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Recently, two-dimensional liquid chromatography (2D-LC) has become a popular approach to analyze complex samples. This is partly due to the introduction of commercial 2D-LC systems. In the past, 2D-LC was carried out on in-house developed setups, typically consisting of several switching valves and sample loops as the interface between the two dimensions. Commercial systems usually offer different 2D-LC modes in combination with specialized software to operate the instrument and analyze the data. This makes them highly user-friendly, however, at an increased cost compared to in-house developed setups. This study aims to make a comparison between an in-house developed 2D-LC setup and a commercially available 2D-LC instrument. The comparison is made based on experimental differences, in addition to more general differences, including cost price, flexibility, and ease of operation. Special attention is also paid to the different strategies to deal with the mobile phase incompatibility between the highly orthogonal separation mechanisms considered in this work: hydrophilic interaction liquid chromatography (HILIC) and reversed-phase LC (RPLC). For the commercial 2D-LC instrument, this is done using active solvent modulation (ASM), a valve-based approach allowing the on-line dilution of the effluent eluting from the first dimension column before transfer to the second dimension (2D) column. For the in-house developed setup, a combination of restriction capillaries and a trap column is used. Using a sample of 28 compounds with a large polarity range, peak shapes and recoveries of the 2D-chromatograms are compared for both setups. For early eluting compounds, the selective comprehensive approach, currently only possible on the commercial 2D-LC instrument, results in the best peak shapes and recoveries, however, at the cost of an increased analysis time. In general, depending on the analytical goal (single heart-cut versus full-comprehensive 2D-LC), an in-house developed system can be satisfactory for the analysis of specific target compounds/samples. For more complex problems, it can be interesting to use a more specialized commercial 2D-LC instrument. Overall, this comparison study provides advice for analytical scientists, who are considering to use 2D-LC, on the type of equipment to consider, depending on the needs of their particular applications.

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Analytical data processing often requires the comparison of data, i.e. finding similarities and differences within separations. In this context, a peak-tracking algorithm was developed to compare multiple datasets in one-dimensional (1D) and two-dimensional (2D) chromatography. Two application strategies were investigated: i) data processing where all chromatograms are produced in one sequence and processed simultaneously, and ii) method optimization where chromatograms are produced and processed cumulatively. The first strategy was tested on data from comprehensive 2D liquid chromatography and comprehensive 2D gas chromatography separations of academic and industrial samples of varying compound classes (monoclonal-antibody digest, wine volatiles, polymer granulate headspace, and mayonnaise). Peaks were tracked in up to 29 chromatograms at once, but this could be upscaled when necessary. However, the peak-tracking algorithm performed less accurate for trace analytes, since, peaks that are difficult to detect are also difficult to track. The second strategy was tested with 1D liquid chromatography separations, that were optimized using automated method-development. The strategy for method optimization was quicker to detect peaks that were still poorly separated in earlier chromatograms compared to assigning a target chromatogram, to which all other chromatograms are compared. Rendering it a useful tool for automated method optimization.

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The typical phenolic profile in grapes is characterized by its complexity both in terms of number of diverse chemical structures and their variation during ripening. Besides, the specific phenolic composition of grapes directly influences the presence of those components in the resulting wine. In this contribution, a new method based on the application of comprehensive two-dimensional liquid chromatography coupled to a diode array detector and tandem mass spectrometry has been developed to obtain the typical phenolic profile of Malbec grapes cultivated in Brazil. Moreover, the method has been demonstrated to be useful to study how the phenolic composition in grapes evolved during a 10-week ripening period. Main detected compounds in grapes and in the wine derived from them were anthocyanins, although a good number of polymeric flavan-3-ols were also tentatively identified, among other compounds. Results show how the amount of anthocyanins present in grapes was increased during ripening up to 5-6 weeks and then decreased towards week 9. The two-dimensional approach applied was demonstrated to be useful for the characterization of the complex phenolic profile of these samples, involving more than 40 different structures and has the potential to be further applied to the study of this important fraction is different grapes and wines systematically.

