Identification of New Ketamine Metabolites and Their Detailed Distribution in the Mammalian Brain.

Ketamine is a common anesthetic used in human and veterinary medicine. This drug has recently received increased medical and scientific attention due to its indications for neurological diseases. Despite being applied for decades, ketamine's entire metabolism and pharmacological profile have not been elucidated yet. Therefore, insights into the metabolism and brain distribution are important toward identification of neurological effects. Herein, we have investigated ketamine and its metabolites in the pig brain, cerebrospinal fluid, and plasma using mass spectrometric and metabolomics analysis. We discovered previously unknown metabolites and validated their chemical structures. Our comprehensive analysis of the brain distribution of ketamine and 30 metabolites describes significant regional differences detected mainly for phase II metabolites. Elevated levels of these metabolites were identified in brain regions linked to clearance through the cerebrospinal fluid. This study provides the foundation for multidisciplinary studies of ketamine metabolism and the elucidation of neurological effects by ketamine.

Rapid and Bifunctional Chemoselective Metabolome Analysis of Liver Disease Plasma Using the Reagent 4-Nitrophenyl-2H-azirine.

Primary sclerosing cholangitis (PSC) is a chronic inflammatory disease of the bile ducts that has been associated with diverse metabolic carboxylic acids. Mass spectrometric techniques are the method of choice for their analysis. However, the broad investigation of this metabolite class remains challenging. Derivatization of carboxylic acids represents a strategy to overcome these limitations but available methods suffer from diverse analytical challenges. Herein, we have designed a novel strategy introducing 4-nitrophenyl-2H-azirine as a new chemoselective moiety for the first time for carboxylic acid metabolites. This moiety was selected as it rapidly forms a stable amide bond and also generates a new ketone, which can be analyzed by our recently developed quant-SCHEMA method specific for carbonyl metabolites. Optimization of this new method revealed a high reproducibility and robustness, which was utilized to validate 102 metabolic carboxylic acids using authentic synthetic standard conjugates in human plasma samples including nine metabolites that were newly detected. Using this sequential analysis of the carbonyl- and carboxylic acid-metabolomes revealed alterations of the ketogenesis pathway, which demonstrates the vast benefit of our unique methodology. We anticipate that the developed azirine moiety with rapid functional group transformation will find broad application in diverse chemical biology research fields.

Immobilized Enzymes on Magnetic Beads for Separate Mass Spectrometric Investigation of Human Phase II Metabolite Classes.

The human body has evolved to remove xenobiotics through a multistep clearance process. Non-endogenous metabolites are converted through a series of phase I and different phase II enzymes into compounds with higher hydrophilicity. These compounds are important for diverse research fields such as toxicology, nutrition, biomarker discovery, doping control, and microbiome metabolism. One of the challenges in these research fields has been the investigation of the two major phase II modifications, sulfation and glucuronidation, and the corresponding unconjugated aglycon independently. We have now developed a new methodology utilizing an immobilized arylsulfatase and an immobilized ß-glucuronidase to magnetic beads for treatment of human urine samples. The enzyme activities remained the same compared to the enzyme in solution. The separate mass spectrometric investigation of each metabolite class in a single sample was successfully applied to obtain the dietary glucuronidation and sulfation profile of 116 compounds. Our new chemical biology strategy provides a new tool for the investigation of metabolites in biological samples with the potential for broad-scale application in metabolomics, nutrition, and microbiome studies.

Identification of nutritional biomarkers through highly sensitive and chemoselective metabolomics.

The importance of a healthy diet for humans is known for decades. The elucidation of key molecules responsible for the beneficial and adverse dietary effects is slowly developing as the tools are missing. Carbonyl-containing metabolites are a common bioproducts through conversion of diet by the microbiome. In here, we have utilized our recently developed mass spectrometric methodology based on chemoselective conjugation of carbonyl-metabolites. The method has been applied for urine sample analysis from a dietary (poly)phenol intervention study (N = 78 individuals) for the first time. We have identified a series of carbonyl-metabolites of dietary origin and the chemical structure was validated for 30 metabolites. Our sensitive analysis led to the discovery of four unknown dietary markers with high sensitivity and selectivity (AUC > 0.91). Our chemical metabolomics method has been successfully applied for large-scale analysis and provides the basis for targeted metabolomics to identify unknown nutritional and disease-related biomarkers.

