Solitons in an isolated helix chain

A molecular chain with helix structure has been investigated in the three-dimensional space in the case when it is considered as an isolated object (not subjected to any substrate potential). Each of the chain molecules is allowed to move in three dimensions, and intermolecular interactions (bonds) are assumed to be of the pair type and to have spherical symmetry. The helix structure is provided by the first- and second-neighbor intermolecular bonds as well as by the nearest-neighbor interactions along the longitudinal direction of the chain, stabilizing the helix backbone which can be considered as a generalization of the well-known one-dimensional Fermi-Pasta-Ulam model to include transverse degrees of freedom of the chain molecules. In the particular case of the α-helix molecular chain, the intermolecular interactions involved into the model are the point-point bonds connecting the first-, second-, and third-nearest neighbors. The set of nonlinear field equations with respect to the longitudinal and transverse (torsional and radial) displacements of the chain molecules has been derived and treated. Stable nontopological soliton solutions which describe supersonic pulses of longitudinal compression propagating together with localized transverse thickening (bulge) and torsional stretching (untwisting) have been found. The stability properties of these (three-component) soliton solutions have been studied by using numerical techniques developed for seeking solitary-wave solutions in complex molecular systems.