A NUMERICAL PROCEDURE TO ESTIMATE KINETIC AND STEADY-STATE CHARACTERISTICS OF INACTIVATING IONIC CURRENTS

The voltage-clamp technique is widely employed to obtain data suitable for the reliable estimation of the steady-state and kinetic parameter s of inactivating ionic currents in neurones and other excitable cells . Yet, the estimation procedure itself remains a difficult numerical p roblem, because of the strong non-linear nature of the currents involv ed. The majority of the numerical methods of parameter estimation make s use of one or another type of non-linear optimization algorithms, an d hence is, by nature, iterative. The optimization criterion is based on the maximum likelihood or the least-square error principle and the search for the optimal values takes place in a multi-dimensional param eter space. It is, therefore, prone to be trapped at some local extrem um of the parameter space. Moreover, a large number of iterations may be needed to find the optimum using up large amount of computing time. In this paper, we introduce a method that avoids these shortcomings i n that it splits up the muti-parameter non-linear fitting problems int o a sequence of linear regressions. Furthermore, it uses the value of t(p), the time at which the current trace reaches its peak value, to e stimate the activation kinetics of the current. Our approach also guar antees that the estimates will be sufficiently close to the 'real' val ues, provided the quality of the experimental records is satisfactory. In order to test our method, we used kinetic and steady-state propert ies of the following three currents as identified in earlier experimen ts: the low-threshold Ca2+ current, I-T, and the K+ currents, I-A and I-K2. Gaussian noise of constant variance was added to the simulated c urrent traces, The method was also tested on experimental traces of I- T.