The goal of this review is to summarize techniques and concepts for in vivo or ex vivo stable isotope labeling in cardiovascular research, to highlight mathematical concepts and their limitations, to describe analytical methods at the tissue and single-cell level, and to discuss opportunities to leverage metabolic models to address important mechanistic questions relevant to all patients with cardiovascular disease.Although metabolic remodeling during cardiovascular diseases has been well-recognized for decades, the recent development of analytical platforms and mathematical tools has driven the emergence of assessing cardiac metabolism using tracers. Metabolism is a critical component of cellular functions and adaptation to stress. The pathogenesis of cardiovascular disease involves metabolic adaptation to maintain cardiac contractile function even in advanced disease stages. Stable-isotope tracer measurements are a powerful tool for measuring flux distributions at the whole organism level and assessing metabolic changes at a systems level  Measurements of metabolic changes in a variety of biological samples are feasible due to advances in chromatographic separation  and improved detection like nuclear magnetic resonance (NMR) and mass spectrometry (MS). However, the interpretation of complex disease models or patient derived samples can be challenging with large scale metabolomics and when a systems-wide understanding of specific pathways is required. Measuring changes in metabolite concentration do not allow to draw any conclusions on metabolic rates or the direction of a flux. Changes in metabolite levels can either result from differential production or utilization of a given intermediate due to increased flux from synthesizing reactions, decreased flux toward consuming reactions, or alterations in transporter activities. For example, during ischemia-reperfusion injury, glycolytic intermediates accumulate despite a reduction in glucose uptake  and to utilize metabolic vulnerabilities as biomarkers or for the development of therapeutics. Targeted or untargeted measurements of metabolites allow to assess the metabolic state in an organism e uptake –3. Theree uptake . In expein vivo conditions as closely as possible  and are used to study in vivo or ex vivo metabolic changes in the heart. There are several clinically relevant radiopharmaceuticals such as 99mtechnetium-sestamibi  (18F]-Fluorodeoxyglucose ([18F]-FDG)  are less sensitive than radioactive probes, but in a single experiments stable isotope labeling approaches allow to assess multiple pathways simultaneously over longer experimental time periods. Like radiopharmaceuticals, stable-isotope tracers allow flux assessments, but at the same time these probes provide more in-depth analysis of metabolism both using targeted and untargeted discovery oriented analytical approaches. Increased availability and advancements in analytical techniques for metabolomics have made stable isotope tracers increasingly popular in studying cardiac metabolism in vivo and ex vivo. In this review, we describe recent advances in applying stable isotope tracers in cardiovascular research and discuss important aspects to consider during data analysis allowing accurate assessments of metabolic changes  in cost-efficient and safe way. At the same time metabolic conversions of labeled nutrients or small molecules allow to track the incorporation of isotopic label  into downstream products and pathways. The detection of specific metabolic products then allows to assess total metabolite changes alongside enzyme activities, flux rates, and overall contribution of specific pathways to the metabolic profile. Tracer studies in isolated perfused murine hearts are commonly used to evaluate metabolic changes in model systems that resemble possible . In vitrdioLite)  or 18F]8F]-FDG)  for inteF8F]-FDG) studies . Stable  changes .in vivo or ex vivo delivery of stable-isotope tracers including oral administration via diets, gavage or drinking water, direct intravenous infusion, injection, or perfusion of the heart  the Langendorff method and (2) the working heart preparation. The aortic perfusion of Langendorff remains a standard preparation and is popular to this date due to its simpler technical requirements and perfusion apparatus  or human participant. Blood or tissue samples are collected before and after tracer infusion, and isotopic enrichment is then analyzed. Another important factor during stable-tracer experiments is the dynamics of tracers and the determination of metabolite pool sizes , as well as turnover  of metabolites . For exapathways , whereas13C, 15N), number of labeled atoms  and position of labeled atoms will determine which products and pathways will incorporate the label. Any of these options increase the complexity of the experimental design and subsequent data analysis. Selecting the right combination of tracers allows delivering multiple probes and interrogation of multiple pathways simultaneously. Parallel tracing experiments are limited to few applications, but recent advances in high resolution mass spectrometry and development of new probes show promise. For a comprehensive overview of stable-isotope tracers and their readouts, readers are referred to Selecting the right tracer depends on the scope of the study and ultimately which metabolic readout is required for a given biological question. The substrate class , type of atoms  of glucose. To gain insight into the systems-wide response during disease development, it is also necessary to assess how metabolic alterations are linked to protein dynamics and posttranslation modifications .Considering the diversity and versatility of stable isotope tracers, which criteria can we apply to select the optimal probe for a given experiment? The chemical properties, including kinetics, specificity, and turnover, are critical components of tracer selection. Tracer kinetics must be almost identical to unlabeled compounds and probes should not accumulate in tissue. Non-specific binding to other proteins and lipids is generally a concern when using radionucleotides but similar demands need to be met by stable isotope tracers. Lastly, turnover time and tissue concentration of tracers should follow the range of non-labelled metabolites to avoid mass effects and optimal signal-to-noise ratios. Selection of tracers can also be based on metabolic read-outs and targeted toward a pathway of interest. Uniformly labeled tracers of common nutrients  can be used to determine how these nutrients are utilized in multiple pathways. Combination with single labeled tracers in parallel experiments then allows to detect specific metabolic fluxes. Different labeling strategies are best described using glucose because of its high abundance, commercial availability, and ease of use in experimental settings. For example, g pathway  82). Li. Li13C]grogenase , respectications , 84. Stag period . The advA prerequisite for accurate metabolic measurements is the sample collection and preparation. Metabolites have different turnover rates and differences in their abundance can easily lead to obfuscation of experimental data. For example, rapid degradation of NADPH and CoA derivatives during sample preparation have been well-documented , 87. Devin silico. In the context of stable-isotope tracer analysis, models are required to estimate flux distributions and explain labeling states for specific metabolites. These modeling approaches can describe the metabolic state of a biological system, but they cannot predict or explain it by identifying regulatory enzymes or principles   .13C vs. 12C and 2H vs. 1H in carbon- and hydrogen-labeling studies, respectively. Stable-isotopomer measurements are interpreted by defining mass-distribution vectors (MDVs) that reflect the incorporation of label from a tracer into downstream metabolites , 9213C vXj  represents the fraction of a metabolite's pool that corresponds to the jth labeled isotopolog and n is the maximum number of labeled atoms that a metabolite can incorporate. The fractional isotope enrichments, Xj, and their sum equal 1 or 100%. In stable isotope labeling, incorporation of j labeled atoms causes a mass shift of j atomic units nominal to the mass M of the unlabeled metabolite. Therefore, the MDV is often denoted as follows:Where each component IC denotes the isotopolog count for a given metabolite j and TC denotes the sum of all isotopolog counts. For example, the MDV for 13C-labeled glucose can be determined as:Where n = 6, because a glucose molecule has six carbon atoms where 13C-label can be incorporated. Xm0 represents the fraction of unlabeled glucose within the total metabolite pool, and Xm2 = 0.1 would indicate that 10% of the total glucose pool carries two 13C-labeled carbons. Based on the MDV it is not possible to assess where the incorporation of label occurred.with n = 1) are being used. For instance, carbon appears in the form for two stable isotopes, 12C and 13C, with a natural occurrence of ~98.9 and 1.1%, respectively. When using 13C-tracers, measurements need to be corrected for this natural occurrence. Several tools have been developed , highly abundant metabolites , or single labeled tracers (oped see  53–56) –56 n = 1jth row of the matrix jth labeled isotopolog. Determining the actual MDVs for each metabolite is a critical step prior to further data analysis and flux interpretation  is a constrained-based modeling technique that relies on balancing fluxes around metabolites within a network stoichiometry . Flux di13C-Metabolic flux analysis (13C-MFA) is most widely used in assessing flux in stable-isotope tracer experiments  are incorporated into a mathematical model of atom transfers and combined with measurements of nutrient uptakes and secretions, and biomass function. The distribution of fluxes throughout a cellular metabolism is mathematically estimated by iteratively solving a least-square regression problem of isotope labeling measurements and extracellular exchanges rates. The models applied to data regression