Concerted motion of protons in hydrogen bonds of DNA-type molecules
V. L. Golo*+, E. I. Kats°, M. Peyrard+
*Department of Mechanics and Mathematics, Moscow University, 119899 Moscow, Russia
°Laue-Langevin Institute, F-38042, Grenoble, France
+Lab. Phys. ENS Lyon, 69364, Lyon, Cedex 07, France
° L. D. Landau Institute for Theoretical Physics, RAS, 117940 Moscow, Russia
PACS: 87.14.Gg, 87.15.-v
We study the dynamical behaviour of the proton transfer in the
hydrogen bonds in the base-pairs of the double helices of the DNA type. Under
the assumption that the elastic and the tunnelling degrees of freedom may be
coupled, we derive a non-linear and non-local Schrodinger equation (SNLNL)
that describes the concerted motion of the proton tunnelling.
Rough estimates of the solutions to the SNLNL show an intimate interplay
between the concerted tunnelling of protons and the symmetry of double helix.