Coupling Flux Balance Analysis with Reactive Transport Modeling through Machine Learning for Rapid and Stable Simulation of Microbial Metabolic Switching

Abstract

Integration of genome-scale metabolic networks with reactive transport models (RTMs) is an advanced simulation technique that enables predicting the changes of microbial growth and metabolism in space and time. Despite promising demonstrations in the past, computational inefficiency has been pointed out as a critical issue to overcome because it requires repeated implementation of linear programming (LP) to get flux balance analysis (FBA) solutions in every time step and every spatial grid. To address this challenge, we propose a new simulation method where we train/validate artificial neural networks (ANNs) using FBA solutions randomly sampled and incorporate the resulting reduced-order FBA model (represented as algebraic equations) into RTMs as source/sink terms. We demonstrate the efficiency of our method via a case study of Shewanella oneidensis MR-1 strain. During the aerobic growth on lactate, S. oneidensis produces metabolic byproducts (such as pyruvate and acetate), which are subsequently consumed as alternative carbon sources when the preferred ones are depleted. Simulating such intricate dynamics posed a considerable challenge, which we overcame by adopting the cybernetic approach that describes metabolic switches as the outcome of dynamic competition among multiple growth options. In both zero-dimensional batch and one-dimensional column configurations, the ANN-based reduced-order models achieved substantial reduction of computational time by several orders of magnitude compared to the original LP-based FBA models. Importantly, the ANN models produced robust solutions without any special measures to prevent numerical instability. These developments significantly promote our ability to utilize genome-scale networks in complex, multi-physics, and multi-dimensional ecosystem modeling.