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

Syed Murtuza Baker,Björn H Junker,C Hart Poskar

doi:10.1186/1687-4153-2011-7

Abstract

In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. What differentiates this approach is the integration of an orthogonal-based local identifiability method into the unscented Kalman filter (UKF), rather than using the more common observability-based method which has inherent limitations. It also introduces a variable step size based on the system uncertainty of the UKF during the sensitivity calculation. This method identified 10 out of 12 parameters as identifiable. These ten parameters were estimated using the UKF, which was run 97 times. Throughout the repetitions the UKF proved to be more consistent than the estimation algorithms used for comparison.

Highlights

The focus of systems biology is to study the dynamic, complex and interconnected functionality of living organisms [1]
We investigated parameter identifiability using a sensitivitybased orthogonal identifiability algorithm proposed by Yao et al [10] with the unscented Kalman filter (UKF) as the method for parameter estimation in a nonlinear biological model
The novelty of this study lies in the fact that we propose to embed a sensitivity-based method for identifiability analysis into the UKF during the estimation of the parameter

Summary

Introduction

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. 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 order to properly describe the dynamics, it is required to have both an accurate and a complete set of parameter values that implement these

Methods

Results

Conclusion