Abstract
We study the dynamical behavior of proton transfer in hydrogen bonds in the base pairs of double helices of the DNA type. Under the assumption that the elastic and tunnelling degrees of freedom may be coupled, we derive a nonlinear and nonlocal Schrödinger equation (NLNLS) that describes the concerted motion of the proton tunnelling. Rough estimates of the solutions to the NLNLS show an intimate interplay between the concerted tunnelling of protons and the symmetry of the double helix.
Similar content being viewed by others
References
A. J. Horsewill, N. H. Jones, and R. Caciuffo, Science 291, 100 (2001).
W. Saenger, Principles of Nucleic Acid Structure (Springer-Verlag, New York, 1984).
F. H. C. Crick, J. Mol. Biol. 19, 548 (1966).
J. L. Leroy, K. Gehring, A. Kettani, and M. Gueron, Biochemistry 32, 6019 (1993); S. Bratos, J. Chem. Phys. 63, 3499 (1975).
N. Bodor, M. J. S. Dewar, and A. J. Hagert, J. Am. Chem. Soc. 92, 2929 (1970).
M. Dreyfus, J. Am. Chem. Soc. 98, 6338 (1976).
V. L. Golo and E. I. Kats, Zh. Éksp. Teor. Fiz. 111, 1830 (1997) [JETP 84, 1003 (1997)]; V. L. Golo, Yu. M. Evdokimov, and E. I. Kats, Pis’ma Zh. Éksp. Teor. Fiz. 70, 766 (1999) [JETP Lett. 70, 780 (1999)].
T. Dauxois, M. Peyrard, and A. R. Bishop, Phys. Rev. E 47, R44 (1993); T. Dauxois, M. Peyrard, and A. R. Bishop, Phys. Rev. E 47, 684 (1993); T. Dauxois and M. Peyrard, Phys. Rev. E 51, 4027 (1995).
A. S. Davydov, Usp. Fiz. Nauk 138(4), 603 (1982) [Sov. Phys. Usp. 251, 898 (1982)].
A. C. Scott, Phys. Rev. A 26, 578 (1982).
D. Antoniou and S. Schwarts, Proc. Natl. Acad. Sci. USA 94, 12360 (1997).
A. Kohen and P. J. Klinman, Acc. Chem. Res. 31, 397 (1998).
V. E. Zakharov and V. S. Synakh, Zh. Éksp. Teor. Fiz. 68, 940 (1975) [Sov. Phys. JETP 41, 465 (1975)]; J. J. Rasmuseen and K. Rypdal, Phys. Scr. 33, 481 (1986).
Author information
Authors and Affiliations
Additional information
From Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 73, No. 4, 2001, pp. 225–229.
Original English Text Copyright © 2001 by Golo, Kats, Peyrard.
This article was submitted by the authors in English.