A Note on the Linearity of Real-valued Functions with Respect to Suitable Metrics

In this paper we prove that for every real-valued Morse function φ on a smooth closed manifold ℳ and every neighborhood U of its critical points a suitable Riemannian metric μ _U exists such that φ is linear outside U     

New Cyclophanes as Initiator Cores for the Construction of Dendritic Receptors: Host-guest complexation in aqueous solutions and structures of solid-state inclusion compounds

Cyclophanes 3 and 4 were prepared as initiator cores for the construction of dendrophanes (dendritic cydophanes) 1 and 2 , respectively, which mimic recognition sites buried in globular proteins. The tetra-oxy[6.1.6.1]paracyclophane 3 was prepared by a short three-step route (Scheme 1) and possesses a cavity binding site shaped by two diphenylmethane units suitable for the inclusion of flat aromatic substrates such as benzene and naphthalene derivatives as was shown by ¹H-NMR binding titrations in basic D₂O phosphate buffer (Table 1). The larger cyclophane 4 , shaped by two wider naphthyl(phenyl)methane spacers, was prepared in a longer, ten-step synthesis (Scheme 2) which included as a key intermediate the tetrabromocyclophane 5 . ¹H-NMR Binding studies in basic borate buffer in D₂O/CD₃OD demonstrated that 4 is an efficient steroid receptor. In a series of steroids (Table 1), complexation strength decreased with increasing substrate polarity and increasing number of polar substituents; in addition, electrostatic repulsion between carboxylate residues of host and guest also affected the binding affinity strongly. The conformationally flexible tetrabromocyclophane 5 displayed a pronounced tendency to form solid-state inclusion compounds of defined stoichiometry, which were analyzed by X-ray crystallography (Fig. 2). 1,2-Dichloroethane formed a cavity inclusion complex 5a with 1:1 stoichiometry, while in the 1:3 inclusion compound 5b with benzene, one guest is fully buried in the macrocyclic cavity and two others are positioned in channels between the Cyclophanes in the crystal lattice. In the 1:2 inclusion compound 5c , two toluene molecules penetrate with their aromatic rings the macrocyclic cavity from opposite sides in an antiparallel fashion. On the other hand, p-xylene (= 1,4-dimethylbenzene) in the 1:1 compound 5d is sandwiched between the cyclophane molecules with its two Me groups penetrating the cavities of the two macrocycles. In the 1:2 inclusion compound 5e with tetralin (= 1,2,3,4-tetrahydronaphthalene), both host and guest are statically disordered. The shape of the macrocycle in 5a – e depends strongly on the nature of the guest (Fig. 4). Characteristic for these compounds is the pronounced tendency of 5 to undergo regular stacking and to form channels for guest inclusion; these channels can infinitely extend across the macrocyclic cavities (Fig. 6) or in the crystal lattice between neighboring cyclophane stacks (Fig. 5). Also, the crystal lattice of 5c displays a remarkable zig-zag pattern of short Br…?O contacts between neighboring macrocycles (Fig. 7).     

Dendrophanes: Water-soluble dendritic receptors as models for buried recognition sites in globular proteins

Water-soluble dendritic cyclophanes (dendrophanes) of first ( 1 , 4 ), second ( 2 5 ), and third generation ( 3 6 ) with poly(ether amide) branching and 12, 36, and 108 terminal carboxylate groups, respectively, were prepared by divergent synthesis, and their molecular recognition properties in aqueous solutions were investigated. Dendrophanes 1 – 3 incorporate as the initiator core a tetraoxa[6.1.6.1]paracyclophane 7 with a suitably sized cavity for inclusion complexation of benzene or naphthalene derivatives. The initiator core in 4 – 6 is the [6.1.6.1]cyclo-phane 8 shaped by two naphthyl(phenyl) methane units with a cavity suitable for steroid incorporation. The syntheses of 1 – 6 involved sequential peptide coupling to monomer 9 , followed by ester hydrolysis (Schemes 1 and 4), Purification by gel-permeation chromatography (GPC; Fig. 3) and full spectral characterization were accomplished at the stage of the intermediate poly(methyl carboxylates) 10 – 12 and 23 – 25 , respectively. The third-generation 108-ester 25 was also independently prepared by a semi-convergent synthetic strategy, starting from 4 (Scheme 5). All dendrophanes with terminal ester groups were obtained in pure form according to the ¹³C-NMR spectral criterion (Figs, 1 and 5). The MALDI-TOF mass spectra of the third-generation derivative 25 (mol. wt. 19328 D) displayed the molecular ion as base peak, accompanied by a series of ions [M – n(1041 ± 7)]⁺, tentatively assigned as characteristic fragment ions of the poly(ether amide) cascade. A similar fragmentation pattern was also observed in the spectra of other higher-generation poly(ether amide) dendrimers. Attempts to prepare monodisperse fourth-generation dendrophanes by divergent synthesis failed. ¹H-NMR and fluorescence binding titrations in basic aqueous buffer solutions showed that dendrophanes 1 – 3 complexed benzene and naphthalene derivatives, whereas 4 – 6 bound the steroid testosterone. Complexation occurred exclusively at the cavity-binding site of the central cyclophane core rather than in fluctuating voids in the dendritic branches, and the association strength was similar to that of the complexes formed by the initiator cores 7 and 8 , respectively (Tables 1 and 3). Fluorescence titrations with 6-(p-toluidino)naphthalene-2-sulfonate as fluorescent probe in aqueous buffer showed that the micropolarity at the cyclophane core in dendrophanes 1 - 3 becomes increasingly reduced with increasing size and density of the dendritic superstructure; the polarity at the core of the third-generation compound 3 is similar to that of EtOH (Table 2). Host-guest exchange kinetics were remarkably fast and, except for receptor 3 , the stabilities of all dendrophane complexes could be evaluated by ¹H-NMR titrations. The rapid complexation-decomplexation kinetics are explained by the specific attachment of the dendritic wedges to large, nanometer-sized cyclophane initiator cores, which generates apertures in the surrounding dendritic superstructure.     

