Model-based fitting of single-channel dwell-time distributions

Single-channel recordings provide unprecedented resolutions on kinetics of conformational changes of ion channels. Several approaches exist for analysis of the data, including the dwell-time histogram fittings and the full maximal-likelihood approaches that fit either the idealized dwell-time sequence or more ambitiously the noisy data directly using hidden Markov modeling. Although the full maximum likelihood approaches are statistically advantageous, they can be time-consuming especially for large datasets and/or complex models. We present here an alternative approach for model-based fitting of one-dimensional and two-dimensional dwell-time histograms. To improve performance, we derived analytical expressions for the derivatives of one-dimensional and two-dimensional dwell-time distribution functions and employed the gradient-based variable metric method for fast search of optimal rate constants in a model. The algorithm also has the ability to allow for a first-order correction for the effects of missed events, global fitting across different experimental conditions, and imposition of typical constraints on rate constants including microscopic reversibility. Numerical examples are presented to illustrate the performance of the algorithm, and comparisons with the full maximum likelihood fitting are discussed.