A study of a diauxic growth experiment using an expanded dynamic flux balance framework

PLOS ONE RESEARCH ARTICLE A study of a diauxic growth experiment using an expanded dynamic flux balance framework Emil Karlsen ID1, Marianne Gylseth1☯, Christian Schulz ID1☯, Eivind Almaas ID1,2* 1 Department of Biotechnology and Food Science, NTNU - Norwegian University of Science and Technology, Trondheim, Norway, 2 K. G. Jebsen Center for Genetic Epidemiology Department of Public Health and General Practice, NTNU - Norwegian University of Science and Technology, Trondheim, Norway a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Karlsen E, Gylseth M, Schulz C, Almaas E (2023) A study of a diauxic growth experiment using an expanded dynamic flux balance framework. PLoS ONE 18(1): e0280077. https:// doi.org/10.1371/journal.pone.0280077 Editor: Chen-Guang Liu, Shanghai Jiao Tong University, CHINA Received: May 16, 2022 Accepted: December 20, 2022 Published: January 6, 2023 Copyright: © 2023 Karlsen et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting information files. ☯ These authors contributed equally to this work. * Abstract Flux balance analysis (FBA) remains one of the most used methods for modeling the entirety of cellular metabolism, and a range of applications and extensions based on the FBA framework have been generated. Dynamic flux balance analysis (dFBA), the expansion of FBA into the time domain, still has issues regarding accessibility limiting its widespread adoption and application, such as a lack of a consistently rigid formalism and tools that can be applied without expert knowledge. Recent work has combined dFBA with enzyme-constrained flux balance analysis (decFBA), which has been shown to greatly improve accuracy in the comparison of computational simulations and experimental data, but such approaches generally do not take into account the fact that altering the enzyme composition of a cell is not an instantaneous process. Here, we have developed a decFBA method that explicitly takes enzyme change constraints (ecc) into account, decFBAecc. The resulting software is a simple yet flexible framework for using genome-scale metabolic modeling for simulations in the time domain that has full interoperability with the COBRA Toolbox 3.0. To assess the quality of the computational predictions of decFBAecc, we conducted a diauxic growth fermentation experiment with Escherichia coli BW25113 in glucose minimal M9 medium. The comparison of experimental data with dFBA, decFBA and decFBAecc predictions demonstrates how systematic analyses within a fixed constraint-based framework can aid the study of model parameters. Finally, in explaining experimentally observed phenotypes, our computational analysis demonstrates the importance of non-linear dependence of exchange fluxes on medium metabolite concentrations and the noninstantaneous change in enzyme composition, effects of which have not previously been accounted for in constraint-based analysis. Funding: EK would like to thank the Norwegian Research Council grant #269084, and CS would like to thank the Norwegian Research Council grant #294605. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Introduction Competing interests: The authors have declared that no competing interests exist. Computer models are invaluable tools in capturing and systematizing new knowledge, especially for the complex phenomena found in biology. Genome-scale metabolic models (GEMs) PLOS ONE | https://doi.org/10.1371/journal.pone.0280077 January 6, 2023 1 / 17 PLOS ONE A study of a diauxic growth experiment using an expanded dynamic flux balance framework are computational models that compile information about the entirety of known metabolic functions in a given organism or cell type. GEMs typically contain a listing of genes, enzymes, and reactions, and relationships of dependence between these. For biochemical reactions, information about substrate, product, and stoichiometry is included in their model representation, i.e. the consumption and production rates for the involved compounds. Based on how compounds participate in different reactions, it is possible to infer a metabolic network: a bipartite network connecting the reactions and metabolites [1]. An additional central component in GEMs is the representation of a biomass objective function (BOF), a pseudo-reaction which represents the metabolites needed for the cell to reproduce. Since it is a key component of these models, the BOF has recently been the target of increased interest in the field [2–6]. Computational models help identify inconsistencies in our current understanding of the phenomena they model. They also predict novel system behavior or connections, and aid in the design of experiments [1, 7–10]. As the use of these models becomes more popular and necessary to improve systems-level understanding of metabolism, so should their ease of use and interpretation. Due to the formulation of the GEMs and the assumptions of steady-state, mass conservation, and optimality of an objective (commonly chosen to be the BOF), the calculation of system-wide flux-states (measured in millimoles per hour per gram of cell dry weight (mmol h−1 gCDW−1) [1]) can be performed using standard tools for constraint-based linear optimization [1]. This allows for very rapid arrival at an optimal solution, even for large networks containing thousands of reactions. The aforementioned analysis and calculation steps are called flux balance analysis (FBA) [1]. In the years since its inception, FBA and related approaches have given rise to a number of derivatives and modifications [11]. Two modifications that in particular improve the utility of FBA are (1) dynamic flux balance analysis (dFBA) and (2) enzyme-constrained flux balance analysis (ecFBA). In dFBA, the goal is to simulate the interaction between the organism’s metabolism and the environment over time [7, 12]. In the ecFBA approach, additional constraints are applied to the flux distribution to account for the fact that the proportion of active enzymes in a cell is only a fraction of the cell mass, and these enzymes have a finite capacity to catalyze biochemical reactions [13, 14]. While first introduced in 1994 [7], dFBA was first explicitly formalized in 2002 [12]. This formalization emphasized two main approaches: the dynamic optimization approach (DOA), and the static optimization approach (SOA) [12]. The essential difference between the two methods is that in DOA, the simulation is solved for a single interval of time (often the total duration of interest) which determines the optimal strategy, whereas in SOA, a regular FBA problem is solved f (...truncated)