%0 Book Section %1 statphys23_0232 %A Krokhin, A.A. %A Bagci, V.M.K. %A Izrailev, F.M. %A Usatenko, O.V. %A Yampolsky, V.A. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K correlations dna edge localization mobility statphys23 topic-10 %T Electron localization in double-stranded DNA molecules %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=232 %X Analytical results are obtained for the electron localization length $l(E)$ in DNA molecule. Double-helix DNA is modelled by two infinite chains (channels) of sites with coupling constant $h$ between the chains and hopping amplitude $t$ between the nearest neighbors in the same chain. For the DNA molecules the typical values of the coupling constants are $t=0.37$ eV, $h =1$ eV, and the site potential takes four values associated with the ionization potential of the basic nucleotides, $\varepsilon_A =8.24 $ eV, $\varepsilon_T = 9.14$ eV, $\varepsilon_G = 7.75$ eV, and $\varepsilon_C = 8.87$ eV. A random sequence of nucleotides is strongly correlated, therefore the results for localization length obtained for white-noise potential$^1$ are inapplicable. The long-range correlations affect the localization length and may give rise to a mobility edge in the energy spectrum of a single-channel system.$^2$ Assuming that the fluctuations of the random potential are weak, which is the case of a sequence of the nucleotides in a DNA molecule, we have derived the formula for the localization length in a double-channel system. This formula accounts for backscattering processes in the both channels with change of the electron momentum by $\Delta k=2k_1$, and $\Delta k=2k_2$ and also cross-channel backscattering with $\Delta k=k_1+k_2$. Accordingly, the binary auto-correlation functions in the both channels and the cross-correlation function give additive contributions to the Lyapunov exponent. Using the data from GenBank Database, (www.ncbi.nlm.nih.gov/Genbank), we calculated the correlation functions and localization lengths for different DNA's. Typical localization length in most of the studied DNA's is about 30-70 base pairs. However, for the Human BRCA gene we found a few narrow regions of energy, where $l(E)10^4 -10^5$. These states are practically delocalized. In figure the localized and delocalized states and the mobility edges for BRCA are clearly seen. Although, it is not clear yet, what is the biological role of the extended states in DNA, they are due to the long-range correlations in the nucleotide sequence. We speculate that these states may be responsible for the transfer of information about mutations along the macromolecule. A direct relation between the conductance and mutations in DNA molecules has been recently demonstrated in the experiment.$^3$ Presence or absence of the mobility edge can be used for classification of the DNA molecules. Supported by the US Department of Energy. \\ 1) D.J. Thouless, Phys. Rev. Lett. 61, 2141 (1988). \\ 2) F. M. Izrailev and A. A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999). \\ 3) J. Hilhath, B. Xu, P. Zhang, N. Tao, Proceedings of National Acad. Sci. 102, 16979 (2005).

@incollection{statphys23_0232, abstract = {Analytical results are obtained for the electron localization length $l(E)$ in DNA molecule. Double-helix DNA is modelled by two infinite chains (channels) of sites with coupling constant $h$ between the chains and hopping amplitude $t$ between the nearest neighbors in the same chain. For the DNA molecules the typical values of the coupling constants are $t=0.37$ eV, $h =1$ eV, and the site potential takes four values associated with the ionization potential of the basic nucleotides, $\varepsilon_A =8.24 $ eV, $\varepsilon_T = 9.14$ eV, $\varepsilon_G = 7.75$ eV, and $\varepsilon_C = 8.87$ eV. A random sequence of nucleotides is strongly correlated, therefore the results for localization length obtained for white-noise potential$^1$ are inapplicable. The long-range correlations affect the localization length and may give rise to a mobility edge in the energy spectrum of a single-channel system.$^2$ Assuming that the fluctuations of the random potential are weak, which is the case of a sequence of the nucleotides in a DNA molecule, we have derived the formula for the localization length in a double-channel system. This formula accounts for backscattering processes in the both channels with change of the electron momentum by $\Delta k=2k_1$, and $\Delta k=2k_2$ and also cross-channel backscattering with $\Delta k=k_1+k_2$. Accordingly, the binary auto-correlation functions in the both channels and the cross-correlation function give additive contributions to the Lyapunov exponent. Using the data from GenBank Database, (www.ncbi.nlm.nih.gov/Genbank), we calculated the correlation functions and localization lengths for different DNA's. Typical localization length in most of the studied DNA's is about 30-70 base pairs. However, for the Human BRCA gene we found a few narrow regions of energy, where $l(E)\sim 10^4 -10^5$. These states are practically delocalized. In figure the localized and delocalized states and the mobility edges for BRCA are clearly seen. Although, it is not clear yet, what is the biological role of the extended states in DNA, they are due to the long-range correlations in the nucleotide sequence. We speculate that these states may be responsible for the transfer of information about mutations along the macromolecule. A direct relation between the conductance and mutations in DNA molecules has been recently demonstrated in the experiment.$^3$ Presence or absence of the mobility edge can be used for classification of the DNA molecules. Supported by the US Department of Energy. \\ 1) D.J. Thouless, Phys. Rev. Lett. {\bf 61}, 2141 (1988). \\ 2) F. M. Izrailev and A. A. Krokhin, Phys. Rev. Lett. {\bf 82}, 4062 (1999). \\ 3) J. Hilhath, B. Xu, P. Zhang, N. Tao, Proceedings of National Acad. Sci. {\bf 102}, 16979 (2005).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Krokhin, A.A. and Bagci, V.M.K. and Izrailev, F.M. and Usatenko, O.V. and Yampolsky, V.A.}, biburl = {https://www.bibsonomy.org/bibtex/21e1cbc87874a804b4e1cac2ea36991a7/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {8dd761adb9534cacb21e1b13117fe2eb}, intrahash = {1e1cbc87874a804b4e1cac2ea36991a7}, keywords = {correlations dna edge localization mobility statphys23 topic-10}, month = {9-13 July}, timestamp = {2007-06-20T10:16:14.000+0200}, title = {Electron localization in double-stranded DNA molecules}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=232}, year = 2007 }