Informational code structures in the improved soliton model for biomembrane and nerves

Unlike the Hodgkin-Huxley picture in which the nerve impulse results from ion exchanges across the cell membrane through ion-gate channels, in the so-called soliton model proposed by Heimburg and Jackson, the impulse is seen as an electromechanical process related to thermodynamical phenomena accompanying the generation of the action potential. In the present work, an improved soliton model for biomembranes and nerves is used to establish that in a low-amplitude approximation, the dynamics of nerve impulses can be described by the damped nonlinear Schrödinger equation (DNLSE) that is shown to admit soliton trains. This solution contains an undershoot beneath the baseline (“hyperpolarization”) and a “refractory period,” i.e., a minimum distance between pulses, and therefore it represents typical nerve profiles. Likewise, the linear stability of wave trains is analyzed. The results from the linear stability analysis show that, in addition to the main periodic wave trains observed in most nerve experiments, five other localized background modes can copropagate along the nerve. These modes could eventually be responsible for various fundamental processes in the nerve such as, phase transitions, electrical and mechanical changes.