Controlled hidden Markov models for dynamically adapting patch clamp experiment to estimate Nernst potential of single-ion channels

This paper presents novel kernel-based stochastic learning algorithms for controlling the kinetics of single-ion channels in a patch clamp experiment. The algorithms yield efficient estimates of the equilibrium (Nernst) potential of an ion channel. The equilibrium potential of an ion channel is the applied external potential difference required to maintain electrochemical equilibrium across the ion channel. The algorithm adaptively controls the exploration of the learning algorithm to achieve an optimal balance between exploration and exploitation. An important feature of the resulting algorithm is that it is guaranteed to minimize the experimental effort. We illustrate the efficiency of the algorithms for the experimentally determined current voltage curve of a bi-ionic single potassium ion channel.