# Optimization-based framework with flux balance analysis (FBA) and metabolic pathway analysis (MPA) for identifying metabolic objective functions

## TL;DR

This paper introduces TIObjFind, a new framework that improves metabolic modeling by identifying key reactions and their contributions to cellular objectives under different conditions.

## Contribution

TIObjFind combines FBA and MPA to dynamically determine reaction importance coefficients for better metabolic predictions.

## Key findings

- TIObjFind reduces prediction errors and aligns model outputs with experimental data in glucose fermentation by Clostridium acetobutylicum.
- The framework successfully captures stage-specific metabolic objectives in a multi-species IBE system.
- Coefficients of Importance enhance the interpretability of complex metabolic networks.

## 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. To address this, we introduce a novel framework (e.g., TIObjFind) that imposes Metabolic Pathway Analysis (MPA) with Flux Balance Analysis (FBA) to analyze adaptive shifts in cellular responses throughout different stages of a biological system. This framework determines Coefficients of Importance (CoIs) that quantify each reaction’s contribution to an objective function, aligning optimization results with experimental flux data. By examining Coefficients of Importance, TIObjFind enhances the interpretability of complex metabolic networks and provides insights into adaptive cellular responses.

Cells adjust their metabolism dynamically in response to environmental changes, and computational models help us understand these adaptations. Flux Balance Analysis is a widely used approach to predict cellular metabolism, but its accuracy relies on selecting an appropriate metabolic objective function. Here, we introduce TIObjFind, a data-driven optimization framework that helps computational models better predict how metabolic networks prioritize reactions under different conditions. TIObjFind identifies key reactions by assigning Coefficients of Importance, which indicate the contribution to cellular objectives. Two case studies illustrate the application of TIObjFind. The first case study focuses on the fermentation of glucose by Clostridium acetobutylicum, where the proposed method is used to determine pathway-specific weighting factors. By applying different weighting strategies, we assess the influence of Coefficients of Importance on flux predictions and demonstrate their impact on reducing prediction errors while improving the alignment with experimental data. The second case study examines a multi-species isopropanol-butanol-ethanol (IBE) system comprising C. acetobutylicum, and C. ljungdahlii. In this case, the weights (or Coefficients of Importance) are used as hypothesis coefficients within the objective function to assess cellular performance. Application of the proposed approach demonstrates a good match with observed experimental data and capturing stage-specific metabolic objectives.