Efficient maximum likelihood estimation of kinetic rate constants from macroscopic currents

A new method is described that accurately estimates kinetic constants, conductance and number of ion channels from macroscopic currents. The method uses both the time course and the strength of correlations between different time points of macroscopic currents and utilizes the property of semiseparability of covariance matrix for computationally efficient estimation of current likelihood and its gradient. The number of calculation steps scales linearly with the number of channel states as opposed to the cubic dependence in a previously described method. Together with the likelihood gradient evaluation, which is almost independent of the number of model parameters, the new approach allows evaluation of kinetic models with very complex topologies. We demonstrate applicability of the method to analysis of synaptic currents by estimating accurately rate constants of a 7-state model used to simulate GABAergic macroscopic currents.