PolyRound: polytope rounding for random sampling in metabolic networks

Rethinking 13C-metabolic flux analysis - The Bayesian way of flux inference

Metabolic reaction rates (fluxes) play a crucial role in comprehending cellular phenotypes and are essential in areas such as metabolic engineering, biotechnology, and biomedical research. The state-of-the-art technique for estimating fluxes is metabolic flux analysis using isotopic labelling (13C-MFA), which uses a dataset-model combination to determine the fluxes. Bayesian statistical methods are gaining popularity in the field of life sciences, but the use of 13C-MFA is still dominated by conventional best-fit approaches. The slow take-up of Bayesian approaches is, at least partly, due to the unfamiliarity of Bayesian methods to metabolic engineering researchers. To address this unfamiliarity, we here outline similarities and differences between the two approaches and highlight particular advantages of the Bayesian way of flux analysis. With a real-life example, re-analysing a moderately informative labelling dataset of E. coli, we identify situations in which Bayesian methods are advantageous and more informative, pointing to potential pitfalls of current 13C-MFA evaluation approaches. We propose the use of Bayesian model averaging (BMA) for flux inference as a means of overcoming the problem of model uncertainty through its tendency to assign low probabilities to both, models that are unsupported by data, and models that are overly complex. In this capacity, BMA resembles a tempered Ockham's razor. With the tempered razor as a guide, BMA-based 13C-MFA alleviates the problem of model selection uncertainty and is thereby capable of becoming a game changer for metabolic engineering by uncovering new insights and inspiring novel approaches.

dingo: a Python package for metabolic flux sampling

We present dingo, a Python package that supports a variety of methods to sample from the flux space of metabolic models, based on state-of-the-art random walks and rounding methods. For uniform sampling, dingo's sampling methods provide significant speed-ups and outperform existing software. Indicatively, dingo can sample from the flux space of the largest metabolic model up to now (Recon3D) in less than a day using a personal computer, under several statistical guarantees; this computation is out of reach for other similar software. In addition, dingo supports common analysis methods, such as flux balance analysis and flux variability analysis, and visualization components. dingo contributes to the arsenal of tools in metabolic modelling by enabling flux sampling in high dimensions (in the order of thousands).

Availability and implementation

The dingo Python library is available in GitHub at https://github.com/GeomScale/dingo and the data underlying this article are available in https://doi.org/10.5281/zenodo.10423335.

Genome scale metabolic network modelling for metabolic profile predictions

Metabolic profiling (metabolomics) aims at measuring small molecules (metabolites) in complex samples like blood or urine for human health studies. While biomarker-based assessment often relies on a single molecule, metabolic profiling combines several metabolites to create a more complex and more specific fingerprint of the disease. However, in contrast to genomics, there is no unique metabolomics setup able to measure the entire metabolome. This challenge leads to tedious and resource consuming preliminary studies to be able to design the right metabolomics experiment. In that context, computer assisted metabolic profiling can be of strong added value to design metabolomics studies more quickly and efficiently. We propose a constraint-based modelling approach which predicts in silico profiles of metabolites that are more likely to be differentially abundant under a given metabolic perturbation (e.g. due to a genetic disease), using flux simulation. In genome-scale metabolic networks, the fluxes of exchange reactions, also known as the flow of metabolites through their external transport reactions, can be simulated and compared between control and disease conditions in order to calculate changes in metabolite import and export. These import/export flux differences would be expected to induce changes in circulating biofluid levels of those metabolites, which can then be interpreted as potential biomarkers or metabolites of interest. In this study, we present SAMBA (SAMpling Biomarker Analysis), an approach which simulates fluxes in exchange reactions following a metabolic perturbation using random sampling, compares the simulated flux distributions between the baseline and modulated conditions, and ranks predicted differentially exchanged metabolites as potential biomarkers for the perturbation. We show that there is a good fit between simulated metabolic exchange profiles and experimental differential metabolites detected in plasma, such as patient data from the disease database OMIM, and metabolic trait-SNP associations found in mGWAS studies. These biomarker recommendations can provide insight into the underlying mechanism or metabolic pathway perturbation lying behind observed metabolite differential abundances, and suggest new metabolites as potential avenues for further experimental analyses.

Bayesian 13C-Metabolic Flux Analysis of Parallel Tracer Experiments in Granulocytes: A Directional Shift within the Non-Oxidative Pentose Phosphate Pathway Supports Phagocytosis

The pentose phosphate pathway (PPP) plays a key role in the cellular regulation of immune function; however, little is known about the interplay of metabolic adjustments in granulocytes, especially regarding the non-oxidative PPP. For the determination of metabolic mechanisms within glucose metabolism, we propose a novel set of measures for 13C-metabolic flux analysis based on ex vivo parallel tracer experiments ([1,2-13C]glucose, [U-13C]glucose, [4,5,6-13C]glucose) and gas chromatography-mass spectrometry labeling measurements of intracellular metabolites, such as sugar phosphates and their fragments. A detailed constraint analysis showed that the permission range for net and irreversible fluxes was limited to a three-dimensional space. The overall workflow, including its Bayesian flux estimation, resulted in precise flux distributions and pairwise confidence intervals, some of which could be represented as a line due to the strength of their correlation. The principal component analysis that was enabled by these behaviors comprised three components that explained 99.6% of the data variance. It showed that phagocytic stimulation reversed the direction of non-oxidative PPP net fluxes from ribose-5-phosphate biosynthesis toward glycolytic pathways. This process was closely associated with the up-regulation of the oxidative PPP to promote the oxidative burst.

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.

One-shot 13 C15 N-metabolic flux analysis for simultaneous quantification of carbon and nitrogen flux

Metabolic flux is the final output of cellular regulation and has been extensively studied for carbon but much less is known about nitrogen, which is another important building block for living organisms. For the tuberculosis pathogen, this is particularly important in informing the development of effective drugs targeting the pathogen's metabolism. Here we performed ¹³ C¹⁵ N dual isotopic labeling of Mycobacterium bovis BCG steady state cultures, quantified intracellular carbon and nitrogen fluxes and inferred reaction bidirectionalities. This was achieved by model scope extension and refinement, implemented in a multi-atom transition model, within the statistical framework of Bayesian model averaging (BMA). Using BMA-based ¹³ C¹⁵ N-metabolic flux analysis, we jointly resolve carbon and nitrogen fluxes quantitatively. We provide the first nitrogen flux distributions for amino acid and nucleotide biosynthesis in mycobacteria and establish glutamate as the central node for nitrogen metabolism. We improved resolution of the notoriously elusive anaplerotic node in central carbon metabolism and revealed possible operation modes. Our study provides a powerful and statistically rigorous platform to simultaneously infer carbon and nitrogen metabolism in any biological system.