Nonlinear multi-objective flux balance analysis of the Warburg Effect

Yi Zhang, Daniel Boley

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Due to its implication in cancer treatment, the Warburg Effect has received extensive in silico investigation. Flux Balance Analysis (FBA), based on constrained optimization, was successfully applied in the Warburg Effect modelling. Yet, the assumption that cell types have one invariant cellular objective severely limits the applicability of the previous FBA models. Meanwhile, we note that cell types with different objectives show different extents of the Warburg Effect. To extend the applicability of the previous model and model the disparate cellular pathway preferences in different cell types, we built a Nonlinear Multi-Objective FBA (NLMOFBA) model by including three key objective terms (ATP production rate, lactate generation rate and ATP yield) into one objective function through linear scalarization. By constructing a cellular objective map and iteratively varying the objective weights, we showed disparate cellular pathway preferences manifested by different cell types driven by their unique cellular objectives, and we gained insights about the causal relationship between cellular objectives and the Warburg Effect. In addition, we obtained other biologically consistent results by using our NLMOFBA model. For example, augmented with the constraint associated with inefficient mitochondria function, low oxygen availability, or limited substrate, NLMOFBA predicts cellular pathways supported by the biology literature. Collectively, our NLMOFBA model can help build a complete understanding towards the Warburg Effect in different cell types. Finally, we investigated the impact of glutaminolysis, an important pathway related to glycolysis, on the occurrence of the Warburg Effect by using linear programming.

Original languageEnglish (US)
Article number111223
JournalJournal of Theoretical Biology
StatePublished - Oct 7 2022

Bibliographical note

Funding Information:
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors have no relevant financial or non-financial interests to disclose. We sincerely thank the reviewers for their helpful suggestions during the revision phase.

Publisher Copyright:
© 2022 Elsevier Ltd


  • Flux balance analysis
  • Multi-objective optimization
  • Nonconvex optimization
  • Theoretical biology


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