Adjusting the metabolic URLanization to the environment by tuning enzyme expression levels is crucial for cellular growth , in particular in a changing environment or during metabolic adaptation . Metabolic networks are often studied with optimization methods applied to constraint-based steady state models. But, a corresponding dynamic modeling framework including a tight interplay between metabolic fluxes and gene expression is currently lacking. Due to that, the cost of producing enzymes so far could not be taken into account in dynamic optimization of metabolic fluxes. Here , we present a modeling framework combining the metabolic network and the enzyme production costs. A rigorous mathematical approximation by a timescale separation yields a coupled model of quasi steady state constraints on the metabolic reactions, and differential equations for the substrate concentrations and biomass composition. Based on this model, we propose a dynamic optimization approach to determine reaction fluxes, explicitly taking production costs for enzymes and enzymatic capacity into account . In contrast to the established dynamic flux balance analysis, the proposed approach thereby allows to analyse dynamic changes in both the metabolic fluxes and the detailed biomass composition in situations of metabolic adaptation .
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 .
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Adjusting the metabolic URLanization to the environment
The regulation of metabolic activity
R
for cellular growth , in particular in a changing environment or during metabolic adaptation
to sustain cellular growth in changing environments
R
with optimization methods applied to constraint-based steady state models. But, a corresponding dynamic modeling framework including a tight interplay between metabolic fluxes and gene expression is currently lacking. Due to that, the cost of producing enzymes so far could not be taken into account in dynamic optimization of metabolic fluxes. Here ,
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
R
modeling framework combining
dynamic optimization framework that integrates
R
and the enzyme production costs. A rigorous mathematical approximation by a timescale separation yields a coupled model of quasi steady state constraints on the metabolic reactions, and differential equations for the substrate concentrations and biomass composition. Based on this model, we propose a dynamic optimization approach to determine reaction fluxes, explicitly taking production costs for enzymes
with the dynamics of biomass production and composition, explicitly taking into account enzyme production costs
D
into account
R
the proposed approach thereby allows to analyse
our approach allows predicting
R
detailed biomass composition in situations of metabolic adaptation
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