How often do simple dynamical processes have infinitely many coexisting sinks?

This work concerns the nature of chaotic dynamical processes. Sheldon Newhouse wrote on dynamical processes (depending on a parameter )x _x+1=T(x _n ; ), wherex is in the plane, such as might arise when studying Poincaré return maps for autonomous differential equations in IR³. He proved that if the system is chaotic there will very often be existing parameter values for which there are infinitely many periodic attractors coexisting in a bounded region of the plane, and that such parameter values would be dense in some interval. The fact that infinitely many coexisting sinks can occur brings into question the very nature of the foundations of chaotic dynamical processes. We prove, for an apparently typical situation, that Newhouse's construction yields only a set of parameter values of measure zero.This research was supported in part by grants from the Air Force Office of Scientific Research AFOSR 81-0217, the Consiglio Nazionale delle Ricerche-Comitato per le Matematiche, and the National Science Foundation DMS 84-19110On leave from: Dipartimento di Matematica G. Castel nuovo Universita di Roma La Sapienza P. le Aldo Moro 5, I-00185 Rome, Italy     

Synthetic erythropoietic proteins: tuning biological performance by site-specific polymer attachment

Chemical synthesis in combination with precision polymer modification allows the systematic exploration of the effect of protein properties, such as charge and hydrodynamic radius, on potency using defined, homogeneous conjugates. A series of polymer-modified synthetic erythropoiesis proteins were constructed that had a polypeptide chain similar to the amino acid sequence of human erythropoietin but differed significantly in the number and type of attached polymers. The analogs differed in charge from +5 to -26 at neutral pH and varied in molecular weight from 30 to 54 kDa. All were active in an in vitro cell proliferation assay. However, in vivo potency was found to be strongly dependent on overall charge and size. The trends observed in this study may serve as starting points for the construction of more potent synthetic EPO analogs in the future.     

Supramolecular helical mesomorphic polymers. Chiral induction through H-bonding

The work described here concerns a challenge of general interest in supramolecular chemistry: the achievement of chiral helical organizations with controlled structures. This work provides a strategy to obtain supramolecular polymers in which a chiral helical conformation has been induced by a noncovalent association, that is, through hydrogen bonding. Polycatenar 2,4,6-triarylamino-1,3,5-triazines, which organize into columnar mesophases and are susceptible to H-bonding interactions, were chosen as a starting point to build up the chiral supramolecular structure. The stacking of these mesogens has been forced to wind in a helical way by means of H-bond association with (R)-3-methyladipic acid, within the mesophase. The optically active columnar organization has been studied in depth by optical microscopy, differential scanning calorimetry (DSC), X-ray diffraction, and circular dichroism. Formation of stable complexes between the triazine units and (R)-3-methyladipic acid has also been investigated by means of NMR diffusion-ordered spectroscopy (DOSY) experiments in chloroform.     

Phase transition and mixed oxide-proton conductivity in germanium oxy-apatites

La_9.75□_0.25(Ge₆O₂₄)O_2.62 oxy-apatite shows a phase transition from triclinic to hexagonal symmetry at approximately 1020 K that has been characterised by high-temperature synchrotron X-ray and neutron powder diffraction, and ionic conductivity measurements. The crystal structure at 1073 K has been determined from joint Rietveld refinements of synchrotron X-ray and neutron powder diffraction data. The study shows that hexagonal-La_9.75□_0.25(Ge₆O₂₄)O_2.62 contains interstitial oxygen at the position previously reported for other oxy-germanates. Changes in the oxide conductivity associated with this structural transition are discussed. The thermal analyses showed a weight loss on heating close to 600 K very likely due to water release. The synchrotron thermodiffractometric study shows an anomaly in the cell parameters evolution at that temperature, which indicates that this residual water is located into the apatite channels. The electrical characterisation under different atmospheres (dry and wet synthetic air) indicates that there is a significant proton contribution to the overall conductivity below 600 K, mainly under wet atmosphere.     

