(373h) Graph-Based Multi-Objective Flux Balance Analysis: A Novel Framework for Determining Optimal Weights in Multi-Objective Functions

Metabolomics-based network analysis poses challenges in identifying and interpreting metabolites due to their complex relationships. To overcome this, networks can be constructed using network graphs where nodes represent metabolites or reaction fluxes and edges represent their connections relationships ^[1]. Network graphs can be built from a variety of stoichiometric network models. Genome-scale metabolic models have gained attention for their comprehensive view of metabolic systems, but their large size often leads to ill-conditioning problems, resulting in inaccurate predictions and high sensitivity to small perturbations ^[2]. To improve the accuracy and robustness of the metabolic models, researchers have compared different objective functions in determining flux values for modeling cell metabolism under specific environmental conditions ^[3]. Choosing the appropriate objective function can significantly impact the results. However, the determination of the objective function may be labor and time-consuming under the limiting understanding of the system.

To deal with these challenges, a novel mass flow graph-based multi-objective flux balance analysis (FBA) framework is proposed. The mass flow graph is a directed and weighted graph where the nodes represent the reaction/ fluxes in the model and the weights are estimated from the metabolic mass fluxes from experiment data. After transforming the network matrix to the graph, the maximum flow algorithm (or minimum cut) is applied to the mass flow graph of the genome-scale metabolic model to extract the featured pathway of the reactions from the source point (sugars) to the desired product point (e.g., solventogenesis ^[5]). The extracted subnetwork provides information about the relationships between the metabolic networks at different stages, and estimates the quantitative priorities of the fluxes of products. The quantitative values can serve as weights of an objective function that will determine the solution and uncover the cellular metabolic priority.

In this study, a complex multi-species isopropanol-butanol-ethanol (IBE) system is used to illustrate the proposed framework ^[4]. In this system, four species are involved (C. acetobutylicum (Cac), C. ljungdahlii (Clj), and fused types of Cac and Clj) and two sugar sources (glucose and fructose). The objective is to predict the flux profiles of solventogenesis products. The result shows that the proposed framework provided a more accurate and robust estimation compared to conventional single objective function analysis, and the extracted pathways allowed for better interpretation and focus on crucial metabolic pathways among thousands-of-reactions involved in the network.

References:

[1] Beguerisse-Díaz, M., Bosque, G., Oyarzún, D., Picó, J., & Barahona, M. (2018). Flux-dependent graphs for metabolic networks. NPJ systems biology and applications, 4(1), 32.

[2] Gábor, A., & Banga, J. R. (2015). Robust and efficient parameter estimation in dynamic models of biological systems. BMC systems biology, 9(1), 1-25.

[3] Gu, C., Kim, G. B., Kim, W. J., Kim, H. U., & Lee, S. Y. (2019). Current status and applications of genome-scale metabolic models. Genome biology, 20, 1-18.

[4] Foster, C., Charubin, K., Papoutsakis, E. T., & Maranas, C. D. (2021). Modeling Growth kinetics, interspecies cell fusion, and metabolism of a Clostridium acetobutylicum/Clostridium ljungdahlii syntrophic coculture. Msystems, 6(1), e01325-20.

[5] Senger, R. S., & Papoutsakis, E. T. (2008). Genome‐scale model for Clostridium acetobutylicum: Part I. Metabolic network resolution and analysis. Biotechnology and bioengineering, 101(5), 1036-1052.