  The regulation of metabolic activity by tuning enzyme expression levels is
crucial to sustain cellular growth in changing environments. Metabolic networks
are often studied at steady state using constraint-based models and
optimization techniques. However, metabolic adaptations driven by changes in
gene expression cannot be analyzed by steady state models, as these do not
account for temporal changes in biomass composition. Here we present a dynamic
optimization framework that integrates the metabolic network with the dynamics
of biomass production and composition, explicitly taking into account enzyme
production costs and enzymatic capacity. In contrast to the established dynamic
flux balance analysis, our approach allows predicting dynamic changes in both
the metabolic fluxes and the biomass composition during metabolic adaptations.
We applied our algorithm in two case studies: a minimal nutrient uptake
network, and an abstraction of core metabolic processes in bacteria. In the
minimal model, we show that the optimized uptake rates reproduce the empirical
Monod growth for bacterial cultures. For the network of core metabolic
processes, the dynamic optimization algorithm predicted commonly observed
metabolic adaptations, such as a diauxic switch with a preference ranking for
different nutrients, re-utilization of waste products after depletion of the
original substrate, and metabolic adaptation to an impending nutrient
depletion. These examples illustrate how dynamic adaptations of enzyme
expression can be predicted solely from an optimization principle.
