Phase transitions and ion currents in a model ferroelectric channel unit

The hypothesis of ferroelectric electrodiffusion is examined mathematically. A thermodynamic potential, the elastic Gibbs function, written in polynomial form, provides the dielectric equation of state for the model. The other equations of electrodiffusion theory complete the model. This system reduces to a second-order partial differential equation, which is formally solved by the phase-plane method. This solution, applied to the Na channel, leads to a propagating phase-transition wave accompanied by movement of ionic charge. This may be readily interpreted as a transmembrane wave traveling along a ferroelectric unit within, and transporting ions through, the channel. Comparison of the temperature dependence of axonal conduction velocity with that of the spontaneous polarization of Rochelle salt suggests that the Na channel of squid axon contains a ferroelectric unit having a lower Curie point, but decomposing before reaching its upper Curie point. Comparison with data from reconstitution experiments suggests that the ferroelectric unit is a carbohydrate enclosed in an intrinsic protein structure to form a glycoprotein channel. The value experimentally estimated for the surface charge of the Na channel is within the range of spontaneous polarizations of typical ferroelectric crystals. It is argued that the ferroelectric probably is a single crystal of the order-disorder type, which undergoes a first-order transition between a ferroelectric and a paraelectric state during excitational activity. The hypothesis of ferroelectric channel units is consistent with the existence and directionality of the observed "gating" currents.