Estimating transition rates in aggregated Markov models of ion channel gating with loops and with nearly equal dwell times

Abstract

A typical task in the application of aggregated Markov models to ion channel data is the estimation of the transition rates between the states. Realistic models for ion channel data often have one or more loops. We show that the transition rates of a model with loops are not identifiable if the model has either equal open or closed dwell times. This non–identifiability of the transition rates also has an effect on the estimation of the transition rates for models which are not subject to the constraint of either equal open or closed dwell times. If a model with loops has nearly equal dwell times, the Hessian matrix of its likelihood function will be ill–conditioned and the standard deviations of the estimated transition rates become extraordinarily large for a number of data points which are typically recorded in experiments.