Trajectory-based model reduction of nonlinear biochemical networks employing the observability normal form

Abstract

AbstractIn the last years, improved measurement devices, automated data generation, and high-throughput methods have initiated a trend to increasingly precise, but also increasingly complex models. Simulating these high-dimensional models and understanding their basic dynamic properties are crucial challenges encountered right now. One way towards these goals is model reduction. In this paper, we propose a trajectory-based method for reducing the input-output (I/O) map of continuous-time nonlinear ordinary differential equations. The method uses a sample of simulated I/O-trajectories, obtained by distributing initial states and input trajectories according to a probability density. Employing Monte-Carlo integration and the observability normal form, parameters of a reduced model are determined by convex optimization from this sample of trajectories. The properties of the method are illustrated using a model of the MAPK cascade. It is shown that redundancies are detected and that the approach can deal with nonlinear dynamics, such as limit-cycle oscillations.