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The combination of hydrophilic interaction chromatography (HILIC) and reversed-phase liquid chromatography (RP-LC) has proved effective in the LC × LC analysis of polyphenols due to the high degree of orthogonality associated with these separation modes for various classes of phenolic compounds. However, despite the growing number of such applications, HILIC is almost exclusively used as the first dimension (1D) separation mode, and RP-LC in the second dimension (2D). This is somewhat surprising in light of the potential advantages of swapping these separation modes. In this contribution, we present a detailed evaluation of the potential of online RP-LC × HILIC-MS for the analysis of phenolic compounds, comparing the performance of this system to the more established HILIC × RP-LC-MS configuration. Method development was performed using a predictive optimisation program, and fixed solvent modulation was employed to combat the solvent incompatibility between HILIC and RP-LC mobile phases. Red wine, rooibos tea, Protea and chestnut phenolic extracts containing a large diversity of phenolic compound classes were analysed by both HILIC × RP-LC- and RP-LC × HILIC-MS in order to compare the separation performance. Overall, the kinetic performance of HILIC × RP-LC was found to be clearly superior, with higher peak capacities and better resolution obtained for the majority of samples compared to RP-LC × HILIC analyses using similar column dimensions. Dilution of the 1D solvent combined with large volume injections proved insufficient to focus especially phenolic acids in the 2D HILIC separation, which resulted in severe 2D peak distortion for these compounds, and negatively impacted on method performance. On the other hand, a noteworthy improvement in the sensitivity of RP-LC × HILIC-MS analyses was observed due to higher ESI-MS response for the 2D HILIC mobile phase and greater sample loading capacity of the 1D RP-LC column, brought on by the high solubility of phenolic samples in aqueous solutions. As a result, a significantly higher number of compounds were detected in the RP-LC × HILIC-MS separations. These findings point to the potential advantage of RP-LC × HILIC as a complementary configuration to HILIC × RP-LC for phenolic analysis.

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Online comprehensive two-dimensional liquid chromatography (LC×LC) is the preferred method currently for the separation of highly complex mixtures of non-volatile compounds. With fully automated commercial instrumentation and software making the method appealing to both researchers and industry, the demand for systems with improved separation capabilities for highly complex mixtures such as those found in natural products or proteomics has increased. In this study we report an approach that enables variable second dimension analysis times based on the use of multiple heart-cutting valves and stop-flow operation to circumvent the requirement for very fast second dimension (2D) analyses in online LC×LC. As application, the HILIC×RP-LC analysis of condensed tannins (proanthocyanidins) in cocoa, grape seed and quebracho extracts is used to demonstrate the performance on the proposed methodology. The method offers increased flexibility compared to conventional online LC×LC separations in that longer 2D gradients can be used to accommodate more complex portions of the chromatogram, while shorter 2D gradients can be used in sections containing fewer peaks, while largely maintaining the benefits of comprehensive separation. We present an evaluation of the performance of the variable gradient time stop-flow HILIC×RP-LC method compared to a comparable, conventional online HILIC×RP-LC system in terms of practical peak capacities using established 2D-LC theory. The improved separation of especially low-level intermediate molecular weight proanthocyanidin oligomers by the former method demonstrates the benefits of the developed approach.

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In this work, three chemometrics-based approaches are compared for quantification purposes when using two-dimensional liquid chromatography (LC×LC-MS), taking as a study case the quantification of amino acids in commercial drug mixtures. Although the approaches have been already used for one-dimensional gas or liquid chromatography, the main novelty of this work is the demonstration of their applicability to LC×LC-MS datasets. Besides, steps such as peak alignment and modelling, commonly applied in this type of data analysis, are not required with the approaches proposed here. In a first step, regions of interest (ROI) strategy is used for the spectral compression of the LC×LC-MS datasets. Then the first strategy consists of building a calibration curve from the areas obtained in this ROI compression step. Alternatively, the ROI intensity matrices can be used as input for a second analysis step employing the multivariate curve resolution alternating least squares (MCR-ALS) method. The main benefit of MCR-ALS is the resolution of elution and spectral profiles for each of the analytes in the mixture, even in the case of strong coelutions and high signal overlapping. Classical MCR-ALS based calibration curve from the peak areas resolved only applying non-negativity constraints (second strategy) is compared to the results obtained when an area correlation constraint is imposed during the ALS optimization (third strategy). All in all, similar quantification results were achieved by the three approaches but, especially in prediction studies, the more accurate quantification is obtained when the calibration curve is built from the peak areas obtained with MCR-ALS when the area correlation constraint is imposed.

