Phase transitions and ion currents in a model ferroelectric channel unit

On molecular steps that activate a voltage sensitive ion channel at critical depolarization

At high transmembrane electric field, a voltage sensitive ion channel is an insulator; when the field is critically reduced, it becomes a conductor of selected ions. The Channel Activation by Electrostatic Repulsion (CAbER) hypothesis proposes that an ordered polarization field of induced dipoles at the high electric field magnitude of the excitable state is overcome by thermal disorder at a critical depolarization. Increased repulsions between positive charges in the S4 segments cause an allosteric transition in which these segments expand and separate in a chiral proteinquake. The increased space allows the P segments to refold and the ion-semiconducting S5 and S6 segments to relax and expand outward in a breathing mode. Stripped permeant ions enter widened hydrogen bonds in the core helices of these segments. Driven by concentration differences and the electric field, the ions hop along transient pathways across the channel, appearing as fractal, stochastic bursts of single-channel currents. To support order amid thermal fluctuations, an object must be of a minimum size. The critical role of an ion channel's size suggests that the evolution of Metazoa became possible only after its DNA had grown enough to code for proteins larger than the correlation length.

Fit of the dielectric anomaly of squid axon membrane near heat-block temperature to the ferroelectric Curie-Weiss law

In a 1969 experiment, Palti and Adelman reported that the capacitance of squid axon membrane rises sharply with temperature between 40 and 50 degrees C. This phenomenon is here explained by the ferroelectric-superionic transition hypothesis, which also explains channel gating and other phenomena observed in excitable membranes. According to this hypothesis gating in the Na channel is due to a first-order phase transition from a ferroelectric (closed) state to a superionic (open) state. From it, the dielectric permittivity of the Na channel, and hence the temperature-dependent component of membrane capacitance, is predicted to obey the ferroelectric Curie-Weiss law near the transition (heat-block) temperature. The Palti-Adelman data are fitted accurately by the predicted relationship. The parameters obtained permit an estimate to be made of the Curie constant of the channel, approximately 6400 K, consistent with an order-disorder ferroelectric. The Na channel appears to be a ferroelectric polymer component of a lyotropic lamellar liquid crystal.

Does the Na channel conduct ions through a water-filled pore or a condensed-state pathway?

Many investigators assert that the ion-conducting pathway of the Na channel is a water-filled pore. This assertion must be reevaluated to clear the way for more productive approaches to channel gating. The hypothesis of an aqueous pore leaves the questions of voltage-dependent gating and ion selectivity unexplained because a column of water can neither serve as a switch nor provide the necessary selectivity. The price of believing in an aqueous pore therefore is a futile search for separate ad hoc mechanisms for gating and selectivity. The fallacy is to assume that only water is available to carry ions rapidly, ignoring the role of the glycoprotein, which can form an elastomeric phase with water. The elastomer is a state of matter, neither liquid nor solid, in which the molecules of a liquid are threaded together with cross-linked polymer chains; it supports fast ion motion (Owen, 1989). An alternative hypothesis for channel gating, based on condensed-state materials science, already exists (Leuchtag, 1988, 1991a). The ferroelectric-superionic transition hypothesis (FESITH) postulates that the Na channel exists in a metastable ordered (closed) state at resting potential and, on threshold depolarization, undergoes a reversible order-disorder phase transition to a less-ordered, ion-conducting (open) state. The ordered state is ferroelectric; the disordered state is a fast ion conductor selective for Li+ and Na+. The basis of the voltage dependence is elevation of transition temperature with electric field, well established in ferroelectrics. FESITH is consistent with single-channel transitions, gating currents, heat and cold block, and other phenomena observed at channel or membrane level. An implication of FESITH, the Curie-Weiss law, has been shown to explain existing data on membrane capacitance versus temperature in squid axon (Leuchtag, 1991c). Only on the basis of a clear understanding of function can we expect new structural data on the Na-channel glycoprotein to generate realistic structure-function models at the molecular level.

Using fractals to understand the opening and closing of ion channels

Looking at an old problem from a new perspective can sometimes lead to new ways of analyzing experimental data which may help in understanding the mechanisms that underlie the phenomena. We show how the application of fractals to analyze the patch clamp recordings of the sequence of open and closed times of cell membrane ion channels has led to a new description of ion channel kinetics. This new information has led to new models that imply: (a) ion channel proteins have many conformational states of nearly equal energy minima and many pathways connecting one conformational state to another, and (b) that these many states are not independent but are linked by physical mechanisms that result in the observed fractal scaling. The first result is consistent with many experiments, simulations, and theories of globular proteins developed over the last decade. The second result has stimulated the suggestion of several different physical mechanisms that could cause the fractal scalings observed.

Indications of the existence of ferroelectric units in excitable-membrane channels

Previous work in excitability has focused primarily on the mathematical description of the phenomena, while mechanisms postulated to explain these were simple mechanical interpretations of the terms of this description. The problem considered here is that of the physical mechanism underlying excitation. The experimental facts to be explained must be not only the electrical behavior of the membrane, but also its electromechanical, electro-optic and thermoelectric behavior. Previous work on the physically grounded electrodiffusion theory foundered not because of the incorrectness of the electrodiffusion approach, but because the assumed description of the dielectric properties of the membrane was too simple. Extension of the dielectric equation of state to a nonlinear polynomial form converts the classical electrodiffusion system of equations into a nonlinear polynomial form converts the classical electrodiffusion system of equations into a ferroelectric electrodiffusion system. The consideration of ferroelectric behavior in excitable channels makes possible straight-forward physical explanation of the phenomena of membrane swelling during action potential, currents induced by temperature changes, transition temperatures, current-voltage hysteresis, nonlinear electrical behavior, voltage-dependent birefringence and rectangular pulses from single channels. The hypothesis is therefore proposed that excitable channels contain ferroelectric transmembrane units. These may be crystals or liquid crystals.