Unscented Kalman filter with parameter identifiability analysis for the estimation of multiple parameters in kinetic models

The focus of systems biology is to study the dynamic, complex and interconnected functionality of living organisms [1]. To have a systems-level understanding of these organisms, it is necessary to integrate experimental and computational techniques to form a dynamic model [1,2]. One such approach to dynamic models is the modeling of metabolic fluxes by their underlying enzymatic reaction rates. These enzymatic reaction rates, or enzyme kinetics, are described by a kinetic rate law. Different rate laws may be used, matching the specific behaviour of the chemical reaction that is catalysed by the enzyme to the most appropriate rate law. These kinetic rate laws are formulated with mathematical functions of metabolite concentration(s) and one or more kinetic parameters. In combination with the stoichiometry of the metabolism, these kinetic rate laws define the function of the cell. In order to properly describe the dynamics, it is required to have both an accurate and a complete set of parameter values that implement these kinetic rate laws. Owing to various limitations in wet lab experiments, it is not always possible to have a measured value for all the required parameters. In these cases, it is necessary to apply computational approaches for the estimation of these unknown parameters.In the past few years, increasing research has been made on the application of several optimization techniques towards parameter estimation in systems biology. These include nonlinear least square (NLSQ) fitting [3], simulated annealing [4] and evolutionary computation [5]. More recently, kinetic modelling has been formulated as a nonlinear dynamic system in state-space form, where the parameter estimation is addressed in the framework of control theory. One of the most widely used methods in control theory for parameter estimation is the Kalman filter [2]. However, the Kalman filter is designed for inference in a linear dynamic system, and subsequently gives inaccurate results when appl