Sparse Estimation in Ordinary Differential Equation Systems

Ordinary differential equation systems are used to model abundances of chemical species as deterministic continuous time processes. Identification of the system from noisy data is a major challenge with applications in systems biology – such as to the inference of phosphoprotein interaction networks as in [3]. For mass action kinetics the system structure – the network – is encoded via sparsity in a parameter vector, whose dimension increases rapidly with the number of species. We have developed an algorithm for simultaneous system identification and parameter estimation via minimisation of a penalised loss function. The global minimiser is difficult to find, and focus has been on computational aspects, as well as variancereduction techniques. Several techniques are combined to cope with the computational and statistical aspects. The resulting method is implemented in an R-package, which handles enzymatic systems of up to 100 chemical species.