Dynamics of an intra-host model of malaria with a constant drug efficiency

In this paper, we investigate the dynamics of an intra-host model of malaria with logistic red blood growth, treatment and immune response. We provide a theoretical study of the model. We derive the basic reproduction number $\mathcal R_f$ which determines the extinction and the persistence of malaria within the body of a host. We compute equilibria and study their stability. More precisely, we show that there exists a threshold parameter $\zeta$ such that if $\mathcal R_f\leq\zeta\leq1$, the disease-free equilibrium is globally asymptotically stable. However, if $\mathcal R_f>1$, there exist two malaria infection equilibria which are locally asymptotically stable: one malaria infection equilibrium without immune response and one malaria infection equilibrium with immune response. The sensitivity analysis of the model has been performed in order to determine the impact of related parameters on outbreak severity. The theory is supported by numerical simulations. We also derive a spatio-temporal model, using Diffusion-Reaction equations to model parasites dispersal. Finally, we provide numerical simulations for parasites spreading, and test different treatment scenarios.     

Contrast of optical activity and rogue wave propagation in chiral materials

Nonlinear Dynamics - We report the contrast of optical activity and properties of nonparaxial optical rogue waves for the higher-order nonparaxial chiral nonlinear Schrödinger (NLS) equation....     

Meet-irreducible submaximal clones determined by nontrivial equivalence relations

Let θ and ρ be a nontrivial equivalence relation and a binary relation on a finite set A, respectively. It is known from Rosenberg’s classification theorem (1965) that the clone Pol θ, which consists of all operations on A that preserve θ, is among the maximal clones on A. In the present paper, we find all binary relations ρ such that the clone Pol ρ is a meet-irreducible maximal subclone of Pol θ.     

New two-step sequence involving a hetero-Diels-Alder and a nonphenolic oxidative coupling reaction: a convergent access to analogs of steganacin

A new family of analogs of steganacin, an important antimitotic compound, was accessed. It takes advantage of a completely stereoselective sequence of two key steps. The central dihydropyrane core is built by a highly diastereoselective and facially controlled hetero-Diels-Alder reaction. It is followed by a nonphenolic biaryl oxidative coupling with a complete atropo-stereoselectivity. It leads to a quick way to form cyclic biaryl lignans.     

Luminol anchors improve the electrochemical-tyrosine-click labelling of proteins

New methods for chemo-selective modifications of peptides and native proteins are important in chemical biology and for the development of therapeutic conjugates. Less abundant and uncharged amino-acid residues are interesting targets to form less heterogeneous conjugates and preserve biological functions. Phenylurazole (PhUr), N-methylphenylurazole (NMePhUr) and N-methylluminol (NMeLum) derivatives were described as tyrosine (Y) anchors after chemical or enzymatic oxidations. Recently, we developed the first electrochemical Y-bioconjugation method coined eY-click to activate PhUr in biocompatible media. In this work, we assessed the limitations, benefits and relative efficiencies of eY-click conjugations performed with a set of PhUr, NMePhUr and NMeLum derivatives. Results evidenced a high efficiency of NMeLum that showed a complete Y-chemoselectivity on polypeptides and biologically relevant proteins after soft electrochemical activation. Side reactions on nucleophilic or heteroaromatic amino-acids such as lysine or tryptophan were never observed during mass spectrometry analysis. Myoglobine, bovine serum albumin, a plant mannosidase, glucose oxidase and the therapeutically relevant antibody trastuzumab were efficiently labelled with a fluorescent probe in a two-step approach combining eY-click and strain-promoted azide–alkyne cyclization (SPAAC). The proteins conserved their structural integrity as observed by circular dichroism and the trastuzumab conjugate showed a similar binding affinity for the natural HER2 ligand as shown by bio-layer interferometry. Compared to our previously described protocol with PhUr, eY-click with NMeLum species showed faster reaction kinetics, higher (complete) Y-chemoselectivity and reactivity, and offers the interesting possibility of the double tagging of solvent-exposed Y.

We assessed the relative efficiencies of tyrosine anchors in the electrochemical conjugation of peptides and proteins. Luminol derivatives showed faster reaction kinetics, complete tyrosine-chemoselectivity, and possible double modification.     

Molecular decompositions and interpolation

Molecular decompositions for functions in weighted Bergman spaces are extended to two homogeneous, non symmetric Siegel domains of type II, as well as interpolation by functions in weighted Bergman spaces. An ingredient in the proof is a generalization of a lemma due to Koranyi. We also specify the hypotheses in the symmetric case.