Optimization-based framework with flux balance analysis (FBA) and metabolic pathway analysis (MPA) for identifying metabolic objective functions
Ching-Mei Wen, Eleftherios Papoutsakis, Marianthi Ierapetritou
Abstract
Metabolic network modeling, especially Flux Balance Analysis (FBA), plays a critical role in systems biology by providing insights into cellular behaviors. Although FBA is the main tool for predicting flux distributions, it can face challenges capturing flux variations under different conditions. Selecting an appropriate objective function is therefore important for accurately representing system performance.
Introduction
Metabolic networks have been extensively used in various fields, such as drug discovery [1], microbial strain improvement [2], systems biology [3], disease diagnosis [4], and understanding evolutionary dynamics [5]. Rather than limiting research to isolated reactions or pathways, a comprehensive analysis of these networks offers insights into the broader interplay of cellular functions.
Materials and method
The following sections describe the graph-based representation of flux solutions, the computation of Coefficients of Importance using the minimum-cut algorithm, and the application of TIObjFind to infer the Coefficients of Importance of metabolic objectives. A list of mathematical notations is provided in S3 Text.
Results and discussion
2.1. Overview of Topology-Informed Objective Find (TIObjFind)
From a practical perspective, researchers often perform FBA with an objective function that assumes a single reaction, such as biomass maximization or metabolite production, as the exclusive optimization goal [29]. Without considering how alternative pathways contribute to overall network function, these static objectives may not always align with observed experimental flux data, particularly under changing environmental conditions.
Acknowledgments
We are grateful to Dr. John Hill and Dr. Jonathan Otten for producing the co-culture experiments. We also appreciate the constructive feedback and assistance provided by members of our research groups.
Citation: Wen C-M, Papoutsakis E, Ierapetritou M (2025) Optimization-based framework with flux balance analysis (FBA) and metabolic pathway analysis (MPA) for identifying metabolic objective functions. PLoS Comput Biol 21(10): e1013635. https://doi.org/10.1371/journal.pcbi.1013635
Editor: Claudio Angione, Teesside University, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
Received: June 24, 2025; Accepted: October 19, 2025; Published: October 27, 2025
Copyright: © 2025 Wen et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All data sets used in this study and codes for running the simulations described 592 in this article can be downloaded from our group’s GitHub page: https://github.com/mgigroup1/Minimum-Cut-Algorithm-example.git. This includes all case study data; metabolic reaction content; flux bounds of E coli, iCAC802, iJL680, hybrid Cac, and hybrid Clj metabolic models; and supplemental MATLAB and py. codes for running the graph-based analysis simulations described in this article.
Funding: This work was supported by a US Department of Energy ARPA-E project under contract AR0001505, part of the ARPA-E program DE-FOA-0002387 “Energy and Carbon Optimized Synthesis for the Bioeconomy (ECOSynBio)”. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
