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. 2018 Sep 20;14(9):e1006412.
doi: 10.1371/journal.pcbi.1006412. eCollection 2018 Sep.

Maintaining Maximal Metabolic Flux by Gene Expression Control

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Free PMC article

Maintaining Maximal Metabolic Flux by Gene Expression Control

Robert Planqué et al. PLoS Comput Biol. .
Free PMC article

Abstract

One of the marvels of biology is the phenotypic plasticity of microorganisms. It allows them to maintain high growth rates across conditions. Studies suggest that cells can express metabolic enzymes at tuned concentrations through adjustment of gene expression. The associated transcription factors are often regulated by intracellular metabolites. Here we study metabolite-mediated regulation of metabolic-gene expression that maximises metabolic fluxes across conditions. We developed an adaptive control theory, qORAC (for 'Specific Flux (q) Optimization by Robust Adaptive Control'), and illustrate it with several examples of metabolic pathways. The key feature of the theory is that it does not require knowledge of the regulatory network, only of the metabolic part. We derive that maximal metabolic flux can be maintained in the face of varying N environmental parameters only if the number of transcription-factor binding metabolites is at least equal to N. The controlling circuits appear to require simple biochemical kinetics. We conclude that microorganisms likely can achieve maximal rates in metabolic pathways, in the face of environmental changes.

Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Experimental evidence indicating that microbes tune their enzyme levels to maximise growth rate.
In each example, the wild type (WT) is shown to express enzyme concentrations at which the growth rate μ is approximately maximal. Axes show enzyme concentrations relative to wild type (WT) levels (abscissa) and growth rates relative to WT. Data adapted from: A, [9]; B, [4, 5, 6], C, [3]; D, [2]. Abbreviations: GAL1, galactokinase; GAL2, Galactose permease; GAL7, Galactose-1-phosphate uridyl transferase; LDH, lactate dehydrogenase; PFK, phosphofructokinase; LAS, las operon; GAPDH, glyceraldehyde 3-phosphate dehydrogenase; Glc, glucose; Succ, succinate. In [9] there are many other examples, including several proteins that do not show levels at which growth rate is optimised.
Fig 2
Fig 2. Biological examples of qORAC.
Four well-characterised metabolic pathways in which a metabolite binds to a transcription factor (TF) to influence gene expression. The qORAC framework applies to each of them: in each case, the qORAC formalism gives rise to the enzyme synthesis rates that steer the metabolic pathway to maximal metabolic rates that are robust to changes in the external concentration (external with respect to the pathway). (A) The lac operon in E. coli, with sensor Allolactose binding to LacI; (B) The galactose uptake system in yeast, with sensor internal galactose binding to gal3p; (C) The control of glycolytic enzymes via sensors FBP (binding to Cra), and cAMP (binding to Crp); (D) The control of the L-Tryptophan biosynthesis pathway by the amino acid binding to TrpR; (E) The general scheme of a qORAC-steered pathway. Abbreviations:Lacout, external lactose; Allolac, allolactose; αKG, α-ketoglutarate;Galout, external galactose; Galin, internal galactose; Gal-1P, galactose-1-phosphate; Glc-1P, glucose-1-phosphate; UDP-Glc, uridine-diphosphate-glucose; UDP-Gal, uridine-diphosphate-galactose; Glu, glucose; FBP, fructose-1,6-biphosphate; PEP, phosphoenolpyruvate; PYR, pyruvate; cAMP, cyclic AMP; ATP, adenosine-triphosphate; Cho, chorismate; Ant, Anthranilate; NAnt, N-(5’-phosphoribosyl)-anthranilate; ECP1P, Enol-1-0-carboxy-phenylamino-1-deoxyribulose phosphate; Ind, Indole-3-glycerol-P; L-Tryp, L-tryptophan.
Fig 3
Fig 3. Integrating qORAC with experimental evidence.
Top, left: We consider a cell which takes up glucose (Glu) and converts it into biomass using a metabolic pathway. A sensor metabolite (S) influences gene expression and hence enzyme levels. Let E be one such enzyme in the active pathway. Top, right: The concentration of E is titrated experimentally under different glucose conditions, Low, Mid and High. In each condition, the maximal growth rate is measured, at different levels of titrated enzyme levels. In the same experiment, the sensor concentration is monitored. Bottom, right: Plotting the optimal enzyme levels at different conditions together with the measured sensor concentrations indicates the input-output relation of the gene network necessary to achieve maximal growth rates. Any gene network that implements such an input-output relation automatically expresses optimal enzyme levels in each condition. Bottom, left: To ensure that the steady state of the combined metabolic-gene system is always optimal, the gene network must presume optimality of the sensor at each time point. If the sensor is not optimal, it will change (and so will the enzyme levels); if it is optimal and stationary, the whole pathway will achieve maximal rates. qORAC also decribes the input-output relation in other conditions than the cell may have experienced (dotted lines in graph bottom right).
Fig 4
Fig 4. Example qORAC dynamics.
The dynamics are illustrated for the network shown in A. The green box depicts a varying external concentration, the blue box denotes the sensor concentration. B: the optimal input-output relations, showing enzyme synthesis rates as a function of changing sensor concentration C′. In plots C1 to C4, the external C concentration is changed after 50 time units, and again after 100 time units. C1: The optimal C concentration predicted by the sensor (red line) converges to the real external C concentration (blue), even when the external concentration changes at t = 50 and t = 100. C2: enzyme dynamics equilibrate after each change in external conditions, and reach their optimal levels. C3: the steered metabolic pathway reaches the optimum after each external change, as the distance to the (periodically changing) optimum reaches zero after some time. C4: flux dynamics equilibrate, showing that the pathway has reached steady state each time the external conditions change. Full equations are given in Box 2, code is given in the SI.
Fig 5
Fig 5. Example dynamics for a more complicated pathway.
A: metabolic network with two inputs and two outputs, and with allosteric cross-inhibition. This pathway is robust to changes in both input and output concentration (in green), which requires four sensors (in blue). B: Each of the external concentrations is changed once, and the system adapts accordingly. C: the metabolite concentrations converge to the (periodically changing) predicted optimum over time. D: enzyme concentration dynamics. See SI text for details of the pathway, and the matlab file daes_double_branched.m for the code.
Fig 6
Fig 6. qORAC for an internal parameter.
In this example qORAC is illustrated for a Km parameter in the third reaction, K3. In A the same pathway is drawn, with sensors in blue. B: metabolite dynamics in which first external concentrations are varied (green) and at the end also K3 is varied. C: K3 (in green) is varied at time t = 2500, and the predicted optimal value (in orange) subsequently converges, illustrating robust adaptive control. An example in which the same pathway is controlled using a different set of sensors, resulting in lack of convergence to the optimum, is found in the SI, S4 Fig.

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Grant support

FJB acknowledges funding of Nederlandse Organisatie NWO-VIDI project No. 864-11-011; BT acknowledges funding of Nederlandse Organisatie NWO-VICI project 865.14.005. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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