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.

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.

Assumptions on decision making and environment can yield multiple steady states in microbial community models.

BACKGROUND: Microbial community simulations using genome scale metabolic networks (GSMs) are relevant for many application areas, such as the analysis of the human microbiome. Such simulations rely on assumptions about the culturing environment, affecting if the culture may reach a metabolically stationary state with constant microbial concentrations. They also require assumptions on decision making by the microbes: metabolic strategies can be in the interest of individual community members or of the whole community. However, the impact of such common assumptions on community simulation results has not been investigated systematically. RESULTS: Here, we investigate four combinations of assumptions, elucidate how they are applied in literature, provide novel mathematical formulations for their simulation, and show how the resulting predictions differ qualitatively. Our results stress that different assumption combinations give qualitatively different predictions on microbial coexistence by differential substrate utilization. This fundamental mechanism is critically under explored in the steady state GSM literature with its strong focus on coexistence states due to crossfeeding (division of labor). Furthermore, investigating a realistic synthetic community, where the two involved strains exhibit no growth in isolation, but grow as a community, we predict multiple modes of cooperation, even without an explicit cooperation mechanism. CONCLUSIONS: Steady state GSM modelling of microbial communities relies both on assumed decision making principles and environmental assumptions. In principle, dynamic flux balance analysis addresses both. In practice, our methods that address the steady state directly may be preferable, especially if the community is expected to display multiple steady states.

PolyRound: polytope rounding for random sampling in metabolic networks.

SUMMARY: Random flux sampling is a powerful tool for the constraint-based analysis of metabolic networks. The most efficient sampling method relies on a rounding transform of the constraint polytope, but no available rounding implementation can round all relevant models. By removing redundant polytope constraints on the go, PolyRound simplifies the numerical problem and rounds all the 108 models in the BiGG database without parameter tuning, compared to ∼50% for the state-of-the-art implementation. AVAILABILITY AND IMPLEMENTATION: The implementation is available on gitlab: https://gitlab.com/csb.ethz/PolyRound. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

HOPS: high-performance library for (non-)uniform sampling of convex-constrained models.

SUMMARY: The C++ library Highly Optimized Polytope Sampling (HOPS) provides implementations of efficient and scalable algorithms for sampling convex-constrained models that are equipped with arbitrary target functions. For uniform sampling, substantial performance gains were achieved compared to the state-of-the-art. The ease of integration and utility of non-uniform sampling is showcased in a Bayesian inference setting, demonstrating how HOPS interoperates with third-party software. AVAILABILITY AND IMPLEMENTATION: Source code is available at https://github.com/modsim/hops/, tested on Linux and MS Windows, includes unit tests, detailed documentation, example applications and a Dockerfile. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Reversible jump MCMC for multi-model inference in Metabolic Flux Analysis.

MOTIVATION: The validity of model based inference, as used in systems biology, depends on the underlying model formulation. Often, a vast number of competing models is available, that are built on different assumptions, all consistent with the existing knowledge about the studied biological phenomenon. As a remedy for this, Bayesian Model Averaging (BMA) facilitates parameter and structural inferences based on multiple models simultaneously. However, in fields where a vast number of alternative, high-dimensional and non-linear models are involved, the BMA-based inference task is computationally very challenging. RESULTS: Here we use BMA in the complex setting of Metabolic Flux Analysis (MFA) to infer whether potentially reversible reactions proceed uni- or bidirectionally, using 13C labeling data and metabolic networks. BMA is applied on a large set of candidate models with differing directionality settings, using a tailored multi-model Markov Chain Monte Carlo (MCMC) approach. The applicability of our algorithm is shown by inferring the in vivo probability of reaction bidirectionalities in a realistic network setup, thereby extending the scope of 13C MFA from parameter to structural inference. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

When a single lineage is not enough: Uncertainty-Aware Tracking for spatio-temporal live-cell image analysis.

MOTIVATION: Microfluidic platforms for live-cell analysis are in dire need of automated image analysis pipelines. In this context, producing reliable tracks of single cells in colonies has proven to be notoriously difficult without manual assistance, especially when image sequences experience low frame rates. RESULTS: With Uncertainty-Aware Tracking (UAT), we propose a novel probabilistic tracking paradigm for simultaneous tracking and estimation of tracking-induced errors in biological quantities derived from live-cell experiments. To boost tracking accuracy, UAT relies on a Bayesian approach which exploits temporal information on growth patterns to guide the formation of lineage hypotheses. A biological study is presented, in which UAT demonstrates its ability to track cells, with comparable to better accuracy than state-of-the-art trackers, while simultaneously estimating tracking-induced errors. AVAILABILITY AND IMPLEMENTATION: Image sequences and Java executables for reproducing the results are available at https://doi.org/10.5281/zenodo.1299526. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

To be certain about the uncertainty: Bayesian statistics for 13 C metabolic flux analysis.

