Identifiability analysis and parameter estimation of a single Hodgkin–Huxley type voltage dependent ion channel under voltage step measurement conditions

Identifiability analysis of a single Hodgkin–Huxley (HH) type voltage dependent ion channel model under voltage clamp circumstances is performed in order to decide if one can uniquely determine the model parameters from measured data in this simple case. It is shown that the two steady-state parameters (m∞m∞, h∞h∞) and the conductance (g) are not globally identifiable together using a single step voltage input. Moreover, no pair from these three parameters is identifiable. Based on the results of the identifiability analysis, a novel optimization-based identification method is proposed and demonstrated on in silico data. The proposed method is based on the decomposition of the parameter estimation problem into two parts using multiple voltage step traces. The results of the article are used to formulate explicit criteria for the design of voltage clamp protocols.