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.