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.     

The reaction of β-aminoenones with substituted acetonitriles. Regiospecific synthesis of 2(1H)-pyridones

Unsymmetrically substituted β-aminoenones react with malononitrile, cyanomethylphenylsulfone, benzoyl-acetonitrile and ethyl cyanoacetate, in very mild conditions, to yield regiospecifically 3-functionalized 2(1H)-pyridones in high yields.     

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.     

Shift reagent 1H NMR study of methoxycoumarins

The complete assignment of the proton chemical shifts of coumarin ( 1 ), all monomethoxy derivatives and the six possible dimethoxyl substituted compounds at the aromatic ring was achieved at 60 MHz in a quantitative study utilizing Pr(fod)₃ as the shift reagent. It was found that in addition to the complexation at the lactone carbonyl a second interaction of the lanthanide shift reagent occurs when two methoxyl groups are found in an ortho distribution. The results are discussed in comparison to data published for flavones in the presence of Pr(fod)₃ shift reagent.     

Langmuir monolayers of the zwitterionic surfactant hexadecyl 1-N-L-tryptophan glycerol ether

We report the formation of Langmuir monolayers of pure zwitterionic hexadecyl 1-N-L-tryptophan glycerol ether (C(16)-TGE) surfactant and mixed monolayers of cationic-zwitterionic surfactant obtained modifying the pH of the subphase. The pressure-area and surface potential-area isotherms and fluorescence microscopy measurements have been used to characterize the surface phase transitions in the monolayers. These transitions appeared at larger areas as the pH decreased from 6.0 to 2.0 and almost disappeared as the pH decreased further. The analysis of the surface potential and the infrared reflection-absorption spectroscopy data suggests that the phase transition is associated with a change of orientation of both the hydrocarbon chain and the aromatic group of the surfactant with respect to the air-water surface. The surface rheology of the monolayers was studied by quasielastic light scattering and by the oscillatory barrier technique. The results indicate that there is at least one relaxation process in the monolayer.