Cellular ion channel-pump system modeling using switched stochastic differential equations

This paper identifies a multidimensional random switched process model of a neuron with embedded Ca⁺⁺ ion channel and pump molecules adiabatically interacting based on local ion concentrations near the cell membrane. The model interprets known physiology of the channels as a coupled set of switched random processes and derives mechanical equations based on concentration flow among different states of the system. Rapid changes to channel barrier energies occurring during channel opening and closing transitions are modeled as another degree of freedom commutating the state of the overall system. An ion reservoir model is used as the primary tool to incorporate stochastic effects in channel operation. The complete model is analyzed numerically and then the equations are used to motivate a stochastic model for closed state dwell times. The result is compared against expected results of a leaky-integrator and known single-channel histograms.