Calibration of Biochemical Network Models

The estimation of parameter values (model calibration) is the bottleneck of the computational analysis of biological systems. Modeling approaches are central in systems biology, as they provide a rational framework to guide systematic strategies for key issues in medicine as well as the pharmaceutical and biotechnological industries. Inter- and intra-cellular processes require dynamic models, that contain the rate constants of the biochemical reactions. These kinetic parameters are often not accessible directly through experiments. Therefore methods that estimate rate constants with the maximum precision and accuracy are needed. We present here a new method for estimating rate coefficients from noisy observations of concentration levels at discrete time points. This is traditionally done by computing the least-squares estimator. However, estimation of the error function generally requires solving the reaction rate equations, which can become computationally unfeasible. We propose an alternative approach based on a probabilistic, generative model of the variations in reactant concentration. Our method returns the rate coefficients, the level of noise and an error range on the estimates of rate constants. Its probabilistic formulation is key to a principled handling of the noise inherent in biological data, and it allows for a number of further extensions. The mathematical procedure presented here has been implemented in a software tool, named KInfer.