Merging Shaker K+ channel electrophysiology with structural data by a nucleation and growth mechanism

An Insight into the Potassium Currents of hERG and Their Simulation

By assuming that a stepwise outward movement of the four S4 segments of the hERG potassium channel determines a concomitant progressive increase in the flow of the permeant potassium ions, the inward and outward potassium currents can be simulated by using only one or two adjustable (i.e., free) parameters. This deterministic kinetic model differs from the stochastic models of hERG available in the literature, which usually require more than 10 free parameters. The K⁺ outward current of hERG contributes to the repolarization of the cardiac action potential. On the other hand, the K⁺ inward current increases with a positive shift in the transmembrane potential, in apparent contrast to both the electric and osmotic forces, which would concur in moving K⁺ ions outwards. This peculiar behavior can be explained by the appreciable constriction of the central pore midway along its length, with a radius < 1 Å and hydrophobic sacks surrounding it, as reported in an open conformation of the hERG potassium channel. This narrowing raises a barrier to the outward movement of K⁺ ions, inducing them to move increasingly inwards under a gradually more positive transmembrane potential.

A historical biophysical dogma vs. an understanding of the structure and function of voltage-gated tetrameric ion channels. A review

The outstanding work of several eminent biophysicists has allowed the functional features of voltage-gated tetrameric ion channels to be disclosed using ingenious and sophisticated electrophysiological techniques. However, the kinetics and mechanism underlying these functions have been heavily conditioned by an arbitrary interpretation of the groundbreaking results obtained by Hodgkin and Huxley (HH) in their investigation of sodium and potassium currents using the voltage clamp technique. Thus, the heavy parametrization of their results was considered to indicate that any proposed sequence of closed states terminates with a single open state. This 'dogma' of HH parametrization has influenced the formulation of countless mechanistic models, mainly stochastic, requiring a high number of free parameters and of often unspecified conformational states. This note aims to point out the advantages of a deterministic kinetic model that simulates the main features of tetrameric ion channels using only two free parameters by assuming their stepwise opening accompanied by a progressively increasing cation flow. This model exploits the electrostatic attractive interactions stemming from the charge distribution shared by all tetrameric ion channels, providing a close connection between their structure and function. Quite significantly, a stepwise opening of all ligand-gated tetrameric ion channels, such as glutamate receptors (GluRs), with concomitant ion flow, is nowadays generally accepted, not having been influenced by this dogma. This provides a unified picture of both voltage-gated and ligand-gated tetrameric ion channels.

Deterministic model of Cav3.1 Ca2+ channel and a proposed sequence of its conformations

A family of current-time curves of T-type Ca_v3.1 Ca²⁺ channels available in the literature is simulated by a kinetic model differing from that used for the interpretation of all salient features of Na⁺ and Shaker K⁺ channels by the insertion of a multiplying factor expressing the difference between the working potential ϕ and the reversal potential ϕ_r. This deterministic model is also used to simulate experimental curves taken from the literature for steady-state 'fast inactivation' and for a gradual passage from fast to 'slow inactivation'. A depolarizing pulse induces fast or slow inactivation depending on whether it lasts 100-500 ms or about 1 min, and is believed to cause a collapse of the central pore near the selectivity filter (SF). A number of features of fast and slow inactivation of Ca_v3.1 Ca²⁺ channels are qualitatively interpreted on the basis of a sequence of conformational states. Briefly, the conformation responsible for 'fast inactivation' is assumed to have the activation gate open and the inactivation gate (i.e., the SF) inactive. Immediately after a depolarizing pulse, this conformation is inactive and requires a sufficiently long rest time at a far negative holding potential to recover from inactivation. 'Slow inactivation' is ascribed to a different conformation with the activation gate closed and the SF inactive.

Role of the time dependence of Boltzmann open probability in voltage-gated proton channels

The modeling and simulation of experimental families of current-time (I-t) curves of dimeric voltage-gated proton channels and of proton-conducting voltage sensing domains (VSDs) with a minimum of free parameters requires the movement of protons to be controlled by the rate of increase of the Boltzmann open probability p over time in passing from the holding to the depolarizing potential. Families of I-t curves of protomers and proton-conducting VSDs can be satisfactorily fitted by the use of a single free parameter expressing the rate constant k_p for the increase of p over time. Families of I-t curves of dimeric H_v1 channels can be fitted by a model that assumes an initial proton current I₁ flowing along the two monomeric units, while they are still operating separately; I₁ is gradually replaced by a slower and more potential-dependent current I₂ flowing when the two monomers start operating jointly under the control of the coiled-coil domain. Here too, p is assumed to increase over time with a rate constant k_p that doubles in passing from I₁ to I₂, with fit requiring three free parameters. Chord conductance yields erroneously high gating charges when fitted by the Boltzmann function, differently from slope conductance.