Propagating fronts,chaos and multistability in a cell replication model

Numerical solutions to a model equation that describes cell population dynamics are presented and analyzed. A distinctive feature of the model equation (a hyperbolic partial differential equation) is the presence of delayed arguments in the time (t) and maturation (x) variables due to the nonzero length of the cell cycle. This transport like equation balances a linear convection with a nonlinear, nonlocal, and delayed reaction term. The linear convection term acts to impress the value of u(t,x=0) on the entire population while the death term acts to drive the population to extinction. The rich phenomenology of solution behaviour presented here arises from the nonlinear, nonlocal birth term. The existence of this kinetic nonlinearity accounts for the existence and propagation of soliton-like or front solutions, while the increasing effect of nonlocality and temporal delays acts to produce a fine periodic structure on the trailing part of the front. This nonlinear, nonlocal, and delayed kinetic term is also shown to be responsible for the existence of a Hopf bifurcation and subsequent period doublings to apparent "chaos" along the characteristics of this hyperbolic partial differential equation. In the time maturation plane, the combined effects of nonlinearity, nonlocality, and delays leads to solution behaviour exhibiting spatial chaos for certain parameter values. Although analytic results are not available for the system we have studied, consistency and validation of the numerical results was achieved by using different numerical methods. A general conclusion of this work, of interest for the understanding of any biological system modeled by a hyperbolic delayed partial differential equation, is that increasing the spatio-temporal delays will often lead to spatial complexity and irregular wave propagation. (c) 1996 American Institute of Physics.     

Geometry and the Jones projection of a state

LetA be a von Neumann algebra and a faithful normal state. ThenO = { ºAd(g ¹) :g G _A }andU = { ºAd(u ^*) :u U _A are homogeneous reductive spaces. IfA is aC ^* algebra,e the Jones projection of the faithful state viewed as a conditional expectation, then we prove that the similarity orbit ofe by invertible elements ofA can be imbedded inAA in such a way thate is carried to 1 1 and the orbit ofe to a homogeneous reductive space and an analytic submanifold ofAA.     

One-pot enantioselective formation of eight-membered rings from alkenyl Fischer carbene complexes and ketone enolates

Eight-membered carbocycles with up to five new stereogenic centers are enantioselectively obtained following a one-pot procedure that involves the coupling of three components: an alkenyl Fischer carbene complex, a ketone enolate, and allyl lithium.     

Interaction between indigo and adsorbed protein as a major factor causing backstaining during cellulase treatment of cotton fabrics

A model microassay system was developed to measure indigo backstaining on cotton fabrics in the presence of enzymes on a small laboratory scale. Backstaining indexes for 11 cellulase samples were measured, and the enzymes were ranked from lower to higher backstaining. Two multienzyme cellulase preparations were separated into fractions using chromatofocusing on a Mono P column. Adsorption ability and backstaining properties of purified enzyme fractions were studied. Evidence was obtained that protein adsorption on cotton fabrics is a crucial parameter causing backstaining (both for crude cellulase samples and purified enzyme components).     

Stability study of simvastatin under hydrolytic conditions assessed by liquid chromatography

In this work, a liquid chromatography stability-indicating method was developed and applied to study the hydrolytic behavior of simvastatin in different pH values and temperatures. The selected chromatographic conditions were a C18 column; acetonitrile-28 mM phosphate buffer solution, pH 4 (65 + 35) as the mobile phase; 251 degrees C column temperature; and flow rate 1 mL/min. The developed method exhibited an adequate repeatability and reproducibility (coefficient of variation 0.54 and 0.74%, respectively) and a recovery higher than 98%. Furthermore, the detection and quantification limits were 9.1 x 10(-7) and 2.8 x 10(-6) M, respectively. The degradation of simvastatin fitted to pseudo-first order kinetics. The degradation was pH dependent, being much higher at alkaline pH than at acid pH. Activation energy, kinetic rate constants (k) at different temperatures, the half life (t1/2) and the time for 10% degradation to occur (t90) values are also reported.     