comprise mass balances and isotopomer balances on all network components, thus often encompasses hundreds of equations. The sum of squared residuals (SSR) is defined as follows:eriments . In 13C-v) are estimated by the assumption of a steady state (equation 7) and minimizing SSRs between simulated (x) and experimentally derived (r) MDVs for a given metabolite S. The stoichiometry matrix of a given metabolic network is represented by N. Uncertainties, σ, can be estimated based on the root-mean square error of unenriched control samples and the standard error of measurement of technical MS replicates. For a metabolite S, steady state implies that the total rate at which it is supplied is equal to the total rate at which it is removed  consists of 64 carbon atom isotopomers , 4,096 hydrogen atom isotopomers , and combined 2.6 × 105 (26 × 212) carbon and hydrogen isotopomers. Therefore, additional methods have been developed to allow the integration of multiple isotopic tracer systems  EMUs are possible. The algorithm allows to identify a minimal set of EMUs to be considered in the simulation model, which reduces the overall number of variables and makes the computational analysis feasible even for multiple-tracer experiments and larger scale models  methods can be used . The output is presented as a mass spectrum where each peak represents a different ion with a specific m/z, and the peak length corresponds with a relative abundance. Combining MS with separation techniques like GC or LC enables analysis of complex samples based on separation times (or retention times) and m/z ratios. The variable ionization of compounds, ion suppression, and instrument cycling times inherently limit the number and type of metabolites that can be distinguished in a single run. Different ionization techniques have been developed including electron ionization (EI) and chemical ionization (CI) for compounds in gas-phase, as well as electrospray ionization (ESI) and matrix-assisted laser desorption/ionization (MALDI) which are suitable for thermally labile and non-volatile analytes . Another advantage over MS is quantifying multiple compounds without the need for calibration curves for each compound. MS and NMR spectrometry have evolved as the most common techniques in stable isotope tracer and metabolomics studies. However, there is no single analytical platform that can achieve a complete quantification and identification of all molecules within a sample. Therefore, more than one method must be employed for comprehensive metabolic profiling. When deciding on an analytical avenue, the choice primarily depends on the focus of the research study and the nature of the samples, and instrument and know-how accessibility.The goal of metabolomics is to comprehensively measure the metabolic composition of a sample in a single analysis. Different analytical platforms combine unbiased, rapid, reproducible, and stable analysis of complex samples in a single run. Each technology has its advantages and disadvantages in terms of sensitivity, throughput, reproducibility, robustness, quantitation, and suitability for specific chemical classes of metabolites. These analytical chemistry techniques range from high-performance liquid chromatography (HPLC), gas chromatography-mass spectrometry (GC-MS), liquid chromatography-mass spectrometry (LC-MS), gas chromatography combustion isotope ratio mass spectrometry (GC-C-IRMS), capillary electrophoresis-mass spectrometry (CE-MS), Fourier transform-ion cyclotron-mass spectrometry (FT-ICR-MS), and nuclear magnetic resonance (NMR). Broadly, analytical chemistry techniques can be divided into (i) separation, (ii) identification, and (iii) quantification of metabolites from a complex sample . The separation of metabolites is accomplished using chromatography  or CE. Sample detection is then achieved using fluorescence, ion conductivity, or spectrometry . MS and NMR are different types of spectrometers that measure physical characteristics over a given spectrum. MS measures masses within a chemical sample through their mass-to-charge ratio (m/z), while NMR measures the variation of nuclear resonant frequencies. Both detection techniques can be combined with a different separation method allowing customized application methods for a specific type of sample and compound. MS and NMR are widely used in metabolomics to detect and analyze stable isotope tracer studies, such as analytes . After iications . ImplemeSingle-cell analysis is a powerful tool to interrogate cellular heterogeneity within the same tissue, allowing for refined assessment of phenotypes and biomarker discovery. Metabolomics at the single-cell level holds the promise to obtain precise spatial and temporal information allowing to assess cell differentiation and division, cell-cell interactions, metabolic cooperation between cell populations and a detailed stress response analysis. In comparison to other omics technology, single-cell metabolomics faces several challenges because of the chemical diversity of metabolites, wide range of concentrations, sample stability, and lack of amplification . Recent in vivo will be critical to identify metabolic vulnerabilities. Ultimately, these efforts may help clinicians to tailor therapeutic interventions based on the metabolic profile of the intact heart.Understanding how reprogrammed metabolism supports cardiac adaptation during stress and diseases requires a systems-wide approach. Translational models that recapitulate cardiac pathophysiology are critical to advance our understanding of CVDs and to utilize metabolic vulnerabilities through the development of novel therapeutics or biomarker identification. Stable-isotope labeling and mathematical modeling require multidisciplinary collaborations to bridging animal models into patients. Likewise, clinical studies should inform animal models for mechanistic hypothesis-driven testing. Challenges persist in accurate estimations of fluxes from stable-isotope tracers and integration into clinical trials. Evidence indicates that metabolic phenotypes are a key determinate of disease development and progression. Advancements in analytical methods to quantify metabolic phenotypes AK designed and wrote the manuscript.This research was supported by R00-HL-141702 and institutional funds from Cedars-Sinai Medical Center to AK.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. 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Escherichia coli, noisy regulation of lower glycolysis and citric acid cycle is responsible for large variations in respiratory metabolism. We found that these variations are Pareto optimal to maximization of growth rate and minimization of lag time, two objectives competing between fermentative and respiratory metabolism. Metabolome-based analysis revealed the role of respiratory metabolism in preventing the accumulation of toxic intermediates of branched chain amino acid biosynthesis, thereby supporting early onset of cell growth after carbon starvation. We propose that optimal metabolic tradeoffs play a key role in shaping and preserving phenotypic heterogeneity and adaptation to fluctuating environments.Despite mounting evidence that in clonal bacterial populations, phenotypic variability originates from stochasticity in gene expression, little is known about noise-shaping evolutionary forces and how expression noise translates to phenotypic differences. Here we developed a high-throughput assay that uses a redox-sensitive dye to couple growth of thousands of bacterial colonies to their respiratory activity and show that in  E. coli can mediate and promote population diversification.It is unclear how noise in gene expression propagates to phenotypic heterogeneity in clonal bacterial populations. Here, the authors explore how variability in central sugar metabolism in  While not always beneficial3, population diversification is a key mechanism to adapt to fluctuating environments4, in that it can allow genotypes to persist in the face of adverse conditions. For example, growth rate heterogeneity in bacterial populations contributes to survival upon exposure to antibiotics6, and differences in the onset of cell division can favor tolerance and evolution of antibiotic resistance9. A number of different molecular mechanisms can give rise to phenotypic heterogeneity12. Typically, these are cellular processes such as stochastic gene expression14 and stochastic partitioning of molecules at cell division15, which ultimately manifest in the variation of protein copy numbers per cell. Recent experimental evidence showed that fluctuations in the expression of growth-limiting enzymes can be responsible for growth fluctuations and the transmission of noise to other genes10. While mounting single-cell studies have shown gene expression to vary within a population of genetically identical cells under constant conditions17, which cellular processes are predominantly affected by noisy gene expression and whether noise propagation is shaped by optimality-based principles are still open questions.Heterogeneity between individual bacterial cells growing under macroscopically identical conditions can have important functional consequences19. However, whether and how fluctuations in metabolite levels can permeate the metabolic state of a cell and affect the ability to adapt to changing environments is unclear. While technological advances enabled monitoring levels of metabolites at single cell21, directly probing cell-to-cell variability in the turnover of metabolites remains challenging22, ultimately hampering the study of metabolic heterogeneity and its functional implications. By developing an assay to directly measure variability in the respiratory rates among colonies of Escherichia coli growing on solid media, we show that noisy transcriptional regulation of lower glycolytic and citric acid (TCA) cycle enzymes can be readily transmitted to metabolic heterogeneity. Surprisingly, we found that individual colonies within an isogenic population exhibit largely different respiratory activities, and