Shock and detonation waves at an interface and the collision of action potentials

Abstract

Action potentials in neurons are known to annihilate each other upon collision, while there are cases where they might penetrate each other. The fate of two waves upon collision is critically dependent on the underlying mechanism of propagation and therefore an understanding of possible outcomes of collision under different conditions is important. Previously, compression waves that travel within the plasma membrane of a neuron have been proposed as a thermodynamic basis for the propagation of action potentials. In this context, it was recently shown that two-dimensional compressive shock waves in the model system of lipid monolayers behave strikingly similar to action potentials in neurons and can even annihilate each other upon head-on collision. However, even a qualitative mechanism remained unclear. To this end, we summarise the fundamentals of shock physics as applied to an interface and recap how it explained the observation of threshold and saturation of shockwaves in the lipid monolayer (all - or - none). We then compare the theory with the soliton model that has the same fundamental premise, i.e. the conservation laws and thermodynamics, and was previously proposed as a model for the nerve pulse propagation. We elaborate on how the two approaches make different predictions with regards to collisions and the detailed structure of the wave-front. As a case study and a new qualitative result, we finally show that previously unexplained annihilation of shock waves in the lipid monolayer is a direct consequence of the nature of state changes, i.e. jump conditions, within these shockwaves.

Keywords: Deflagration; Detonation; Hugoniots; Lipids; Nonlinear acoustics; Phase transition.