Hybrid Reductions of Computational Models of Ion Channels Coupled to Cellular Biochemistry

Computational models of cellular physiology are often too complex to be analyzed with currently available tools. By model reduction we produce simpler models with less variables and parameters, that can be more easily simulated and analyzed. We propose a reduction method that applies to ordinary differential equations models of voltage and ligand gated ion channels coupled to signaling and metabolism. These models are used for studying various biological functions such as neuronal and cardiac activity, or insulin production by pancreatic beta-cells. Models of ion channels coupled to cell biochemistry share a common structure. For such models we identify fast and slow sub-processes, driving and slaved variables, as well as a set of reduced models. Various reduced models are valid locally and can change on a trajectory. The resulting reduction is hybrid, implying transitions from one reduced model (mode) to another one.