Ion channel data are an exemplary example of a stochastic process described by the chemical master equation (CME). Fundamental to the description by the CME is that the dynamics of ion channels satisfy Markov models. These are discrete state models of a continuous conformational process. The discrete states delineate the macroscopic chemical properties of the protein at a given time. On the time scales resolved by the data, they symbolize metastable states that an ion channel or receptor can assume. The transition rates of the Markov model determine the change between the states and thus their probability distributions.
We generalize a Kalman filter with a more general model of the experimental signal to determine the Bayesian posterior distribution of the parameters. The generalized Kalman filter called Bayesian filter is based on a Fokker-Planck approximation of the CME, which determines the unknown parameters from the Markov model of macroscopic ion channel data. We were able to demonstrate the superiority of our software over classical rate equation approaches (Münch 2022) From the Markov models, the basic chemical and biological properties of the protein, open probability as a function of the existing physical chemical environment and its free energy, can be derived.
Currently, model selection criteria, minimum-informative prior distributions, and parameter identifiability are being investigated. In particular, parameter unidentifiability is a problem for both Bayesian estimation and the frequentist likelihood approach. Here, the superior Bayesian information fusion capabilities can be profitably applied to parameter identification.