Area-Minimizing Currents mod 2Q: Linear Regularity Theory

We establish a theory of Q -valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents mod(p) when p = 2Q , and to establish a first general partial regularity theorem for every p in any dimension and codimension . © 2020 Wiley Periodicals LLC.     

Protic Anions [H(B12X12)]− (X=F,Cl, Br,I) That Act as Brønsted Acids in the Gas Phase

The acidity of protic cations and neutral molecules has been studied extensively in the gas phase, and the gas‐phase acidity has been established previously as a very useful measure of the intrinsic acidity of neutral and cationic compounds. However, no data for any anionic acids were available prior to this study. The protic anions [H(B₁₂X₁₂)]^? (X=F, Cl, Br, I) are expected to be the most acidic anions known to date. Therefore, they were investigated in this study with respect to their ability to protonate neutral molecules in the gas phase by using a combination of mass spectrometry and quantum‐chemical calculations. For the first time it was shown that in the gas phase protic anions are also able to protonate neutral molecules and thus act as Brønsted acids. According to theoretical calculations, [H(B₁₂I₁₂)]^? is the most acidic gas‐phase anion, whereas in actual protonation experiments [H(B₁₂Cl₁₂)]^? is the most potent gas‐phase acidic anion for the protonation of neutral molecules. This discrepancy is explained by ion pairing and kinetic effects.     

Type S Non-Ribosomal Peptide Synthetases for the Rapid Generation of Tailormade Peptide Libraries**

Bacterial natural products in general, and non-ribosomally synthesized peptides in particular, are structurally diverse and provide us with a broad range of pharmaceutically relevant bioactivities. Yet, traditional natural product research suffers from rediscovering the same scaffolds and has been stigmatized as inefficient, time-, labour- and cost-intensive. Combinatorial chemistry, on the other hand, can produce new molecules in greater numbers, cheaper and in less time than traditional natural product discovery, but also fails to meet current medical needs due to the limited biologically relevant chemical space that can be addressed. Consequently, methods for the high throughput generation of new natural products would offer a new approach to identifying novel bioactive chemical entities for the hit to lead phase of drug discovery programs. As a follow-up to our previously published proof-of-principle study on generating bipartite type S non-ribosomal peptide synthetases (NRPSs), we now envisaged the de novo generation of non-ribosomal peptides (NRPs) on an unreached scale. Using synthetic zippers, we split NRPSs in up to three subunits and rapidly generated different bi- and tripartite NRPS libraries to produce 49 peptides, peptide derivatives, and de novo peptides at good titres up to 145 mg L⁻¹. A further advantage of type S NRPSs not only is the possibility to easily expand the created libraries by re-using previously created type S NRPS, but that functions of individual domains as well as domain-domain interactions can be studied and assigned rapidly.     

On the rate of convergence in the global central limit theorem for random sums of uniformly strong mixing random variables

Lithuanian Mathematical Journal - We present upper bounds of the integral $$ {\int}_{-\infty}^{\infty }{\left|x\right|}^l\left|\mathrm{P}\left\{{Z}_N0\left({S}_N{X}_1+\dots +{X}_N\right) $$ of...     

Modular Synthetic Approach to Carboranyl‒Biomolecules Conjugates

The development of novel, tumor-selective and boron-rich compounds as potential agents for use in boron neutron capture therapy (BNCT) represents a very important field in cancer treatment by radiation therapy. Here, we report the design and synthesis of two promising compounds that combine meta-carborane, a water-soluble monosaccharide and a linking unit, namely glycine or ethylenediamine, for facile coupling with various tumor-selective biomolecules bearing a free amino or carboxylic acid group. In this work, coupling experiments with two selected biomolecules, a coumarin derivative and folic acid, were included. The task of every component in this approach was carefully chosen: the carborane moiety supplies ten boron atoms, which is a tenfold increase in boron content compared to the l-boronophenylalanine (l-BPA) presently used in BNCT; the sugar moiety compensates for the hydrophobic character of the carborane; the linking unit, depending on the chosen biomolecule, acts as the connection between the tumor-selective component and the boron-rich moiety; and the respective tumor-selective biomolecule provides the necessary selectivity. This approach makes it possible to develop a modular and feasible strategy for the synthesis of readily obtainable boron-rich agents with optimized properties for potential applications in BNCT.     

Tuning Human Serum Albumin (HSA) Hydrogels through Albumin Glycation

The changes of technological properties of albumin-based hydrogels induced by increasing degrees of post-translational modification of the protein are reported. Maillard-type modification of amino acids arginine and lysine of albumin is achieved through glyoxal as an α-dicarbonyl compound. The degrees of modification are fine-tuned using different molar ratios of glyoxal. Hydrogels are thermally induced by heating highly concentrated precursor solutions above the protein's denaturation temperature. While the post-translational modifications are determined and quantified with mass spectrometry, continuous-wave (CW) electron paramagnetic resonance (EPR) spectroscopy shed light on the protein fatty acid binding capacity and changes thereof in solution and in the gel state. The viscoelastic behavior is characterized as a measure of the physical strength of the hydrogels. On the nanoscopic level, the modified albumins in low concentration solution reveal lower binding capacities with increasing degrees of modification. On the contrary, in the gel state, the binding capacity remains constant at all degrees of modifications. This indicates that the loss of fatty acid binding capacity for individual albumin molecules is partially compensated by new binding sites in the gel state, potentially formed by modified amino acids. Such, albumin glycation offers a fine-tuning method of technological and nanoscopic properties of these gels.