A combinatorial approach to obtain affinity media with binding properties towards the aflatoxins

In our work we performed a combinatorial solid-phase synthesis in aqueous medium to prepare peptide libraries from which to select an amino acid sequence with binding properties towards aflatoxins.We used polystyrene beads, functionalised with carboxylic groups as solid support and eight amino acids as monomers. During the first step 64 different sequences of two amino acids were prepared by exploiting the principles of combinatorial chemistry; then the binding properties of all sequences towards aflatoxin B(1 )were checked. We determined binding constants towards aflatoxin B(1) and towards aflatoxins B(2), G(1) and G(2). Results were promising, so we prepared a new library by using the selected dipeptide as the starting solid phase. After selecting the best tetrapeptide sequences, we determined binding constants towards the quoted aflatoxins. We obtained binding constants ( K>10(4) M(-1)) similar to those shown by human serum albumin for similar compounds. Preliminary studies on an extraction column were promising for the development of an SPE system and for its application in food matrices.     

Synthesis of some 4-substituted-2-(o-halogenophenyl)-1,2,3-triazoles

Mesoaldehyde 1,3-dioxime was treated with either 2,4,6-trichlorophenyl- (a), o-fluorophenyl- (b), or o-bromophenyl- (c) hydrazine to give the corresponding mesoaldehyde 1,3-dioxime-2-halogenophenylhydrazones (1a,b,c). The latter were O-acetylated with acetic anhydride, and cyclized to triazole 4-oximes (3b, c) or triazole 4-O-acetyloximes ( 6a,b,c ) with cesium carbonate, then converted to nitriles ( 7a,b,c ) by refluxing with acetic anhydride followed by pyrolysis, or to aldehydes ( 4a,b,c ) by hydrolysis. The nitriles ( 7a,b,c ) were also converted to acids ( 9a,b,c ), esters ( 10a,b,c ), amides ( 8a,c ), an alcohol (11a), and an amine ( 12a ). In addition, tetrazoles of two types were prepared. The first ( 13d,e ) were obtained from the acid chlorides by the action of 5-aminotetrazole, whereas the second ( 14f ) was produced from the respective nitrile by the action of ammonium azide.     

Identification of extracellular nanoparticle subsets by nuclear magnetic resonance

Exosomes are a subset of secreted lipid envelope-encapsulated extracellular vesicles (EVs) of 50–150 nm diameter that can transfer cargo from donor to acceptor cells. In the current purification protocols of exosomes, many smaller and larger nanoparticles such as lipoproteins, exomers and microvesicles are typically co-isolated as well. Particle size distribution is one important characteristics of EV samples, as it reflects the cellular origin of EVs and the purity of the isolation. However, most of the physicochemical analytical methods today cannot illustrate the smallest exosomes and other small particles like the exomers. Here, we demonstrate that diffusion ordered spectroscopy (DOSY) nuclear magnetic resonance (NMR) method enables the determination of a very broad distribution of extracellular nanoparticles, ranging from 1 to 500 nm. The range covers sizes of all particles included in EV samples after isolation. The method is non-invasive, as it does not require any labelling or other chemical modification. We investigated EVs secreted from milk as well as embryonic kidney and renal carcinoma cells. Western blot analysis and immuno-electron microscopy confirmed expression of exosomal markers such as ALIX, TSG101, CD81, CD9, and CD63 in the EV samples. In addition to the larger particles observed by nanoparticle tracking analysis (NTA) in the range of 70–500 nm, the DOSY distributions include a significant number of smaller particles in the range of 10–70 nm, which are visible also in transmission electron microscopy images but invisible in NTA. Furthermore, we demonstrate that hyperpolarized chemical exchange saturation transfer (Hyper-CEST) with ¹²⁹Xe NMR indicates also the existence of smaller and larger nanoparticles in the EV samples, providing also additional support for DOSY results. The method implies also that the Xe exchange is significantly faster in the EV pool than in the lipoprotein/exomer pool.

Diffusion and xenon NMR based methods to determine a very broad range of sizes and sub-sets of extracellular vesicles.     

