  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.
