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 parameters of inactivating ionic currents in neurones and other excitable cells. Yet, the estimation procedure itself remains a difficult numerical problem, because of the strong non-linear nature of the currents involved. The majority of the numerical methods of parameter estimation makes use of one or another type of non-linear optimization algorithms, and 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 parameter space. It is, therefore, prone to be trapped at some local extremum 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 in that it splits up the multi-parameter non-linear fitting problems into a sequence of linear regressions. Furthermore, it uses the value of tp, the time at which the current trace reaches its peak value, to estimate the activation kinetics of the current. Our approach also guarantees that the estimates will be sufficiently close to the 'real' values, provided the quality of the experimental records is satisfactory. In order to test our method, we used kinetic and steady-state properties of the following three currents as identified in earlier experiments: the low-threshold Ca2+ current, IT, and the K+ currents, IA and IK2. Gaussian noise of constant variance was added to the simulated current traces. The method was also tested on experimental traces of IT.