Chemoselective bicyclobutane-based mass spectrometric detection of biological thiols uncovers human and bacterial metabolites.

Sulfur is an essential element of life. Thiol-containing metabolites in all organisms are involved in the regulation of diverse biological processes. Especially, the microbiome produces bioactive metabolites or biological intermediates of this compound class. The analysis of thiol-containing metabolites is challenging due to the lack of specific tools, making these compounds difficult to investigate selectively. We have now developed a new methodology comprising bicyclobutane for chemoselective and irreversible capturing of this metabolite class. We utilized this new chemical biology tool immobilized onto magnetic beads for the investigation of human plasma, fecal samples, and bacterial cultures. Our mass spectrometric investigation detected a broad range of human, dietary and bacterial thiol-containing metabolites and we even captured the reactive sulfur species cysteine persulfide in both fecal and bacterial samples. The described comprehensive methodology represents a new mass spectrometric strategy for the discovery of bioactive thiol-containing metabolites in humans and the microbiome.

A frame-shift mutation in COMTD1 is associated with impaired pheomelanin pigmentation in chicken.

The biochemical pathway regulating the synthesis of yellow/red pheomelanin is less well characterized than the synthesis of black/brown eumelanin. Inhibitor of gold (IG phenotype) is a plumage colour variant in chicken that provides an opportunity to further explore this pathway since the recessive allele (IG) at this locus is associated with a defect in the production of pheomelanin. IG/IG homozygotes display a marked dilution of red pheomelanin pigmentation, whilst black pigmentation (eumelanin) is only slightly affected. Here we show that a 2-base pair insertion (frame-shift mutation) in the 5th exon of the Catechol-O-methyltransferase containing domain 1 gene (COMTD1), expected to cause a complete or partial loss-of-function of the COMTD1 enzyme, shows complete concordance with the IG phenotype within and across breeds. We show that the COMTD1 protein is localized to mitochondria in pigment cells. Knockout of Comtd1 in a mouse melanocytic cell line results in a reduction in pheomelanin metabolites and significant alterations in metabolites of glutamate/glutathione, riboflavin, and the tricarboxylic acid cycle. Furthermore, COMTD1 overexpression enhanced cellular proliferation following chemical-induced transfection, a potential inducer of oxidative stress. These observations suggest that COMTD1 plays a protective role for melanocytes against oxidative stress and that this supports their ability to produce pheomelanin.

Sensitive quantification of short-chain fatty acids combined with global metabolomics in microbiome cultures.

The microbiome has been identified to have a key role for the physiology of their human host. One of the major impacts is the clearance of bacterial pathogens. We have now developed a chemoselective probe methodology for the absolute quantification of short-chain fatty acids at low nM concentrations, with high reproducibility and spiked isotope labelled internal standards. Immobilization to magnetic beads allows for separation from the matrix and the tagged metabolites upon bioorthogonal cleavage can be analyzed via UHPLC-MS. The major advantage of our sensitive method is the simple combination with global metabolomics analysis as only a small sample volume is required. We have applied this chemical metabolomics strategy for targeted SCFA analysis combined with global metabolomics on gut microbiome co-cultures with Salmonella and investigated the effect of antibiotic treatment.

Mucosal and Plasma Metabolomes in New-onset Paediatric Inflammatory Bowel Disease: Correlations with Disease Characteristics and Plasma Inflammation Protein Markers.

