Monopropionate analogues of DOTA4- and DTPA5-: kinetics of formation and dissociation of their lanthanide(III) complexes

The replacement of an acetate function of the macrocyclic DOTA4-(DO3A-Nprop4-) or the acyclic DTPA5- in terminal position (DTTA-Nprop5-) has been recently shown to result in a significant increase of the water exchange rate on the Gd3+ complexes, which makes these chelates potential contrast agents for MRI applications. Here, two novel and straightforward synthetic routes to H4DO3A-Nprop are described. Protonation constants of DO3A-Nprop4- and stability constants with several alkaline earth and transition metal ions have been determined by potentiometry. For each metal, the thermodynamic stability constant is decreased in comparison to the DOTA chelates. The formation reaction of LnDO3A-Nprop- complexes (Ln=Ce, Gd and Yb) proceeds via the rapid formation of a diprotonated intermediate and its subsequent deprotonation and rearrangement in a slow, OH- catalyzed process. The stability of the LnH2DO3A-Nprop* intermediates is similar to those reported for the corresponding DOTA analogues. The rate constants of the OH- catalyzed deprotonation step increase with decreasing lanthanide ion size, and are slightly higher than for DOTA complexes. The kinetic inertness of GdDTTA-Nprop2- was characterized by the rates of its exchange reactions with Zn2+ and Eu3+. The rate of the reaction between GdDTTA-Nprop2- and Zn2+ increases with Zn2+ concentration, while it is independent of pH, implying that the exchange takes place predominantly via direct attack of the metal ion on the complex. In the Eu3+ exchange, the rate decreases with increasing concentration of the exchanging ion which is accounted for by the transitional formation of a dinuclear GdDTTA-NpropEu+ species. The kinetic inertness of the monopropionate GdDTTA-Nprop2- is decreased in comparison to GdDTPA2-: all rate constants, characterizing the dissociation reaction via either proton- or metal-catalyzed pathways being higher by 1-2 orders of magnitude. Similarly, a study of the acid-catalyzed dissociation of the macrocyclic CeDO3A-Nprop- showed a partial loss of the kinetic inertness with regard to the tetraacetate derivative CeDOTA-.     

Optimal design accounting for uncertainty in loading amplitudes: A numerical investigation

A numerical investigation is performed addressing the optimal design of stiff structures accounting for uncertainty in loading amplitudes. A minimum volume problem is endowed with a stochastic compliance constraint handling normal distributions and solved adopting mathematical programming. The formulation, originally conceived for a single load case, is extended to handle multiple load cases. Numerical simulations are performed to test the proposed algorithms, pointing out features of the numerical procedures and peculiarities of the stochastic-based optimal solutions achieved for different values of the second-order moments. Comparisons with respect to conventional deterministic layouts are provided as well.     

Co2(CO)8-induced domino reactions of ethyl diazoacetate, carbon monoxide and ferrocenylimines leading to 2-(1-ferrocenyl-methylidene)-malonic acid derivatives

Novel 2-(1-ferrocenyl-methylidene)-malonic acid derivatives are obtained upon reacting ethyl diazoacetate, carbon monoxide and ferrocenylimines in the presence of Co₂(CO)₈ as catalyst under mild conditions. Presumably, the reaction involves three steps taking place in a domino fashion, (i) carbonylation of ethyl diazoacetate leading to a ketene derivative, (ii) [2+2] cycloaddition of the ketene with the ferrocenylimine present in the reaction mixture resulting in the formation of a β-lactam and (iii) N(1)-C(4) cleavage of the β-lactam ring. In most cases, 2-(1-ferrocenyl-methylidene)-malonic acid derivatives are obtained as a separable mixture of E- and Z-isomers in ratios depending on the structure of the imine component.     

Condensation of β‐Diester Titanium Enolates with Carbonyl Substrates: A Combined DFT and Experimental Investigation

The condensation of dialkyl β‐diesters with various aldehydes promoted by TiCl₄ has been studied by DFT approaches and experimental methods, including NMR, IR and UV/Vis spectroscopy. Various possible reaction pathways have been investigated and their energy profiles evaluated to find out a plausible mechanism of the reaction. Theoretical results and experimental evidence point to a three‐step mechanism: 1) Ti‐induced formation of the enolate ion; 2) aldol reaction between the enolate ion and the aldehyde, both coordinated to titanium; and 3) intramolecular elimination that leads to a titanyl complex. The presented mechanistic hypothesis allows one to better understand the pivotal role of titanium(IV) in the reaction.     

