New representation and factorizations of the higher-order ultraspherical-type differential equations

The paper deals with the class of linear differential equations of any even order 2α+4$2\alpha +4$, α∈_N0$\alpha \in {\mathbb{N}}_0$, which are associated with the so-called ultraspherical-type polynomials. These polynomials form an orthogonal system on the interval [−1,1]$[-1,1]$ with respect to the ultraspherical weight function (1−x²)^α${(1-x^2)}^{\alpha }$ and additional point masses of equal size at the two endpoints. The differential equations of “ultraspherical-type” were developed by R. Koekoek in 1994 by utilizing special function methods. In the present paper, a new and completely elementary representation of these higher-order differential equations is presented. This result is used to deduce the orthogonality relation of the ultraspherical-type polynomials directly from the differential equation property. Moreover, we introduce two types of factorizations of the corresponding differential operators of order 2α+4$2\alpha +4$ into a product of α+2$\alpha +2$ linear second-order operators.     

Batch versus Flow Photochemistry: A Revealing Comparison of Yield and Productivity

The use of flow photochemistry and its apparent superiority over batch has been reported by a number of groups in recent years. To rigorously determine whether flow does indeed have an advantage over batch, a broad range of synthetic photochemical transformations were optimized in both reactor modes and their yields and productivities compared. Surprisingly, yields were essentially identical in all comparative cases. Even more revealing was the observation that the productivity of flow reactors varied very little to that of their batch counterparts when the key reaction parameters were matched. Those with a single layer of fluorinated ethylene propylene (FEP) had an average productivity 20 % lower than that of batch, whereas three‐layer reactors were 20 % more productive. Finally, the utility of flow chemistry was demonstrated in the scale‐up of the ring‐opening reaction of a potentially explosive [1.1.1] propellane with butane‐2,3‐dione.     

Chemical Probing of the Human Sirtuin 5 Active Site Reveals Its Substrate Acyl Specificity and Peptide‐Based Inhibitors

Sirtuins are NAD⁺‐dependent deacetylases acting as sensors in metabolic pathways and stress response. In mammals there are seven isoforms. The mitochondrial sirtuin 5 is a weak deacetylase but a very efficient demalonylase and desuccinylase; however, its substrate acyl specificity has not been systematically analyzed. Herein, we investigated a carbamoyl phosphate synthetase 1 derived peptide substrate and modified the lysine side chain systematically to determine the acyl specificity of Sirt5. From that point we designed six potent peptide‐based inhibitors that interact with the NAD⁺ binding pocket. To characterize the interaction details causing the different substrate and inhibition properties we report several X‐ray crystal structures of Sirt5 complexed with these peptides. Our results reveal the Sirt5 acyl selectivity and its molecular basis and enable the design of inhibitors for Sirt5.     

Endless: A Purine‐Binding RNA Motif that Can Be Expressed in Cells

It is becoming increasingly clear that nature uses RNAs extensively for regulating vital functions of the cell, and short sequences are frequently used to suppress gene expression. However, controlling the concentration of small molecules intracellularly through designed RNA sequences that fold into ligand‐binding structures is difficult. The development of “endless”, a triplex‐based folding motif that can be expressed in mammalian cells and binds the second messenger 3′,5′‐cyclic guanosine monophosphate (cGMP), is described. In vitro, DNA or RNA versions of endless show low micromolar to nanomolar dissociation constants for cGMP. To test its functionality in vivo, four endless RNA motifs arranged in tandem were co‐expressed with a fluorescent cGMP sensor protein in murine vascular smooth muscle cells. Nitric oxide induced endogenous cGMP signals were suppressed in endless‐expressing cells compared to cells expressing a control motif, which suggests that endless can act as a genetically encoded cGMP sink to modulate signal transduction in cells.     

Long-Lived Charge-Transfer State Induced by Spin-Orbit Charge Transfer Intersystem Crossing (SOCT-ISC) in a Compact Spiro Electron Donor/Acceptor Dyad

We prepared conceptually novel, fully rigid, spiro compact electron donor (Rhodamine B, lactam form, RB)/acceptor (naphthalimide; NI) orthogonal dyad to attain the long-lived triplet charge-transfer (³CT) state, based on the electron spin control using spin-orbit charge transfer intersystem crossing (SOCT-ISC). Transient absorption (TA) spectra indicate the first charge separation (CS) takes place within 2.5 ps, subsequent SOCT-ISC takes 8 ns to produce the ³NI* state. Then the slow secondary CS (125 ns) gives the long-lived ³CT state (0.94 μs in deaerated n-hexane) with high energy level (ca. 2.12 eV). The cascade photophysical processes of the dyad upon photoexcitation are summarized as ¹NI*→¹CT→³NI*→³CT. With time-resolved electron paramagnetic resonance (TREPR) spectra, an EEEAAA electron-spin polarization pattern was observed for the naphthalimide-localized triplet state. Our spiro compact dyad structure and the electron spin-control approach is different to previous methods for which invoking transition-metal coordination or chromophores with intrinsic ISC ability is mandatory.     

