MODELING AND IDENTIFICATION OF COUPLED MARKOV-CHAIN MODEL WITH APPLICATION

A parametrized Markov chain model is developed to model the action of a biological ion channel. The proposed model takes the form of a set o f identical binary chains which are dependent according to a coupling parameter. The outputs of these chains combine additively to give a re cord of ion current buried in large amounts of noise versus time. When varied, the coupling parameter realizes a range of behaviours from ti ght coupling to complete independence. Other model parameters describe the intrinsic characteristics of the binary chains as well as their b ehaviour when fully coupled. An identification procedure for the model parameters is developed based on hidden Markov modelling ideas but in corporating a gradient descent estimation algorithm. In this way we co pe with the non-linear form of the dependence of the model on the para meters. The model and identification methods are tested and verified o n simulated data and real biological data.