Large-scale statistical parameter estimation in complex systems with an application to metabolic models

The estimation of a large number of parameters in a complex dynamic multicompartment model in the presence of insufficient data is a difficult and challenging problem. Such problems arise in many applications, e.g., in biology, physiology, and environmental sciences. The model consists of a large system of coupled nonlinear ordinary differential equations, the data consisting of the values of few components at given observation times. The estimation problems are usually ill-posed and severely underdetermined, while the quality of the scarce data is far from optimal. Therefore, a successful solution necessarily requires additional information about the parameters. A natural framework to introduce a priori information into the model is the Bayesian paradigm. In this article we develop a Bayesian methodology that is able to utilize various types of prior constraints such as approximate algebraic constraints for the parameters or inequality constraints for the solutions and integrate them into a parametric prior distribution. The subsequent parameter estimation is based on a combination of optimization methods and statistical sampling techniques. We apply the methodology to a skeletal muscle metabolism model, in which we are able to simultaneously estimate more than 100 parameters from one fifth as many measured data points.