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Taylor JA, Rapaport A, Dochain D. Convex Representation of Metabolic Networks with Michaelis-Menten Kinetics. Bull Math Biol 2024; 86:65. [PMID: 38671332 PMCID: PMC11052807 DOI: 10.1007/s11538-024-01293-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 04/08/2024] [Indexed: 04/28/2024]
Abstract
Polyhedral models of metabolic networks are computationally tractable and can predict some cellular functions. A longstanding challenge is incorporating metabolites without losing tractability. In this paper, we do so using a new second-order cone representation of the Michaelis-Menten kinetics. The resulting model consists of linear stoichiometric constraints alongside second-order cone constraints that couple the reaction fluxes to metabolite concentrations. We formulate several new problems around this model: conic flux balance analysis, which augments flux balance analysis with metabolite concentrations; dynamic conic flux balance analysis; and finding minimal cut sets of networks with both reactions and metabolites. Solving these problems yields information about both fluxes and metabolite concentrations. They are second-order cone or mixed-integer second-order cone programs, which, while not as tractable as their linear counterparts, can nonetheless be solved at practical scales using existing software.
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Affiliation(s)
- Josh A Taylor
- Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ, USA.
| | - Alain Rapaport
- MISTEA, Université de Montpellier, INRAE, Institut Agro, Montpellier, France
| | - Denis Dochain
- Université Catholique de Louvain, Louvain-la-Neuve, Belgium
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2
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Klamt S, Mahadevan R, von Kamp A. Speeding up the core algorithm for the dual calculation of minimal cut sets in large metabolic networks. BMC Bioinformatics 2020; 21:510. [PMID: 33167871 PMCID: PMC7654042 DOI: 10.1186/s12859-020-03837-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Accepted: 10/23/2020] [Indexed: 12/16/2022] Open
Abstract
Background The concept of minimal cut sets (MCS) has become an important mathematical framework for analyzing and (re)designing metabolic networks. However, the calculation of MCS in genome-scale metabolic models is a complex computational problem. The development of duality-based algorithms in the last years allowed the enumeration of thousands of MCS in genome-scale networks by solving mixed-integer linear problems (MILP). A recent advancement in this field was the introduction of the MCS2 approach. In contrast to the Farkas-lemma-based dual system used in earlier studies, the MCS2 approach employs a more condensed representation of the dual system based on the nullspace of the stoichiometric matrix, which, due to its reduced dimension, holds promise to further enhance MCS computations. Results In this work, we introduce several new variants and modifications of duality-based MCS algorithms and benchmark their effects on the overall performance. As one major result, we generalize the original MCS2 approach (which was limited to blocking the operation of certain target reactions) to the most general case of MCS computations with arbitrary target and desired regions. Building upon these developments, we introduce a new MILP variant which allows maximal flexibility in the formulation of MCS problems and fully leverages the reduced size of the nullspace-based dual system. With a comprehensive set of benchmarks, we show that the MILP with the nullspace-based dual system outperforms the MILP with the Farkas-lemma-based dual system speeding up MCS computation with an averaged factor of approximately 2.5. We furthermore present several simplifications in the formulation of constraints, mainly related to binary variables, which further enhance the performance of MCS-related MILP. However, the benchmarks also reveal that some highly condensed formulations of constraints, especially on reversible reactions, may lead to worse behavior when compared to variants with a larger number of (more explicit) constraints and involved variables. Conclusions Our results further enhance the algorithmic toolbox for MCS calculations and are of general importance for theoretical developments as well as for practical applications of the MCS framework.
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Affiliation(s)
- Steffen Klamt
- Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, 39106, Magdeburg, Germany.
