Effect of hydrogen bond anharmonicity on supersonic discrete Davydov soliton propagation

We consider the propagation of energy along a protein chain in the Davydov approximation. We study the fully discrete Davydov equations including the anharmonic corrections in the hydrogen bond potential and find approximate variational solutions. We show analytically that for the harmonic interaction of the hydrogen bonds of the Davydov model the waves travel with velocities less than half the sound velocity for the relevant biological parameters. We find, for weak nonlinearity of the hydrogen bonds, two branches of soliton solutions. The first one gives a new type of strongly stable cusped discrete supersonic soliton. The second branch captures the main component of a more complicated breather solution compared to the one studied by Gaididei and reproduces the Davydov soliton of the continuum limit. These results show the possibility of coherent protein chain deformation due to the anharmonicity of the hydrogen bond interactions. These supersonic waves are shown to provide a viable mechanism for energy transport in spite of the temperature influence in the soliton lifetime.