Quantifying the propagation of parametric uncertainty on flux balance analysis

A quantitative description of light-limited cyanobacterial growth using flux balance analysis

The metabolism of phototrophic cyanobacteria is an integral part of global biogeochemical cycles, and the capability of cyanobacteria to assimilate atmospheric CO2 into organic carbon has manifold potential applications for a sustainable biotechnology. To elucidate the properties of cyanobacterial metabolism and growth, computational reconstructions of genome-scale metabolic networks play an increasingly important role. Here, we present an updated reconstruction of the metabolic network of the cyanobacterium Synechocystis sp. PCC 6803 and its quantitative evaluation using flux balance analysis (FBA). To overcome limitations of conventional FBA, and to allow for the integration of experimental analyses, we develop a novel approach to describe light absorption and light utilization within the framework of FBA. Our approach incorporates photoinhibition and a variable quantum yield into the constraint-based description of light-limited phototrophic growth. We show that the resulting model is capable of predicting quantitative properties of cyanobacterial growth, including photosynthetic oxygen evolution and the ATP/NADPH ratio required for growth and cellular maintenance. Our approach retains the computational and conceptual simplicity of FBA and is readily applicable to other phototrophic microorganisms.

Model validation and selection in metabolic flux analysis and flux balance analysis

13C-Metabolic Flux Analysis (13C-MFA) and Flux Balance Analysis (FBA) are widely used to investigate the operation of biochemical networks in both biological and biotechnological research. Both methods use metabolic reaction network models of metabolism operating at steady state so that reaction rates (fluxes) and the levels of metabolic intermediates are constrained to be invariant. They provide estimated (MFA) or predicted (FBA) values of the fluxes through the network in vivo, which cannot be measured directly. These fluxes can shed light on basic biology and have been successfully used to inform metabolic engineering strategies. Several approaches have been taken to test the reliability of estimates and predictions from constraint-based methods and to compare alternative model architectures. Despite advances in other areas of the statistical evaluation of metabolic models, such as the quantification of flux estimate uncertainty, validation and model selection methods have been underappreciated and underexplored. We review the history and state-of-the-art in constraint-based metabolic model validation and model selection. Applications and limitations of the χ2 -test of goodness-of-fit, the most widely used quantitative validation and selection approach in 13C-MFA, are discussed, and complementary and alternative forms of validation and selection are proposed. A combined model validation and selection framework for 13C-MFA incorporating metabolite pool size information that leverages new developments in the field is presented and advocated for. Finally, we discuss how adopting robust validation and selection procedures can enhance confidence in constraint-based modeling as a whole and ultimately facilitate more widespread use of FBA in biotechnology.

Characterising the metabolic rewiring of extremely slow growing Komagataella phaffii

Retentostat cultivations have enabled investigations into substrate-limited near-zero growth for a number of microbes. Quantitative physiology at these near-zero growth conditions has been widely discussed, yet characterisation of the fluxome is relatively under-reported. We investigated the rewiring of metabolism in the transition of a recombinant protein-producing strain of Komagataella phaffii to glucose-limited near-zero growth rates. We used cultivation data from a 200-fold range of growth rates and comprehensive biomass composition data to integrate growth rate dependent biomass equations, generated using a number of different approaches, into a K. phaffii genome-scale metabolic model. Here, we show that a non-growth-associated maintenance value of 0.65 mmol ATP g CDW - 1 h - 1 and a growth-associated maintenance value of 108 mmol ATP g CDW - 1 lead to accurate growth rate predictions. In line with its role as energy source, metabolism is rewired to increase the yield of ATP per glucose. This includes a reduction of flux through the pentose phosphate pathway, and a greater utilisation of glycolysis and the TCA cycle. Interestingly, we observed activity of an external, non-proton translocating NADH dehydrogenase in addition to the malate-aspartate shuttle. Regardless of the method used for the generation of biomass equations, a similar, yet different, growth rate dependent rewiring was predicted. As expected, these differences between the different methods were clearer at higher growth rates, where the biomass equation provides a much greater constraint than at slower growth rates. When placed on an increasingly limited glucose diet, the metabolism of K. phaffii adapts, enabling it to continue to drive critical processes sustaining its high viability at near-zero growth rates.

