voltage dependent transition in a kinetic scheme
A voltage dependent rate for a state transition in a kinetic scheme. It follows the same form as Borg-Graham's modified Hodgkin-Huxley equations. The equivalent gating charge is z, half potential, Vhalf (mV), and position of the activation particle within the transit of the gating particle is gamma: 0 < gamma < 1. The transition rates are expressed through their reciprocals, the characteristic timescales, tau-x near Vhalf, and tau-m (tau-m << tau-x), the saturation timescale for extreme potentials.
The transition is computed from the forward and reverse rates, alpha and beta, given by:
private final double alpha (double v) {
double a = Math.exp (ebykt * (gamma) * z * (v - Vhalf)) / tau_x;
a = 1. / (1. / a + tau_m);
return a;
}
private final double beta (double v) {
double b = Math.exp (-ebykt * (1. - gamma) * z * (v - Vhalf)) / tau_x;
b = 1. / (1. / b + tau_m);
return b;
}