Geodesic
Adiabatic approximation for the calculation of the charge mobility in the DNA Holstein model
Matematičeskaâ biologiâ i bioinformatika, Tome 6 (2011) no. 2, pp. 264-272.

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In Holstein’ model the charge transfer along a site chain is described using self- consistent ODE system (polaron model). To estimate the charge mobility at temperature prescribed, linear adiabatic approximation is suggested wherein the charge moving does not act on the site displacements. In this approximation computations are fast. Comparison of calculating results for the polaron model and the adiabatic model shows agreement of diffusion coefficients with accuracy up to one standard deviation. 
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D. A. Tikhonov; E. V. Sobolev; V. D. Lakhno; N. S. Fialko. Adiabatic approximation for the calculation of the charge mobility in the DNA Holstein model. Matematičeskaâ biologiâ i bioinformatika, Tome 6 (2011) no. 2, pp. 264-272. http://geodesic.mathdoc.fr/item/MBB_2011_6_2_a7/

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

[2] Nanobioelectronics – for Electronics, Biology, and Medicine, eds. Offenhäusser A., Rinaldi R., Springer, New York, 2009, 337 pp.

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

[4] Fialko N.S., Lakhno V.D., “Nonlinear dynamics of excitations in DNA”, Physics Letters A, 278 (2000), 108–111 | DOI

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

[6] Komineas S., Kalosakas G., Bishop A.R., “Effects of intrinsic base-pair fluctuations on charge transport in DNA”, Physical Review E, 65 (2002), 061905 | DOI

[7] Lakhno V.D., Fialko N.S., Dinamicheskie modeli protsessov v kletkakh i subkletochnykh strukturakh, eds. Riznichenko G.Yu., Rubin A.B., NITs Regulyarnaya i khaoticheskaya dinamika, M.–Izhevsk, 2010, 11–67

[8] Voityuk A.A., Rösch N., Bixon M., Jortner J., “Electronic Coupling for Charge Transfer and Transport in DNA”, The Journal of Physical Chemistry B, 104 (2000), 9740–9745 | DOI

[9] Jortner J., Bixon M., Voityuk A.A., Rösch N., “Superexchange Mediated Charge Hopping in DNA”, The Journal of Physical Chemistry A, 106 (2002), 7599–7606 | DOI

[10] Lewis F.D., Wu Y., “Dynamics of superexchange photoinduced electron transfer in duplex DNA”, Journal of Photochemistry and Photobiology C: Photochemistry Reviews, 2 (2001), 1–16 | DOI

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

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

[13] Magnus W., “On the exponential solution of differential equations for a linear operator”, Communications on Pure and Applied Mathematics, 7 (1954), 649–673 | DOI | MR | Zbl

[14] Del Buono N., Lopez L., “A survey on methods for computing matrix exponentials in numerical schemes for ODEs”, Computational Science – ICCS 2003, eds. Sloot P., Abramson D., Bogdanov A., Gorbachev Y., Dongarra J., Zomaya A., Springer, Berlin/Heidelberg, 2003, 111–120 | MR | Zbl

[15] Gallopoulos G., Saad Y., “Efficient solution of parabolic equations by Krylov approximation methods”, SIAM Journal on Scientific and Statistical Computing, 13 (1992), 1236–1264 | DOI | MR | Zbl

[16] Lu Y.Y., Exponentials of Symmetric Matrices through Tridiagonal Reductions URL: (data obrascheniya: 15.11.2011) http://math.cityu.edu.hk/~mayylu/papers/matexp.pdf

[17] Fialko N.V., Perenos zaryada v DNK. Chislennoe modelirovanie protsessov perenosa zaryada v diskretnykh molekulyarnykh tsepochkakh, Lambert Academic Publishing, Saarbrucken, Germany, 2010, 93 pp.

[18] Lakhno V.D., Sultanov V.B, “O vozmozhnosti sverkhbystrogo perenosa zaryada v DNK”, Matematicheskaya biologiya i bioinformatika, 4 (2009), 46–51 ; URL: (дата обращения: 15.11.2011) http://www.matbio.org/downloads/Lakhno2009(4_46).pdf | Zbl