Balancing biomass reaction stoichiometry and measured fluxes in flux balance analysis

MOTIVATION

Flux balance analysis (FBA) is widely recognized as an important method for studying metabolic networks. When incorporating flux measurements of certain reactions into an FBA problem, it is possible that the underlying linear program may become infeasible, e.g. due to measurement or modeling inaccuracies. Furthermore, while the biomass reaction is of central importance in FBA models, its stoichiometry is often a rough estimate and a source of high uncertainty.

RESULTS

In this work, we present a method that allows modifications to the biomass reaction stoichiometry as a means to (i) render the FBA problem feasible and (ii) improve the accuracy of the model by corrections in the biomass composition. Optionally, the adjustment of the biomass composition can be used in conjunction with a previously introduced approach for balancing inconsistent fluxes to obtain a feasible FBA system. We demonstrate the value of our approach by analyzing realistic flux measurements of E.coli. In particular, we find that the growth-associated maintenance (GAM) demand of ATP, which is typically integrated with the biomass reaction, is likely overestimated in recent genome-scale models, at least for certain growth conditions. In light of these findings, we discuss issues related to the determination and inclusion of GAM values in constraint-based models. Overall, our method can uncover potential errors and suggest adjustments in the assumed biomass composition in FBA models based on inconsistencies between the model and measured fluxes.

AVAILABILITY AND IMPLEMENTATION

The developed method has been implemented in our software tool CNApy available from https://github.com/cnapy-org/CNApy.

The Quantitative Measurement of Peptidoglycan Components Obtained from Acidic Hydrolysis in Gram-Positive and Gram-Negative Bacteria via Hydrophilic Interaction Liquid Chromatography Coupled with Mass Spectrometry

The high throughput in genome sequencing and metabolic model (MM) reconstruction has democratised bioinformatics approaches such as flux balance analysis. Fluxes' prediction accuracy greatly relates to the deepness of the MM curation for a specific organism starting from the cell composition. One component is the cell wall, which is a functional barrier (cell shape, exchanges) with the environment. The bacterial cell wall (BCW), including its thickness, structure, and composition, has been extensively studied in Escherichia coli but poorly described for other organisms. The peptidoglycan (PG) layer composing the BCW is usually thinner in Gram- bacteria than in Gram+ bacteria. In both bacteria groups, PG is a polymeric mesh-like structure of amino acids and sugars, including N-acetylglucosamine, N-acetylmuramic acid, and amino acids. In this study, we propose a high-throughput method to characterise and quantify PG in Gram-positive and Gram-negative bacteria using acidic hydrolysis and hydrophilic interaction liquid chromatography coupled with mass spectrometry (HILIC-MS). The method showed a relatively short time frame (11 min analytical run), low inter- and intraday variability (3.2% and 4%, respectively), and high sensitivity and selectivity (limits of quantification in the sub mg/L range). The method was successfully applied on two Gram-negative bacteria (Escherichia coli K12 MG1655, Bacteroides thetaiotaomicron DSM 2079) and one Gram-positive bacterium (Streptococcus salivarius ssp. thermophilus DSM20259). The PG concentration ranged from 1.6% w/w to 14% w/w of the dry cell weight. The results were in good correlation with previously published results. With further development, the PG concentration provided by this newly developed method could reinforce the curation of MM.

Practical sampling of constraint-based models: Optimized thinning boosts CHRR performance

Thinning is a sub-sampling technique to reduce the memory footprint of Markov chain Monte Carlo. Despite being commonly used, thinning is rarely considered efficient. For sampling constraint-based models, a highly relevant use-case in systems biology, we here demonstrate that thinning boosts computational and, thereby, sampling efficiencies of the widely used Coordinate Hit-and-Run with Rounding (CHRR) algorithm. By benchmarking CHRR with thinning with simplices and genome-scale metabolic networks of up to thousands of dimensions, we find a substantial increase in computational efficiency compared to unthinned CHRR, in our examples by orders of magnitude, as measured by the effective sample size per time (ESS/t), with performance gains growing with polytope (effective network) dimension. Using a set of benchmark models we derive a ready-to-apply guideline for tuning thinning to efficient and effective use of compute resources without requiring additional coding effort. Our guideline is validated using three (out-of-sample) large-scale networks and we show that it allows sampling convex polytopes uniformly to convergence in a fraction of time, thereby unlocking the rigorous investigation of hitherto intractable models. The derivation of our guideline is explained in detail, allowing future researchers to update it as needed as new model classes and more training data becomes available. CHRR with deliberate utilization of thinning thereby paves the way to keep pace with progressing model sizes derived with the constraint-based reconstruction and analysis (COBRA) tool set. Sampling and evaluation pipelines are available at https://jugit.fz-juelich.de/IBG-1/ModSim/fluxomics/chrrt.

