A direct optimization approach to hidden Markov modeling for single channel kinetics

Hidden Markov modeling (HMM) provides an effective approach for modeling si ngle channel kinetics. Standard HMM is based on Baum's reestimation. As app lied to single channel currents, the algorithm has the inability to optimiz e the rate constants directly. We present here an alternative approach by c onsidering the problem as a general optimization problem. The quasi-Newton method is used for searching the likelihood surface. The analytical derivat ives of the likelihood function are derived, thereby maximizing the efficie ncy of the optimization. Because the rate constants are optimized directly, the approach has advantages such as the allowance for model constraints an d the ability to simultaneously fit multiple data sets obtained at differen t experimental conditions. Numerical examples are presented to illustrate t he performance of the algorithm. Comparisons with Baum's reestimation sugge st that the approach has a superior convergence speed when the likelihood s urface is poorly defined due to, for example, a low signal-to-noise ratio o r the aggregation of multiple states having identical conductances.