Mechanical Surface Waves Accompany Action Potential Propagation

Abstract: Many studies have shown that a mechanical displacement of the axonal membrane accompanies the electrical pulse defining the Action Potential (AP). Despite a large and diverse body of experimental evidence, there is no theoretical consensus either for the physical basis of this mechanical wave nor its interdependence with the electrical signal. In this manuscript we present a model for these mechanical displacements as arising from the driving of surface wave modes in which potential energy is stored in elastic properties of the neuronal membrane and cytoskeleton while kinetic energy is carried by the axoplasmic fluid. In our model these surface waves are driven by the traveling wave of electrical depolarization that characterizes the AP, altering the compressive electrostatic forces across the membrane as it passes. This driving leads to co-propagating mechanical displacements, which we term Action Waves (AWs). Our model for these AWs allows us to predict, in terms of elastic constants, axon radius and axoplasmic density and viscosity, the shape of the AW that should accompany any traveling wave of voltage, including the AP predicted by the Hodgkin and Huxley (HH) equations. We show that our model makes predictions that are in agreement with results in experimental systems including the garfish olfactory nerve and the squid giant axon. We expect our model to serve as a framework for understanding the physical origins and possible functional roles of these AWs in neurobiology.