High performance liquid chromatography post-column chemiluminescence determination of sulfonamide residues in milk at low concentration levels using bis[4-nitro-2-(3,6,9-trioxadecyloxycarbonyl)phenyl] oxalate as chemiluminescent reagent

The determination of seven sulfonamides by means of HPLC with chemiluminescence detection is proposed for the first time. The analytes are derivatized with fluorescamine, separated and subsequently they participate in the post-column chemiluminescence (CL) peroxyoxalate system using imidazole as a catalyst. Among the different peroxyoxalates tested, bis[4-nitro-2-(3,6,9-trioxadecyloxycarbonyl)phenyl] oxalate provides higher sensitivities and stabilities, avoiding precipitation problems. A rigorous optimization of the significant variables by means of experimental designs has been developed in order to reconcile the chromatographic conditions with the CL reaction. The method provides detection limits in the low microgl(-1) range and has been satisfactorily applied to the analysis of spiked raw milk samples.     

Synthesis and characterization of Cu,Ni and Zn binding capability of some amino- and imidazole hydroxamic acids: Effects of substitution of side chain amino-N for imidazole-N or hydroxamic-N-H for -N-CH3 on metal complexation

Solution equilibrium studies on Cu(II)-, Ni(II)- and Zn(II)-N-Me-β-Alaninehydroxamic acid (N-Me-β-Alaha), -N-Me-α-alaninehydroxamic acid (N-Me-α-Alaha), -Imidazole-4-carbohydroxamic acid (Im-4-Cha), -N-Me-imidazole-4-carbohydroxamic acid (N-Me-Im-4-Cha) and -Imidazole-4-acetohydroxamic acid (Im-4-Aha) systems have been performed by pH-potentiometry, UV–Vis spectrophotometry, EPR, CD, ESI-MS and ¹H NMR methods. According to the results: (i) the amino-N atoms are more basic in N-Me-α-Alaha and N-Me-β-Alaha than the hydroxamate function, but the trend is just the opposite between the imidazole-N(3) and hydroxamate. (ii) The metal ion anchor is always the hydroxamate part in the amino acid derivatives, while it is always the imidazole-N(3) in the studied imidazolehydroxamic acids. (iii) The three studied N-Me derivatives do not form metallacrowns. Only hydroxamate type chelate is formed with N-Me-β-Alaha, but with N-Me-α-Alaha a new type of coordination mode (via amino-N and hydroxamate-O) also exists. N-Me-Im-4-Cha also forms a dinuclear complex, [M₂L₃], with Cu(II) and Ni(II) (but not with Zn(II)). In this complex, one of the three ligands might bridge the two metal ions (five-membered hydroxamate-(O,O) plus five-membered (N_im, O_carb) bridging bis-chelating mode), while each of the additional two ligands binds to one metal. (iv) The two studied N–H derivatives, having dissociable proton on the hydroxamic-N, are able to form metallacrown species. A pentanuclear complex, [M₅L₄H₋₄], is exclusively formed above pH 4 between Cu(II) and Im-4-Aha. Interestingly, this 12-metallacrown-4 type complex, although together with various mononuclear binding isomers, appears also with Ni(II) and Zn(II). Unfortunately, the complexes of Im-4-Cha are not soluble in water at physiological pH at all.     

Study of metal-loaded activated charcoals for the separation and determination of selenium species by energy dispersive X-ray fluorescence analysis

Conversion of adsorption properties of activated charcoal (C^∗) by metal modification towards selenite, selenate and seleno-dl-methionine (Se-Met) was studied. Several metals were included in modification studies and also a procedure was developed for the separation and independent determination of microgram quantities of these selenium species in aqueous solution. Selenium species were collected one by one from the same sample solution onto collector material by adsorbing them directly or after complex formation onto different metal-loaded activated charcoals (MgC^∗ and FeC^∗). The mass of selenium in these collectors was measured directly by energy dispersive X-ray fluorescence spectrometry (EDXRF). Detection limits for all three selenium species were better than 6 μg corresponding to concentration of 60 μg/l with 0.100 l of initial sample volume.