Parameter Estimation of Biological Phenomena: An Unscented Kalman Filter Approach

Abstract

Recent advances in high-throughput technologies for biological data acquisition have spurred a broad interest in the construction of mathematical models for biological phenomena. The development of such mathematical models relies on the estimation of unknown parameters of the system using the time-course profiles of different metabolites in the system. One of the main challenges in the parameter estimation of biological phenomena is the fact that the number of unknown parameters is much more than the number of metabolites in the system. Moreover, the available metabolite measurements are corrupted by noise. In this paper, a new parameter estimation algorithm is developed based on the stochastic estimation framework for nonlinear systems, namely the unscented Kalman filter (UKF). A new iterative UKF algorithm with covariance resetting is developed in which the UKF algorithm is applied iteratively to the available noisy time profiles of the metabolites. The proposed estimation algorithm is applied to noisy time-course data synthetically produced from a generic branched pathway as well as real time-course profile for the Cad system of E. coli. The simulation results demonstrate the effectiveness of the proposed scheme.