Parameter identification of biological networks using extended Kalman filtering and χ2 criteria

Parameter estimation is a central issue in systems biology, as it represents the key step in obtaining information from computational models of biological systems. The extended Kalman filter (EKF) in its various implementations has been proposed as a parameter estimator by several authors. However, in many cases, and in particular when the estimation problem involves a large number of unknown parameters, the EKF can perform poorly. In this paper we show how the knowledge of the statistics of the measurement noise can be used to validate or invalidate the estimates provided by the filter, and to refine them in case they turn out not to be satisfactory. We demonstrate these ideas on a simple gene expression model, and we show how the proposed method offer advantages over classical techniques such as least-squares estimation.