Absolute Configuration of Small Molecules by Co‐Crystallization

The most reliable method to determine the absolute configuration of chiral molecules is X‐ray crystallography, but small molecules can be difficult to crystallize. We report rapid co‐crystallization of tetraaryladamantanes with small molecules as different as n‐decane to nicotine to produce crystals for X‐ray analysis and the assignment of absolute configuration when the molecules are chiral. A screen of 52 diverse compounds gave inclusion in co‐crystals for 88 % of all cases and a high‐resolution structure in 77 % of cases. Furthermore, starting from three milligrams of analyte, a combination of NMR spectroscopy and X‐ray crystallography produced a full structure in less than three days using an adamantane crystallization chaperone that encapsulates the analyte at room temperature.     

Investigation of polynuclear Zr(IV) hydroxide complexes by nanoelectrospray mass-spectrometry combined with XAFS

Polynuclear species of zirconium in acidic aqueous solution are investigated by combining X-ray absorption spectroscopy (XAFS) and nanoelectrospray mass spectrometry (ESI-MS). Species distributions are measured between pH_C 0 and pH_C 3 for [Zr] = 1.5–10 mM. While the monomer remains a minor species, with increasing pH the degree of polymerization increases and the formation of tetramers, pentamers, octamers, and larger polymers is observed. The high resolution of the mass spectrometer permits the unambiguous determination of polynuclear zirconium hydroxide complexes by means of their isotopic patterns. The relative abundances of mononuclear and polynuclear species present simultaneously in solution are measured, even if one of the species contributes only 0.1% of the Zr concentration. For the first time it has been directly observed that the hydrolysis of polynuclear Zr species is a continuous process which leads to charge compensation through the sequential substitution of water molecules by hydroxide ligands until doubly charged polymers dominate at conditions (H⁺ and Zr concentrations) close to the solubility of Zr(OH)₄(am). The invasiveness of the electrospray process was minimized by using very mild declustering conditions, leaving the polynuclear species within a solvent shell of approximately 20 water molecules. Figure Schematic Diagram of Multiplexed Measurement of 9 Anti-Nuclear Antibodies Using the AtheNa Multilyte Assay     

DNA‐Hybrid‐Gated Multifunctional Mesoporous Silica Nanocarriers for Dual‐Targeted and MicroRNA‐Responsive Controlled Drug Delivery

The design of an ideal drug delivery system with targeted recognition and zero premature release, especially controlled and specific release that is triggered by an exclusive endogenous stimulus, is a great challenge. A traceable and aptamer‐targeted drug nanocarrier has now been developed; the nanocarrier was obtained by capping mesoporous silica‐coated quantum dots with a programmable DNA hybrid, and the drug release was controlled by microRNA. Once the nanocarriers had been delivered into HeLa cells by aptamer‐mediated recognition and endocytosis, the overexpressed endogenous miR‐21 served as an exclusive key to unlock the nanocarriers by competitive hybridization with the DNA hybrid, which led to a sustained lethality of the HeLa cells. If microRNA that is exclusively expressed in specific pathological cell was screened, a combination of chemotherapy and gene therapy should pave the way for a targeted and personalized treatment of human diseases.     

Long‐Lived Charge‐Transfer State Induced by Spin‐Orbit Charge Transfer Intersystem Crossing (SOCT‐ISC) in a Compact Spiro Electron Donor/Acceptor Dyad

We prepared conceptually novel, fully rigid, spiro compact electron donor (Rhodamine B, lactam form, RB)/acceptor (naphthalimide; NI) orthogonal dyad to attain the long‐lived triplet charge‐transfer (³CT) state, based on the electron spin control using spin‐orbit charge transfer intersystem crossing (SOCT‐ISC). Transient absorption (TA) spectra indicate the first charge separation (CS) takes place within 2.5 ps, subsequent SOCT‐ISC takes 8 ns to produce the ³NI* state. Then the slow secondary CS (125 ns) gives the long‐lived ³CT state (0.94 μs in deaerated n‐hexane) with high energy level (ca. 2.12 eV). The cascade photophysical processes of the dyad upon photoexcitation are summarized as ¹NI*→¹CT→³NI*→³CT. With time‐resolved electron paramagnetic resonance (TREPR) spectra, an EEEAAA electron‐spin polarization pattern was observed for the naphthalimide‐localized triplet state. Our spiro compact dyad structure and the electron spin‐control approach is different to previous methods for which invoking transition‐metal coordination or chromophores with intrinsic ISC ability is mandatory.