Gadolinium Photocatalysis: Dearomative [2+2] Cycloaddition/Ring‐Expansion Sequence with Indoles

Lanthanide photocatalysts are much less investigated in synthetic chemistry than rare and expensive late transition metals. We herein introduce Gd^III photocatalysis of a highly regioselective, intermolecular [2+2] photocycloaddition/ring‐expansion sequence with indoles, which could provide divergent access to cyclopenta[b]indoles and indolines. A simple and commercially available Gd(OTf)₃ salt is sufficient for this visible‐violet‐light‐induced transformation. The reaction proceeds either through a transient or start‐to‐end dearomatization cascade and shows excellent regioselectivity (usually >95:5 r.r.), broad scope (59 examples), good functional group tolerance and facile scale‐up under mild, direct visible‐light‐excitation conditions. Mechanistic investigations reveal that direct excitation of the Gd(OTf)₃/indole mixture gives an excited state intermediate, which undergoes the subsequent [2+2] cycloaddition and cyclobutane‐expansion cascade.     

Synthesis of Small‐Molecule Fluorescent Probes for the In Vitro Imaging of Calcium‐Activated Potassium Channel KCa3.1

Small‐molecule probes for the in vitro imaging of K_Ca3.1 channel‐expressing cells were developed. Senicapoc, showing high affinity and selectivity for the K_Ca3.1 channels, was chosen as the targeting component. BODIPY dyes 15 – 20 were synthesized and connected by a Cu^I‐catalyzed azide–alkyne [3+2]cycloaddition with propargyl ether senicapoc derivative 8 , yielding fluorescently labeled ligands 21 – 26 . The dimethylpyrrole‐based imaging probes 25 and 26 allow staining of K_Ca3.1 channels in NSCLC cells. The specificity was shown by removing the punctate staining pattern by pre‐incubation with senicapoc. The density of K_Ca3.1 channels detected with 25 and by immunostaining was identical. The punctate structure of the labeled channels could also be observed in living cells. Molecular modeling showed binding of the senicapoc‐targeting component towards the binding site within the ion channel and orientation of the linker with the dye along the inner surface of the ion channel.     

Coordination polymers and a dinuclear complex constructed from zinc(II) ions and fluorescein: iodine adsorption and optical properties

Abstract

1-D coordination polymers, ¹_∞[Zn(fl)₂]·2EtOH and ¹_∞[Zn(fl)₂]·2MeOH, and a dinuclear complex, [{Zn(fl)₂}₂(dienpip)]·4H₂O·4EtOH (dienpip?= N,N′-bis(2-aminoethyl)piperazine), were obtained using Zn(II) ions and fluorescein anions (fl). Thermal analysis shows stability of the polymers after solvent removal up to more than 400?°C. Crystallization solvent molecules were removed under reduced pressure with the preservation of the polymeric structure, ¹_∞[Zn(fl)₂]. Desolvated crystals were exposed to I₂ vapors and the crystal structure determination by X-ray diffraction confirmed the presence of I₂ molecules in the channels generated in crystals by the metal-organic framework. The iodine content, evaluated by X-ray diffraction, corresponds to the overall formula ¹_∞[Zn(fl)₂]·0.3I₂. The optical properties of the coordination polymers and the dinuclear complex have been investigated.     

Crystal energy functions via the charge in types A and C

The Ram–Yip formula for Macdonald polynomials (at t = 0) provides a statistic which we call charge. In types A and C it can be defined on tensor products of Kashiwara–Nakashima single column crystals. In this paper we prove that the charge is equal to the (negative of the) energy function on affine crystals. The algorithm for computing charge is much simpler and can be more efficiently computed than the recursive definition of energy in terms of the combinatorial R-matrix.     

On a parabolic–elliptic chemotactic model with coupled boundary conditions

This paper deals with a nonlinear system of parabolic–elliptic type with a logistic source term and coupled boundary conditions related to pattern formation. We prove the existence of a unique positive global in time classical solution. We also analyze the associated stationary problem. Moreover it is proved, under the assumption of sufficiently strong logistic damping, that there is only one nonzero homogeneous equilibrium, and all the solutions to the nonstationary problem tend to this steady state for large times.     

A relativistic quark-diquark model for the nucleon

We developed a constituent quark-diquark model for the nucleon and its resonances using a harmonic oscillator potential for the interaction. The effects due to relativistic kinetic energy correction are studied. Finally, charge form factor of the model is calculated and compared with experimental data.      

Thinking Transport as a Twist

The determination of the conductivity of a deterministic or stochastic classical system coupled to reservoirs at its ends can in general be mapped onto the problem of computing the stiffness (the ‘energy’ cost of twisting the boundaries) of a quantum-like system. The nature of the coupling to the reservoirs determines the details of the mechanical coupling of the torque at the ends.     

Duality and Hidden Symmetries in Interacting Particle Systems

In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the “hidden” symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil its SU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.