Het(aryl)isatin to het(aryl)aminoindoline scaffold hopping: A route to selective inhibitors of matrix metalloproteinases

Matrix metalloproteinases (MMPs) are a large family of zinc-dependent endoproteases known to exert multiple regulatory roles in tumor progression. A variety of chemical classes have been explored for targeting individual MMP isoforms. In the present study, we further developed our isatin based scaffold BB0223107 capable of binding to and inactivating MMP-2 in a zinc-independent manner (Agamennone et al., 2016). Forty four new compounds were synthesized based on the modified BB0223107. All compounds were tested in enzyme inhibition assays against MMP-2, ?8 and ?13. SAR studies demonstrated that 5-het(aryl)-3-aminoindolin-2-ones (37–39) were active toward MMP-2 and MMP-13. The most potent compounds 33 and 37 displayed an IC₅₀ of 3 µM against MMP-13 and showed a negligible activity toward MMP-8; almost all new compounds were inactive toward MMP-8. Replacement of the isatin ring with a biaryl system (compound 33) did not decrease the potency against MMP-13 but reduced the selectivity. Structure-based computational studies were carried out to rationalize the inhibitory activity data. The analysis of binding geometries confirmed that all fragments occupied the S1′ site in the three enzymes while no ligand was able to bind the catalytic zinc ion. To the best of our knowledge, this is the first example of 3-aminoindolin-2-one-based MMP inhibitors that, based on the computer modeling study, do not coordinate the zinc ion. Thus, the het(aryl)-3-aminoindolin-2-one derivatives emerge as a drug-like and promising chemotype that, along with the hetaryl variations, represents an alternative and thrifty tool for chemical space exploration aimed at MMP inhibitor design.     

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Versatile Near-Infrared Super-Resolution Imaging of Amyloid Fibrils with the Fluorogenic Probe CRANAD-2

CRANAD-2 is a fluorogenic curcumin derivative used for near-infrared detection and imaging in vivo of amyloid aggregates, which are involved in neurodegenerative diseases. We explore the performance of CRANAD-2 in two super-resolution imaging techniques, namely stimulated emission depletion (STED) and single-molecule localization microscopy (SMLM), with markedly different fluorophore requirements. By conveniently adapting the concentration of CRANAD-2, which transiently binds to amyloid fibrils, we show that it performs well in both techniques, achieving a resolution in the range of 45–55 nm. Correlation of SMLM with atomic force microscopy (AFM) validates the resolution of fine features in the reconstructed super-resolved image. The good performance and versatility of CRANAD-2 provides a powerful tool for near-infrared nanoscopic imaging of amyloids in vitro and in vivo.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Synthesis and characterization of VO–vanillin complex immobilized on MCM-41 and its facile catalytic application in the sulfoxidation reaction,and synthesis of 2,3-dihydroquinazolin-4(1H)-ones and disulfides in green media

In this work, a vanillin complex is immobilized onto MCM-41 and characterized by FT-IR, X-ray diffraction, scanning electron microscopy, energy dispersive spectroscopy, thermogravimetric analysis, and BET techniques. This supported Schiff base complex was found to be an efficient and recoverable catalyst for the chemoselective oxidation of sulfides into sulfoxides and thiols into their corresponding disulfides (using hydrogen peroxide as a green oxidant) and also a suitable catalyst for the preparation of 2,3-dihydroquinazolin-4(1H)-one derivatives in water at 90°C. Using this protocol, we show that a variety of disulfides, sulfoxides, and 2,3-dihydroquinazolin-4(1H)-one derivatives can be synthesized in green conditions. The catalyst can be recovered and recycled for further reactions without appreciable loss of catalytic performance.     

Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.