Aggregated markov model using time series of single molecule dwell times with minimum excessive information

Statistics of the dwell times, the stationary state distributions (SSDs), are often studied to infer the underlying kinetics from a single molecule finite-level time series. However, it is well known that the underlying kinetic scheme, a hidden Markov model (HMM), cannot be identified uniquely from the SSDs because some features of the underlying HMM are hidden by finite-level measurements. Here, we quantify the amount of excessive information in a given HMM that is not warranted by the measured SSDs and extract the HMM with minimum excessive information as the most objective representation of the data. The method is applied to a single molecule enzymatic turnover experiment, and the origin of dynamic disorder is discussed in terms of the network properties of the HMM.