Biochemical network models simplified by balanced truncation

Modelling of biochemical systems usually focuses on certain pathways, while the concentrations of so-called external metabolites are considered fixed. This approximation ignores feedback loops mediated by the environment, that is, via external metabolites and reactions. To achieve a more realistic, dynamic description that is still numerically efficient, we propose a new methodology: the basic idea is to describe the environment by a linear effective model of adjustable dimensionality. In particular, we (a) split the entire model into a subsystem and its environment, (b) linearize the environment model around a steady state, and (c) reduce its dimensionality by balanced truncation, an established method for large-scale model reduction. The reduced variables describe the dynamic modes in the environment that dominate its interaction with the subsystem. We compute metabolic response coefficients that account for complexity-reduced dynamics of the environment. Our simulations show that a dynamic environment model can improve the simulation results considerably, even if the environment model has been drastically reduced and if its kinetic parameters are only approximately known. The speed-up in computation gained by model reduction may become vital for parameter estimation in large cell models.