| | - Radhakrishnan Mahadevan
- Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College Street, Toronto, ON, M5S 3E5, Canada
| | - Axel von Kamp
- Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, 39106, Magdeburg, Germany
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Schneider P, von Kamp A, Klamt S. An extended and generalized framework for the calculation of metabolic intervention strategies based on minimal cut sets. PLoS Comput Biol 2020; 16:e1008110. [PMID: 32716928 PMCID: PMC7410339 DOI: 10.1371/journal.pcbi.1008110] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Revised: 08/06/2020] [Accepted: 06/30/2020] [Indexed: 02/07/2023] Open
Abstract
The concept of minimal cut sets (MCS) provides a flexible framework for analyzing properties of metabolic networks and for computing metabolic intervention strategies. In particular, it has been used to support the targeted design of microbial strains for bio-based production processes. Herein we present a number of major extensions that generalize the existing MCS approach and broaden its scope for applications in metabolic engineering. We first introduce a modified approach to integrate gene-protein-reaction associations (GPR) in the metabolic network structure for the computation of gene-based intervention strategies. In particular, we present a set of novel compression rules for GPR associations, which effectively speedup the computation of gene-based MCS by a factor of up to one order of magnitude. These rules are not specific for MCS and as well applicable to other computational strain design methods. Second, we enhance the MCS framework by allowing the definition of multiple target (undesired) and multiple protected (desired) regions. This enables precise tailoring of the metabolic solution space of the designed strain with unlimited flexibility. Together with further generalizations such as individual cost factors for each intervention, direct combinations of reaction/gene deletions and additions as well as the possibility to search for substrate co-feeding strategies, the scope of the MCS framework could be broadly extended. We demonstrate the applicability and performance benefits of the described developments by computing (gene-based) Escherichia coli strain designs for the bio-based production of 2,3-butanediol, a chemical, that has recently received much attention in the field of metabolic engineering. With our extended framework, we could identify promising strain designs that were formerly unpredictable, including those based on substrate co-feeding.
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Affiliation(s)
- Philipp Schneider
- Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
| | - Axel von Kamp
- Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
| | - Steffen Klamt
- Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
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Röhl A, Riou T, Bockmayr A. Computing irreversible minimal cut sets in genome-scale metabolic networks via flux cone projection. Bioinformatics 2020; 35:2618-2625. [PMID: 30590390 DOI: 10.1093/bioinformatics/bty1027] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2017] [Revised: 12/06/2018] [Accepted: 12/14/2018] [Indexed: 12/19/2022] Open
Abstract
MOTIVATION Minimal cut sets (MCSs) for metabolic networks are sets of reactions which, if they are removed from the network, prevent a target reaction from carrying flux. To compute MCSs different methods exist, which may fail to find sufficiently many MCSs for larger genome-scale networks. RESULTS Here we introduce irreversible minimal cut sets (iMCSs). These are MCSs that consist of irreversible reactions only. The advantage of iMCSs is that they can be computed by projecting the flux cone of the metabolic network on the set of irreversible reactions, which usually leads to a smaller cone. Using oriented matroid theory, we show how the projected cone can be computed efficiently and how this can be applied to find iMCSs even in large genome-scale networks. AVAILABILITY AND IMPLEMENTATION Software is freely available at https://sourceforge.net/projects/irreversibleminimalcutsets/. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Annika Röhl
- Department of Mathematics and Computer Science, FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany
| | - Tanguy Riou
- Department FRANCE, Ecole Centrale de Nantes, Nantes, France
| | - Alexander Bockmayr
- Department of Mathematics and Computer Science, FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany
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Ullah E, Yosafshahi M, Hassoun S. Towards scaling elementary flux mode computation. Brief Bioinform 2019; 21:1875-1885. [PMID: 31745550 DOI: 10.1093/bib/bbz094] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2019] [Revised: 07/04/2019] [Accepted: 07/05/2019] [Indexed: 01/05/2023] Open
Abstract
While elementary flux mode (EFM) analysis is now recognized as a cornerstone computational technique for cellular pathway analysis and engineering, EFM application to genome-scale models remains computationally prohibitive. This article provides a review of aspects of EFM computation that elucidates bottlenecks in scaling EFM computation. First, algorithms for computing EFMs are reviewed. Next, the impact of redundant constraints, sensitivity to constraint ordering and network compression are evaluated. Then, the advantages and limitations of recent parallelization and GPU-based efforts are highlighted. The article then reviews alternative pathway analysis approaches that aim to reduce the EFM solution space. Despite advances in EFM computation, our review concludes that continued scaling of EFM computation is necessary to apply EFM to genome-scale models. Further, our review concludes that pathway analysis methods that target specific pathway properties can provide powerful alternatives to EFM analysis.
