The steady-state metabolism of microorganisms has evolved to optimize growth under ambient conditions
]. However, under suboptimal conditions or upon perturbation, organisms must maintain homeostasis and adapt their modes of operation to ensure viability
]. Maintenance of homeostasis has already been addressed in the context of studying system’s robustness
]. The underlying mechanisms stabilize a cellular function under changing conditions and often involve feedback control
]. In turn, adaptability refers to adjustment in systemic properties (e.g.
, utilization of available nutrients) in order to facilitate the transition between conditions. The two properties—robustness and adaptability—do not exclude each other since both arise from the necessity of an organism to cope with its environment.
While robustness has been widely studied
], (metabolic) adaptability has not been systematically investigated, largely due to the lack of a precise formulation and its global effects on the organism. Therefore, any approach to capture and analyze adaptation-related processes requires the consideration of a comprehensive network of metabolic pathways in order to capture the complex interplay of network constituents.
Several approaches that integrate data with graph-theoretic methods have been applied to obtain subnetworks engaged under different conditions. For instance,
] uses transcriptomics data in combination with protein-protein interaction networks to identify active subnetworks that show levels in differential expression for particular subsets of conditions. However, graph-theoretic approaches neglect the stoichiometry of the considered biochemical reactions. Thus, it is difficult to relate the findings from these approaches to network functionality and growth.
With the increasing availability and quality of genome-scale metabolic models and high-throughput data, constraint-based methods that integrate these data have found broad applications. For instance, a genome-scale metabolic model has been coupled with transcriptomics data, based on Boolean logic, to improve flux predictions
]. Thereby, a flux is constrained to zero, if the respective transcript has not been observed. Another attempt employs transcriptomics and proteomics data to derive tissue-specific metabolic activity
] and is based on a trivalued logic to maximize the number of reactions in the network that are consistent with the expression data. To overcome the issue of selecting an arbitrary threshold value in considering a gene “on” or “off”, a method, referred to as MADE, was proposed. It employs the statistical significance of changes in gene or protein expression data between two cellular states to extract metabolic models (subnetworks) that reflect the expression dynamics
While constraint-based methods usually provide solutions that optimize a certain objective, elementary flux modes (EFMs) capture the whole spectrum of metabolic steady states of a given network. An EFM is defined as a minimal set of reactions that can operate at steady state
]. EFM-based analysis have been applied to study robustness
] and explore structural properties of new pathways
]. Although promising attempts for enumerating subsets of EFMs, identifying pathways in genome-scale metabolic networks
], as well as for sampling a given number of EFMs
] have been proposed, the problem of combinatorial explosion restrains the computation of EFMs to networks of moderate size
Flux-based, i.e., constraint- and EFM-based, approaches have proven useful in characterizing stationary metabolic states of an organism. However, the adaptation of metabolism to changing conditions is a temporal process, and the state of the organism strongly depends on the time scale after the perturbation. Therefore, in order to capture adaptation-related processes, it is necessary to develop and apply a computational method which allows the integration of time-series data, uses the advantages of flux-based methods, and overcomes some of the shortcomings of the briefly reviewed approaches.
Here we present a novel method, which we term Adaptation of Metabolism (AdaM), to identify reactions and pathways that enable system adaptation upon external perturbation. AdaM integrates time-series transcriptomics data with flux-based bilevel optimization to extract minimal operating networks from a given large-scale metabolic model. The minimality of the extracted networks enables the computation of EFMs for each time point. These sets of EFMs are in turn used to characterize the transitional behavior of the network as well as of individual reactions (see Figure
). The theoretical framework is applied to recently obtained transcriptomics data for cold and heat stress from E. coli
] and is compared to MADE. Our findings reveal differences in response patterns for the two investigated conditions and characterize (de)activation patterns associated to temperature stress. The model-based and data-driven predictions are verified with respect to results from the existing experimental studies. Finally, our results are used to posit novel hypotheses related to temperature-associated metabolic adaptation processes.
Figure 1 Schematic depiction of the computational approach. A genome-scale network and time-series transcriptomics data are used to extract time- and condition-specific minimal networks. Data for different environmental conditions are analyzed to weight genes (more ...)