Quantitative results for the limiting semigroup generated by the multidimensional Bernstein operators

Semigroup Forum - A quantitative estimate for the Trotter’s approximation theorem for the limiting semigroup of operators generated by the multidimensional Bernstein operators on a simplex is...     

An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube

Transport in Porous Media - In this paper, we derive upscaled equations for modeling biofilm growth in porous media. The resulting macroscale mathematical models consider permeable multi-species...     

The Proteome‐Wide Potential for Reversible Covalency at Cysteine

Reversible covalency, achieved with, for instance, highly electron‐deficient olefins, offers a compelling strategy to design chemical probes and drugs that benefit from the sustained target engagement afforded by irreversible compounds, while avoiding permanent protein modification. Reversible covalency has mainly been evaluated for cysteine residues in individual kinases and the broader potential for this strategy to engage cysteines across the proteome remains unexplored. Herein, we describe a mass‐spectrometry‐based platform that integrates gel filtration with activity‐based protein profiling to assess cysteine residues across the human proteome for both irreversible and reversible interactions with small‐molecule electrophiles. Using this method, we identify numerous cysteine residues from diverse protein classes that are reversibly engaged by cyanoacrylamide fragment electrophiles, revealing the broad potential for reversible covalency as a strategy for chemical‐probe discovery.     

Unprecedented Relaxivity Gap in pH-Responsive FeIII-Based MRI Probes

Two mononuclear ferric complexes are reported that respond to a pH change with a 27- and 71-fold jump, respectively, in their capacity to accelerate the longitudinal relaxation rate of water-hydrogen nuclei, and this starting from a negligible base value of only 0.06. This unprecedented performance bodes well for tackling the sensitivity issues hampering the development of Molecular MRI. The two chelates also excel in the fully reversible and fatigue-less nature of this phenomenon. The structural reasons for this performance reside in the macrocyclic nature of the hexa-dentate ligand, as well as the presence of a single pendant arm displaying a five-membered lactam or carbamate which show (perturbed) pK_a values of 3.5 in the context of this N6 N5O1 coordination motif.     

Positive radial solutions for Dirichlet problems via a Harnack-type inequality

We deal with the existence and localization of positive radial solutions for Dirichlet problems involving $\varphi$-Laplacian operators in a ball. In particular, $p$-Laplacian and Minkowski-curvature equations are considered. Our approach relies on fixed point index techniques, which work thanks to a Harnack-type inequality in terms of a seminorm. As a consequence of the localization result, it is also derived the existence of several (even infinitely many) positive solutions.