that while costly23, increased respiratory activity facilitates the early onset of cell growth after starvation by preventing the accumulation of toxic intermediates. We propose that variability in respiro-/fermentative metabolism can be fitness invariant, allowing cells to maintain a greater variation in enzyme expression and potentially employ diverse adaptive strategies to environmental changes.Despite the expectations that stochasticity of biochemical reactions should have negligible effect, theoretical models demonstrate how noise in transcription and translation of metabolic enzymes can affect levels of metabolic reactantsE. coli13   processes affected by standard noise levels consist of lowly expressed genes involved in DNA repair, DNA recombination, and chemotaxis  exhibit larger than expected cell-to-cell variability relative to other proteins with similar expression levels , indicating that there may be selective pressures for noise reduction26. These results suggest that, despite the key role in bacterial fitness of proteins involved in central metabolism, fluctuations in their expression, translation, or degradation may have been preserved by evolution and can be a major source of phenotypic heterogeneity. To test if deviations of proteins from mean-noise levels could be the results of stochasticity in their gene expression regulation, we searched for transcription factors (TFs) regulating the expression of proteins with large deviating noise. We found that Cra, a key regulator of flux in lower glycolysis27, is significantly enriched  for targets that exhibit high deviating noise levels  Fig. 13, we hyxis Fig. , we founxis Fig. . More spls Figs.  and S1. els Fig. . Altoget28. However, whether and which noisy enzymes are able to cause fluctuations in the rates of the corresponding enzymatic reactions, and hence may affect phenotypic heterogeneity, is still unclear. To address this question, we integrated bulk measurements of protein copy-numbers29 and metabolic fluxes30 in E. coli growing in minimal media with seven different carbon sources. By quantifying the linear dependency between changes in the copy number of 40 enzymes and 25 rates of the corresponding metabolic reactions, we found that changes in the abundance of enzymes in lower glycolysis  and citric acid (TCA) cycle  directly scale with changes in fluxes  at the single-cell level are lagging behind. As a result, much less is known about heterogeneity at the level of metabolism, and whether such variability can have direct functional consequences. To overcome this problem, instead of single-cell analytical methods we developed a multiparametric assay that monitors phenotypic and metabolic heterogeneity of thousands of colonies-forming E. coli growing on solid agar media   reduction in the variability of respiratory rates as well as lag times , we observed a continuum of colonies exploiting different metabolic strategies. How can this metabolic diversity be maintained? While in a given constant environment, only one strategy is optimal, in a naturally fluctuating environment the advantages of short lag time or fast growth rate might average out. We hypothesized that variability in respiro-/fermentative metabolism is fitness-neutral—i.e., cells can be equally optimal in spite of different metabolic strategies. Colonies that find an optimal compromise between two competing objectives are called Pareto optimal41—i.e., a colony is Pareto optimal if there exists no other colony that is at least as good in all objectives, but strictly better in at least one objective. By using a simple exponential model of bacterial growth, one can derive that in equally fit cells—i.e., cells able to reach the same number of divisions in a fixed period of time—growth rate and lag time are inversely related (Supplementary text). Hence, according to our hypothesis, the space of feasible growth rates and lag times should be delimited by a Pareto front41 approximating an inverse relationship between the two. Moreover, natural selection of optimal fitness will force colonies to operate metabolism in the proximity of the optimal tradeoffs42, and hence colonies shall not randomly occupy the space of feasible growth rates and lag times. Moreover, because of the already known direct proportionality between fermentative metabolism and growth rate23, we expect that in Pareto optimal colonies, growth rate negatively scales with the respiratory rate (Supplementary text: lag time vs. growth rate). Our theory is consistent with growth kinetics observed in wild-type E. coli colonies growing on glucose as the sole carbon source  operate metabolism so as to require a minimum adjustment between growth on glucose and acetate42, we predicted that FSw would favor respiratory metabolism, while slow-switchers (SSw) would feature higher fermentative metabolism . To test our predictions we used previously published data42 measuring growth rate, glucose-uptake, and acetate secretion for seven FSw and eight SSw randomly selected clones grown in liquid glucose minimal medium. In agreement with our predictions, we found that FSw on average have significantly  higher respiratory activity and slower growth rates than SSw  with an isopropyl β-D-1-thiogalactopyranoside (IPTG) inducible promoter to modulate the arcA expression (arcA+). ArcA is a key repressor of genes involved in the TCA cycle and oxidative phosphorylation. While arcA deletion causes an increased carbon flux into the TCA cycle44, respiration is inhibited and acetate fermentation increased upon arcA overexpression45. Hence, we expect lag times to increase with an increased expression of arcA. To test this hypothesis, we grew wild-type E. coli, the ΔarcA and arcA+ strains in batch liquid cultures of glucose minimal medium up to mid-exponential phase ~1), washed the cells, and incubated them in M9 medium without carbon sources together with the IPTG inducer (0.02 mM) for 2 h. Next, we resuspended cells in M9 medium with glucose and monitored OD600 in a plate reader using different levels of IPTG inducer. Consistent with a previous study45, mild induction of arcA (below 0.03 mM IPTG) is able to improve growth rate with respect to the wild-type  or gluconeogenic  substrate as sole carbon sources  lower levels of biosynthetic intermediates in branched-chain amino acids (BCAA) , including the main precursor pyruvate and the end product valine leucine  often involves negative feedback loops in which metabolites can directly regulate transcription factors activity56. Such type of regulatory interactions can function as negative integral feedback and provide quasi-adaptation to small perturbations58, thereby increasing the number of generations that are necessary for daughter cells to significantly diverge from the transcription factor activity of the ancestor. Therefore, while clearly different from single-cell measurements, by simultaneously monitoring thousands of colonies and their variation in growth kinetic parameters and respiratory rates, we could make experimentally testable predictions on the functional impact of metabolic diversity on phenotypic heterogeneity.Here we monitored phenotypic and metabolic heterogeneity arising at a single colony level. A key advantage of this approach is the ability to directly monitor the variability in metabolic rates rather than reporting on the level of individual metabolites. It is worth noting that bacterial colonies develop in complex 3D structures in which individual bacteria can experience different metabolic gradientsIn this study, we showed that the regulation of key proteins involved in funneling carbon into the TCA cycle plays a fundamental role in the phenotypic heterogeneity of colonies growing on solid media. While not all regulatory solutions can be equally optimal, the existence of multiple and largely diverse metabolic tradeoffs that are fitness-invariant can be a major driving force preserving and shaping phenotypic heterogeneity and plasticity—i.e., the ability to develop varied phenotypes under fluctuating environmental conditions. Independent experimental evidence of planktonic cultures that evolve in coexisting subpopulations exhibiting the same predicted tradeoffs between lag time, growth rate, and respiratory activity, suggests that the same concepts can be generalized to largely diverse growth conditions.arcA deletion significantly suppresses resistance evolution59, provides a basis to link independent experimental evidence relating lag time and energy metabolism61 to antibiotic tolerance and resistance7. Consistent with our findings, mounting evidence associated evolutionary adaptation of bacterial persistence to mutations in enzymes of the respiratory metabolism, such as the proton-pumping NADH:ubiquinone oxidoreductase (Nuo complex)62. We demonstrated that homeostasis in BCAA can play a fundamental role during the early growth phases. We propose that valine/leucine and isoleucine and possibly intermediates in their biosynthesis can function similarly to toxin–antitoxin systems mediating bacterial dormancy. Toxin–antitoxin modules, such as HipAB63, have well-established roles in regulating the bistability of clonal populations64 and in the formation of growth-arrested persisters63. In a similar way, the accumulation of toxic BCAA intermediates in clonal cells with different metabolic activities can lead to cellular stasis by inhibiting BCAA biosynthesis and/or carbon uptake49, ultimately affecting the biosynthesis of essential components for cell growth and division. The existence of different Pareto-optimal metabolic strategies within a clonal bacterial population, on the one hand, could represent a form of metabolic «division of labor»65 and, on the other hand, could provide a bet-hedging strategy to withstand unforeseen challenges, such as periods of nutrient limitations or antibiotic treatments6.Moreover, explaining colony-to-colony variations in growth rate and lag time by changes in respiro-/fermentative metabolism, together with the observation that an 8. The existence of a tradeoff between