Parameter identifiability and identifiable combinations in generalized Hodgkin-Huxley models

TL;DR

This paper analyzes the structural identifiability of parameters in generalized Hodgkin-Huxley models using voltage clamp data, revealing which parameters can be uniquely estimated and under what conditions.

Contribution

It provides a comprehensive identifiability analysis of generalized HH models, introducing methods to determine which parameters are estimable from voltage clamp data.

Findings

Steady-state gating variables are not identifiable without initial conditions.

The product of gating variables and conductance is an identifiable combination.

Time constants are identifiable, and exponents are identifiable in the two-gate case.

Abstract

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.