Document Open Access Logo

Mixed-Integer Optimization for Loopless Flux Distributions in Metabolic Networks

Authors Hannah Troppens , Mathieu Besançon , St. Elmo Wilken , Sebastian Pokutta

PDF

File

Thumbnail PDF
PDF
LIPIcs.SEA.2025.26.pdf
  • Filesize: 1.45 MB
  • 18 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Mathematical optimization
  • Applied computing → Operations research
  • Applied computing → Biological networks
Keywords
  • Systems biology
  • mixed-integer optimization
  • disjunctive optimization
  • flux balance analysis

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Constraint-based metabolic models can be used to investigate the intracellular physiology of microorganisms. These models couple genes to reactions, and typically seek to predict metabolite fluxes that optimize some biologically important metric. Classical techniques, like Flux Balance Analysis (FBA), formulate the metabolism of a microbe as an optimization problem where growth rate is maximized. While FBA has found widespread use, it often leads to thermodynamically infeasible solutions that contain internal cycles (loops). To address this shortcoming, Loopless-Flux Balance Analysis (ll-FBA) seeks to predict flux distributions that do not contain these loops. ll-FBA is a disjunctive program, usually reformulated as a mixed-integer program, and is challenging to solve for biological models that often contain thousands of reactions and metabolites. In this paper, we compare various reformulations of ll-FBA and different solution approaches. 
Overall, the combinatorial Benders' decomposition is the most promising of the tested approaches with which we could solve most instances. However, the model size and numerical instability pose a challenge to the combinatorial Benders' method.

Cite As Get BibTex

Hannah Troppens, Mathieu Besançon, St. Elmo Wilken, and Sebastian Pokutta. Mixed-Integer Optimization for Loopless Flux Distributions in Metabolic Networks. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SEA.2025.26

Author Details

Hannah Troppens
  • Zuse Institute Berlin, Germany
Mathieu Besançon
  • Université Grenoble Alpes, Inria, LIG, CNRS, France
St. Elmo Wilken
  • Institute of Quantitative and Theoretical Biology, Heinrich Heine University Düsseldorf, Germany
Sebastian Pokutta
  • Zuse Institute Berlin, Germany
  • Technische Universität Berlin, Germany

Funding

  • Besançon, Mathieu: This research benefited from the support of the FMJH Program PGMO.
  • Wilken, St. Elmo: This research benefited from the support of the FMJH Program PGMO.
  • Pokutta, Sebastian: Research reported in this paper was partially supported through the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund numbers 05M14ZAM,05M20ZBM) and the Deutsche Forschungsgemeinschaft (DFG) through the DFG Cluster of Excellence MATH+.

