Unifying metabolic networks, regulatory constraints, and resource allocation
Metabolic and gene regulatory networks are two classic models of systems biology. Biologically, gene regulatory networks are the control system of protein expression while metabolic networks, especially the genome-scale reconstructions consist of thousands of enzymatic reactions breaking down nutrients into precursors and energy to support the cellular survival. Metabolic-genetic networks, in addition, include the translational processes as an integrated model of classical metabolic networks and the gene expression machinery. Conversely, genetic regulation is also affected by the metabolic activities that provide feedbacks and precursors to the regulatory system. Thus, the two systems are highly interactive and depend on each other. Up to now, various efforts have been made to bridge the two network types. Yet, the dynamic integration of metabolic networks and genetic regulation remains a major challenge in computational systems biology. This PhD thesis is a contribution to mathematical modeling approaches for studying metabolic-regulatory systems. Inspired by regulatory flux balance analysis (rFBA), we first propose an analytic pipeline to explore the optimal solution space in rFBA. Then, our efforts focus on the dynamic combination of metabolic networks together with enzyme production costs and genetic regulation. For this purpose, we first explore the intuitive idea that incorporates Boolean regulatory rules while iterating resource balance analysis. However, with the iterative strategy, the gene expression states are only updated in discrete time steps. Furthermore, formalizing the metabolic-regulatory networks (MRNs) by hybrid automata provides a new mathematical framework that allows the quantitative integration of the metabolic-genetic network with the genetic regulation in a hybrid discrete-continuous system. For the application of this theoretical formalization, we develop a constraint-based approach regulatory dynamic enzyme-cost flux balance analysis (r-deFBA) as an optimal control strategy for the hybrid automata representing MRNs. This allows the prediction of optimal regulatory state transitions, dynamics of metabolism, and resource allocation capable of achieving a maximal biomass production over a time interval. Finally, this PhD project ends with a chapter on perspectives; we apply the theory of product automata to model the dynamics at population-level, integrating continuous metabolism and discrete regulatory states.