Biological systems such as metabolic and regulatory networks are often well-described using ordinary differential equations to describe mass-action kinetics. Several problems arise while building and constraining these models. For example in metabolic systems the rate-limiting steps can vary depending on the experimental conditions. This can lead to uncertainty in the appropriate model structure to describe a system and in the identifiability of the model prameters. In principle we would like to build models which capture these rate limiting steps in a principled way and where either all parameters can be identified or the uncertainty is charactered. I will describe our work on different approaches to building models from dynamic data, including methods for sparse model selection and parameter estimation for system where only a subsets of the variables are directly measured.