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Favipiravir finished dosage was approved for emergency use in many countries to treat SARS-CoV-2 patients. A specific, accurate, linear, robust, simple, and stability-indicating HPLC method was developed and validated for the determination of degradation impurities present in favipiravir film-coated tablets. The separation of all impurities was achieved from the stationary phase (Inert sustain AQ-C18, 250 × 4.6 mm, 5-µm particle) and mobile phase. Mobile phase A contained KH2 PO4 buffer (pH 2.5 ± 0.05) and acetonitrile in the ratio of 98:2 (v/v), and mobile phase B contained water and acetonitrile in the ratio of 50:50 (v/v). The chromatographic conditions were optimized as follows: flow rate, 0.7 mL/min; UV detection, 210 nm; injection volume, 20 µL; and column temperature, 33°C. The proposed method was validated per the current International Conference on Harmonization Q2 (R1) guidelines. The recovery study and linearity ranges were established from the limit of quantification to 150% optimal concentrations. The method validation results were found to be between 98.6 and 106.2% for recovery and r2  = 0.9995-0.9999 for linearity of all identified impurities. The method precision results were achieved below 5% of relative standard deviation. Forced degradation studies were performed in chemical and physical stress conditions. The compound was sensitive to chemical stress conditions. During the study, the analyte degraded and converted to unknown degradation impurities, and its molecular mass was found using the LC-MS technique and established degradation pathways supported by reaction of mechanism. The developed method was found to be suitable for routine analysis of research and development and quality control.

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Rhus coriaria L. (Anacardiaceae), commonly known as sumac, has been used since ancient times for many different applications, and nowadays is used mostly as a spice obtained from its in the Mediterranean and the Middle ground fruits and employed for flavoring and garnishing food, predominantly Eastern regions. Traditionally, sumac has been also used in popular medicine for the treatment of many ailments including hemorrhoids, wound healing, diarrhea, ulcers, and eye inflammation. Sumac drupes are indeed rich in various classes of phytochemicals including organic acids, flavonoids, tannins, and others, which are responsible of their powerful antioxidant capacity, from which treatment of many common diseases such as cardiovascular disease, diabetes, and cancer could benefit. In this work we evaluated the influence of fruit ripeness, conservation, and processing. To this aim, a phytochemical characterization of six different samples of Rhus coriaria L. was carried out. Specifically, headspace solid-phase micro extraction gas chromatography coupled to mass spectrometry and comprehensive two-dimensional liquid chromatography coupled to photodiode array and mass spectrometry detection, were employed. A total of 263 volatile compounds, including terpene hydrocarbons, acids, and aldehydes, as well as 83 polyphenolic compounds, mainly gallic acid derivatives, were positively identified. All samples showed a significant antioxidant activity by means of oxygen radical absorbance capacity, in line with their polyphenolic content and composition. Such findings set a solid ground to support the utilization of this plant as an attractive target for novel nutraceutical approaches and for drug discovery.

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This research reports on the development of a comprehensive two-dimensional liquid chromatography (2D-LC) method hyphenated to inline DAD-UV and ESI-QTOF-MS/MS-detection for the separation of conjugated polyunsaturated fatty acid isomers and structurally related (saturated, unconjugated, oxidized) compounds. In pharmaceutical lipid formulations conjugated fatty acids can be found as impurities, generated by oxidation of polyunsaturated fatty acids. Due to the structural complexity of resultant multi-component samples one dimensional liquid chromatography may be suboptimal for quality control and impurity profiling. The screened reversed-phase columns showed a lack of selectivity for the conjugated fatty acid isomers but the resolutions improved with the shape selectivity of the stationary phases (C18- < C30- < cholesteryl-ether-bonded). Further enhanced selectivity for the non-chiral conjugated FAs could be achieved with amylose/cellulose-based chiral stationary phases (CSPs) which harbor cavities for selective inclusion depending on E/Z configurations of the double bonds of the analytes. Amylose-based CSPs showed higher selectivity for conjugated fatty acids than the cellulose-based polysaccharide CSPs. Hyphenating the chiral and reversed-phase columns in a comprehensive 2D-LC-setup was favorable since they showed orthogonality and good compatibility, because both were operated under RP-conditions. The chiral dimension (1D) mainly separated the different isomers, while the reversed-phase dimension (2D) separated according to number of double bonds and degree of oxidation. Using this setup, advanced structural annotation of unknowns was possible based on UV-, MS1- and MS2-spectra. Data-independent acquisition (by SWATH) enabled differentiation of positional isomers of oxidized lipids by characteristic MS2-fragments and elucidation of co-eluted compounds by selective extracted ion chromatograms of fragment ions (MS2 EICs).

