Regulatory dynamic enzyme-cost flux balance analysis: A unifying framework for constraint-based modeling

Integrated modeling of metabolism and gene regulation continues to be a major challenge in computational biology. While there exist approaches like regulatory flux balance analysis (rFBA), dynamic flux balance analysis (dFBA), resource balance analysis (RBA) or dynamic enzyme-cost flux balance analysis (deFBA) extending classical flux balance analysis (FBA) in various directions, there have been no constraint-based methods so far that allow predicting the dynamics of metabolism taking into account both macromolecule production costs and regulatory events. In this paper, we introduce a new constraint-based modeling framework named regulatory dynamic enzyme-cost flux balance analysis (r-deFBA), which unifies dynamic modeling of metabolism, cellular resource allocation and transcriptional regulation in a hybrid discrete-continuous setting. With r-deFBA, we can predict discrete regulatory states together with the continuous dynamics of reaction fluxes, external substrates, enzymes, and regulatory proteins needed to achieve a cellular objective such as maximizing biomass over a time interval. The dynamic optimization problem underlying r-deFBA can be reformulated as a mixed-integer linear optimization problem, for which there exist efficient solvers.