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Affiliation(s)
- Ehsan Ullah
- Qatar Computing Research Institute, Hamad Bin Khalifa University, Doha, Qatar
| | - Mona Yosafshahi
- Qatar Computing Research Institute, Hamad Bin Khalifa University, Doha, Qatar
| | - Soha Hassoun
- Department of Computer Science, Tufts University, Medford MA 02155, USA
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Vijayakumar S, Conway M, Lió P, Angione C. Seeing the wood for the trees: a forest of methods for optimization and omic-network integration in metabolic modelling. Brief Bioinform 2019; 19:1218-1235. [PMID: 28575143 DOI: 10.1093/bib/bbx053] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2017] [Indexed: 11/13/2022] Open
Abstract
Metabolic modelling has entered a mature phase with dozens of methods and software implementations available to the practitioner and the theoretician. It is not easy for a modeller to be able to see the wood (or the forest) for the trees. Driven by this analogy, we here present a 'forest' of principal methods used for constraint-based modelling in systems biology. This provides a tree-based view of methods available to prospective modellers, also available in interactive version at http://modellingmetabolism.net, where it will be kept updated with new methods after the publication of the present manuscript. Our updated classification of existing methods and tools highlights the most promising in the different branches, with the aim to develop a vision of how existing methods could hybridize and become more complex. We then provide the first hands-on tutorial for multi-objective optimization of metabolic models in R. We finally discuss the implementation of multi-view machine learning approaches in poly-omic integration. Throughout this work, we demonstrate the optimization of trade-offs between multiple metabolic objectives, with a focus on omic data integration through machine learning. We anticipate that the combination of a survey, a perspective on multi-view machine learning and a step-by-step R tutorial should be of interest for both the beginner and the advanced user.
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Affiliation(s)
| | - Max Conway
- Computer Laboratory, University of Cambridge, UK
| | - Pietro Lió
- Computer Laboratory, University of Cambridge, UK
| | - Claudio Angione
- Department of Computer Science and Information Systems, Teesside University, UK
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Apaolaza I, José-Eneriz ES, Agirre X, Prósper F, Planes FJ. COBRA methods and metabolic drug targets in cancer. Mol Cell Oncol 2017; 5:e1389672. [PMID: 29404389 PMCID: PMC5791858 DOI: 10.1080/23723556.2017.1389672] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2017] [Revised: 10/03/2017] [Accepted: 10/05/2017] [Indexed: 02/09/2023]
Abstract
The identification of therapeutic strategies exploiting the metabolic alterations of malignant cells is a relevant area in cancer research. Here, we discuss a novel computational method, based on the COBRA (COnstraint-Based Reconstruction and Analysis) framework for metabolic networks, to perform this task. Current and future steps are presented.
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Affiliation(s)
- Iñigo Apaolaza
- CEIT and Tecnun, University of Navarra, Manuel de Lardizábal 13, San Sebastián, Spain
| | - Edurne San José-Eneriz
- Area de Hemato-Oncología, IDISNA, Ciberonc, Centro de Investigación Médica Aplicada (CIMA), University of Navarra, Pío XII 55, Pamplona, Spain
| | - Xabier Agirre
- Area de Hemato-Oncología, IDISNA, Ciberonc, Centro de Investigación Médica Aplicada (CIMA), University of Navarra, Pío XII 55, Pamplona, Spain
| | - Felipe Prósper
- Area de Hemato-Oncología, IDISNA, Ciberonc, Centro de Investigación Médica Aplicada (CIMA), University of Navarra, Pío XII 55, Pamplona, Spain
| | - Francisco J Planes
- CEIT and Tecnun, University of Navarra, Manuel de Lardizábal 13, San Sebastián, Spain
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Apaolaza I, San José-Eneriz E, Tobalina L, Miranda E, Garate L, Agirre X, Prósper F, Planes FJ. An in-silico approach to predict and exploit synthetic lethality in cancer metabolism. Nat Commun 2017; 8:459. [PMID: 28878380 PMCID: PMC5587678 DOI: 10.1038/s41467-017-00555-y] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2016] [Accepted: 07/07/2017] [Indexed: 02/02/2023] Open
Abstract
Synthetic lethality is a promising concept in cancer research, potentially opening new possibilities for the development of more effective and selective treatments. Here, we present a computational method to predict and exploit synthetic lethality in cancer metabolism. Our approach relies on the concept of genetic minimal cut sets and gene expression data, demonstrating a superior performance to previous approaches predicting metabolic vulnerabilities in cancer. Our genetic minimal cut set computational framework is applied to evaluate the lethality of ribonucleotide reductase catalytic subunit M1 (RRM1) inhibition in multiple myeloma. We present a computational and experimental study of the effect of RRM1 inhibition in four multiple myeloma cell lines. In addition, using publicly available genome-scale loss-of-function screens, a possible mechanism by which the inhibition of RRM1 is effective in cancer is established. Overall, our approach shows promising results and lays the foundation to build a novel family of algorithms to target metabolism in cancer. Exploiting synthetic lethality is a promising approach for cancer therapy. Here, the authors present an approach to identifying such interactions by finding genetic minimal cut sets (gMCSs) that block cancer proliferation, and apply it to study the lethality of RRM1 inhibition in multiple myeloma.
