 | DOI