Modeling Ion Channel Kinetics with Parameter Constraints

Abstract

Ion channel gating mechanisms can be complex and difficult to extract from experimental data. A solution is to apply parameter constraints, which reflect prior knowledge or tested hypotheses and reduce model complexity and speed up computation. Soft constraints balance the existing knowledge with the new experimental data and limit the parameter search engine to a smaller space of more acceptable values. In contrast, hard constraints enforce a mathematical relationship involving one or more parameters of the model. These constraints can be formulated as an invertible transformation between a set of model parameters and a set of “free” parameters. Each constraint reduces the number of free parameters by one. Linear constraints, such as microscopic reversibility or scaling between sequential transitions, can be conveniently obtained with the singular value decomposition. Here, we show how this method can be generalized to implement arbitrary linear constraints. We also show how to make these constraints depend on arbitrary model parameters. This can be applied, for example, to enforce allosteric constraints where the allosteric factor itself is a free parameter. Furthermore, we explore some useful ways for implementing soft constraints.