shortest lag time and maximum growth rate and the ability to shift between these cellular objectives by modulating respiro-/fermentative metabolism can pave the way to alternative therapeutic strategies fighting the emergence of tolerant cells and eventually the appearance of drug resistance67, potentially beyond antimicrobial treatments68.Overall, our findings can have important implications in diverse theoretical and applicative fields. Understanding the origin and functional impact of metabolic heterogeneity can open new opportunities in metabolic engineering and synthetic biology, to incorporate noise transmission in the design of more efficient biosynthetic strategies. Moreover, fluctuations in respiro-/fermentative metabolism can be of particular significance in the design and interpretation of experimental evolutionE. coli BW25113 or mutants listed in Table 2HPO4 2H2O, 3.0 g KH2PO4, 1.5 g (NH4)2SO4, and 0.5 g NaCl and was adjusted to pH 7 before autoclaving. The following components were filter-sterilized separately and then added : 1 mL of 1 M MgSO4, 1 mL of 0.1 M CaCl2, 1 mL 0.1 M FeCl3, and 10 mL of a trace element solution containing (per liter) 180 mg ZnSO4 7H2O, 120 mg MnSO4 H2O, 180 mg CoCl2 6H2O, and 120 mg CuCl2 2H2O. Carbon source solutions were filter-sterilized and added separately to the medium, 5 g/L glucose, fructose, acetate. Agar plates were made by adding 15 g/L of Agar.For all growth experiments, Strains used for the experiments discussed in the main text, their origin, and corresponding reference.600 in 96-well plates with the multiwell reader Infinite  at 37 °C with shaking. The growth rates were extracted by fitting the exponential part of the growth. An iterative approach was used to find the time window of at least 100 min with the maximum exponential growth rate. The intersection between the initial OD of the inoculum and the extension of the exponential growth curve yielded the lag time69.The growth rate and lag time in batch liquid culture were measured by monitoring OD70. When necessary, p values were corrected for multiple tests by q value estimation71. The network of TF-target genes reported in72 was used to identify TF regulating proteins with large deviating noise.Statistical analyses were performed using Matlab R2018b (MathWorks). Gene ontology and metabolic pathway enrichment analysis, and enrichment of noisy enzymes in TF-target genes were based on an iterative hypergeometric test described in Ref. x and y coordinate on the plate, size at each time point, and RGB intensity. Full details and computer codes are available on GitHub https://github.com/Dfernand1795/PetriScanner2.Overnight cultures were diluted in LB or M9 media 1:1000. Cells were grown up to an OD of 1 before plating at appropriate dilutions on solid agar medium. Standard PC scanners  were used to acquire images at 800 dpi resolution of Petri dishes every 10 min. Acquired images were analyzed with an in-house image analysis software implemented in ImageJ IJ1 Macro and Python. In order to improve the accuracy in detection of bacterial colonies the software corrects for changes in light across plates , performs colony segmentation  and tracking. Finally, outliers/artifacts are filtered out. The final data returns for each colony p) abundance and noise from single-cells of E. coli from13. Consistent with other studies, at low copy number (μp) the noise  is dominated by intrinsic noise , while at high expression levels noise is dominated by extrinsic factors, such as fluctuations in ribosomes, polymerase, transcription factors and partitioning of the population between the cell-cycle stages75. To estimate average noise levels at different protein abundance, we used a moving average smoothing method on the data reported for 1018 proteins13. Specifically, we used the malowess function in Matlab, where for each protein, the expected average noise level  and lag-time (Tlag). Fitting was performed in Matlab 2018b using the lsqcurvefit function using the Truest-region algorithm for optimization from 50 multiple start points . To determine the maximum respiratory rate we use a linear model and found the time interval (consisting of at least ten time points) with the largest proportional coefficient between time and average red intensity of a colony. α is the estimate for maximum respiratory rate (AU/h) and β is an offset value.The Gompertz function is able to describe asymmetrical growth curves assuming that at the time of inflection 21 was transformed into E. coli bacterial strains BW25113 and BW25113-ΔarcA (Keio:JW4364) expressing a T7 RNA polymerase (araB::T7RNAP-tetA). For each sample, a single bacterial colony was grown in LB medium for 6 h at 37 °C under agitation (170 RPM). 30 microliters of culture were pelleted, resuspended in 3 ml of M9 medium and further diluted 1:10 in 3 ml of M9 medium supplemented with Glucose 0.5%, ampicillin 50 µg/ml and arabinose 0.01%. Cultures were grown for 16 h at 37 °C under agitation (170 RPM) and typically reached OD600 values between 0.05 and 0.3. For the starvation procedure, cells were washed twice and resuspended in 3 mL of M9 medium only supplemented with ampicillin 50 µg/ml. Samples were brought back to the shaker for two hours before addition of glucose at 0.5%. Cultures were sampled for FACS analysis right before the starvation phase, after 30 and 120 min of starvation and after one and 15 min after addition of glucose. 30 µl of sampled culture was diluted in PBS containing propidium iodide . FACS measurements were performed on a BD FACSaria III Cell sorter. Fluorescence was measured with the following channels Ex488_LP495_BP514/30-H, Ex405_LP502_BP530/30-H and Ex488_LP610_BP616/23-H .The low concentration ATP reporter plasmid pRS-QUE7muΔarcA E. coli overnight cultures growing on M9 minimal medium were diluted in fresh M9 glucose minimal media and grown at 37 °C until exponential phase and an OD600 of 1. Cells were washed twice with M9 medium without carbon source and 700 μL cell cultures were distributed in 96 deep well plates and incubated at 37 °C until shaking at 2 RCF. Samples for metabolomics profiling were taken during exponential growth prior to carbon deprivation and 5, 10, 15, 30, 60, 90 and 120 min after carbon starvation. In total, 50 μl of whole cell broth was directly transferred to 150 μl extraction liquid solution containing 50% (v/v) methanol and 50% (v/v) acetonitrile at −20 °C. The extraction was carried out by incubating the samples for 1 h at −20 °C. Samples were centrifuged for 5 min at 1789 RCFand 80 μl of the supernatant was transferred to 96 well storage plates and stored at −80 °C (Supplementary Data 77. Mass spectra were recorded from m/z 50 to 1000 using the highest resolving power (4 GHz HiRes). All steps of mass spectrometry data processing and analysis were performed with MATLAB . Detected ions were matched to a list of metabolites based on the corresponding molar mass78. For the full list of metabolites used for annotation see Supplementary Data Wild-type and Further information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Reporting Summary


Saccharomyces cerevisiae. Although yeast physiology in laboratory strains is well-studied, the metabolic states under industrially relevant scenarios such as winemaking are still not sufficiently understood, especially as there is considerable variation in metabolism between commercial strains. To study the potential causes of strain-dependent variation in the production of volatile compounds during enological conditions, random flux sampling and statistical methods were used, along with experimental extracellular metabolite flux data to characterize the differences in predicted intracellular metabolic states between strains.Metabolomics coupled with genome-scale metabolic modeling approaches have been employed recently to quantitatively analyze the physiological states of various organisms, including It was observed that four selected commercial wine yeast strains  produced variable amounts of key volatile organic compounds (VOCs). Principal component analysis was performed on extracellular metabolite data from the strains at three time points of cell cultivation . Separation of the strains was observed at all three time points. Furthermore, Uvaferm at 24 h, for instance, was most associated with propanol and ethyl hexanoate. R2 was found to be associated with ethyl acetate and Opale could be associated with isobutanol while Elixir was most associated with phenylethanol and phenylethyl acetate. Constraint-based modeling (CBM) was employed using the latest genome-scale metabolic model of yeast (Yeast8) and random flux sampling was performed with experimentally derived fluxes at various stages of growth as constraints for the model. The flux sampling simulations allowed us to characterize intracellular metabolic flux states and illustrate the key parts of metabolism that likely determine the observed strain differences. Flux sampling determined that Uvaferm and Elixir are similar while R2 and Opale exhibited the highest degree of differences in the Ehrlich pathway and carbon metabolism, thereby causing strain-specific variation in VOC production. The model predictions also established the top 20 fluxes that relate to phenotypic strain variation (e.g. at 24 h). These fluxes indicated that Opale had a higher median flux for pyruvate decarboxylase reactions compared with the other strains. Conversely, R2 which was lower in all VOCs, had higher median fluxes going toward central metabolism. For Elixir and Uvaferm, the differences in metabolism were most evident in fluxes pertaining to transaminase and hexokinase associated reactions. The applied analysis of metabolic divergence unveiled strain-specific differences in yeast metabolism linked to fusel alcohol and ester production.Overall, this approach proved useful in elucidating key reactions in amino acid, carbon, and glycerophospholipid metabolism which suggest genetic divergence in activity in metabolic subsystems among these wine strains related to the observed differences