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Liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) has become a mainstay analytical technique in pharmaceutical research and development and clinical diagnosis due to several advantages including excellent selectivity, specificity, and high sensitivity. LC-MS/MS has become the method of choice for steroids analysis due to its fast analytical time and improved specificity yet has a challenge in the separation and measurement of isomers with the same product ions. Here we describe a high-sensitivity LC/LC-MS/MS method that combines chiral chromatography and reverse-phase chromatography (LC/LC) along with MS/MS to rapidly separate and quantify steroid isomers of 11ß-methyl-19-nortestosterone (11ß-MNT) and endogenous testosterone in serum.

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Phenolic compounds are an interesting class of natural products because of their proposed contribution to health benefits of foods and beverages and as a bio-source of organic (aromatic) building blocks. Phenolic extracts from natural products are often highly complex and contain compounds covering a broad range in molecular properties. While many 1D-LC and mass spectrometric approaches have been proposed for the analysis of phenolics, this complexity inevitably leads to challenging identification and purification. New insights into the composition of phenolic extracts can be obtained through online comprehensive two-dimensional liquid chromatography (LC × LC) coupled to photodiode array and mass spectrometric detection. However, several practical hurdles must be overcome to achieve high peak capacities and to obtain robust methods with this technique. In many LC × LC configurations, refocusing of analytes at the head of the 2D column is hindered by the high eluotropic strength of the solvent transferred from the 1D to the 2D, leading to peak breakthrough or broadening. LC × LC combinations whereby a purely aqueous mobile phase is used in the 1D and RPLC is used in the 2D are unaffected by these phenomena, leading to more robust methods. In this contribution, the combination of temperature-responsive liquid chromatography (TRLC) with RPLC is used for the first time for the analysis of phenolic extracts of natural origin to illustrate the potential of this alternative combination for natural product analyses. The possibilities of the combination are investigated through analysis of wine extracts by TRLC × RPLC-DAD and TRLC × RPLC-ESI-MS.

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We report on activity-guided investigation of the key antisweet principles of Gymnema sylvestre. Orosensory-guided fractionation by means of solid phase extraction, preparative 2D-LC, and semipreparative HPLC followed by accurate MS and 1D/2D NMR experiments revealed six known and three previously unknown gymnemic acids as the key constituents of seven highly sensory-active fractions. Localized via a modified comparative taste dilution analysis (cTDA) and taste modulation probability (TMP) based screening techniques, a strong intrinsic bitterness was also observed for gymnemic acids. In addition, the suppressive effects of the most abundant acids on the response of the human sweet taste receptor to sucrose were verified by means of a functional hTAS1R2/hTAS1R3 sweet taste receptor assay. This in vitro screening revealed large differences in antisweet activity among the isolated compounds, where gymnemic acids XV and XIX showed the highest sweet suppressing activity. This broad-based molecular characterization of the sweet taste inhibiting activity of Gymnema sylvestre will enable further insight into the molecular basis of sweet taste modulation at the receptor level.

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Biofilms are aggregates of microbial cells encased in a highly hydrated matrix made up of self-produced extracellular polymeric substances (EPS) which consist of polysaccharides, proteins, nucleic acids, and lipids. While biofilm matrix polysaccharides are unraveled, there is still poor knowledge about the identity and function of matrix-associated proteins. With this work, we performed a comprehensive proteomic approach to disclose the identity of proteins associated with the matrix of biofilm-growing Burkholderia multivorans C1576 reference strain, a cystic fibrosis clinical isolate. Transmission electron microscopy showed that B. multivorans C1576 also releases outer membrane vesicles (OMVs) in the biofilm matrix, as already demonstrated for other Gram-negative species. The proteomic analysis revealed that cytoplasmic and membrane-bound proteins are widely represented in the matrix, while OMVs are highly enriched in outer membrane proteins and siderophores. Our data suggest that cell lysis and OMVs production are the most important sources of proteins for the B. multivorans C1576 biofilm matrix. Of note, some of the identified proteins are lytic enzymes, siderophores, and proteins involved in reactive oxygen species (ROS) scavenging. These proteins might help B. multivorans C1576 in host tissue invasion and defense towards immune system assaults.