Glutamate receptor incorporated in a mixed hybrid bilayer lipid membrane array, as a sensing element of a biosensor working under flowing conditions

The realization of a reliable receptor biosensor requires stable, long-lasting, reconstituted biomembranes able to supply a suitable biomimetic environment where the receptor can properly work after incorporation. To this end, we developed a new method for preparing stable biological membranes that couple the biomimetic properties of BLMs (bilayer lipid membranes) with the high stability of HBMs (hybrid bilayer membranes); this gives rise to an innovative assembly, named MHBLM (mixed hybrid bilayer lipid membrane). The present work deals with the characterization of biosensors achieved by embedding an ionotropic glutamate receptor (GluR) on MHBLM. Thanks to signal (transmembrane current) amplification, which is typical of natural receptors, the biosensor here produced detects glutamate at a level of nmol L(-1). The transmembrane current changes linearly vs glutamate up to 100 nmol L(-1), while the limit of detection is 1 nmol L(-1). In addition, the biosensor response can be modulated both by receptor agonists (glycine) and antagonists (Mg(2+)) as well, and by exploiting the biosensor response, the distribution of different kinds of ionotropic GluR present in the purified sample, and embedded in MHBLM, was also evaluated. Finally, one of the most important aspects of this investigation is represented by the high stability of the biomimetic system, which allows the use of biosensor under flowing conditions, where the solutions flow on both biomembrane faces.     

Snake Venom Components: Tools and Cures to Target Cardiovascular Diseases

Cardiovascular diseases (CVDs) are considered as a major cause of death worldwide. Therefore, identifying and developing therapeutic strategies to treat and reduce the prevalence of CVDs is a major medical challenge. Several drugs used for the treatment of CVDs, such as captopril, emerged from natural products, namely snake venoms. These venoms are complex mixtures of bioactive molecules, which, among other physiological networks, target the cardiovascular system, leading to them being considered in the development and design of new drugs. In this review, we describe some snake venom molecules targeting the cardiovascular system such as phospholipase A2 (PLA2), natriuretic peptides (NPs), bradykinin-potentiating peptides (BPPs), cysteine-rich secretory proteins (CRISPs), disintegrins, fibrinolytic enzymes, and three-finger toxins (3FTXs). In addition, their molecular targets, and mechanisms of action—vasorelaxation, inhibition of platelet aggregation, cardioprotective activities—are discussed. The dissection of their biological effects at the molecular scale give insights for the development of future snake venom-derived drugs.     

Straight-Line Rectangular Drawings of Clustered Graphs

We show that every c-planar clustered graph has a straight-line c-planar drawing in which each cluster is represented by an axis-parallel rectangle, thus solving a problem posed by Eades, Feng, Lin, and Nagamochi (Algorithmica 44(1):1–32, 2006).     

Enhancing the dynamic range of targeted energy transfer in acoustics using several nonlinear membrane absorbers

In order to enhance the robustness and the energy range of efficiency of targeted energy transfer (TET) phenomena in acoustics, we discuss in this paper about the use of multiple nonlinear membrane absorbers (called nonlinear energy sinks or NES) placed in parallel. We show this way, mainly thanks to an experimental set-up with two membranes, that the different absorbers have additional effects that extend the efficiency and the possibilities of observation of TET. More precisely, we present the different behavior of the system under sinusoidal forcing and free oscillations, characterizing the phenomena for all input energies. The frequency responses are also presented, showing successive clipping of the original resonance peak of the system, and strongly modulated regimes (SMR). A model is finally used to generalize these results to more than two NES and to simulate the case of several very similar membranes in parallel which shows how to extend the existence zone of TET.     

Synthetic receptors for CG base pairs

Hydrogen-bond-mediated complexation of a CG base pair by a hexylureido phthalimide and a hexylureido isoindolin-1-one was studied by (1)H NMR spectroscopy in an organic solvent. Chemical shift data indicate that both receptors effectively bind the CG base pair from the major groove side.