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Affiliation(s)
- Iñigo Apaolaza
- CEIT and Tecnun, University of Navarra, Manuel de Lardizábal 13, 20018, San Sebastián, Spain
| | - Edurne San José-Eneriz
- Area de Hemato-Oncología, IDISNA, Ciberonc, Centro de Investigación Médica Aplicada (CIMA), University of Navarra, Pío XII 55, 31008, Pamplona, Spain
| | - Luis Tobalina
- CEIT and Tecnun, University of Navarra, Manuel de Lardizábal 13, 20018, San Sebastián, Spain.,Faculty of Medicine, Joint Research Centre for Computational Biomedicine, RWTH Aachen University, MTI2 Wendlingweg 2, D-52074, Aachen, Germany
| | - Estíbaliz Miranda
- Area de Hemato-Oncología, IDISNA, Ciberonc, Centro de Investigación Médica Aplicada (CIMA), University of Navarra, Pío XII 55, 31008, Pamplona, Spain
| | - Leire Garate
- Area de Hemato-Oncología, IDISNA, Ciberonc, Centro de Investigación Médica Aplicada (CIMA), University of Navarra, Pío XII 55, 31008, Pamplona, Spain
| | - Xabier Agirre
- Area de Hemato-Oncología, IDISNA, Ciberonc, Centro de Investigación Médica Aplicada (CIMA), University of Navarra, Pío XII 55, 31008, Pamplona, Spain
| | - Felipe Prósper
- Area de Hemato-Oncología, IDISNA, Ciberonc, Centro de Investigación Médica Aplicada (CIMA), University of Navarra, Pío XII 55, 31008, Pamplona, Spain.
| | - Francisco J Planes
- CEIT and Tecnun, University of Navarra, Manuel de Lardizábal 13, 20018, San Sebastián, Spain.
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von Kamp A, Klamt S. Growth-coupled overproduction is feasible for almost all metabolites in five major production organisms. Nat Commun 2017; 8:15956. [PMID: 28639622 PMCID: PMC5489714 DOI: 10.1038/ncomms15956] [Citation(s) in RCA: 79] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2016] [Accepted: 05/16/2017] [Indexed: 12/13/2022] Open
Abstract
Computational modelling of metabolic networks has become an established procedure in the metabolic engineering of production strains. One key principle that is frequently used to guide the rational design of microbial cell factories is the stoichiometric coupling of growth and product synthesis, which makes production of the desired compound obligatory for growth. Here we show that the coupling of growth and production is feasible under appropriate conditions for almost all metabolites in genome-scale metabolic models of five major production organisms. These organisms comprise eukaryotes and prokaryotes as well as heterotrophic and photoautotrophic organisms, which shows that growth coupling as a strain design principle has a wide applicability. The feasibility of coupling is proven by calculating appropriate reaction knockouts, which enforce the coupling behaviour. The study presented here is the most comprehensive computational investigation of growth-coupled production so far and its results are of fundamental importance for rational metabolic engineering.
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Affiliation(s)
- Axel von Kamp
- ARB Group, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, Magdeburg 39106, Germany
| | - Steffen Klamt
- ARB Group, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, Magdeburg 39106, Germany
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