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This study aimed to evaluate the polyphenolic composition along with the biological activity of guabiroba (Campomanesia xanthocarpa Berg.) fruits using comprehensive two-dimensional liquid chromatography (LC × LC). A simplex centroid design comprising three solvents (methanol, 2% acetic acid, and acetonitrile) was used to optimize the extraction mixture for polyphenols from ripe and unripe guabiroba fruits. A quantitative LC × LC platform was proposed to characterize the guabiroba extracts using a RP-Amide column and a C18 column in the first and second dimensions, respectively. Antidiabetic properties, using in vitro enzyme assay models and in vivo antioxidant activity with the eukaryote model Saccharomyces cerevisiae, was measured. Total phenolics compounds were more efficiently extracted with 2% acetic acid solution and acetonitrile (50:50, v/v). A total of 37 different compounds were identified and quantified using the proposed LC × LC method (linearity ranging from 0.9990 to 0.9994, intra- and interday precision from 0.40 to 10.57% and, accuracy from 81.89 to 108.98%). Significant differences were observed between ripe and unripe guabiroba fruits, especially for the compounds geraldone and methyl galangin isomer. Guabiroba fruits showed significant antidiabetic and antioxidant properties and may be potentially adopted as part of dietary strategies in the management of early stages of type 2 diabetes and associated complications.

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Beer is one the most consumed alcoholic beverage in the world and its contamination with mycotoxins is of public health concern. This study reports a fast and automated analytical procedure based on a multi-heart-cutting two-dimensional liquid chromatography tandem mass spectrometry method using electrospray ionization for the determination of seven mycotoxins (aflatoxins B1, B2, G2 and G1, ochratoxin A, fumonisins B1 and B2) in beers. The developed method was based on the heart-cutting 2D- HPLC technique in which only the specific portions of the first dimension, in the retention time of analytes, were transferred into the second dimension for the further separation and successive determination. The method uses two different chromatographic columns; in the first dimension, 50 µL of sample was injected on first column, and mycotoxins elution regions were collected in a loop and transferred into the second column for the separation of analytes. Each column operated in gradient elution mode in order to eliminate interfering compounds and improve separation and peak shape. After the optimization, the method has been validated according to EU regulation and finally applied for the analysis of forty beer samples collected from Italian supermarkets. Among all mycotoxins studied, fumonisins B1 was the most widely distributed in analysed beers (>21%) in the range from 0.6 to 12.3 ng mL-1. The automated methodology developed was able to determine accurately and simultaneously seven mycotoxins in beer. This provided a significant reduction of sample handle and, consequently of analysis time.

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From a structural point of view, the complete characterization of ADCs is a challenging task due to their high complexity. ADCs combine the heterogeneity of the initial antibody to the variability associated with the conjugation strategy, the manufacturing process, and the storage. Given the inherent complexity of these biomolecules, online comprehensive two-dimensional liquid chromatography (LC × LC) is an attractive technique to address the challenges associated with ADC characterization. Compared to conventional one-dimensional liquid chromatography techniques (1D-LC), LC × LC combines two different and complementary separation systems. In the context of ADC analysis, LC × LC has been proven to be a rapid and efficient analytical tool: (1) to provide a higher resolving power by increasing the overall peak capacity and thus allowing to gain more information within a single run and (2) to allow mass spectrometry (MS) coupling with some chromatographic techniques that are not MS-compatible and hence to facilitate the structural elucidation of ADCs. In this chapter, we present the coupling of different chromatographic techniques including hydrophobic interaction chromatography (HIC), reversed phase liquid chromatography (RPLC), size exclusion chromatography (SEC), ion exchange chromatography (IEX), and hydrophilic liquid chromatography (HILIC). The interest of HIC × SEC, SEC × SEC, HIC × RPLC, IEX × RPLC, RPLC × RPLC, and HILIC × RPLC, all hyphenated to high-resolution mass spectrometry (HRMS), is discussed in the context of the characterization of ADCs.