BACKGROUND AND AIMS: To advance the understanding of inflammatory bowel disease [IBD] pathophysiology, we compared the mucosal and plasma metabolomes between new-onset paediatric IBD patients and symptomatic non-IBD controls, and correlated plasma inflammation markers and disease characteristics with the altered metabolites. METHODS: Paired colonic and ileal biopsies and plasma from 67 treatment-naïve children with incident Crohn's disease [CD; n = 47], ulcerative colitis [UC; n = 9], and non-IBD controls [n = 11] were analysed using ultra-performance liquid chromatography-mass spectrometry [UPLC-MS/MS]. Inflammatory plasma proteins [n = 92] were assessed. RESULTS: The metabolomes in inflamed mucosal biopsies differed between IBD patients and controls. In CD, mucosal levels of several lysophospholipids [lysophosphatidylcholines, lysophosphatidyletanolamines, lysophosphatidylinositols, and lysophosphatidylserines] were decreased, correlating with various plasma metabolites including amino acid analogues and N-acetylated compounds. In both CD and UC, mucosal sphingolipids, including ceramide [d18:2/24:1, d18:1/24:2], lactosyl-N-palmitoyl-sphingosine [d18:1/16:0], behenoyl sphingomyelin [d18:1/22:0], lignoceroyl sphingomyelin [d18:1/24:0], and/or sphingomyelin [d18:1/24:1, d18:2/24:0] were increased, correlating with sphingolipids, bile acids, and/or N-acetylated metabolites in plasma. Among proteins associated with CD, interleukin-24 correlated with plasma metabolites, including lactosyl-N-palmitoyl sphingosine [d18:1/16:0] and phosphatidyletanolamine [18:1/18:1], haemoglobin, and faecal calprotectin. In UC, interleukin-24, interleukin-17A, and C-C motif chemokine 11 correlated with several plasma metabolites, including N-acetyltryptophan, tryptophan, glycerate, and threonate, and with the Paediatric Ulcerative Colitis Activity Index, C-reactive protein, and faecal calprotectin. CONCLUSIONS: Mucosal perturbations of lysophospholipids and sphingolipids characterised the metabolome in new-onset paediatric IBD and correlated with plasma metabolites. By integrating plasma metabolomics data with inflammatory proteins and clinical data, we identified clinical and inflammatory markers associated with metabolomic signatures for IBD.

Enhanced cytotoxicity of a novel family of ATPase inhibitors in colorectal cancer cells with high NAT2 activity.

Loss of heterozygosity (LOH) is a hallmark feature of cancer genomes that reduces allelic variation, thereby creating tumor specific vulnerabilities which could be exploited for therapeutic purposes. We previously reported that loss of drug metabolic arylamine N-acetyltransferase 2 (NAT2) activity following LOH at 8p22 could be targeted for collateral lethality anticancer therapy in colorectal cancer (CRC). Here, we report a novel compound CBK034026C that exhibits specific toxicity towards CRC cells with high NAT2 activity. Connectivity Map analysis revealed that CBK034026C elicited a response pattern related to ATPase inhibitors. Similar to ouabain, a potent inhibitor of the Na+/K+-ATPase, CBK034026C activated the Nf-kB pathway. Further metabolomic profiling revealed downregulation of pathways associated with antioxidant defense and mitochondrial metabolism in CRC cells with high NAT2 activity, thereby weakening the protective response to oxidative stress induced by CBK034026C. The identification of a small molecule targeting metabolic vulnerabilities caused by NAT2 activity provides novel avenues for development of anticancer agents.

Analysis of Growth Phases of Enterotoxigenic Escherichia coli Reveals a Distinct Transition Phase before Entry into Early Stationary Phase with Shifts in Tryptophan, Fucose, and Putrescine Metabolism and Degradation of Neurotransmitter Precursors.

Enterotoxigenic Escherichia coli (ETEC) is a major cause of diarrhea in children and adults in endemic areas. Gene regulation of ETEC during growth in vitro and in vivo needs to be further evaluated, and here we describe the full transcriptome and metabolome of ETEC during growth from mid-logarithmic growth to early stationary phase in rich medium (LB medium). We identified specific genes and pathways subjected to rapid transient alterations in gene expression and metabolite production during the transition from logarithmic to stationary growth. The transient phase was found to be different from the subsequent induction of early stationary phase-induced genes. The transient phase was characterized by the repression of genes and metabolites involved in organic substance transport. Genes involved in fucose and putrescine metabolism were upregulated, and genes involved in iron transport were repressed. Expression of toxins and colonization factors were not changed, suggesting retained virulence from mid-logarithmic to the start of the stationary phase. Metabolomic analyses showed that the transient phase was characterized by a drop of intracellular amino acids, e.g., l-tyrosine, l-tryptophan, l-phenylalanine, l-leucine, and l-glutamic acid, followed by increased levels at induction of stationary phase. A pathway enrichment analysis of the entire combined transcriptome and metabolome revealed that significant pathways during progression from logarithmic to early stationary phase are involved in the degradation of neurotransmitters aminobutyrate (GABA) and precursors of 5-hydroxytryptamine (serotonin). This work provides a comprehensive framework for further studies on transcriptional and metabolic regulation in pathogenic E. coli. IMPORTANCE We show that E. coli, exemplified by the pathogenic subspecies enterotoxigenic E. coli (ETEC), undergoes a stepwise transcriptional and metabolic transition into the stationary phase. At a specific entry point, E. coli induces activation and repression of specific pathways. This leads to a rapid decrease of intracellular levels of certain amino acids. The resulting metabolic activity leads to an intense but short peak of indole production, suggesting that this is the previously described "indole peak," rapid decrease of intermediate molecules of bacterial neurotransmitters, increased putrescine and fucose uptake, increased glutathione levels, and decreased iron uptake. This specific transient shift in gene expression and metabolome is short-lived and disappears when bacteria enter the early stationary phase. We suggest that these changes mainly prepare bacteria for ceased growth, but based on the pathways involved, we could suggest that this transient phase substantially influences survival and virulence.