Mitigating biomass composition uncertainties in flux balance analysis using ensemble representations

The biomass equation is a critical component in genome-scale metabolic models (GEMs): it is used as the de facto objective function in flux balance analysis (FBA). This equation accounts for the quantities of all known biomass precursors that are required for cell growth based on the macromolecular and monomer compositions measured at certain conditions. However, it is often reported that the macromolecular composition of cells could change across different environmental conditions and thus the use of the same single biomass equation in FBA, under multiple conditions, is questionable. Herein, we first investigated the qualitative and quantitative variations of macromolecular compositions of three representative host organisms, Escherichia coli, Saccharomyces cerevisiae and Cricetulus griseus, across different environmental/genetic variations. While macromolecular building blocks such as RNA, protein, and lipid composition vary notably, changes in fundamental biomass monomer units such as nucleotides and amino acids are not appreciable. We also observed that flux predictions through FBA is quite sensitive to macromolecular compositions but not the monomer compositions. Based on these observations, we propose ensemble representations of biomass equation in FBA to account for the natural variation of cellular constituents. Such ensemble representations of biomass better predicted the flux through anabolic reactions as it allows for the flexibility in the biosynthetic demands of the cells. The current study clearly highlights that certain component of the biomass equation indeed vary across different conditions, and the ensemble representation of biomass equation in FBA by accounting for such natural variations could avoid inaccuracies that may arise from in silico simulations.

Integrating Omics Data in Genome-Scale Metabolic Modeling: A Methodological Perspective for Precision Medicine

Recent advancements in omics technologies have generated a wealth of biological data. Integrating these data within mathematical models is essential to fully leverage their potential. Genome-scale metabolic models (GEMs) provide a robust framework for studying complex biological systems. GEMs have significantly contributed to our understanding of human metabolism, including the intrinsic relationship between the gut microbiome and the host metabolism. In this review, we highlight the contributions of GEMs and discuss the critical challenges that must be overcome to ensure their reproducibility and enhance their prediction accuracy, particularly in the context of precision medicine. We also explore the role of machine learning in addressing these challenges within GEMs. The integration of omics data with GEMs has the potential to lead to new insights, and to advance our understanding of molecular mechanisms in human health and disease.

Evaluating proteome allocation of Saccharomyces cerevisiae phenotypes with resource balance analysis

Saccharomyces cerevisiae is an important model organism and a workhorse in bioproduction. Here, we reconstructed a compact and tractable genome-scale resource balance analysis (RBA) model (i.e., named scRBA) to analyze metabolic fluxes and proteome allocation in a computationally efficient manner. Resource capacity models such as scRBA provide the quantitative means to identify bottlenecks in biosynthetic pathways due to enzyme, compartment size, and/or ribosome availability limitations. ATP maintenance rate and in vivo apparent turnover numbers (k_app) were regressed from metabolic flux and protein concentration data to capture observed physiological growth yield and proteome efficiency and allocation, respectively. Estimated parameter values were found to vary with oxygen and nutrient availability. Overall, this work (i) provides condition-specific model parameters to recapitulate phenotypes corresponding to different extracellular environments, (ii) alludes to the enhancing effect of substrate channeling and post-translational activation on in vivo enzyme efficiency in glycolysis and electron transport chain, and (iii) reveals that the Crabtree effect is underpinned by specific limitations in mitochondrial proteome capacity and secondarily ribosome availability rather than overall proteome capacity.

Inspecting the Solution Space of Genome-Scale Metabolic Models

Genome-scale metabolic models are frequently used in computational biology. They offer an integrative view on the metabolic network of an organism without the need to know kinetic information in detail. However, the huge solution space which comes with the analysis of genome-scale models by using, e.g., Flux Balance Analysis (FBA) poses a problem, since it is hard to thoroughly investigate and often only an arbitrarily selected individual flux distribution is discussed as an outcome of FBA. Here, we introduce a new approach to inspect the solution space and we compare it with other approaches, namely Flux Variability Analysis (FVA) and CoPE-FBA, using several different genome-scale models of lactic acid bacteria. We examine the extent to which different types of experimental data limit the solution space and how the robustness of the system increases as a result. We find that our new approach to inspect the solution space is a good complementary method that offers additional insights into the variance of biological phenotypes and can help to prevent wrong conclusions in the analysis of FBA results.