Nonlinear Multi-Objective Flux Balance Analysis of the Warburg Effect

TL;DR

This paper introduces a nonlinear multi-objective flux balance analysis model to better understand the Warburg Effect across different cell types, revealing how cellular objectives influence metabolic pathway preferences and aligning with biological observations.

Contribution

The study develops a novel NLMOFBA model that incorporates multiple cellular objectives, enabling analysis of diverse cell type behaviors in Warburg Effect modeling.

Findings

Different cell types show distinct pathway preferences based on their objectives.

The model predicts pathways consistent with biological literature under various constraints.

Insights into the causal relationship between cellular objectives and the Warburg Effect.

Abstract

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 or limited substrate, NLMOFBA predicts cellular pathways supported by the biology literature. Collectively, NLMOFBA can help build a complete understanding towards the Warburg Effect in different cell types.