Squaric acid as a new chemoselective moiety for mass spectrometry-based metabolomics analysis of amines.

The investigation of microbiome-derived metabolites is important to understand metabolic interactions with their human host. New methodologies for mass spectrometric discovery of undetected metabolites with unknown bioactivity are required. Herein, we introduce squaric acid as a new chemoselective moiety for amine metabolite analysis in human fecal samples.

Chemoselective and Highly Sensitive Quantification of Gut Microbiome and Human Metabolites.

The microbiome has a fundamental impact on the human host's physiology through the production of highly reactive compounds that can lead to disease development. One class of such compounds are carbonyl-containing metabolites, which are involved in diverse biochemical processes. Mass spectrometry is the method of choice for analysis of metabolites but carbonyls are analytically challenging. Herein, we have developed a new chemical biology tool using chemoselective modification to overcome analytical limitations. Two isotopic probes allow for the simultaneous and semi-quantitative analysis at the femtomole level as well as qualitative analysis at attomole quantities that allows for detection of more than 200 metabolites in human fecal, urine and plasma samples. This comprehensive mass spectrometric analysis enhances the scope of metabolomics-driven biomarker discovery. We anticipate that our chemical biology tool will be of general use in metabolomics analysis to obtain a better understanding of microbial interactions with the human host and disease development.

Common and mutation specific phenotypes of KRAS and BRAF mutations in colorectal cancer cells revealed by integrative -omics analysis.

BACKGROUND: Genes in the Ras pathway have somatic mutations in at least 60 % of colorectal cancers. Despite activating the same pathway, the BRAF V600E mutation and the prevalent mutations in codon 12 and 13 of KRAS have all been linked to different clinical outcomes, but the molecular mechanisms behind these differences largely remain to be clarified. METHODS: To characterize the similarities and differences between common activating KRAS mutations and between KRAS and BRAF mutations, we used genome editing to engineer KRAS G12C/D/V and G13D mutations in colorectal cancer cells that had their mutant BRAF V600E allele removed and subjected them to transcriptome sequencing, global proteomics and metabolomics analyses. RESULTS: By intersecting differentially expressed genes, proteins and metabolites, we uncovered (i) two-fold more regulated genes and proteins when comparing KRAS to BRAF mutant cells to those lacking Ras pathway mutation, (ii) five differentially expressed proteins in KRAS mutants compared to cells lacking Ras pathway mutation (IFI16, S100A10, CD44, GLRX and AHNAK2) and 6 (CRABP2, FLNA, NXN, LCP1, S100A10 and S100A2) compared to BRAF mutant cells, (iii) 19 proteins expressed differentially in a KRAS mutation specific manner versus BRAF V600E cells, (iv) regulation of the Integrin Linked Kinase pathway by KRAS but not BRAF mutation, (v) regulation of amino acid metabolism, particularly of the tyrosine, histidine, arginine and proline pathways, the urea cycle and purine metabolism by Ras pathway mutations, (vi) increased free carnitine in KRAS and BRAF mutant RKO cells. CONCLUSIONS: This comprehensive integrative -omics analysis confirms known and adds novel genes, proteins and metabolic pathways regulated by mutant KRAS and BRAF signaling in colorectal cancer. The results from the new model systems presented here can inform future development of diagnostic and therapeutic approaches targeting tumors with KRAS and BRAF mutations.

Differential regulation of oxidative stress, microbiota-derived, and energy metabolites in the mouse brain during sleep.

