Markov Models
Markov models describe the channel as a set off states, such as the conductance states seen in single channel recordings, as well as the non conducting states through which a channel must pass to reach them. Transitions between states are described by rate constants which can be functions of concentrations or voltages, or fixed. These is a variables for each state which represent the portion of channels in a cell which are in that state. As such, the sum of state variables is unity. A Hodgkin-Huxley made can be converted to a Markov model by considering a gating variable as a two state model. However, the advantage of the Markov representation is its ability to model drug interaction. Essentially, drug binding doubles the number of possible states in an ionic model, augmenting the original states with drug-bound versions. One may easily limit drug binding to a particular subset of channel states, and more finely control channel kinetics.