Gibbs-Wilbraham splines

If a function with a jump discontinuity is approximated in the norm ofL ²[–1,1] by a periodic spline of orderk with equidistant knots, a behavior analogous to the Gibbs-Wilbraham phenomenon for Fourier series occurs. A set of cardinal splines which play the role of the sine integral function of the classical phenomenon is introduced. It is then shown that ask becomes large, the phenomenon for splines approaches the classical phenomenon.Communicated by Ronald A. DeVore.     

Time response of a coupled atoms-cavity system

We study the time response of a quantum optical system to a step excitation. The system is composed of a collection of N two-level atoms coupled to a single mode of the electromagnetic field of an optical cavity. The size of the step excitation is not limited to the low-intensity regime. Before the system reaches steady state there is an oscillatory exchange of energy between the atoms and the cavity. We compare the experimental results quantitatively with theoretical calculations and with previous transmission spectroscopy measurements.     

Activation of heat shock protein 70 promoter with meso-tetrahydroxyphenyl chlorin photodynamic therapy reported by green fluorescent protein in vitro and in vivo

Cellular responses to photodynamic therapy (PDT) include induction of heat shock proteins (HSP). We examined meso-tetrahydroxyphenyl chlorin (mTHPC) PDT-mediated HSP activation in EMT6 cells stably transfected with a plasmid containing the gene for green fluorescent protein (GFP) driven by an hsp70 promoter. mTHPC incubation induced concentration-dependent GFP expression. Irradiation of cells exposed to a sensitizer concentration that induced a slight increase in GFP and no loss of cell viability resulted in fluence-dependent GFP accumulation. In response to drug only and to PDT, GFP levels increased to a maximum of four- to five-fold above control levels with increasing drug or fluence and then decreased at higher doses. A trypan blue-exclusion assay confirmed that decreased GFP levels in both cases were due to a loss of cell viability. For initial evaluation in vivo, HSP70/ GFP-transfected EMT6 tumors were grown in BALB/c mice and subjected to mTHPC-PDT with a fluence of 1 J/cm2. Six hours after PDT, GFP fluorescence was imaged in these tumors through the intact skin in vivo. These results indicate that sublethal doses of mTHPC-PDT stimulate GFP expression under the control of an hsp70 promoter and illustrate the potential of noninvasively monitoring reporter protein fluorescence as a measure of molecular response to PDT.     

Cell-cell contact and membrane spreading in an ultrasound trap

An ultrasonic standing wave trap [Langmuir 19 (2003) 3635] in which the morphologies of 2-D latex–microparticle aggregates, forming a pressure node plane, were characterised has been applied here to different cell suspensions with increasing order of specificity of cross-linking molecule, i.e. polylysine with chondrocytes; wheat germ agglutinin (WGA) with erythrocytes and surface receptors on neural cells. The outcome of initial cell–cell contact, i.e. whether the cells stuck at the point of contact (collision efficiency=1) or rolled around each other (collision efficiency=0), was monitored in situ by video-microscopy. The perimeter fractal dimensions (FD) of 2-D hexagonally symmetric, closely packed aggregates of control erythrocytes and chondrocytes were 1.16 and 1.18, respectively while those for the dendrititc aggregates formed initially by erythrocytes in 0.5 μg/ml WGA and chondrocytes in 20 μg/ml polylysine were 1.49 and 1.66. The FDs for control and molecularly cross-linked cells were typical of reaction-limited aggregation (RLA) and transport diffusion-limited aggregation (DLA), respectively. The FDs of the aggregates of cross-linked cells decreased with time to give more closely packed aggregates without clear hexagonal symmetry. Suspensions of neural cells formed dendritic aggregates. Spreading of inter-cellular membrane contact area occurred over 15 min for both erythrocyte and neural cell dendritic aggregates. The potential of the technique to characterise and control the progression of cell adhesion in suspension away from solid substrata is discussed.     

Custom synthesis of molecular imprinted polymers for biotechnological application: Preparation of a polymer selective for tylosin

A molecularly imprinted polymer (MIP) selective for tylosin was designed and synthesised using a computational method (MIP “dialling”). In re-binding experiments the MIP demonstrated high affinity for tylosin in aqueous solutions and in organic solvents. The synthesised polymer was tested for re-binding with the template and related metabolites such as tylactone, narbomycin and picromycin. The HPLC analysis showed that the computationally designed polymer is specific and capable of separating the template from its structural analogues. The MIP was capable of recovering tylosin from broth samples. The polymer capacity for tylosin was estimated as 6.4 mg/g for MIP, which was suitable for practical application and tylosin recovery from broth samples. Among the advantages of this was the possibility to adsorb tylosin from a complex media with easy removal of oils and other impurities which are present in significant quantities, which can create problems for its chromatographic purification procedure. The MIP “dialling” procedure can have a general significance for the fast preparation of specific adsorbents for biotechnological applications.