Cascade alkenyl amination/Heck reaction promoted by a bifunctional palladium catalyst: a novel one-pot synthesis of indoles from o-haloanilines and alkenyl halides

A novel approach for the synthesis of the important indole ring is described. Indoles are obtained from o-bromoanilines and alkenyl halides in a Pd-catalyzed cascade process that involves an alkenyl amination followed by an intramolecular Heck reaction. The overall process represents the first example of the participation of alkenyl amination reactions in Pd-catalyzed cascade reactions. Initially, the relative reactivity of aryl and alkenyl bromides and chlorides towards Pd-catalyzed amination was investigated. Competition experiments were carried out in the presence of primary and secondary amines, and these revealed the reactivity order alkenyl bromides > aryl bromides > alkenyl chlorides > aryl chlorides, as well as very high chemoselectivity; the more reactive halide was always favored. Thereafter, optimized reaction conditions for the sequential alkenyl amination/Heck cyclization to give indoles were investigated with the model reaction of o-bromoaniline with alpha-bromostyrene. An extensive screening of ligands, bases, and reaction conditions revealed that the [Pd2(dba)3]/DavePhos, NaOtBu, toluene combination at 100 degrees C were the optimized reaction conditions to carry out the cascade process (dba=dibenzylideneacetone, DavePhos=2-dicyclohexylphosphino-2'-N,N-dimethylaminobiphenyl). The reaction proceeds with aryl, alkyl, and functionalized substitutents in both starting reactants. The cyclization was also studied with N-substituted o-bromoanilines (which would give rise to N-substituted indoles); however, in this case, indole formation occurred only with 1-substituted-2-bromoalkenes. Finally, the application of this methodology to o-chloroanilines required further optimization. Although the catalyst based on DavePhos failed to promote the cascade process, a catalytic combination based on [Pd2(dba)3]/X-Phos promoted the formation of the indole ring also from the less reactive chloroanilines.     

Whey proteins eluted reversed phase gradients

The behavior of bovine whey proteins in Reversed-Phase High Performance Liquid Chromatography (RP-HPLC) systems has been investigated. The Linear Solvent Strength (LSS) model has been applied to the separation of these proteins studying how their retention time and band broadening change when different gradient parameters are modified. From our results it is deduced that the LSS model describes the behaviour of the whey proteins in RP-HPLC. Also, it seems that t_s (the retention time for non-retained solutes) depends on the size of these proteins. The good fit observed between experimental data and the equations deduced from the LSS model allows the prediction of a gradient shape that permits a rapid analysis of the above mentioned proteins.     

New physically adsorbed polymer coating for reproducible separations of basic and acidic proteins by capillary electrophoresis

In this work, a new physically adsorbed coating for capillary electrophoresis (CE) is presented. The coating is based on a N,N-dimethylacrylamide-ethylpyrrolidine methacrylate (DMA-EPyM) copolymer synthesized in our laboratory. The capillary coating is simple and easy to obtain as only requires flushing the capillary with a polymer aqueous solution for 2 min. It is shown that by using these coated capillaries the electrostatic adsorption of a group of basic proteins onto the capillary wall is significantly reduced allowing their analysis by CE. Moreover, the DMA-EPyM coating provides reproducible separations of the basic proteins with RSD values for migration times lower than 0.75% for the same day (n = 5) and lower than 3.90% for three different days (n = 15). Interestingly, the electrical charge of the coated capillary wall can be modulated by varying the pH of the running buffer which makes possible the analysis of basic and acidic proteins in the same capillary. The usefulness of this coating is further demonstrated via the reproducible separation of whey (i.e. acidic) proteins from raw milk. The coating protocol should be compatible with both CE in microchips and CE-MS of different types of proteins.     

The Role of Intramolecular Hydrogen Bonds vs. Other Weak Interactions on the Conformation of Hyponitrous Acid and Its Mono- and Dithio-Derivatives

High level ab initio and density functional theory calculations have been carried out to investigate the relative stability of the different conformers of hyponitrous acid and its mono- and dithio-derivatives. Geometries and vibrational frequencies were obtained at the B3LYP/6-311+G(d,p) level and final energies through B3LYP/6-311++G(3df,2pd) single point calculations. The reliability of this theoretical scheme has been assessed by comparing these DFT results with those obtained at the G3 level of theory, for some suitable cases. The cis conformers of hyponitrous acid and its mono- and dithio-derivatives are systematically more stable than the trans ones because in the cis conformation a dative interaction between the nitrogen-lone pairs and the σ_NX^* antibonding orbital is significantly favored. Quite interestingly, in general, the conformers presenting an intramolecular hydrogen bond (IHB) are not the global minima of the corresponding potential energy surfaces and only for hyponitrous acid the conformer with a OH ⋅s O IHB is slightly more stable than the cis conformer without IHB. The low stability of the tautomers with IHB is closely related with another weak intramolecular interaction which involves the lone-pairs of the chalcogen atoms and the π_NN^* antibondig orbital, and which is significantly perturbed when the IHB is formed.