Genome-scale metabolic networks (GEMs) provide a high-resolution view of the interplay between genes, proteins, metabolites, and reactions within microbial cells. Flux balance analysis (FBA) is a widely-used standard method to estimate condition-specific flux distributions within complex GEMs. FBA solutions are obtained by implementing linear programming (LP) in order to optimize a specified metabolic objective (such as biomass production or other relevant metabolic functions) under particular environmental conditions and/or omics data-based constraints. Due to this capability, there is an increasing interest in integrating GEMs with reactive-transport models (RTMs) for the accurate simulation of microbial processes varying in space and time. However, the integration of GEMs (composed of thousands of reactions and metabolites) with RTMs (governed by partial differential equations) presents a computational challenge due to significant computational burden caused by iterative implementations of LP at each time and spatial grid throughout simulations. To address this challenge, we developed a novel machine learning-based method that enables computationally efficient and robust coupling of FBA and RTMs (Song et al., 2023). Our strategy is to train artificial neural networks (ANNs) as surrogate FBA models and use the resulting reduced-order models (represented as algebraic equations) as source/sink terms in RTMs. We demonstrate the effectiveness of our method through the case study of the
Shewanella oneidensis MR-1 strain. Dynamic metabolic modeling of
S. oneidensis is not a taxing task due to complex metabolic switches experimentally observed. During aerobic growth on lactate,
S. oneidensis produces metabolic byproducts (such as pyruvate and acetate), which are subsequently consumed as alternative carbon sources when preferred substrates are depleted (Song et al., 2013). Typical kinetics-based approaches are ineffective in accounting for such complex dynamic regulation in
S. oneidensis, requiring more advanced modeling techniques. To address this issue, we adopted the cybernetic approach that specializes in predicting metabolic switches resulting from dynamic competition among multiple growth options. The cybernetic model provides a rational description of metabolic regulation based on an optimal control theory, avoiding the difficulty in accounting for all mechanistic details of metabolic regulation, which are generally unknown (Ramkrishna and Song, 2018; Ramkrishna and Song, 2012). In zero-dimensional batch and one-dimensional column reactors, our ANN-based reduced-order models achieved a significant reduction in computational time, up to several orders of magnitude compared to the original LP-based FBA models. Furthermore, unlike the LP-based FBA approach, our ANN-based models produced robust solutions without the need for special measures to prevent numerical instability. Due to these promising performance and properties, our ANN-based FBA modeling method is currently being used as a core component of CompLab, a simulation tool of fluid flow and solute transport in porous media (Jung et al., 2023). Overall, the new capability demonstrated in this work will facilitate linking molecular-level metabolic data/models with large-scale RTMs with enhanced computational efficiency.
References:
Jung H, Song HS, Meile C. CompLaB v1. 0: a scalable pore-scale model for flow, biogeochemistry, microbial metabolism and biofilm dynamics. Geoscientific Model Development. 2023 Mar 27;16(6):1683-96.
Ramkrishna D, Song HS. Cybernetic Modeling for Bioreaction Engineering. Cambridge University Press; 2018 Oct 18.
Ramkrishna D, Song HS. Dynamic models of metabolism: Review of the cybernetic approach. AIChE Journal. 2012 Apr;58(4):986-97.
Song HS, Ahamed F, Lee JY, Henry CC, Edirisinghe JN, Nelson WC, Chen X, Moulton JD, Scheibe TD. Coupling Flux Balance Analysis with Reactive Transport Modeling through Machine Learning for Rapid and Stable Simulation of Microbial Metabolic Switching. bioRxiv. 2023:2023-02.
Song HS, Ramkrishna D, Pinchuk GE, Beliaev AS, Konopka AE, Fredrickson JK. Dynamic modeling of aerobic growth of Shewanella oneidensis. Predicting triauxic growth, flux distributions, and energy requirement for growth. Metabolic Engineering. 2013 Jan 1; 15:25-33.
