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

Francesco d’Ovidio^*

Henrik Georg Bohr^†

Per-Anker Lindgård^‡

Mediterranean Institute of Advanced Studies IMEDEA (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain

Centre for Quantum Protein, Department of Physics, Technical University of Denmark, DK 2800 Lyngby, Denmark

Materials Research Department, Risø National Laboratory, 4000 Roskilde, Denmark and Centre for Quantum Protein, Department of Physics, Technical University of Denmark, DK 2800 Lyngby, Denmark

^*Email address: dovidio@imedea.uib.es
^†Email address: hbohr@fysik.dtu.dk
^‡Email address: p.a.lindgard@risoe.dk

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Phys. Rev. E 71, 026606 – Published 15 February, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.026606

Abstract

We study the propagation of solitons along the hydrogen bonds of an $α$ 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 $α$ helices may help to explain recent x-ray experiments on long $α$ helices in Rhodopsin where a long lifetime of the vibrational modes has been observed.

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References (20)

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

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