On the Distribution of the Information Density of Gaussian Random Vectors: Explicit Formulas and Tight Approximations.

Based on the canonical correlation analysis, we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as a general formula to calculate the central moments. Using the general results, we give closed-form expressions of the PDF and CDF and explicit formulas of the central moments for important special cases. Furthermore, we derive recurrence formulas and tight approximations of the general series representations, which allow efficient numerical calculations with an arbitrarily high accuracy as demonstrated with an implementation in Python publicly available on GitLab. Finally, we discuss the (in)validity of Gaussian approximations of the information density.

Biodiesel synthesis by direct transesterification of microalga Botryococcus braunii with continuous methanol reflux.

Direct transesterification of Botryococcus braunii with continuous acyl acceptor reflux was evaluated. This method combines in one step lipid extraction and esterification/transesterification. Fatty acid methyl esters (FAME) synthesis by direct conversion of microalgal biomass was carried out using sulfuric acid as catalyst and methanol as acyl acceptor. In this system, once lipids are extracted, they are contacted with the catalyst and methanol reaching 82%wt of FAME yield. To optimize the reaction conditions, a factorial design using surface response methodology was applied. The effects of catalyst concentration and co-solvent concentration were studied. Hexane was used as co-solvent for increasing lipid extraction performance. The incorporation of hexane in the reaction provoked an increase in FAME yield from 82% (pure methanol) to 95% when a 47%v/v of hexane was incorporated in the reaction. However, the selectivity towards non-saponifiable lipids such as sterols was increased, negatively affecting biodiesel quality.

Novel description of mcl-PHA biosynthesis by Pseudomonas chlororaphis from animal-derived waste.

A novel description of mcl-PHA biosynthesis by Ps. chlororaphis from tallow-based biodiesel as an inexpensive carbon feed stock is presented. Fermentation protocols, kinetic analysis, an efficient product recovery strategy, and product characterization are included. Maximum specific growth rates (µmax.) of 0.08 h(-1), 0.10 h(-1) and 0.13 h(-1), respectively, were achieved in three different fermentation set-ups. Volumetric productivity for mcl-PHA amounted to 0.071 g/L h, 0.094 g/L h and 0.138 g/L h, final intracellular PHA contents calculated from the sum of active biomass and PHA from 22.1 to 29.4 wt.-%, respectively. GC-FID analysis showed that the obtained biopolyester predominantly consists of 3-hydroxyoctanoate and 3-hydroxydecanoate, and, to a minor extent, 3-hydroxydodecanoate, 3-hydroxynonanoate, 3-hydroxyhexanoate, and 3-hydroxyheptanoate monomers. The overall distribution of the monomers remained similar, regardless to working volumes, biodiesel concentrations and pre-treatment of the inoculum.

Mathematical modeling of poly[(R)-3-hydroxyalkanoate] synthesis by Cupriavidus necator DSM 545 on substrates stemming from biodiesel production.

Two low structured mathematical models for fed-batch production of polyhydroxybutyrate and poly[hydroxybutyrate-co-hydroxyvalerate] by Cupriavidus necator DSM 545 on renewable substrates (glycerol and fatty acid methyl esters-FAME) combined with glucose and valeric acid, were established. The models were used for development/optimization of feeding strategies of carbon and nitrogen sources concerning PHA content and polymer/copolymer composition. Glycerol/glucose fermentation featured a max. specific growth rate of 0.171 h(-1), a max. specific production rate of 0.038 h(-1) and a PHB content of 64.5%, whereas the FAME/valeric acid fermentation resulted in a max. specific growth rate of 0.046 h(-1), a max. specific production rate of 0.07 h(-1) and 63.6% PHBV content with 4.3% of 3-hydroxyvalerate (3HV) in PHBV. A strong inhibition of glycerol consumption by glucose was confirmed (inhibition constant ki,G=4.28×10(-4) g L(-1)). Applied concentration of FAME (10-12 g L(-1)) positively influenced on PHBV synthesis. HV/PHBV ratio depends on applied VA concentration.

Novel sensitive determination of steryl glycosides in biodiesel by gas chromatography-mass spectroscopy.

A new method was developed for the quantitative analysis of steryl glycosides in biodiesel (fatty acid methyl esters). This method is much more sensitive than existing methods and has minimum limits of quantification of 50 µg/kg, compared to previously published minimum limits of quantification of about 15 mg/kg. The analysis is based on gas chromatography-mass spectroscopy determination of simple pre-treated and silylated samples via single ion monitoring at 204, 217, 247 m/z, which are specific ions for the silylated sugar moiety. Quantification was carried out using cholesteryl ß-D-glucopyranoside as internal standard. The modified synthesis and purification of the internal standard is also presented as well as the characterization by NMR and mass spectroscopy. The advantage of the method compared with other approaches is the simplified sample preparation avoiding extra pre-treatment steps coupled with complete derivatization of the sugar hydroxyl groups by using N,O-bis(trimethylsilyl)acetamide with 5% trimethylchlorosilane as derivatization reagent. On the given conditions high recovery rates ≥ 89% can be obtained. Evaluation of lab specific variance and intermediate precision underline the robustness of the method which will be further assessed by Round robin tests.

