Metabolomics profiling for accurate and reliable quantification of organic acids that carry a carboxylic acid functional group in complex biological samples, remains a major analytical challenge in clinical chemistry research. Several procedural barriers associated with quantification of clinically important carboxylic containing metabolites (CCMs) including spontaneous decarboxylation during ionization, poor chromatographic resolution, and retention on a reverse-phase column, limit the sensitivity, specificity, and reproducibility of multiple-reaction monitoring (MRM) based LC-MS assay development. We report a targeted metabolomics-based analytical method for the quantification of CCMs using phenylenediamine derivatization. Accurate and sensitive quantification of CCMs is successfully demonstrated in an array of biological matrices. Recovery of metabolites from different matrices (plasma, serum, urine, saliva, tissues, and cell extracts), ranged from 90% to 105%, with all the CVs ≤ 10%. The method showed linearity over a broad dynamic range from 0.1 ng/mL to 10 µg/mL with linear regression coefficients of 0.99 for most of the metabolites tested herein, that covers broad-based applicability with the analysis of biological samples. In most cases the LODs were as low as 0.01 ng/mL. The phenylenediamine-based derivatization of carboxyl acid library consisting of more than 70 endogenous metabolites was constructed for metabolite identification, which spanned more than 40 biological pathways. The library included a wide-variety of structurally variant CCMs such as amino acids/conjugates, short to medium chain organic acids, di/tri-carboxylic acids/conjugates, fatty acids and some ring-containing CCMs. We compared the CCMs profiles of pancreatic cancer cells with normal pancreatic epithelial cells to test and validate the biological utility of this method. The comparative profiling between cancerous and normal cells resulted in the identification of potential biomarkers in pancreatic cancer, and their correlation with several key metabolic pathways such as central carbon energy metabolism, protein metabolism, including TCA cycle, glycolysis, Gln-Glu pathway, and biosynthesis of amino acids and unsaturated fatty acids was established. The method, described herein, for the first time enables the sensitive and highly specific quantification of CCMs on small sample size with high reproducibility in a high throughput manner. Given the biological and functional significance of this class of metabolites, this mass spectrometry based targeted quantitative assay, fills an important gap and is likely to support a wide range of applications for basic, clinical, and translational research.

Wheat is one of the global strategic crops and ranks third in terms of cereals production. Wheat crop is exposed to many fungal infections during the cultivation stages, some of which have the ability to secrete numbers of toxic secondary metabolites that threaten the quality of grains, consumer health, producer economics and global trade exchange. Fifty-four random samples were collected from wheat which originated from different countries. The samples included 14 of soft wheat to study the extent of their contamination with Deoxynivalenol (DON) and T-2 toxin by auto-ELISA technology and r-biopharm Microtiter plate. All samples were contaminated with DON toxin except one sample, and the contamination average ranged between 40.7 and 1018.8 µg kg-1. The highest contamination rates were in Lithuanian and the lowest in Indian wheat. Meanwhile the highest average level of T-2 toxin contamination was in Lithuanian wheat grains with a rate of 377.4µg kg-1 and the lowest in Polish wheat with an average of 115.3µg kg-1. GC-MS/MS and multiple reaction monitoring mode (MRM), was used to detect 15 triazole derivatives in collected samples, which may be used to combat fungal diseases on wheat during the growing season. Only 9 derivatives were found; Simeconazole, Penconazole, Hexaconazole, Cyproconazole, Diniconazole, Tebuconazole, Metconazole, Fenbuconazole and Difenoconazole. These derivatives varied according to the origin of wheat samples as well as their its concentration whereas, another 6 derivatives were not detected in all samples. A direct inverse relationship was found between the DON concentration in the samples and the residues of Simeconazole, Penconazole, Diniconazole, Tebuconazole, Metconazole, Fenbuconazole and Difenoconazole and the T-2 toxin showed the same relationship except for Tebuconazole. The safe and rational use of some triazole derivatives may be a new approach and a promising strategy not only to reduce plant diseases and their problems, but also to get rid of some mycotoxins as contaminates.

The present study employed a modifed QuEChERS method to systematically analyze the presence of fifteen Quinolones and seven Tetracyclines antibiotic residues in local animal food. Additionally, a multi-level-four-factor Box-Behnken design (BBD) within the framework of Response surface methodology (RSM) was utilized to evaluate the various factors affecting the detection efficiency of the sample pretreament procedure. The optimization was performed by Design Expert®, the factors including volume of the acetonitrle, the addition of formic acid, the duration of extract and the addition of EDTA were combined to experiment design until reach an optimal solution. Finally, the sample test was conducted by ultra-high performance liquid chromatography-quadrupole-linear ion trap mass spectrometry in both multiple reaction monitoring (MRM) and enhanced product ion (EPI) scan modes on a QTRAP® 5500 instrument. The overall average recoveries from actual samples fortified with 22 antibiotics at three levels ranged from 74.7 to 122.6% based on the use of matrix-fortified calibration with the variation ranging from 2.1 to 18.2% (n=6). The limits of detection and quantification were 0.3 μg kg-1 and 1.0 μg kg-1, respectively.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.