Perturbative study of classical Ablowitz-Ladik type soliton dynamics in relation to energy transport in alpha-helical proteins

Classical Ablowitz-Ladik type soliton dynamics from three closely related c lassical nonlinear equations is studied using a perturbative method. Model nonintegrable equations are derived by assuming nearest neighbor hopping of an exciton(vibron) in the presence of a full exciton(vibron)-phonon intera ction in soft molecular chains in general and spines of alpha-helices in pa rticular. In all cases, both trapped and moving solitons are found implying activation energy barrier for propagating solitons. Analysis further shows that staggered and nearly staggered trapped solitons will have a negative effective mass. In some models the exciton(vibron)-phonon coupling affects the hopping. For these models, when the conservation of probability is take n into account, only propagating solitons with a broad profile are found to be acceptable solutions. Of course, for the soliton to be a physically mea ningful entity, total nonlinear coupling strength should exceed a critical value. On the basis of the result, a plausible modification in the mechanis m for biological energy transport involving conformational change in alpha- helix is proposed. Future directions of the work are also mentioned.