Supplementary material from "Parameter inference for stochastic reaction models of ion channel gating from whole-cell voltage-clamp data"

Mathematical models of ion channel gating describe the changes in ion channel configurations due to the electrical activity of the cell membrane. Experimental findings suggest that ion channels behave randomly, and therefore stochastic models of ion channel gating should be more realistic than deterministic counterparts. Whole-cell voltage-clamp data allows us to calibrate the parameters of ion channel models. However, standard methods for deterministic models do not distinguish between stochastic channel gating and measurement error noise, resulting in biased estimates, whereas conventional approaches for stochastic models are computationally demanding. We propose a state-space model of ion channel gating based on stochastic reaction networks, and a maximum likelihood inference procedure to estimate the unknown parameters. Simulation studies show that: (1) our proposed method infers the unknown parameters with low uncertainty and outperforms standard approaches whilst being computationally efficient, and (2) considering stochastic mechanisms of flickering between conducting and non-conducting open states improves the estimates in the total number of ion channels. Finally, the application of our method to experimental data correctly distinguished the 50Hz measurement error from noise due to stochastic gating. This method improves data-driven models of ion channel dynamics, by accounting for stochastic gating and measurement errors during inference.