Sleep has evolved as a universal core function to allow for restorative biological processes. Detailed knowledge of metabolic changes necessary for the sleep state in the brain is missing. Herein, we have performed an in-depth metabolic analysis of four mouse brain regions and uncovered region-specific circadian variations. Metabolites linked to oxidative stress were altered during sleep including acylcarnitines, hydroxylated fatty acids, phenolic compounds, and thiol-containing metabolites. These findings provide molecular evidence of a significant metabolic shift of the brain energy metabolism. Specific alterations were observed for brain metabolites that have previously not been associated with a circadian function including the microbiome-derived metabolite ergothioneine that suggests a regulatory function. The pseudopeptide ß-citryl-glutamate has been linked to brain development and we have now discovered a previously unknown regioisomer. These metabolites altered by the circadian rhythm represent the foundation for hypothesis-driven studies of the underlying metabolic processes and their function.

Regional Brain Analysis of Modified Amino Acids and Dipeptides during the Sleep/Wake Cycle.

Sleep is a state in which important restorative and anabolic processes occur. Understanding changes of these metabolic processes during the circadian rhythm in the brain is crucial to elucidate neurophysiological mechanisms important for sleep function. Investigation of amino acid modifications and dipeptides has recently emerged as a valuable approach in the metabolic profiling of the central nervous system. Nonetheless, very little is known about the effects of sleep on the brain levels of amino acid analogues. In the present study, we examined brain regional sleep-induced alterations selective for modified amino acids and dipeptides using Ultra-high performance liquid chromatography-MS/MS (UHPLC-MS/MS) based metabolomics. Our approach enabled the detection and identification of numerous amino acid-containing metabolites in the cortex, the hippocampus, the midbrain, and the cerebellum. In particular, analogues of the aromatic amino acids phenylalanine, tyrosine and tryptophan were significantly altered during sleep in the investigated brain regions. Cortical levels of medium and long chain N-acyl glycines were higher during sleep. Regional specific changes were also detected, especially related to tyrosine analogues in the hippocampus and the cerebellum. Our findings demonstrate a strong correlation between circadian rhythms and amino acid metabolism specific for different brain regions that provide previously unknown insights in brain metabolism.

Investigation of the individual human sulfatome in plasma and urine samples reveals an age-dependency.

Metabolic microbiome interaction with the human host has been linked to human physiology and disease development. The elucidation of this interspecies metabolite exchange will lead to identification of beneficial metabolites and disease modulators. Their discovery and quantitative analysis requires the development of specific tools and analysis of specific compound classes. Sulfated metabolites are considered a readout for the co-metabolism of the microbiome and their host. This compound class is part of the human phase II clearance process of xenobiotics and is the main focus in drug or doping metabolism and also includes dietary components and microbiome-derived compounds. Here, we report the targeted analysis of sulfated metabolites in plasma and urine samples in the same individuals to identify the core sulfatome and similarities between these two sample types. This analysis of 27 individuals led to the identification of the core sulfatome of 41 metabolites in plasma and urine samples as well as an age effect for 15 metabolites in both sample types.

Comparison of two arylsulfatases for targeted mass spectrometric analysis of microbiota-derived metabolites.

Sulfation of metabolites is the second highest phase II modification in humans, which plays a critical role in the xenobiotics clearance process and gut microbiota-host co-metabolism. Besides the main function to remove xenobiotics from the body, sulfated metabolites have also been linked to inflammation, bacterial pathogenesis and metabolic disorders. A better understanding of how these metabolites impact the human body has turned into an important research area. Analytical methods for selective identification of this metabolite class are scarce. We have recently developed an assay utilizing the arylsulfatase from Helix pomatia due to a high substrate promiscuity combined with state-of-the-art metabolomics bioinformatic analysis for the selective identification of O-sulfated metabolites in human samples. This enzyme requires a multistep purification process as highest purity is needed for the developed mass spectrometric assay. In this study, we have utilized a new and recombinant overexpressed arylsulfatase (ASPC) for the selective identification of organic sulfate esters in human urine samples. We have compared the substrate conversion in urine samples and substrate specificity of this enzyme with purified arylsulfatase from Helix pomatia. Our analysis of urine samples revealed that both enzymes can be utilized for the selective analysis and discovery of sulfated metabolites with high promiscuity as demonstrated by equal hydrolysis of 108 substrates including sulfated conjugates of 27 metabolites of microbial origin. Importantly, we also identified 21 substrates in human urine samples that are exclusively hydrolyzed by ASPC and application of this enzyme increases the discovery of unknown sulfated metabolites with a higher scaffold diversity.

