The stability of solitons in biomembranes and nerves

Abstract

We examine the stability of a class of solitons, obtained from a generalization of the Boussinesq equation, which have been proposed to be relevant for pulse propagation in biomembranes and nerves. These solitons are found to be stable with respect to small amplitude fluctuations. They emerge naturally from non-solitonic initial excitations and are robust in the presence of dissipation.

Solitary electromechanical pulses in lobster neurons

“…Such transitions have been found in various biological membranes (15). It is thought that the soliton consists of a region of ordered lipid membrane traveling in the otherwise liquid membrane with a speed somewhat less than the speed of sound in the membrane (14,16). This is shown schematically in Fig.…”

“…Recently, there have been various reports, both theoretical and experimental, regarding the possibility of mechanical pulse propagation in artificial systems close to transitions and in nerves (14,16,17,21,22,(31)(32)(33). Heimburg and Jackson (14) argued that, close to the phase transitions found in biological tissue, electromechanical solitons with properties similar to those of the action potential can travel along the nerve axons.…”

Evidence for two-dimensional solitary sound waves in a lipid controlled interface and its implications for biological signalling

“…Rather, it is the variation in velocity as a function of state c g (p, T ), variation in pulse shape as a function of degree of nonlinearity c 0 g (p, T) and the existence of a threshold that can be explained thermodynamically [22,[53][54][55], as seen in this study. But before making further such comparisons, the amplitude velocity relation [56,57], the existence of refractory period [58] and the behaviour of two pulses under collision need to be explored for a comprehensive understanding of these nonlinear effects. For example in nonlinear systems, two pulses might change or annihilate in general on collision (like action potentials) or remain unaffected like solitons under special circumstances [7,57,[59][60][61][62].…”

High-fidelity numerical simulation of solitons in the nerve axon

“…It has been suggested (see for example [25,4]) that the HH model does not accurately describe certain phenomena observed in experiments. While the HH model describes various aspects of the voltage pulse traveling along the nerve axon in a satisfactory manner (e.g., its velocity and the pulse amplitude), it fails to describe several other aspects of the nerve pulse that are of nonelectrical nature.…”

“…In a series of recent publications by Heimburg et al [17,18,26,40,25] an alternative thermodynamic model is proposed in which nerve pulses are described as a reversible electro-mechanical density pulse (soliton) in the axon membrane. This model will be referred to as the nerve soliton (NS) model in the present study.…”