Adiabatic approximation for the calculation of the charge mobility in the DNA Holstein model

Mathematical Biology & Bioinformatics. 2011;6(2):264-272.

doi: 10.17537/2011.6.264.

1. Lakhno VD. DNA nanobioelectronics. International Journal of Quantum Chemistry. 2008;108:1970-1981. doi: 10.1002/qua.21717
2. Nanobioelectronics – for Electronics, Biology, and Medicine. Offenhäusser A, Rinaldi R Eds. New York: Springer, 2009:337.
3. Lakhno VD, Fialko NS. Hole mobility in a homogeneous nucleotide chain. JETP Letters. 2003;78:336-338. doi: 10.1134/1.1625737
4. Fialko NS, Lakhno VD. Nonlinear dynamics of excitations in DNA. Physics Letters A. 2000;278:108-111. doi: 10.1016/S0375-9601(00)00755-6
5. Holstein T. Studies of polaron motion: Part I. The molecular-crystal model. Annals of Physics. 1959;8:325-342. doi: 10.1016/0003-4916(59)90002-8
6. Komineas S, Kalosakas G, Bishop AR. Effects of intrinsic base-pair fluctuations on charge transport in DNA. Physical Review E. 2002;65:061905. doi: 10.1103/PhysRevE.65.061905
7. Lakhno VD, Fialko NS. In: Dinamicheskie modeli processov v kletkah i subkletochnyh strukturah (Dynamical Models of Processes in Cells and Subcellular Structures). Riznichenko GYu, Rubin AB Eds. Moscow – Izhevsk: SPC Regular and Chaotic Dynamics, 2010:11-67 (in Russ.).
8. Voityuk AA, Rösch N, Bixon M, Jortner J. Electronic Coupling for Charge Transfer and Transport in DNA. The Journal of Physical Chemistry B. 2000;104:9740-9745. doi: 10.1021/jp001109w
9. Jortner J, Bixon M, Voityuk AA, Rösch N. Superexchange Mediated Charge Hopping in DNA. The Journal of Physical Chemistry A. 2002;106:7599-7606. doi: 10.1021/jp014232b
10. Lewis FD, Wu Y. Dynamics of superexchange photoinduced electron transfer in duplex DNA. Journal of Photochemistry and Photobiology C: Photochemistry Reviews. 2001;2:1-16. doi: 10.1016/S1389-5567(01)00008-9
11. Lakhno VD. Davydov's solitons in homogeneous nucleotide chain. International Journal of Quantum Chemistry. 2010;110:127-137. doi: 10.1002/qua.22264
12. Greenside HS, Helfand E. Numerical integration of stochastic differential equations II. Bell System Technical Journal. 1981;60:1927-1940. doi: 10.1002/j.1538-7305.1981.tb00303.x
13. Magnus W. On the exponential solution of differential equations for a linear operator. Communications on Pure and Applied Mathematics. 1954;7:649-673. doi: 10.1002/cpa.3160070404
14. Del Buono N, Lopez L. A survey on methods for computing matrix exponentials in numerical schemes for ODEs. In: Computational Science — ICCS 2003. Sloot P, Abramson D, Bogdanov A, Gorbachev Y, Dongarra J, Zomaya A Eds. Berlin/Heidelberg: Springer, 2003:111-120.
15. Gallopoulos G, Saad Y. Efficient solution of parabolic equations by Krylov approximation methods. SIAM Journal on Scientific and Statistical Computing. 1992;13:1236-1264. doi: 10.1137/0913071
16. Lu YY. Exponentials of Symmetric Matrices through Tridiagonal Reductions. Available at: http://math.cityu.edu.hk/~mayylu/papers/matexp.pdf (accessed 15 November 2011).
17. Fialko NS. Perenos zarjada v DNK. Chislennoe modelirovanie processov perenosa zarjada v diskretnyh molekuljarnyh cepochkah (Charge Transfer in DNA. Numerical Modeling of charge migration in discrete molecular chains). Saarbrucken, Germany: Lambert Academic Publishing, 2010:93 p. (in Russ.).
18. Lakhno VD, Sultanov VB. On the Possibility of Superfast Charge Transfer in DNA. Mathematical biology and bioinformatics. 2009;4:1-6. doi: 10.17537/2009.4.1.