in VOC formation. The findings in this study could steer more focused research endeavors in developing or selecting optimal aroma-producing yeast stains for winemaking and other types of alcoholic fermentations.The online version contains supplementary material available at 10.1186/s12934-021-01694-0. Saccharomyces cerevisiae (S. cerevisiae)) strains to complete alcoholic fermentation and produce desirable aroma compounds, so-called volatile organic compounds (VOCs). It has been assessed that wines contain more than 1000 different VOCs of which more than 400 are directly attributed to yeasts [The ability to produce wines with specific sensory profiles would be immensely beneficial to the global wine industry. In addition to characteristics coming from the grape juice, this optimal production is heavily contingent upon commercial yeast  was used to analyze fluxes relative to the stage of fermentation. Fig. . From thIn order to reveal the important fluxes that drive the variation in different time points , a variable factor map was plotted, and these variables are shown with a color scale based on their cos2 values ). The top 20 reactions based on absolute differences are listed in Table Flux sampling was applied using Yeast 8.4.2 and constrained using experimental flux data at several times during yeast cell growth  . The clustergrams were constructed from the median values of the flux sampling analysis of the top 20 absolute different reactions Fig. . This waIn this work, a CBM of random flux sampling was used to examine the differences in intracellular metabolic flux states of commercial wine yeasts under typical enological fermentation conditions. The fluxes were derived from experimental measurements of numerous nutrients, including amino acids and sugars, as well as primary and secondary products, including key VOCs at different phases of cell growth. They were used to constrain the model for flux sampling analysis. The intracellular metabolic flux states were successfully characterized without the need of designating an objective function for optimal states as was necessary in earlier works , 38, 40.While several earlier studies have focused on integrating extracellular metabolite concentration or flux measurements with yeast GSMMs, those studies pertained to nutrient-rich media or aerobic processes , 43, 44.Opale yeast was associated with isobutanol, isoamylol, and isoamyl acetate, therefore it makes sense that it was higher in median flux of the pyruvate decarboxylase reaction (r_0959) because this reaction leads to isoamylaldehyde which is a precursor for isoamylol and isoamyl acetate. On the other hand, R2 which was lower in all VOCs, has higher median fluxes going toward central metabolism  and a lower median flux in the reaction associated with glycerol-3-phosphate dehydrogenase (NAD) (r_0491) which is related to the synthesis of secondary metabolites (VOCs). The other two strains, Elixir and Uvaferm, were associated with 2-phenylethanol, propanol, and ethyl hexanoate. Therefore, it is reasonable that the median fluxes for reactions r_0216, r_0219, r_0064, and r_0491 were higher as these reactions lead to the precursors for these VOCs. Since these two strains were lower in isoamylol and isobutanol, it makes sense that the median flux for the hexokinase associated reaction (r_0534) was higher than that for Opale.In this work, it was observed that Uvaferm and Elixir strains behaved similarly while Opale and R2 were the most distinct. The results point to amino acid and pyruvate metabolism being more active in Opale. Therefore, Opale is associated with isoamylol, isobutanol, and isoamyl acetate. R2 was shown to have lower activity in amino acid and pyruvate metabolism, and hence has lower levels of VOCs than the other strains. Uvaferm and Elixir are similar to each other when examining central carbon, pyruvate, amino acid, and fatty acid degradation metabolism where we predicted higher median fluxes. That would explain why Uvaferm and Elixir produce higher amounts of 2-phenylethyl acetate and ethyl hexanoate, and lower amounts of ethyl acetate. Overall, the phenotypic differences among the strains are predicted to stem from major differences in pyruvate, tyrosine, glycine, serine, threonine and central carbon metabolism. Random flux sampling also predicted substantial differences in metabolic pathways responsible for the generation of secondary metabolites such as Ehrlich pathway. Using Yeast 8.4.2 coupled with our flux sampling approach allowed us to compare predicted fluxes of relevant pathways at different growth phases among the commercial yeast strains. Moreover, by using genome-scale CBM, some insight could be gathered into the global, interconnected pathways responsible for the variation in metabolism and, thus, aroma-producing capabilities among the strains. This work indicates central carbon, amino acid, sulfur, and lipid metabolism play varying roles throughout fermentation to lead to strain-specific characteristics. Results highlighted here reveal the need for more studies to comprehensively investigate nitrogen and lipid metabolism as well as central carbon metabolism to understand their impact on yeast aroma formation. For instance, studies have confirmed the essential role acetaldehyde has within core carbon metabolism and have linked the enzyme ADH2 to oxidizing ethanol to form acetaldehyde . SubsequFrom the flux sampling analysis, it was observed that not only ADH2 associated reactions are accounted for the strain variation, but also PDC1, PDC5, and PDC6 pyruvate decarboxylase as well as 3-methyl-2-oxopentanoate decarboxylase related reactions. This result highlights the interdependent relationship of carbon and nitrogen metabolism and how the expression of intricate pathways can lead to aroma differences. PDC1, PDC5, and PDC6 are involved in the Ehrlich pathway, leading to the irreversible decarboxylation of the α-keto acid to an aldehyde . This paThe CBM approach utilized in this work analyzed and compared the various predicted intracellular metabolic flux states of commercial yeast strains during enological fermentation, including examining the metabolic shifts within the production of VOCs and the consumption of nutrients . The intracellular flux distribution predictions show qualitative agreement with the specific variations found from performing principal component analysis on extracellular flux values. Furthermore, these results indicate elaborate fluctuations and distinctness in nitrogen, carbon, and lipid metabolism that lead to strain-specific differences in VOC formation. From the changing metabolic flux distributions among the strains, the differences in GPR activity were compared and highlighted. Therefore, probable genetic differences among the strains could be inferred and targets for genetic modification could be explored. Although the results in this study identified nitrogen metabolism which is supported by other works as causing VOC specific strain behavior, the results also show carbon and lipid metabolism play a role in VOC formation. This revelation points to the need for additional studies to explore impact of other parts of metabolism on VOC formation in yeasts. Overall, the approach and insight gained here were in good agreement with experimental observations and other studies, making this a promising approach for future use in studies related to individual fluxes of important metabolites in enological conditions and comparing metabolic differences between commercial wine yeast strains. In addition, this work help spur new quests in creating more precise aroma producing wine yeast strains.The experimental data used in this study is from Scott et al. . In thisTM(Uvaferm), Lalvin R2TM (R2), Lalvin ICV OpaleTM , and VitilevureTM Elixir YSEO (Elixir). All strains were Lallemand  commercial yeast strains. In addition, all yeast strains were obtained from the UC Davis Enology Culture Collection containing the following culture collection numbers: Uvaferm (UCD4004), R2 (UCD2033), Opale (UCD2797), and Elixir (UCD4008). These yeast strains were selected based on the different fermentation and aroma-producing performance attributes reported by the manufacturer.The yeast strains used in experiments were Uvaferm 43Yeast 8.4.2 [S. cerevisiae, S288C, a laboratory yeast strain not typically used in industrial settings. However, since this study was applied to fermentations under enological conditions, the GSMM was modified to reflect the anaerobic state of metabolism appropriately. Here, a strategy was applied as described by Heavner et al. [Yeast 8.4.2 includes expanded coverage of aroma-associated pathways such as an extended Ehrlich pathway, more ester formation reactions, and enhanced sulfur reduction pathways as previously performed and described in the literature [The GSMM employed in this study was st 8.4.2 , which ir et al. , constraz et al. , 53 . Principal component analysis (PCA) was conducted using the FactoMineR package [Data analysis was performed using R . ) and many were considered irrelevant because they are reactions describing transport between compartments. Finally, histograms were generated to characterize the solution space of the 20 key reactions, which contributed the metabolic difference among the strains related to experimental criteria. These histograms illustrated respective reaction fluxes along with solution frequencies. Random sampling was performed using Cobra Toolbox 3.0 [https://github.com/opencobra/COBRA.tutorials/tree/master/analysis/uniformSampling).Random flux sampling is an adept approach used to characterize the solution space within a GSMM network. This method involves obtaining a statistically significant number of solutions that have been uniformly distributed throughout the entire solution space . By usinlbox 3.0  functionModeling was performed in MATLAB® 2018b  using Cobra Toolbox 3.0  and implAdditional file 1: Table S1. The top 20 reactions that hat represented the greatest percent flux variation among the distributions among yeast strains for every condition.


