The chemical equation describing behavior of n

The kinetic reaction scheme for n is simply the back-and-forth movement of the "particle" between one side of the membrane and the other. Today we conceptualize this notion as the movement of a charge group from one position to another within the potassium channel.

As with any chemical reaction, the rates at which this movement takes place are set by rate constants. The constant of the forward reaction (the direction in which the probability of the channels opening increases) is "alpha n" and that of the backwards reaction is "beta n."

In spite of the name rate constants, the values are not constant at all but depend on the potential across the membrane.

For depolarizations, "alpha n" is larger than "beta n," causing a steady value of n to build up. For repolarizations, the balance shifts such that n returns to zero.

Finding the values of the alphas and betas for n

The onset and reset of the conductance curves had to be fitted with time courses of n^4. In those days, the fitting was often done by making transparent templates of curves with a range of parameter values to overlay data traces. Interpolations and iterations were used to improve the resolution in the data values.

In this figure (Fig. 2) from the fourth paper in the Hodgkin-Huxley 1952 series, (view larger figure with legend) the n^4 curve fits the conductance data points (circles) quite well.

First Hodgkin and Huxley had to carry out these tedious procedures: