Millard, Smallbone and Mendes (2017) built a detailed kinetic model of Escherichia coli central carbon and energy metabolism and showed, by randomly varying enzyme levels over orders of magnitude, that metabolite-level (metabolic) regulation alone — enzyme saturation and allosteric modulation by small molecules — can reproduce the robust coordination of glucose uptake, catabolism, energy production and growth seen across hundreds of experiments, without invoking regulation of gene expression. The authors themselves delimited the claim: it holds only for moderate changes of enzyme levels, with the flux through the tricarboxylic acid (TCA) cycle as a notable exception, and they stated that expanding the kinetic model to incorporate gene-expression regulation will ultimately be needed to understand the interplay between the two regulatory levels. The open problem is therefore to determine quantitatively how metabolic and hierarchical (transcriptional, translational, post-translational) regulation jointly implement the observed global coordination, and to identify the perturbation magnitudes, timescales, and subsystems — such as the TCA-cycle flux partition, which the authors flag as a notable exception where enzymes exert higher control — in which metabolic regulation alone is insufficient.

Background

Escherichia coli takes up glucose mainly through the phosphotransferase system (PTS), a transport chain in which glucose import is coupled to its phosphorylation, and routes the carbon through glycolysis, the pentose phosphate pathway, and the tricarboxylic acid (TCA) cycle, which oxidizes acetyl-CoA and generates the NADH that fuels respiration; the resulting ATP, redox power, and precursors support growth. Fluxes through these pathways are controlled at two distinct layers. Metabolic regulation (also called metabolite-level regulation) acts directly on enzyme activity: substrate and product concentrations set the degree of enzyme saturation, and metabolites act as allosteric activators or inhibitors (allosteric regulation means binding of a small molecule at a site other than the active site, changing enzyme activity). This layer acts within seconds and without any change in enzyme amounts. Hierarchical regulation acts on enzyme capacity: transcription factors, translational control, and post-translational modification change enzyme concentration or activity state, typically on slower, minutes-to-hours timescales. Two modeling traditions describe the network. Constraint-based (stoichiometric) models such as those used in flux balance analysis impose only mass balance at steady state, defining a space of feasible flux distributions without kinetics. Kinetic models instead write explicit rate laws with kinetic parameters for each reaction, so they can represent metabolite-level regulation and transient dynamics. Millard, Smallbone and Mendes (2017) constructed a kinetic model of E. coli central carbon and energy metabolism (available in the standard SBML model-exchange format, runnable in the COPASI biochemical simulator, as BioModels entry MODEL1505110000, calibrated to glucose-limited chemostat culture, i.e., continuous culture at a fixed dilution rate) and showed that it reproduces data from hundreds of experiments. Strikingly, when enzyme levels were randomized over orders of magnitude, the model retained the experimentally observed functional couplings — between ATP and NADH production, between flux sums and ATP yield, and between growth rate and glucose uptake — and kept intracellular metabolite pools within a few-fold of the calibrated state, while individual reaction fluxes remained flexible. The authors concluded that metabolic regulation is sufficient for the global and robust coordination of catabolism, energy production and growth, and that it does not significantly shrink the stoichiometric solution space for the variables examined, so evolution must have discovered the advantageous kinetic-parameter region rather than being forced into it by kinetic constraints. This conclusion has precedent and context: the flux partition between respiratory and fermentative routes is robust even to deletion of global transcriptional regulators, which was previously interpreted as weak hierarchical control (Haverkorn van Rijsewijk et al. 2011); E. coli metabolism operates close to a multi-dimensional optimum of competing objectives (Schuetz et al. 2012); and metabolites themselves feed back onto gene expression through flux-sensing mechanisms (Kotte et al. 2010; Kochanowski et al. 2013, 2017), while small-scale quantitative models combining carbon catabolite repression with metabolism had long existed for specific subsystems (Kremling et al. 2015). The sufficiency claim is, however, explicitly bounded by its own authors: it was established only for moderate changes of enzyme levels, with the flux through the TCA cycle as a notable exception where enzymes exert higher control, and the paper states that expanding the kinetic model to incorporate regulation of gene expression will be needed ultimately to understand the interplay between metabolic and hierarchical regulation. To date no validated integrated kinetic model of E. coli central metabolism that dissects the division of labor between the two regulatory layers has been built.

Problem Statement

Determine how metabolite-level (metabolic) regulation and hierarchical (gene-expression) regulation combine to produce the global, robust coordination of glucose uptake, catabolism, energy production and growth in Escherichia coli. Concretely: construct and validate an integrated quantitative account of metabolic and hierarchical (gene-expression) regulation that (i) still reproduces the experimental behaviors that the metabolic-regulation-only model reproduces, (ii) quantifies the contribution of each regulatory layer to each coordinated property (functional couplings, metabolite homeostasis, growth coordination) across perturbation magnitudes and timescales, and (iii) identifies the regimes in which metabolic regulation alone is insufficient and hierarchical regulation is required — including large, non-moderate enzyme-level changes such as massive overexpression or deletion of global regulators, and the robustness of the TCA-cycle flux partition. The sufficiency result of the source paper is the baseline to be delimited, not the target to be re-proven.

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