Supplementary Materials

References

  1. Egon Balas. Disjunctive programming. In P.L. Hammer, E.L. Johnson, and B.H. Korte, editors, Discrete Optimization II, volume 5 of Annals of Discrete Mathematics, pages 3-51. Elsevier, 1979. URL: https://doi.org/10.1016/S0167-5060(08)70342-X.
  2. Daniel A. Beard, Eric Babson, Edward Curtis, and Hong Qian. Thermodynamic constraints for biochemical networks. Journal of Theoretical Biology, 228(3):327-333, 2004. URL: https://doi.org/10.1016/j.jtbi.2004.01.008.
  3. Ksenia Bestuzheva, Mathieu Besançon, Wei-Kun Chen, Antonia Chmiela, Tim Donkiewicz, Jasper van Doornmalen, Leon Eifler, Oliver Gaul, Gerald Gamrath, Ambros Gleixner, Leona Gottwald, Christoph Graczyk, Katrin Halbig, Alexander Hoen, Christopher Hojny, Rolf van der Hulst, Thorsten Koch, Marco Lübbecke, Stephen J. Maher, Frederic Matter, Erik Mühmer, Benjamin Müller, Marc E. Pfetsch, Daniel Rehfeldt, Steffan Schlein, Franziska Schlösser, Felipe Serrano, Yuji Shinano, Boro Sofranac, Mark Turner, Stefan Vigerske, Fabian Wegscheider, Philipp Wellner, Dieter Weninger, and Jakob Witzig. Enabling Research through the SCIP Optimization Suite 8.0. ACM Trans. Math. Softw., 49(2), 2023. URL: https://doi.org/10.1145/3585516.
  4. Suresh Bolusani, Mathieu Besançon, Ksenia Bestuzheva, Antonia Chmiela, João Dionísio, Tim Donkiewicz, Jasper van Doornmalen, Leon Eifler, Mohammed Ghannam, Ambros Gleixner, et al. The SCIP Optimization Suite 9.0, 2024. URL: https://arxiv.org/abs/2402.17702.
  5. Gianni Codato and Matteo Fischetti. Combinatorial Benders' Cuts for Mixed-Integer Linear Programming. Operations Research, 54(4):756-766, 2006. Publisher: INFORMS. URL: https://doi.org/10.1287/opre.1060.0286.
  6. Abdelmoneim Amer Desouki, Florian Jarre, Gabriel Gelius-Dietrich, and Martin J. Lercher. CycleFreeFlux: Efficient Removal of Thermodynamically Infeasible Loops from Flux Distributions. Bioinformatics, 31(13):2159-2165, 2015. URL: https://doi.org/10.1093/bioinformatics/btv096.
  7. Christopher S. Henry, Linda J. Broadbelt, and Vassily Hatzimanikatis. Thermodynamics-Based Metabolic Flux Analysis. Biophysical Journal, 92(5):1792-1805, 2007. URL: https://doi.org/10.1529/biophysj.106.093138.
  8. Q. Huangfu and J. A. J. Hall. Parallelizing the dual revised simplex method. Mathematical Programming Computation, 10(2):119-142, 2018. URL: https://doi.org/10.1007/s12532-017-0130-5.
  9. Zachary A. King, Justin Lu, Andreas Dräger, Philip Miller, Stephen Federowicz, Joshua A. Lerman, Ali Ebrahim, Bernhard O. Palsson, and Nathan E. Lewis. BiGG Models: A platform for integrating, standardizing and sharing genome-scale models. Nucleic Acids Research, 44(D1):D515-D522, October 2015. URL: https://doi.org/10.1093/nar/gkv1049.
  10. Miroslav Kratochvíl, Laurent Heirendt, St Elmo Wilken, Taneli Pusa, Sylvain Arreckx, Alberto Noronha, Marvin van Aalst, Venkata P Satagopam, Oliver Ebenhöh, Reinhard Schneider, Christophe Trefois, and Wei Gu. COBREXA.jl: constraint-based reconstruction and exascale analysis. Bioinformatics, 38(4):1171-1172, 2021. URL: https://doi.org/10.1093/bioinformatics/btab782.
  11. Benoît Legat, Oscar Dowson, Joaquim Dias Garcia, and Miles Lubin. MathOptInterface: a data structure for mathematical optimization problems. INFORMS Journal on Computing, 34(2):672-689, 2021. URL: https://doi.org/10.1287/ijoc.2021.1067.
  12. Nathan E. Lewis, Kim K. Hixson, Tom M. Conrad, Joshua A. Lerman, Pep Charusanti, Ashoka D. Polpitiya, Joshua N. Adkins, Gunnar Schramm, Samuel O. Purvine, Daniel Lopez-Ferrer, Karl K. Weitz, Roland Eils, Rainer König, Richard D. Smith, and Bernhard Ø. Palsson. Omic Data from Evolved E. coli Are Consistent with Computed Optimal Growth from Genome-Scale Models. Molecular Systems Biology, 6(1):390, 2010. URL: https://doi.org/10.1038/msb.2010.47.
  13. Hongzhong Lu, Feiran Li, Le Yuan, Iván Domenzain, Rosemary Yu, Hao Wang, Gang Li, Yu Chen, Boyang Ji, Eduard J Kerkhoven, and Jens Nielsen. Yeast metabolic innovations emerged via expanded metabolic network and gene positive selection. Molecular Systems Biology, 17(10):e10427, 2021. URL: https://doi.org/10.15252/msb.202110427.
  14. Miles Lubin, Oscar Dowson, Joaquim Dias Garcia, Joey Huchette, Benoît Legat, and Juan Pablo Vielma. JuMP 1.0: Recent Improvements to a Modeling Language for Mathematical Optimization. Mathematical Programming Computation, 2023. URL: https://doi.org/10.1007/s12532-023-00239-3.
  15. Elad Noor, Nathan E. Lewis, and Ron Milo. A proof for loop-law constraints in stoichiometric metabolic networks. BMC Systems Biology, 6(1):140, 2012. URL: https://doi.org/10.1186/1752-0509-6-140.
  16. Jeffrey D. Orth, Ines Thiele, and Bernhard Ø. Palsson. What is flux balance analysis? Nature Biotechnology, 28(3):245-248, 2010. URL: https://doi.org/10.1038/nbt.1614.
  17. Bernhard Ø. Palsson. Systems Biology: Constraint-based Reconstruction and Analysis. Cambridge University Press, 2015. URL: https://doi.org/10.1017/CBO9781139854610.
  18. Karthik Raman. An Introduction to Computational Systems Biology: Systems-Level Modelling of Cellular Networks. Chapman and Hall/CRC, 2021. URL: https://doi.org/10.1201/9780429486951.
  19. Arne C. Reimers. Metabolic Networks, Thermodynamic Constraints, and Matroid Theory. Phd dissertation, Freie Universität Berlin, 2014. URL: https://refubium.fu-berlin.de/handle/fub188/11116.
  20. Benjamín J Sánchez, Cheng Zhang, Avlant Nilsson, Petri‐Jaan Lahtvee, Eduard J Kerkhoven, and Jens Nielsen. Improving the phenotype predictions of a yeast genome‐scale metabolic model by incorporating enzymatic constraints. Molecular Systems Biology, 13(8):935, 2017. URL: https://doi.org/10.15252/msb.20167411.
  21. Jan Schellenberger, Nathan E. Lewis, and Bernhard Ø. Palsson. Elimination of Thermodynamically Infeasible Loops in Steady-State Metabolic Models. Biophysical Journal, 100(3):544-553, 2011. URL: https://doi.org/10.1016/j.bpj.2010.12.3707.
  22. Matthew Scott, Carl W. Gunderson, Eduard M. Mateescu, Zhongge Zhang, and Terence Hwa. Interdependence of Cell Growth and Gene Expression: Origins and Consequences. Science, 330(6007):1099-1102, 2010. URL: https://doi.org/10.1126/science.1192588.
  23. Hannah Troppens, Mathieu Besançon, St. Elmo Wilken, and Sebastian Pokutta. hannahtro/Loopless_Fluxes_with_Mixed_Integer_Optimization. Software, swhId: https://archive.softwareheritage.org/swh:1:dir:9c41495c7f2ecd9e7459fa0c51d4be32fa0c033e (visited on 2025-07-03). URL: https://github.com/hannahtro/Loopless_Fluxes_with_Mixed_Integer_Optimization, URL: https://doi.org/10.4230/artifacts.23821.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact