Estimating kinetic mechanisms with prior knowledge I: Linear parameter constraints

Abstract

To understand how ion channels and other proteins function at the molecular and cellular levels, one must decrypt their kinetic mechanisms. Sophisticated algorithms have been developed that can be used to extract kinetic parameters from a variety of experimental data types. However, formulating models that not only explain new data, but are also consistent with existing knowledge, remains a challenge. Here, we present a two-part study describing a mathematical and computational formalism that can be used to enforce prior knowledge into the model using constraints. In this first part, we focus on constraints that enforce explicit linear relationships involving rate constants or other model parameters. We develop a simple, linear algebra–based transformation that can be applied to enforce many types of model properties and assumptions, such as microscopic reversibility, allosteric gating, and equality and inequality parameter relationships. This transformation converts the set of linearly interdependent model parameters into a reduced set of independent parameters, which can be passed to an automated search engine for model optimization. In the companion article, we introduce a complementary method that can be used to enforce arbitrary parameter relationships and any constraints that quantify the behavior of the model under certain conditions. The procedures described in this study can, in principle, be coupled to any of the existing methods for solving molecular kinetics for ion channels or other proteins. These concepts can be used not only to enforce existing knowledge but also to formulate and test new hypotheses.