I "understand" the concept that if we have the reaction

A <--> B

With the forward rate Kf and the backwards rate Kb, then we can say

dA/dt = -Kf . A + Kb . B

From that, I understand, when it comes to HH kinetics, we could say, in the DERIVATIVE block

n' = alpha(v)*(1-n) - beta(v)*n

However, I very rarely see NMODL coded in that form. It is normally in the form...

n' = (n_inf - n) / tau_n

which is calculated from

tau_n = 1 / (alpha(v) + beta(v))

n_inf = alpha(v) / (alpha(v) + beta(v))

This, I do not understand. I assume these later "alpha" and "beta" functions are not identical to the former ones, if the mechanism was to produce an identical current? How do I think about these alphas and betas... are they still foward and backward rate constants? Why do people not use the first form that seems more intuitive? It seems hard to believe it is for a computation advantage. Finally, and most importantly, how do I adjust said alpha and beta functions to adjust the kinetics in terms an electrophysiologist would understand, i.e. the V50, the activation kinetics etc?

For reference sake, here is the alpha and beta from the mechanism I am looking at

alpha = 0.032 * (15-v2) / ( exp((15-v2)/5) - 1)

beta = 0.5 * exp((10-v2)/40)