Analytical tools for solitons and periodic waves corresponding to phonons on Lennard-Jones lattices in helical proteins

Francesco D'ovidio, Henrik Bohr, Per-Anker Lindgård

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Abstract

We study the propagation of solitons along the hydrogen bonds of an alpha helix. Modeling the hydrogen and peptide bonds with Lennard-Jones potentials, we show that the solitons can appear spontaneously and have long lifetimes. Remarkably, even if no explicit solution is known for the Lennard-Jones potential, the solitons can be characterized analytically with a good quantitative agreement using formulas for a Toda potential with parameters fitted to the Lennard-Jones potential. We also discuss and show the robustness of the family of periodic solutions called cnoidal waves, corresponding to phonons. The soliton phenomena described in the simulations of alpha helices may help to explain recent x-ray experiments on long alpha helices in Rhodopsin where a long lifetime of the vibrational modes has been observed.
Original languageEnglish
JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume71
Issue number2
Pages (from-to)026606
Number of pages9
ISSN1063-651X
DOIs
Publication statusPublished - 2005

Bibliographical note

Copyright 2005 American Physical Society

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