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Ebenhöh O, Ebeling J, Meyer R, Pohlkotte F, Nies T. Microbial Pathway Thermodynamics: Stoichiometric Models Unveil Anabolic and Catabolic Processes. Life (Basel) 2024; 14:247. [PMID: 38398756 PMCID: PMC10890395 DOI: 10.3390/life14020247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2023] [Revised: 01/29/2024] [Accepted: 02/05/2024] [Indexed: 02/25/2024] Open
Abstract
The biotechnological exploitation of microorganisms enables the use of metabolism for the production of economically valuable substances, such as drugs or food. It is, thus, unsurprising that the investigation of microbial metabolism and its regulation has been an active research field for many decades. As a result, several theories and techniques were developed that allow for the prediction of metabolic fluxes and yields as biotechnologically relevant output parameters. One important approach is to derive macrochemical equations that describe the overall metabolic conversion of an organism and basically treat microbial metabolism as a black box. The opposite approach is to include all known metabolic reactions of an organism to assemble a genome-scale metabolic model. Interestingly, both approaches are rather successful at characterizing and predicting the expected product yield. Over the years, macrochemical equations especially have been extensively characterized in terms of their thermodynamic properties. However, a common challenge when characterizing microbial metabolism by a single equation is to split this equation into two, describing the two modes of metabolism, anabolism and catabolism. Here, we present strategies to systematically identify separate equations for anabolism and catabolism. Based on metabolic models, we systematically identify all theoretically possible catabolic routes and determine their thermodynamic efficiency. We then show how anabolic routes can be derived, and we use these to approximate biomass yield. Finally, we challenge the view of metabolism as a linear energy converter, in which the free energy gradient of catabolism drives the anabolic reactions.
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Affiliation(s)
- Oliver Ebenhöh
- Institute of Quantitative and Theoretical Biology, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
- Cluster of Excellence on Plant Sciences, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
| | - Josha Ebeling
- Institute of Quantitative and Theoretical Biology, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
| | - Ronja Meyer
- Institute of Quantitative and Theoretical Biology, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
| | - Fabian Pohlkotte
- Institute of Quantitative and Theoretical Biology, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
| | - Tim Nies
- Institute of Quantitative and Theoretical Biology, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
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Wilken SE, Besançon M, Kratochvíl M, Foko Kuate CA, Trefois C, Gu W, Ebenhöh O. Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models. Metab Eng 2022; 74:72-82. [PMID: 36152931 DOI: 10.1016/j.ymben.2022.09.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2022] [Revised: 09/08/2022] [Accepted: 09/10/2022] [Indexed: 10/31/2022]
Abstract
Metabolic models are typically characterized by a large number of parameters. Traditionally, metabolic control analysis is applied to differential equation-based models to investigate the sensitivity of predictions to parameters. A corresponding theory for constraint-based models is lacking, due to their formulation as optimization problems. Here, we show that optimal solutions of optimization problems can be efficiently differentiated using constrained optimization duality and implicit differentiation. We use this to calculate the sensitivities of predicted reaction fluxes and enzyme concentrations to turnover numbers in an enzyme-constrained metabolic model of Escherichia coli. The sensitivities quantitatively identify rate limiting enzymes and are mathematically precise, unlike current finite difference based approaches used for sensitivity analysis. Further, efficient differentiation of constraint-based models unlocks the ability to use gradient information for parameter estimation. We demonstrate this by improving, genome-wide, the state-of-the-art turnover number estimates for E. coli. Finally, we show that this technique can be generalized to arbitrarily complex models. By differentiating the optimal solution of a model incorporating both thermodynamic and kinetic rate equations, the effect of metabolite concentrations on biomass growth can be elucidated. We benchmark these metabolite sensitivities against a large experimental gene knockdown study, and find good alignment between the predicted sensitivities and in vivo metabolome changes. In sum, we demonstrate several applications of differentiating optimal solutions of constraint-based metabolic models, and show how it connects to classic metabolic control analysis.
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Affiliation(s)
- St Elmo Wilken
- Institute of Quantitative and Theoretical Biology, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany; Cluster of Excellence on Plant Sciences, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany.
| | - Mathieu Besançon
- Department for AI in Society, Science, and Technology, Zuse Institute Berlin, Takustraße 7, 14195, Berlin, Germany
| | - Miroslav Kratochvíl
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Campus Belval, L-4367, Belvaux, Luxembourg
| | - Chilperic Armel Foko Kuate
- Institute of Quantitative and Theoretical Biology, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
| | - Christophe Trefois
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Campus Belval, L-4367, Belvaux, Luxembourg
| | - Wei Gu
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Campus Belval, L-4367, Belvaux, Luxembourg
| | - Oliver Ebenhöh
- Institute of Quantitative and Theoretical Biology, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany; Cluster of Excellence on Plant Sciences, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
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