Analysis of the stoichiometric structure of metabolic networks provides insights into the relationships between structure, function, and regulation of metabolic systems. Based on knowledge of only reaction stoichiometry, certain aspects of network functionality and robustness can be predicted. Current theories focus on breaking a metabolic network down into non-decomposable pathways able to operate in steady state. The physics underlying these theories is based on mass balance and the laws of thermodynamics. However, due to the inherent nonlinearity of the thermodynamic constraints on metabolic fluxes, computational analysis of large-scale biochemical systems can be expensive. In this study, it is shown how the feasible reaction directions may be determined by either computing the allowable ranges under the mass-balance and thermodynamic constraints or by analyzing the stoichiometric structure of the network. The computed reaction directions translate into a set of linear constraints necessary for thermodynamic feasibility. This set of necessary linear constraints is shown to be sufficient to guarantee feasibility in certain cases, thus translating the nonlinear thermodynamic constraints to linear. We show that for a reaction network of 44 internal reactions representing energy metabolism, the computed linear inequality constraints represent necessary and sufficient conditions for thermodynamic feasibility.
"A known flux mode – i.e., active reactions and flux directions – can help restrict the possible flux distributions. Flux directions can either be constrained ad hoc or based on general principles: thermodynamic laws, for instance, restrict fluxes to run from higher to lower chemical potentials       , which make certain cycle fluxes impossible. Within these physical limits, various flux distributions remain possible and cells can choose between them, at least partially, by their enzyme abundances. "
[Show abstract][Hide abstract] ABSTRACT: Metabolic fluxes are governed by physical and economic principles.
Stationarity constrains them to a subspace in flux space and thermodynamics
makes them lead from higher to lower chemical potentials. At the same time,
fluxes in cells represent a compromise between metabolic performance and enzyme
cost. To capture this, some flux prediction methods penalise larger fluxes by
heuristic cost terms. Economic flux analysis, in contrast, postulates a balance
between enzyme costs and metabolic benefits as a necessary condition for fluxes
to be realised by kinetic models with optimal enzyme levels. The constraints
are formulated using economic potentials, state variables that capture the
enzyme labour embodied in metabolites. Generally, fluxes must lead from lower
to higher economic potentials. This principle, which resembles thermodynamic
constraints, can complement stationarity and thermodynamic constraints in flux
analysis. Futile modes, which would be incompatible with economic potentials,
are defined algebraically and can be systematically removed from flux
distributions. Enzymes that participate in potential futile modes are likely
targets of regulation. Economic flux analysis can predict high-yield and
low-yield strategies, and captures preemptive expression, multi-objective
optimisation, and flux distributions across several cells living in symbiosis.
Inspired by labour value theories in economics, it justifies and extends the
principle of minimal fluxes and provides an intuitive framework to model the
complex interplay of fluxes, metabolic control, and enzyme costs in cells.
"A → B → C → A) in their GEMs, sets of reactions for which the overall thermodynamic driving force is zero, and through which no net flux can occur (steps 51–58 in the reconstruction guidelines). Unfortunately, while there have been a number of studies on SBCs (Beard et al., 2002; 2004; Qian et al., 2003; Yang et al., 2005; Schellenberger et al., 2011b), no universal approach has yet been developed to identify and eliminate them. As techniques for handling SBCs are developed, these could be incorporated into the reconstruction and simulation platforms. "
[Show abstract][Hide abstract] ABSTRACT: Systems-level analyses of microbial metabolism are facilitated by genome-scale reconstructions of microbial biochemical networks. A reconstruction provides a structured representation of the biochemical transformations occurring within an organism, as well as the genes necessary to carry out these transformations, as determined by the annotated genome sequence and experimental data. Network reconstructions also serve as platforms for constraint-based computational techniques which facilitate biological studies in a variety of applications, including evaluation of network properties, metabolic engineering, and drug discovery. Bottom-up metabolic network reconstructions have been developed for dozens of organisms, but until recently the pace of reconstruction has failed to keep up with advances in genome sequencing. To address this problem, a number of software platforms have been developed to automate parts of the reconstruction process, thereby alleviating much of the manual effort previously required. Here, we review four such platforms in the context of established guidelines for network reconstruction. While many steps of the reconstruction process have been successfully automated, some manual evaluation of the results is still required to ensure a high-quality reconstruction. Widespread adoption of these platforms by the scientific community is underway and will be further enabled by exchangeable formats across platforms.
"Computationally, a number of different approaches have been developed for GSMs to increase the predictive capabilities or elucidate alternative pathway usage. These approaches have included the incorporation of regulatory mechanisms   , the inclusion of thermodynamic parameters  , proton and redox balancing , elucidation of alternate optimal solutions , and the alpha-spectrum . These approaches all contribute to increasing the accuracy and usability of GSMs. "
[Show abstract][Hide abstract] ABSTRACT: Constraint-based genome-scale metabolic models are becoming an established tool for using genomic and biochemical information to predict cellular phenotypes. While these models provide quantitative predictions for individual reactions and are readily scalable for any biological system, they have inherent limitations. Using current methods, it is difficult to computationally elucidate a specific network state that directly depicts an in vivo state, especially in the instances where the organism might be functionally in a suboptimal state. In this study, we generated RNA sequencing data to characterize the transcriptional state of the cellulolytic anaerobe, Clostridium thermocellum, and algorithmically integrated these data with a genome-scale metabolic model. The phenotypes of each calculated metabolic flux state were compared to 13 experimentally determined physiological parameters to identify the flux mapping that best matched the in vitro growth of C. thermocellum. By this approach we found predicted fluxes for 88 reactions to be changed between the best solely computational prediction (flux balance analysis) and the best experimentally derived prediction. The alteration of these 88 reaction fluxes led to a detailed network-wide flux mapping that was able to capture the suboptimal cellular state of C. thermocellum.
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