13 C Metabolic Fluxes Analysis (13 C MFA) remains to be the most powerful approach to determine intracellular metabolic reaction rates. Decisions on strain engineering and experimentation heavily rely upon the certainty with which these fluxes are estimated. For uncertainty quantification, the vast majority of 13 C MFA studies relies on confidence intervals from the paradigm of Frequentist statistics. However, it is well known that the confidence intervals for a given experimental outcome are not uniquely defined. As a result, confidence intervals produced by different methods can be different, but nevertheless equally valid. This is of high relevance to 13 C MFA, since practitioners regularly use three different approximate approaches for calculating confidence intervals. By means of a computational study with a realistic model of the central carbon metabolism of E. coli, we provide strong evidence that confidence intervals used in the field depend strongly on the technique with which they were calculated and, thus, their use leads to misinterpretation of the flux uncertainty. In order to provide a better alternative to confidence intervals in 13 C MFA, we demonstrate that credible intervals from the paradigm of Bayesian statistics give more reliable flux uncertainty quantifications which can be readily computed with high accuracy using Markov chain Monte Carlo. In addition, the widely applied chi-square test, as a means of testing whether the model reproduces the data, is examined closer.

Determination of essential phenotypic elements of clusters in high-dimensional entities-DEPECHE.

Technological advances have facilitated an exponential increase in the amount of information that can be derived from single cells, necessitating new computational tools that can make such highly complex data interpretable. Here, we introduce DEPECHE, a rapid, parameter free, sparse k-means-based algorithm for clustering of multi- and megavariate single-cell data. In a number of computational benchmarks aimed at evaluating the capacity to form biologically relevant clusters, including flow/mass-cytometry and single cell RNA sequencing data sets with manually curated gold standard solutions, DEPECHE clusters as well or better than the currently available best performing clustering algorithms. However, the main advantage of DEPECHE, compared to the state-of-the-art, is its unique ability to enhance interpretability of the formed clusters, in that it only retains variables relevant for cluster separation, thereby facilitating computational efficient analyses as well as understanding of complex datasets. DEPECHE is implemented in the open source R package DepecheR currently available at github.com/Theorell/DepecheR.

Intracellular Mycobacterium tuberculosis Exploits Multiple Host Nitrogen Sources during Growth in Human Macrophages.

Nitrogen metabolism of Mycobacterium tuberculosis (Mtb) is crucial for the survival of this important pathogen in its primary human host cell, the macrophage, but little is known about the source(s) and their assimilation within this intracellular niche. Here, we have developed 15N-flux spectral ratio analysis (15N-FSRA) to explore Mtb's nitrogen metabolism; we demonstrate that intracellular Mtb has access to multiple amino acids in the macrophage, including glutamate, glutamine, aspartate, alanine, glycine, and valine; and we identify glutamine as the predominant nitrogen donor. Each nitrogen source is uniquely assimilated into specific amino acid pools, indicating compartmentalized metabolism during intracellular growth. We have discovered that serine is not available to intracellular Mtb, and we show that a serine auxotroph is attenuated in macrophages. This work provides a systems-based tool for exploring the nitrogen metabolism of intracellular pathogens and highlights the enzyme phosphoserine transaminase as an attractive target for the development of novel anti-tuberculosis therapies.

Current state and challenges for dynamic metabolic modeling.

While the stoichiometry of metabolism is probably the best studied cellular level, the dynamics in metabolism can still not be well described, predicted and, thus, engineered. Unknowns in the metabolic flux behavior arise from kinetic interactions, especially allosteric control mechanisms. While the stoichiometry of enzymes is preserved in vitro, their activity and kinetic behavior differs from the in vivo situation. Next to this challenge, it is infeasible to test the interaction of each enzyme with each intracellular metabolite in vitro exhaustively. As a consequence, the whole interacting metabolome has to be studied in vivo to identify the relevant enzymes properties. In this review we discuss current approaches for in vivo perturbation experiments, that is, stimulus response experiments using different setups and quantitative analytical approaches, including dynamic carbon tracing. Next to reliable and informative data, advanced modeling approaches and computational tools are required to identify kinetic mechanisms and their parameters.