Determination of the composition of acetylglycerol mixtures by (1)H NMR followed by GC investigation.

Commercially available partly acetylated glycerols (mono- and diacetins) are a mixture of glycerol, 1- and 2-acetylglycerol, 1,2- and 1,3-diacetylglycerol, and triacetin. No exact analysis method is available. Comparisons of (1)H NMR measurements obtained using deuterated dimethyl sulfoxide (DMSO-d6) and DMSO-d6/15% D2O are sufficient to identify and determine quickly all the components. Advantages compared with the commonly used NMR solvent CDCl3 for fatty acid glycerides include the solubility of all the components and a highly informative OH signal pattern in a region between 4.36 and 5.26 ppm almost free of other signals. 2-Acetylglycerol (2-acetin) is shown to disproportionate even at 50 degrees C into a mixture of glycerol and acetylglycerol thereby making it difficult to quantify by liquid chromatography (LC) and gas chromatography (GC) methods. Complete (1)H chemical shift data for all five components allow for the identification of the components in the mixture and thus the determination of the composition. The NMR method with DMSO-d6 as solvent was used for acetins, propionins, and butyrins. Semipreparative high-performance liquid chromatography (HPLC) on an RP18 column led to moderately pure 1-monoacetin and a mixture of diacylated species. Electron impact mass spectra show for all the components very characteristic fragmentation patterns with loss of AcOCH2 radicals, in contrast to the well-known pattern of longer-chained fatty acid derivatives that show preferred first-step loss of acyl-O radicals.

Tandem mass spectrometric analysis of a complex triterpene saponin mixture of Chenopodium quinoa.

A nano-HPLC electrospray ionization multi-stage tandem mass spectrometry (nLC-ESI-MS/MS) approach was applied to a complex crude triterpene saponin extract of Chenopodium quinoa seed coats. In ESI-MS/MS spectra of triterpene saponins, characteristic fragmentation reactions are observed and allow the determination of aglycones, saccharide sequences, compositions, and branching. Fragmentation of aglycones provided further structural information. The chemical complexity of the mixture was resolved by a complete profiling. Eighty-seven triterpene saponins comprising 19 reported and 68 novel components were identified and studied by MS. In addition to four reported, five novel triterpene aglycones were detected and characterized according to their fragmentation reactions in ESI-MS/MS and electron ionization mass spectrometry (EI-MS). As a novelty fragmentation pathways were proposed and analyzed based upon quantum chemical calculations using a hybrid Hartree-Fock density functional method. Accuracy of the assignment procedure was proven by isolation and structure determination of a novel compound. As the relative distribution and composition of saponins varies between different cultivars and soils, the presented strategy allows a rapid and complete analysis of Chenopodium quinoa saponin distribution and composition, and is particularly suitable for quality control and screening of extracts designated for pharmaceutical, agricultural, and industrial applications.

Quantification of primary fatty acid amides in commercial tallow and tallow fatty acid methyl esters by HPLC-APCI-MS.

Primary fatty acid amides are a group of biologically highly active compounds which were already identified in nature. Here, these substances were determined in tallow and tallow fatty acid methyl esters for the first time. As tallow is growing in importance as an oleochemical feedstock for the soap manufacturing, the surfactant as well as the biodiesel industry, the amounts of primary fatty acid amides have to be considered. As these compounds are insoluble in tallow as well as in the corresponding product e.g. tallow fatty acid methyl esters, filter plugging can occur. For the quantification in these matrices a purification step and a LC-APCI-MS method were developed. Although quantification of these compounds can be performed by GC-MS, the presented approach omitted any derivatization and increased the sensitivity by two orders of magnitude. Internal standard calibration using heptadecanoic acid amide and validation of the method yielded a limit of detection of 18.5 fmol and recoveries for the tallow and fatty acid methyl ester matrices of 93% and 95%, respectively. A group of commercially available samples were investigated for their content of fatty acid amides resulting in an amount of up to 0.54%m/m (g per 100 g) in tallow and up to 0.16%m/m (g per 100 g) in fatty acid methyl esters.

Novel 12-deoxy-16-hydroxyphorbol diesters isolated from the seed oil of Jatropha curcas.

Six unstable intramolecular diterpene esters were isolated from the seed oil of Jatropha curcas. Five of these, Jatropha factors C(2)-C(6) (3-7), are new natural products, and the structure of the known Jatropha factor C(1) (2) has been revised. All compounds possess the same diterpene moiety, namely, 12-deoxy-16-hydroxyphorbol (1). The dicarboxylic acid moieties of 2-5 contain a bicyclo[3.1.0]hexane unit, and those of 6 and 7 a cyclobutane unit, which is described for the first time within this compound class. Compounds 4 and 5 are C-8' epimers. The structures of 2-7 were elucidated by spectroscopic methods and give an insight into the biogenesis of the characterized substances.