A novel approach to dynamic flux balance analysis that accounts for the dynamic transfer of information by internal metabolites

Understanding the dynamics of information feedback amongst components of complex biological systems is crucial to the success of engineering desirable metabolic phenotypes. Flux Balance Analysis (FBA) is a structural metabolic modelling procedure that allows for local topological constraints to be related to steady-state global behaviors of metabolic systems. A vast majority of biological systems of interest, such as microbial communities, however do not exist under steady-state conditions. Therefore, extending FBA methods to the dynamical setting has been a major challenge to metabolic modelling. In dynamic FBA (dFBA), the representation of feedback dynamics is made possible by combining the methods of FBA with those of Ordinary Differential Equations (ODE). Although numerous dFBA models have been constructed to date, very little effort has gone into the theoretical analysis of how static FBA models and dynamic ODE models should be combined in dFBA. To develop a better understanding of the mathematical structure of dFBA, we investigate the properties of FBA. In order to predict time-derivatives of population growth, every dFBA model must make the assumption that the underlying metabolic network modeled via FBA optimizes a phenotypic function of growth rate. We show however, that under certain circumstances, this requirement introduces a rigid correspondence between growth rate, and a related quantity, the growth yield. The consequence of this is that the dFBA models become rigid in its predictions, effectively becoming a near-static representation of metabolism. In this thesis, we show that this tight correspondence between yield and rate may be broken by combining two inversely related approaches to formulating the FBA problem.