The diameter game

A large class of Positional Games are defined on the complete graph on n vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his subgraph has a given — usually monotone — property. Here we introduce the d‐diameter game, which means that Maker wins iff the diameter of his subgraph is at most d. We investigate the biased version of the game; i.e., when the players may take more than one, and not necessarily the same number of edges, in a turn. Our main result is that we proved that the 2‐diameter game has the following surprising property: Breaker wins the game in which each player chooses one edge per turn, but Maker wins as long as he is permitted to choose 2 edges in each turn whereas Breaker can choose as many as (1/9)n^1/8/(lnn)^3/8. In addition, we investigate d‐diameter games for d ≥ 3. The diameter games are strongly related to the degree games. Thus, we also provide a generalization of the fair degree game for the biased case. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

A priori resolution of the intermediate spectra in the bacteriorhodopsin photocycle: the time evolution of the L spectrum revealed

Resolution of the spectra of the intermediates in the photocycle of wild-type bacteriorhodopsin (BR) was achieved by singular value decomposition with exponential-fit-assisted self-modeling (SVD-EFASM) treatment of multichannel difference spectra measured at 5 degrees C during the course of the photocycle. New is the finding that two spectrally distinct L intermediates, L(1) and L(2), form sequentially. Our conclusion is that the photocycle is more complex than most published schemes. The dissection of the spectrally different L forms eliminates stoichiometric discrepancies usually appearing as systematically varying total intermediate concentrations before the onset of BR recovery. In addition, our analysis reveals that the red tails in the spectra of K and L(1) are more substantial than those of L(2) and BR. We suggest that these subtle differences in the shapes of the spectra reflect torsional and/or environmental differences in the retinyl chromophore.     

Electrophoretic mobility and molecular distribution studies of poly(amidoamine) dendrimers of defined charges

Generation 5 ethylenediamine (EDA)-cored poly(amidoamine) (PAMAM) dendrimers (E5, E denotes the EDA core and 5 the generation number) with different degrees of acetylation and carboxylation were synthesized and used as a model system to investigate the effect of charge and the influence of dendrimer surface modifications on electrophoretic mobility (EM) and molecular distribution. The surface-modified dendrimers were characterized by size-exclusion chromatography, 1H NMR, MALDI-TOF-MS, PAGE, and CE. The focus of our study was to determine how EM changes as a function of particle charge and molecular mass, and how the molecular distribution changes due to surface modifications. We demonstrate that partially modified dendrimers have much broader migration peaks than those of fully surface functionalized or unmodified E5 dendrimers due to variations in the substitution of individual dendrimer surfaces. EM decreased nonlinearly with increases in surface acetylation for both PAMAM acetamides and PAMAM succinamic acids, indicating a complex migration activity in CE separations that is not solely due to charge/mass ratio changes. These studies provide new insights into dendrimer properties under an electric field, as well as into the characterization of dendrimer-based materials being developed for medical applications.     

Almost all triangle-free triple systems are tripartite

A triangle in a triple system is a collection of three edges isomorphic to {123,124,345}. A triple system is triangle-free if it contains no three edges forming a triangle. It is tripartite if it has a vertex partition into three parts such that every edge has exactly one point in each part. It is easy to see that every tripartite triple system is triangle-free. We prove that almost all triangle-free triple systems with vertex set [n] are tripartite. Our proof uses the hypergraph regularity lemma of Frankl and R?dl [13], and a stability theorem for triangle-free triple systems due to Keevash and the second author [15].     

A Kotz and Steutel type of characterization of the gamma family

Let X and Y be independent identically distributed (i.i.d.) nondegenerate and positive random variables with a common absolutely continuous distribution function F(x). We use the notation Z?=?max(X, Y) and W?=?min(X, Y). In the present paper, we prove that ${\frac{(Z - W)}{(Z + W)}}$ and (Z +?W) are independent if and only if X and Y have gamma distribution.