MODELING A NONINACTIVATING DELAYED RECTIFIER CARDIAC CURRENT USING VOLTAGE-CLAMP DATA

This paper describes a new parameter estimation method applicable to e xperimental voltage-clamp records. The method is based on the Hodgkin- Huxley (HH) representation of a generic non-inactivating delayed recti fier current (I-K) which can be assimilated to the delayed rectifier p otassium current of cardiac cells. The model involves a single gating variable of activation (x) of degree (lambda(x)). Its parameters inclu de the voltage-dependent steady-state characteristic (x(infinity)), ti me constant tau(x), the degree lambda(x) as a positive integer, and th e maximal conductance ($) over bar(K). The method is based on linear o ptimization. It implements a series of least-squares minimization step s to calculate a first estimate of each model parameter, followed by g lobal minimization to obtain final estimates. The required data, in th e form of ionic current responses, correspond to standard voltage-clam p protocols. The effects of noise are minimized by avoiding the use of the time derivative of I-K in the calculations. Simulated voltage-cla mp data using either a HH model or a five-state Markov chain (MC) mode l 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 mode l was obtained by fitting its current responses to those of the HH mod el. Rate constants of the nominal MC model were then modified and volt age-clamp current responses were generated. Excellent results were obt ained 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 produ ce substantial effects. Nevertheless, a given MC data set can be fitte d quite closely by a HH model. In the light of these simulation result s it is indicated that an hybrid HH-MC representation of I-K data woul d be more flexible than a straight HH model by removing some of the co nstraints between the rate constants, and less cumbersome than a strai ght MC model by substantially reducing the number of parameters to be estimated.