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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.
Highlights
The structure in most proteins consists of ␣ helices and the  sheets connected by loops
We study the propagation of solitons along the hydrogen bonds of an ␣ helix
In a previous work9͔, we considered a similar geometry of points connected by Toda potentials. We showed that such a system admits a solitary wave propagating along the whole helix when an instantaneous perturbation parallel to the hydrogen bonds is given to the first amino acid of the chain
Summary
The structure in most proteins consists of ␣ helices and the  sheets connected by loops. The fact that there are no local vibrational modes corresponding to such an energy points to the interpretation of the long-lived excitations as collective modes, that is, modes that involve a large number of amino acids. We show that soliton solutions exist in the more realistic Lennard-JonesLJpotential as well, and we demonstrate that the Toda description is accurate in a surprisingly large interval of energies. It has been proven theoretically11͔ that the Toda solutions are robust under small perturbations away from exact integrability. An excitation on the H bonds is certainly to be expected near the observed frequency Both phonons and solitons could exist on the chain in a nonharmonic potential. The nonlinearities are expected to play a role at the high level of pumping in the pump-probe experiments5͔
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