Rapid Preparation of a Large Sulfated Metabolite Library for Structure Validation in Human Samples.

Metabolomics analysis of biological samples is widely applied in medical and natural sciences. Assigning the correct chemical structure in the metabolite identification process is required to draw the correct biological conclusions and still remains a major challenge in this research field. Several metabolite tandem mass spectrometry (MS/MS) fragmentation spectra libraries have been developed that are either based on computational methods or authentic libraries. These libraries are limited due to the high number of structurally diverse metabolites, low commercial availability of these compounds, and the increasing number of newly discovered metabolites. Phase II modification of xenobiotics is a compound class that is underrepresented in these databases despite their importance in diet, drug, or microbiome metabolism. The O-sulfated metabolites have been described as a signature for the co-metabolism of bacteria and their human host. Herein, we have developed a straightforward chemical synthesis method for rapid preparation of sulfated metabolite standards to obtain mass spectrometric fragmentation pattern and retention time information. We report the preparation of 38 O-sulfated alcohols and phenols for the determination of their MS/MS fragmentation pattern and chromatographic properties. Many of these metabolites are regioisomers that cannot be distinguished solely by their fragmentation pattern. We demonstrate that the versatility of this method is comparable to standard chemical synthesis. This comprehensive metabolite library can be applied for co-injection experiments to validate metabolites in different human sample types to explore microbiota-host co-metabolism, xenobiotic, and diet metabolism.

Comparative dietary sulfated metabolome analysis reveals unknown metabolic interactions of the gut microbiome and the human host.

The gut microbiome converts dietary compounds that are absorbed in the gastrointestinal tract and further metabolized by the human host. Sulfated metabolites are a major compound class derived from this co-metabolism and have been linked to disease development. In the present multidisciplinary study, we have investigated human urine samples from a dietary intervention study with 22 individuals collected before and after consumption of a polyphenol rich breakfast. These samples were analyzed utilizing our method combining enzymatic metabolite hydrolysis using an arylsulfatase and mass spectrometric metabolomics. Key to this study is the validation of 235 structurally diverse sulfated metabolites. We have identified 48 significantly upregulated metabolites upon dietary intervention including 11 previously unknown sulfated metabolites for this diet. We observed a large variation in subjects based on their potential to sulfate metabolites, which may be the foundation for classification of subjects as high and low sulfate metabolizers in future large cohort studies. The reported sulfatase-based method is a robust tool for the discovery of unknown microbiota-derived metabolites in human samples.

DNA surface exploration and operator bypassing during target search.

Many proteins that bind specific DNA sequences search the genome by combining three-dimensional diffusion with one-dimensional sliding on nonspecific DNA1-5. Here we combine resonance energy transfer and fluorescence correlation measurements to characterize how individual lac repressor (LacI) molecules explore the DNA surface during the one-dimensional phase of target search. To track the rotation of sliding LacI molecules on the microsecond timescale, we use real-time single-molecule confocal laser tracking combined with fluorescence correlation spectroscopy (SMCT-FCS). The fluctuations in fluorescence signal are accurately described by rotation-coupled sliding, in which LacI traverses about 40 base pairs (bp) per revolution. This distance substantially exceeds the 10.5-bp helical pitch of DNA; this suggests that the sliding protein frequently hops out of the DNA groove, which would result in the frequent bypassing of target sequences. We directly observe such bypassing using single-molecule fluorescence resonance energy transfer (smFRET). A combined analysis of the smFRET and SMCT-FCS data shows that LacI hops one or two grooves (10-20 bp) every 200-700 µs. Our data suggest a trade-off between speed and accuracy during sliding: the weak nature of nonspecific protein-DNA interactions underlies operator bypassing, but also speeds up sliding. We anticipate that SMCT-FCS, which monitors rotational diffusion on the microsecond timescale while tracking individual molecules with millisecond resolution, will be applicable to the real-time investigation of many other biological interactions and will effectively extend the accessible time regime for observing these interactions by two orders of magnitude.