Optimal scheduling for parameter estimation of cell signaling pathway models - A gradient approach

Modeling of cell signaling pathways attracted a lot of interest in recent years. Such models let scientists to understand mechanisms governing the cell functioning which plays a crucial role in many areas, for example in a new drug development. To obtain a mathematical model that behaves similarly to observed biological process the estimation of model's parameters is required after writing mathematical equations. In case of cell signaling pathways appropriate measurements, for example DNA microarrays or different blotting techniques, are relatively expensive. Hence it is very important to choose right times of measurements in order to obtain low variances of estimates of parameters. This problem is somehow similar to estimation of parameters in pharmacokinetics. The classical approach is to use the Fisher information matrix (FIM), which inverse, under some assumptions, is a lower bound for the covariance matrix of parameter's estimates. One of possible approach to sampling schedule optimization is to maximize the determinant of FIM. In this paper we derive formulas for calculation of the gradient of FIM in space of sampling times under the assumption that the model is given in state space. Then the gradient-based approach is proposed. Numerical examples confirm the correctness and usefulness of the presented method.