Dynamic optimization of metabolic networks coupled with gene expression

Abstract

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. An approximation by a timescale separation leads to a coupled model of quasi steady state constraints on the metabolic reactions, and differential equations for the substrate concentrations and biomass composition. We propose a dynamic optimization approach to determine reaction fluxes for this model, 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. Discretization of the optimization problems leads to a linear program that can be efficiently solved.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.

Cellular trade-offs and optimal resource allocation during cyanobacterial diurnal growth

“…Building upon previous works (1,6,15,18,23,25,26), our approach is based on the fact that growth is inherently autocatalytic: The cellular machinery to sustain metabolism is itself a product of metabolism. Our foci have therefore been the net stoichiometric and energetic implications of diurnal growth on the de novo synthesis of proteins and other cellular macromolecules.…”

“…1. In contrast to conventional FBA, and following recent developments in constraint-based analysis (18,(23)(24)(25)(26), the capacity constraints of individual reactions are explicitly part of the model.…”

“…Our model significantly improves upon previous computational analyses of diurnal phototrophic growth (14,(16)(17)(18) and takes recent developments in constraintbased analysis into account (19)(20)(21)(22). Our approach is closely related to resource balance analysis (23,24) and dynamic enzymecost flux balance analysis (25), as well as integrated metabolism and gene expression (ME) models (21,26), but explicitly accounts for the properties of diurnal phototrophic growth.…”

Synthetic biology and regulatory networks: where metabolic systems biology meets control engineering

“…DFBA also provides a suitable framework for multi-scale metabolic modelling, where the interplay of different cell types and tissues is taken into account [69]. More recently, DFBA has been extended to metabolic networks coupled with gene expression of the corresponding enzymes, where it incorporated constraints on resource allocation [70,71]. -FBA and nonlinearity.…”

Network Analysis and Modeling in Systems Biology

“…Second, the FBG can be readily used to quantify metabolic robustness via graph statistics upon node (e.g., reaction) removal (Smart, Amaral, and Ottino 2008). Third, the proposed approach can be extended to include dynamic adaptations of metabolic activity, for example, by using dynamic extensions of FBA (Mahadevan, Edwards, and Doyle 2002;Rügen, Bockmayr, and Steuer 2015;Waldherr, Oyarzún, and Bockmayr 2015), or by incorporating static (Colijn et al 2009) and time-varying (Oyarzún 2011) enzyme concentrations. Fourth, the FBG could provide a novel route for robustness analysis of FBA solutions (Gudmundsson and Thiele 2010).…”