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The green microalga Haematococcus pluvialis has been widely studied due to its capacity to accumulate great amounts of astaxanthin, a high-value carotenoid with biological activities. In the present work, two green compressed fluid-based processes, pressurized liquid extraction (PLE) and supercritical antisolvent fractionation (SAF), are integrated to obtain an astaxanthin-enriched extract from this microalga. PLE was carried out using pressurized ethanol as solvent, for 20 min, at 10 MPa, and 50 °C as extraction temperature. Subsequently, the obtained extract was processed by SAF to further purify the carotenoid fraction. The SAF process was optimized using a 3-level factorial experimental design and considering three experimental variables: (i) CO2 pressure (10-30 MPa), (ii) percentage of water in the PLE extract (20-50%), and (iii) PLE extract/supercritical-CO2 flow rate ratio (0.0125-0.05). Total carotenoid content was evaluated in both extracts and raffinates. Best results were obtained at 30 MPa, 0.05 feed/SC-CO2 mass flow rate, and 20% (v/v) of water in the feed solution, achieving values of 120.3 mg g-1 carotenoids in extract (in the SAF extract fraction), which were significantly higher than those obtained in the original PLE extract. In parallel, a new fast two-dimensional comprehensive liquid chromatography (LC×LC) method was optimized to get the full carotenoid profile of these extracts in less than 25 min. This is the first time that the use of a C30 column is reported in an on-line LC×LC system. Graphical abstract.

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Modern food analysis is directed to the characterization of as many components as possible in food and food-related materials. The use of -omics technologies within a Foodomics approach requires the use of high throughput analytical techniques able to offer increased resolving power and capability to separate a high number of compounds. From this perspective, two-dimensional liquid chromatography has the potential to unravel very complex food matrices, providing with high resolving power and enhanced identification potential, particularly when coupled to mass spectrometry. This review presents an overview including the most notable two-dimensional liquid chromatography applications developed in the last ten years to study food safety, food quality and the relationship between health and food as well as for the characterization of particular groups of food components within a Foodomics perspective. Moreover, the latest developments and advances, limitations, future evolution and needs related to the use of this technique are critically discussed and commented.

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Omega-3 poly-unsaturated fatty acids have been shown to have beneficial effects on several inflammatory-driven endpoints such as cardiovascular diseases. The anti-inflammatory effects of docosahexaenoic acid (DHA) are largely mediated through various oxylipins. Yet, mechanistic insights are limited. Here, we measured 53 oxylipins using LC-MS/MS in an in vitro model of endothelial cell inflammation, and compared the changes induced by DHA to hydrocortisone, a well-established anti-inflammatory drug. DHA modified several oxylipins derived from different precursors such as DHA, AA, LA and EPA. In response to a TNFα and IL-1-ß challenge, DHA clearly reduced many COX-derived pro-inflammatory oxylipins, yet to a minor extent when compared to hydrocortisone. DHA also upregulated metabolites from the CYP and LOX pathways as opposed to hydrocortisone. Thus, DHA reduced pro-inflammation and enhanced pro-resolution, while hydrocortisone blunted both the pro- and anti-inflammatory pathways. Our results may fuel further research on the mitigation of corticosteroids adverse side-effects.

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Agrifood by-products are perfect candidates to be further processed under the concept of circular economy, in order to produce their valorization. Although significant amounts of food-related wastes that are discarded are produced worldwide, these might still be rich in valuable compounds. A strategy to further valorize agrifood-related by-products is based on pyrolysis processes. The result of this process is a liquid product termed bio-oil which is composed of an organic phase and an aqueous phase. This bio-oil is rich on a variety of components and its analysis implies several challenges. In this work, quantitative on-line comprehensive two-dimensional liquid chromatography (LC × LC) is proposed for the first time to characterize several aqueous phases of different bio-oils. Rice husk, peanut shell, spent coffee grounds, peach core and Eucalyptus sawdust biomasses were analyzed. The developed quantitative LC × LC method presented very good linearity, precision, reproducibility, recovery and LODs and LOQs as low as 0.05 µg mL-1 and 0.16 µg mL-1, respectively. As much as 28 components were simultaneously separated and quantified in those samples. Our results found that the composition of these bio-oils was different but strongly related to the agrifood by-product submitted to pyrolysis. The developed methodology is foreseen as a valuable tool for the quantitative study of other bio-oils, considering the great complexity and high dimensionality of these samples.

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