  The use of Hodgkin-Huxley (HH) equations abounds in the literature, but the
identifiability of the HH model parameters has not been broadly considered.
Identifiability analysis addresses the question of whether it is possible to
estimate the model parameters for a given choice of measurement data and
experimental inputs. Here we explore the structural identifiability properties
of a generalized form of HH from voltage clamp data. Through a scaling
argument, we conclude that the steady-state gating variables are not
identifiable from voltage clamp data, and then further show that their product
together with the conductance term forms an identifiable combination. We
additionally show that these parameters become identifiable when the initial
conditions for each of the gating variables are known. The time constants for
each gating variable are shown to be identifiable, and a novel method for
estimating them is presented. Finally, the exponents of the gating variables
are shown to be identifiable in the two-gate case, and we conjecture these to
be identifiable in the general case. These results are broadly applicable to
models using HH-like formalisms, and show in general which parameters and
combinations of parameters are possible to estimate from voltage clamp data.