Data of muscle pH and metabolite accumulation were based on published research for intense exercise to contractile failure within ~3 min, from which capacities and time profiles were modeled. Data were obtained from prior research for multiple competitive cation dissociation constants of metabolites and the chemical reactions of non‐mitochondrial energy catabolism, and pH dependent calculations of ~H+e from specific chemical reactions. Data revealed that the 3 min of intense exercise incurred a total ATP turnover of 142.5 mmol L−1, with a total intramuscular ~H+ exchange (‐‘ve = release) of −187.9 mmol L−1. Total ~H+ metabolic consumption was 130.6 mmol L−1, revealing a net total ~H+e (~H+te) of −57.3 mmol L−1. Lactate production had a ~H+te of 44.2 mmol L−1 (for a peak accumulation = 45 mmol L−1). The net ~H+te for the sum of the CK, AK, and AMPD reactions was 36.33 mmol L−1. The ~H+te from ATP turnover equaled −47.5 mmol L−1. The total ~H+ release to lactate ratio was 4.3 (187.9/44). Muscle ~H+ release during intense exercise is up to ~4‐fold larger than previously assumed based on the lactic acid construct.The purpose of this investigation was to present calculations of fractional H + exchange (~H+e) from the chemical reactions of non‐mitochondrial energy catabolism were performed to quantify the extent of ~H+ release during 3 min of intense muscle contractions. The total ~H+ release was −187.9 mmol L−1 and total ~H+ consumption was 130.6 mmol L−1. The largest sources of ~H+ release were from glycolysis and ATP hydrolysis and the largest contributor to ~H+ consumption was lactate production (44.2 mmol L−1).Calculations of fractional H For example, the Nobel Prize work of Hill and Meyerhoff in 1922  consumer and as such opposes not contributes to metabolic ~H+ release. For example, Robergs et al.  for binding with ionizable groups of metabolites  and many reactions presented in biochemical textbooks do not present ~H+ balanced chemical reactions, thereby misleading readers of the actual involvement of ~H+ release or consumption in many reactions of cytosolic energy catabolism. Even reactions that do not directly involve covalent H+e still have ~H+e due to differences in weak ~H+ dissociation or association between the substrates and/or products of the reaction across the physiological pH range  as proposed by Stewart Stewart, , 1983. T+ from muscle to blood , though each method has its own limitations as explained in the Discussion.Regardless of the mechanism(s) accounting for cellular metabolic acidosis, the last 80 years of research inquiry of muscle metabolic acidosis during intense exercise documents a clear cellular acidosis that directly alters systemic  acidosis by multiple transport mechanisms of H+e of the creatine kinase (CK) reaction prior to the meaningful activation of and substrate flux through the glycolytic pathway , which was further compared to the data for ATPto from Bangsbo et al.  were used as an external validation of the computed data for ATPto from this research.The list of metabolites and reactions included in this computational evaluation of skeletal muscle ~Hs et al.  and are s et al. , 1987b wo et al.  and Medbo et al. . The ATP−1 dry wt. or mmol kg−1 wet wt. to mmol L−1 muscle water based on the assumption of the cellular mass being 76% water   Table . For lacn Figure . Thereaft et al. .+ exchange coefficients (~H+) of each reaction from Robergs et al. (2017) were imported into the software. Metabolite data were then corrected based on the subtraction of resting values (ΔM) (Equation incr) at 1 Hz . The polynomial coefficients for the accumulation of each metabolite and also the pH dependent fractional HEquation  and thenEquation .a), which was assumed to represent production in this anoxic model, the increment metabolite data were adjusted based on the equations of Table a was equal to the accumulation (or breakdown) of pertinent substrates or products based on the integral of the increment data . Noted examples of this approach are for the LDH and CK reactions. For reactions involved in sequential multiple reaction pathways, Mf was based on adjustment to the final accumulating product of the pathway. For glycolysis during the modeled ATP demand of this study, this was lactate. As such, the muscle lactate accumulation data were used to derive all other metabolite flux calculations from glycogenolysis and glycolysis, as presented in Table f was quantified by adding the profiled Ma of muscle pyruvate accumulation to the Mf of the LDH reaction . This pyruvate kinase Mf was then added to the Ma of phosphoenolpyruvate to compute the enolase reaction Mf. The enolase Mf was then used as the core component of the preceding reaction, as shown in the equations of Table To compute metabolite accumulation (MEquation . For reatf) was the integral of the Mf data corrected for carbon numbers, the multiple reactions of aldolase and TPI at the start of phase‐II of glycolysis, as well as for the summation of the AK and AMPD reactions to account for flux through the AK reaction. Note that for several reactions, where limited data exist for their accumulation in skeletal muscle, metabolite accumulation for G1P, F1,6P, DHP, G3P, 3PG, 2PG, and PEP were assumed to fit the same profile.Total metabolite flux  pH dependent calculation of the ~H+ exchange (H+e). For this, the Mf data were multiplied by the pH dependent ~H+ coefficient data (42) for the given pH at each data point, and then each ~H+e metabolite array for the 3 min exercise condition was integrated to yield the total ~H+e (H+te) for the specific reaction .The calculation of MEquation . The onlto, the flux of substrate through the reactions that regenerate ATP were summed to produce total ATPto  pH. This mathematical relationship is expressed in Equation (+) buffering  as this (after baseline correction) equaled the LDH Mf and was the basis for Mf and Mtf estimation of all reactions of glycolysis  and chemical reactions, and the subsequent H+e and H+te  was able to be calculated from the Mf of the ATP regenerating reactions  added to the temporal profile of the decrease in muscle [ATP]  equated to 142.46 mmol L−1, and PFK reaction corrected ATPto equated to 111.35 mmol L−1. The net release of inorganic phosphate (Pi) (19.74 mmol L−1) is the balance of Pi release from the PFK reaction corrected ATPto minus the Pi consumption in the phosphorylase and G3PDH reactions which equaled 91.61 mmol L−1. This simultaneous Pi release and metabolic consumption during cytosolic energy catabolism adds complexity to understanding the role of Pi as a H+ buffer, as will be explained in the Discussion. Also, note that the negative data for Pi release in Figure a.The M] Figure . The diff and H+e did not conform to a standard polynomial function of any order. Consequently, figure data of the temporal profiles of the pH dependent H+e for the main reactions of interest  total buffering capacity  equated to 187.86 Slykes. The total ~H+ release to lactate accumulation ratio was 4.27 (187.86/44). Use of the now outdated and incorrect stoichiometric lactate derivation of H+ release would have revealed an erroneous buffer capacity of 44 Slykes (ΔLa to ΔpH ratio); an error factor equal to the H+ release to [La−] ratio.Total H+ balance and ADP balance revealed large changes of −12.63 and 24.63 mmol L−1 respectively. For NAD+ balance, this means that there was a decrease in NAD+ of this amount by the end of the exercise bout, which then means that the relative redox potential would have had a 25.26‐fold decrease. For ADP balance, this is a remarkably large ADP release which clearly does not result in an appreciable ADP accumulation, and such a result discrepancy is explained in the Discussion.Each of NAD4+e for all chemical reactions of non‐mitochondrial energy catabolism to model cytosolic Mf during 3 min of intense exercise to contractile failure. Data for Mf and ~H+e was used to calculate the H+te for all pertinent reactions. The results revealed an appreciably large ~H+te for each of glycolysis and ATP hydrolysis, and a fourfold larger total ~H+ release to lactate ratio than previously assumed from the lactic acidosis construct. The most ~H+ releasing reaction of glycolysis was the G3PDH reaction, which involves a more complex understanding of cellular inorganic phosphate metabolism than currently acknowledged. It will be argued that this research provides the most accurate and thorough quantification of cellular ~H+e to date and the implications of these results to the biochemistry of cellular energy catabolism and metabolic acidosis will be discussed in detail.This research used prior published data of muscle metabolite accumulation in combination with prior documentation of the pH dependent multiple competitive cation ~Hf and then ~H+e. Discussion will then be directed to the implications of these results to the biochemistry of metabolic acidosis, past theories that have been proposed to cause metabolic acidosis, and finally to the limitations of this study.The Discussion content to follow will be structured by metabolic energy system, with each consisting of M4.131P MRS documents larger concentrations of resting muscle CrP (30–40 mmol L−1 muscle water) than research based on muscle biopsy (15–20 mmol L−1), and this is understandable given the invasiveness and inherent delays in tissue sample excision and freezing for the biopsy procedure  degradation during exercise of different intensities, as well as CrP regeneration during the exercise recovery interval . As such, the resting cellular [ATP] is not an energy store, as it is essential to stabilize the concentrations of all the phosphorylated adenylate molecules  to ensure sufficient free energy release from ATP hydrolysis. This has been repeatedly verified by the relatively meagre reductions (<30%) in cellular [ATP] despite extreme conditions of voluntary and involuntary contraction‐induced ATP demand  + Δ[CrP] + (2 × Δ[ATP]) − Δ[ADP])/time (s) /time (s) )/time (s)  is a form of chemical work, and ATPto should be based on the total amount of ATP regeneration from energy catabolism. The value for ATPto from this study exceeded all prior integrated totals from the pertinent studies presented in Figure to across multiple prior research studies and researchers provides remarkable external validation of the methods and data results of this research.The slight discrepancies between these equations are problematic due to subsequent differences in validity. However, the more important concern pertains to the lactate constant of 1.5 used in these equations, as this is an adjustment of the gross 4 ATP yield from the production of 2 La+e during intense muscle contractions . Clearly, ATP hydrolysis has a meaningful capacity of ~H+ release in transition from neutral and acidic cellular conditions and should not be overlooked as a potential contributor to the development of metabolic acidosis.Researchers who have focused on ATP hydrolysis as a potential major contributor to net cellular ~Hes Kemp, . For thier Table , which w4.43−2]) occur from an imbalance in ATP turnover (excess) and mitochondrial ATP regeneration (limited), where the latter is an important consumer of Pi as a substrate in oxidative phosphorylation. During cytosolic energy catabolism, Pi is also a substrate for the phosphorylase and G3PDH reactions. The data of Table −1  and that Pi consumption during glycogenolysis and glycolysis equated to 91.61 mmol L−1, revealing a net Pi release of 19.74 mmol L−1.Increased intracellular concentrations of inorganic phosphate  occuto. However, before comparisons to past research, it is important to clarify the differences in absolute concentrations of phosphate metabolites obtained from muscle biopsy research versus research from 31‐phosphorous magnetic resonance (31P MRS) methodologies.The relatively small Pi accumulation calculated for this modelling represents just 63% of the decrease in CrP, and only 18% of the PFK adjusted total ATP31P MRS, it is important to acknowledge the influence of magnetic field strength. Early research (pre‐2000) of 31P MRS was confined to magnetic field strengths <2 Tesla, whereas in recent years it is now common to see use of large bore magnets between 3–10 Tesla. For a given tissue sampling volume, the larger the magnetic field strength the greater the resolution of peaks for different phosphate metabolites, as well as the increased signal intensity for each metabolite and more rapid nuclear relaxation time, thereby allowing higher signal to noise, higher acquisition frequencies, reduced averaging of spectra and thereby improved temporal resolution. Whereas early studies required up to 1–2 min of signal averaging at anywhere from 2 to 5 s acquisition intervals, current high field strength studies now produce quality data with approximately 6–15 s of spectra averaging at 1–2 s acquisition intervals . Added to these assumptions is the difficulty in resolving the pure Pi peak for intense exercise conditions, and this is especially true for lower magnetic field strength magnets, as the increasing accumulation of the hexose and triose phosphate intermediates of glycolysis have resonance frequencies close to that of Pi and as such appear as a broad shoulder off the Pi peak, though this resolution is improved in higher magnetic field strength magnets.Research from 31P MRS of muscle metabolism during intense exercise, there are large discrepancies in the extent of muscle Pi accumulation. For example, Taylor et al.  of 119.5%. More recent research from 31P MRS has revealed peak Pi accumulation during intense exercise that is considerably lower than that of Taylor et al.  were acquired every 2 s (each contraction cycle gated to end recovery), and each spectra was an average of 4 FIDs, resulting in an 8 s time average. Similarly, Layec et al. , and this can be seen from the G3PDH reaction H+e curve of Figure 2PO4−1 from 0.3599 at pH 7.0 to 0.849 at pH 6.0. This ~H+ association of Pi increases the ~H+ release for each of the reactions where Pi is a substrate (phosphorylase and G3PDH). For sustained intense exercise to contractile failure and volitional exhaustion, as modeled in this research, the anapleurotic nature of Pi in cellular energy catabolism complicates how to interpret the buffering nature of Pi, as the integral of the ~H+e of the phosphorylase and G3PDH can cause a net ~H+ release that exceeds the perceived ~H+ buffering by Pi accumulation.The metabolic role of Pi becomes even more interesting when you compute the pH dependent ~H4.5+. How do these competing rates of NADH and NAD+ appearance and disappearance influence net cytosolic NAD+/NADH proportions (redox) once the specific substrate flux through these reactions are integrated over time? Based on the observed increase in substrate flux for preceding reactions to the LDH reaction as you backtrack along phase II of glycolysis, more NADH is produced from the G3PDH reaction than NAD+ regenerated from the LDH reaction. As such, it is simple biochemical logic for the NAD+ to NADH redox ratio to gradually fall and remain low as lactate production increases. This deficiency in lactate coupled NAD+ regeneration integrates to a 24‐fold relative change at the end of the exercise condition. This relative decrease in cytosolic NAD+ is likely to be a significant contributor to a gradual decrease in substrate flux through glycolysis during intense exercise, which in‐turn would gradually compromise ATPto necessitating the gradual decrease in muscle [ATP] with simultaneous increases in [Pi], [ADP], and contractile failure.Glycolysis produces NADH, while lactate production oxidizes NADH and reduces pyruvate to lactate, regenerating cytosolic NAD−1. This is remarkably large and no research of muscle metabolism during intense exercise has calculated intramuscular ADP accumulation anywhere near close to this extent. As explained for muscle ATP metabolism, a cell would not tolerate such increases in [ADP] based purely on drastic alterations of the free energy transfer of ATP hydrolysis, or indeed any reaction where ADP is a product. Clearly, the cellular handling of ADP is complex, and it is assumed that cellular mitochondria must act as a sink for ADP during intense muscle contractions. To some extent, this is logical as there would then be a readily available supply of ADP substrate, and presumably also Pi and H+ for oxidative phosphorylation to respond to the improved oxygenation from increased blood flow and perfusion during the recovery from intense muscle contractions. Such a rapid response ATP supply is also important for the rapid regeneration of CrP by the CK reaction in the immediate post‐exercise recovery period. Perhaps this is further evidence for the importance of the creatine kinase shuttle in connecting phosphate transfer between the mitochondria and the cytosol  regulate the pH of biological fluids.Given that cells do not produce lactic acid, the only remaining theory of the cause of metabolic acidosis is Peter Stewart's physico‐chemical theory Corey, , 1983. S3O+] of biological solutions being a dependent variable. In other words, there was no cellular or systemic source of H+ separate to this electro‐chemical correction (see Introduction)  pre pre16) pEquation . Based o Robergs , the neg+e and therefore the pH of body fluids. A new model is needed to improve the construct validity of understanding metabolic acidosis and perhaps the broader acid‐base regulation of biological systems. This approach would need to account for cellular determinants to intracellular pH and the cell to extracellular transport of H+. In this context, there needs to be experimental verification or refutation of many of the assumptions of the Stewart approach, and based on this evidence, a new computation model can be developed.Peter Stewart has to be acknowledged for his attempt at explaining body fluid pH based on physico‐chemical principles, but is it clear that despite some clinical acceptance of this approach Corey, , the mod4.7tf, and H+te, and such preliminary evidence across a shortened exercise duration to 1.5 min has already been published  and H+ (~H+e) in inverse proportion to the exercise duration, with minimal influence on the integral of these measures. The minimal changes that did occur were because of how changes in the temporal profile of Mf for each metabolite and cellular pH differed to their relative profiles of this study.The duration of intense exercise was chosen to be 3 min due to repeated studies documenting the validity of this duration to the maximal accumulated oxygen deficit and muscle anaerobic capacity  of this ~H+ release. New insights were also provided on the capacity of ~H+ release and consumption for specific reactions of the phosphagen, glycogenolytic, and glycolytic energy systems. We now know that the ~H+e from chemical reactions during times of high metabolic demand are remarkably large, and that despite considerable ~H+ consumption, cellular energy catabolism during intense exercise exceeding mitochondrial capacities is net ~H+ releasing, with the exact numerics of the release being dependent on cellular pH and the extent of mitochondrial deficiency.The lactic acidosis construct has been an accepted component within acid‐base chemistry and physiology, and related topics, for more than 100 years. Such acceptance had prevented the need to research alternative causes of ~H+e of chemical reactions may or may not be involved in the determination of the cellular and systemic acid‐base balance of biological solutions.The data may have important implications to understanding the cause of metabolic acidosis coincident with increased cellular metabolic demand. Nevertheless, considerably more research is required to establish how the ~HThe author has no competing interests or conflicts of interest in the completion of this research and publication of the manuscript.


