Modeling a non-inactivating delayed rectifier cardiac current using voltage clamp data

This paper describes a new parameter estimation method applicable to experimental voltage-clamp records. The method is based on the Hodgkin-Huxley (HH) representation of a generic non-inactivating delayed rectifier current (IK) which can be assimilated to the delayed rectifier potassium current of cardiac cells. The model involves a single gating variable of activation (chi) of degree (lambda chi). Its parameters include the voltage-dependent steady-state characteristic (chi infinity), time constant tau chi, the degree lambda chi as a positive integer, and the maximal conductance gK. The method is based on linear optimization. It implements a series of least-squares minimization steps to calculate a first estimate of each model parameter, followed by global minimization to obtain final estimates. The required data, in the form of ionic current responses, correspond to standard voltage-clamp protocols. The effects of noise are minimized by avoiding the use of the time derivative of IK in the calculations. Simulated voltage-clamp data using either a HH model or a five-state Markov chain (MC) model served two purposes: (i) to test the performance of the HH parameter estimation method, and (ii) to study the suitability of the HH model to reproduce data generated by models other than HH. A nominal MC model was obtained by fitting its current responses to those of the HH model. Rate constants of the nominal MC model were then modified and voltage-clamp current responses were generated. Excellent results were obtained with HH and nominal MC data. Data sets generated by a 20% change in the rate constants of the nominal MC model showed that the closed-state rate constants have only a limited influence on the HH parameter estimates, whereas changes in the closed-to-open rate constants produce substantial effects. Nevertheless, a given MC data set can be fitted quite closely by a HH model. In the light of these simulation results it is indicated that an hybrid HH-MC representation of IK data would be more flexible than a straight HH model by removing some of the constraints between the rate constants, and less cumbersome than a straight MC model by substantially reducing the number of parameters to be estimated.