An improved constraint filtering technique for inferring hidden states and parameters of a biological model

In systems biology, kinetic models represent the biological system using a set of ordinary differential equations (ODEs). The correct values of the parameters within these ODEs are critical for a reliable study of the dynamic behaviour of such systems. Typically, it is only possible to experimentally measure a fraction of these parameter values. The rest must be indirectly determined from measurements of other quantities. In this article, we propose a novel statistical inference technique to computationally estimate these unknown parameter values. By characterizing the ODEs with non-linear state-space equations, this inference technique models the unknown parameters as hidden states, which can then be estimated from noisy measurement data. Here we extended the square-root unscented Kalman filter SR-UKF proposed by Merwe and Wan to include constraints with the state estimation process. We developed the constrained square-root unscented Kalman filter (CSUKF) to estimate parameters of non-linear state-space models. This probabilistic inference technique was successfully used to estimate parameters of a glycolysis model in yeast and a gene regulatory network. We showed that our method is numerically stable and can reliably estimate parameters within a biologically meaningful parameter space from noisy observations. When compared with the two common non-linear extensions of Kalman filter in addition to four widely used global optimization algorithms, CSUKF is shown to be both accurate and computationally efficient. With CSUKF, statistical analysis is straightforward, as it directly provides the uncertainty on the estimation result. Matlab code available upon request from the author. Supplementary data are available at Bioinformatics online.