Moreover, this combination of approaches produces testable predictions for the assembly of experimental microbial communities with specific properties and can facilitate rational environmental design processes for complex microbiomes.Despite a growing understanding of how environmental composition affects microbial communities, it remains difficult to apply this knowledge to the rational design of synthetic multispecies consortia. This is because natural microbial communities can harbour thousands of different organisms and environmental substrates, making up a vast combinatorial space that precludes exhaustive experimental testing and computational prediction. Here, we present a method based on the combination of machine learning and metabolic modelling that selects optimal environmental compositions to produce target community phenotypes. In this framework, dynamic flux balance analysis is used to model the growth of a community in candidate environments. A genetic algorithm is then used to evaluate the behaviour of the community relative to a target phenotype, and subsequently adjust the environment to allow the organisms to approach this target. We apply this iterative process to thousands of  In adin silico analogues of these experiments . As such, the objective of the GA was to minimize this quantity. We found that, by iteratively searching this large combinatorial space, the GA framework successfully identified environments that allowed each organism to reach a high relative abundance while allowing the remaining two to reach low, but nonzero abundances (a–c). Notably, the algorithm converged on multiple such environmental compositions, indicating a type of metabolic flexibility with regard to specific final taxonomic compositions.To search this larger combinatorial space, we carried out dFBA simulations of our community in the selected environments as they were produced by the GA, instead of generating a full environment–phenotype mapping undances a–c. Notad–f). For example, in one of the environments that was selected to have B. subtilis dominate the community, our dFBA simulation revealed that it was the exclusive consumer of two out of three primary nutrients, while the third nutrient was shared between the three organisms (d). A similar structure was also observed for the environments that optimized dominance of E. coli and S. coelicolor , as well as in the other compositions selected by the GA , suggesting that nutrient specificity was a major driving force of organism dominance in these communities. We also observed dense networks of metabolic byproduct exchange, with molecules such as acetate, formate, glycine and succinate being frequently transferred between organisms, paralleling previous experimental observations of organic acid transfer [We examined the highest scoring environmental compositions in greater detail, identifying common interaction network structures that conferred the desired community phenotypes d–f. For rganisms d. A simielicolor e,f, as wtransfer –75. Give. 3in silico microbial communities to show how their ecological properties can be modulated via environmental modification and presented a search algorithm to identify specific nutrient combinations that would result in desired phenotypes. We showed how this algorithm was quickly able to identify high-quality solutions for a variety of ecological objectives: from overall taxonomic balance to specific organism abundances and patterns of metabolic secretion and exchange. Given these capabilities, this method represents a computationally inexpensive way to rapidly screen very large combinatorial spaces to produce desired community properties. Therefore, in addition to optimizing the various objectives tested here, our dFBA–GA framework can be extended to encompass a greater number of important environmental attributes and experimental designs such as varying nutrient concentrations, continuous culture platforms, spatio-temporal nutrient variation and periodic changes in species abundances [The rational design of multispecies communities toward defined phenotypes is an enticing, yet challenging, goal of synthetic ecology. As the phenotypic traits of microbiomes in complex settings remain difficult to predict ,76,77, fundances ,48,81. Iundances ,82, thisin vitro will inevitably require experimental validation of modelling predictions. Our approach can be applied to this goal in two ways. First, in silico analogues of the desired community may be iteratively screened as we have performed here, and the final environments generated by the GA may then be explicitly tested experimentally. In this way, our method serves as a way to generate an accessible number of testable hypotheses pertaining to specific ecological systems. The pairing of flux balance models and confirmatory experiments in this way has been used extensively to obtain a greater understanding of organism function, as well as to explore previously unknown phenotypes [Despite the flexibility and mechanistic insight afforded by a dFBA approach, engineering synthetic ecosystems enotypes ,83–86. Henotypes ,88, (ii)enotypes  and  and formulations (e.g. population size and scoring) that can aid its applicability to experimental systems. We therefore propose that, given the increasing accessibility of high-throughput platforms for microbial ecology  [A second strategy can thus forgo the dFBA component altogether and use the evolutionary algorithm as a way to search through experimentally derived community phenotypic data. As we showed how the GA was able to reach high-quality solutions with relatively few experimental data points, one could envision implementing a similar framework alongside the eriments ,42. It is, etc.) –45, a se. 4. 4.1in silico minimal medium with limiting quantities of a set of carbon sources. This minimal medium, modelled after the composition of M9, contained nonlimiting concentrations of molecules necessary for growth such as water and ions, as well as sources of nitrogen, phosphorus and sulfur. Limiting amounts of 20 carbon sources were then added on an environment-by-environment basis. These nutrients, an assortment of sugars, organic acids and amino acids , were added in all combinations of up to 4 at equimolar ratios such that the total concentration of carbon in each environment was 50 mM C in 400 µl. This scheme resulted in 6196 unique environmental compositions. (ii) Genome-scale reconstructions [in silico media compositions. These organism-specific models span a wide range of taxa and metabolic strategies and were selected to maximize variation in endpoint community composition and interactions across our combinatorial environments . Based on an approximate total inoculum of OD600 0.05 corresponding to in silico media at equal ratios of We employed a dFBA method  to test ructions ,32 of 13ht (gDW) , all 13 f 0.01 h . A more a), we first computed Spearman correlation coefficients between the species relative abundance vectors under each environment. We then performed hierarchical clustering on these coefficients using the ‘clustergram' function in MATLAB, which calculated distances between clusters using the UPGMA method based on Euclidean distance.To determine whether our communities had stopped growing by the end of the 24 h timespan, we analysed the growth curves of each organism in each environment. If the derivative of the organism's growth curve was greater than zero at least once during the simulation (i.e. the organism grew), and was less than or equal to zero at the end of the simulation, we determined that organism to have stopped growing. For our visualization of the clustered relative abundances of our communities a, we firH asi in a community. Organisms in a community with a larger H have more equal relative abundances, while those in one with a smaller H are less equal, due for example to a single organism outcompeting the rest.We calculated the Shannon entropy for each community in order to quantify their degrees of taxonomic balance. We define Shannon entropy B. subtilis, E. coli and S. coelicolor ) from our list of 13 were used and inoculated into our environments at initial amounts of For our second, exploratory application of the GA, a larger pool of 154 carbon sources was used from which a maximum of three nutrients were selected per environment, resulting in 596 904 unique environmental compositions. Here, we did not explicitly simulate the community phenotypes in all combinatorial environments. Instead, only the environmental compositions selected by the GA in each generation were tested and their performance recorded as above. For these simulations, three organism genome-scale reconstructions  the total number of metabolic exchanges, (iv) the total metabolic flux directed at each of the 13 in silico organisms, (v) the total secretion flux of 24 different metabolic byproducts and (vi) the approximation of target relative abundances. The modifications of different solutions take place over the course of multiple ‘generations', in which each solution is scored according to the phenotype being optimized, and the best solutions are used to seed a new generation of candidate solutions. This process continues with the intent of converging on a set of optimal solutions.A GA is a search heuristic based on the principle of evolution by natural selection, which optimizes a particular objective function via the modification of a population of individual solutions . Our selP environmental compositions. In order to demonstrate its extensibility to be used in parallel to an in vitro experimental system, we sought to minimize the number of environmental compositions P tested in each generation. Therefore, we limited the number of compositions to an experimentally tractable  1.P environments are initialized with random assortments of up to N nutrients (The  2.in vitro system) are recorded and used to assign fitness values to each environment.The community phenotypes resulting from each environment in the population  and mutation (existing nutrients are replaced with new randomly sampled ones). In our implementation, the parent nutrient vectors are linearized, and the remaining Having selected a set of  5.Steps 2–4 are repeated for the new environmental compositions until convergence criteria are met, or for a predetermined number of generations.Our implementation of the GA begins with a randomly generated population made up of B. subtilis and (iii) maximization of the total number of metabolic exchanges. We then varied the values of S. This score is based on a combination of two metrics: (i) the number of generations required for a set of solutions to surpass the 99th percentile of a given objective S is defined as follows:S can range from 0 to 2. We found that the best S to changing mutation probabilities We determined optimal values for the crossover and mutation probabilities r values , our cal 1.Populations are internally consistent: the difference between the best fitness and the average fitness within a generation is less than 10% of the average fitness of that generation. 2.Solutions have reached a maximum: the scaled difference in fitness between the best individual in the current generation and the best individual ever discovered is less than 0.01. 3.t-test.No further improvement: the fitness scores of the individuals in a generation have not shown a statistically significant increase from those of the preceding generation for at least 10 generations, as determined using a one-tailed To determine whether the algorithm has converged to an optimum, we implemented a set of three criteria based on the fitness values of each tested environmental composition. All three of these criteria, based on those previously implemented in evolutionary algorithms ,94, must