Abstract
An action potential is typically described as a purely electrical change that propagates along the membrane of excitable cells. However, recent experiments have demonstrated that non-linear acoustic pulses that propagate along lipid interfaces and traverse the melting transition, share many similar properties with action potentials. Despite the striking experimental similarities, a comprehensive theoretical study of acoustic pulses in lipid systems is still lacking. Here we demonstrate that an idealized description of an interface near phase transition captures many properties of acoustic pulses in lipid monolayers, as well as action potentials in living cells. The possibility that action potentials may better be described as acoustic pulses in soft interfaces near phase transition is illustrated by the following similar properties: correspondence of time and velocity scales, qualitative pulse shape, sigmoidal response to stimulation amplitude (an ‘all-or-none’ behavior), appearance in multiple observables (particularly, an adiabatic change of temperature), excitation by many types of stimulations, as well as annihilation upon collision. An implication of this work is that crucial functional information of the cell may be overlooked by focusing only on electrical measurements.
Highlights
Excitable cells generate a characteristic transient change in transmembrane voltage that propagates along the cell membrane in response to suitable stimuli
One conjecture, which is the focus of this manuscript, is that Action potentials (APs) are acoustic pulses that propagate along the lipid interface and cross the phase-transition from the so called liquid-expanded to the liquid-condensed phase[20,21]
Stimulation was shown to prompt a sigmoidal response of density pulses in lipid interfaces near phase transition[27], and these pulses were demonstrated to annihilate upon collision[36]
Summary
Our purpose is to investigate the properties of isentropic traveling waves which exist near a phase transition. To allow for a continuous transition between the two phases, we follow van der Waals’ hypothesis that the energy of a system depends on the gradient of density (the so called capillarity term)[43,44]. Both curves meet at the critical point (wc, pc, θc), where the distinction between the two phases disappears. These scales were used to derive a dimensionless form of the model equations (Supplemental Materials, Eqs (S3)–(S5)), that depends on only three parameters: the (dimensionless) heat capacity, thermal conductivity and capillarity coefficient c v cvθc , pc wc k = kθc , pc wcζ. Θ is the Heaviside function, and λ is the width of excitation
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