Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

G1 arrest and down-regulation of cyclin E/cyclin-dependent kinase 2 by the protein kinase inhibitor staurosporine are dependent on the retinoblastoma protein in the bladder carcinoma cell line 5637.

The protein kinase inhibitor staurosporine has been shown to induce G1 phase arrest in normal cells but not in most transformed cells. Staurosporine did not induce G1 phase arrest in the bladder carcinoma cell line 5637 that lacks a functional retinoblastoma protein (pRB-). However, when infected with a pRB-expressing retrovirus [Goodrich, D. W., Chen, Y., Scully, P. & Lee, W.-H. (1992) Cancer Res. 52, 1968-1973], these cells, now pRB+, were arrested by staurosporine in G1 phase. This arrest was accompanied by the accumulation of hypophosphorylated pRB. In both the pRB+ and pRB- cells, cyclin D1-associated kinase activities were reduced on staurosporine treatment. In contrast, cyclin-dependent kinase (CDK) 2 and cyclin E/CDK2 activities were inhibited only in pRB+ cells. Staurosporine treatment did not cause reductions in the protein levels of CDK4, cyclin D1, CDK2, or cyclin E. The CDK inhibitor proteins p21(Waf1/Cip1) and p27 (Kip1) levels increased in staurosporine-treated cells. Immunoprecipitation of CDK2, cyclin E, and p2l from staurosporine-treated pRB+ cells revealed a 2.5- to 3-fold higher ratio of p2l bound to CDK2 compared with staurosporine-treated pRB- cells. In pRB+ cells, p2l was preferentially associated with Thrl6O phosphorylated active CDK2. In pRB- cells, however, p2l was bound preferentially to the unphosphorylated, inactive form of CDK2 even though the phosphorylated form was abundant. This is the first evidence suggesting that G1 arrest by 4 nM staurosporine is dependent on a functional pRB protein. Cell cycle arrest at the pRB- dependent checkpoint may prevent activation of cyclin E/CDK2 by stabilizing its interaction with inhibitor proteins p2l and p27.

On the classification of binary shifts of finite commutant index

We provide a complete classification up to conjugacy of the binary shifts of finite commutant index on the hyperfinite II1, factor. There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.

Dynamics and orientation of N+(CD3)3-bromoacetylcholine bound to its binding site on the nicotinic acetylcholine receptor

Dynamic and structural information has been obtained for an analogue of acetylcholine while bound to the agonist binding site on the nicotinic acetylcholine receptor (nAcChoR), using wide-line deuterium solid-state NMR. Analysis of the deuterium lineshape obtained at various temperatures from unoriented nAcChoR membranes labeled with deuterated bromoacetylcholine (BAC) showed that the quaternary ammonium group of the ligand is well constrained within the agonist binding site when compared with the dynamics observed in the crystalline solids. This motional restriction would suggest that a high degree of complementarity exists between the quaternary ammonium group of the ligand and the protein within the agonist binding site. nAcChoR membranes were uniaxially oriented by isopotential centrifugation as determined by phosphorous NMR of the membrane phospholipids. Analysis of the deuterium NMR lineshape of these oriented membranes enriched with the nAcChoR labeled with N+(CD3)3-BAC has enabled us to determine that the angle formed between the quaternary ammonium group of the BAC and the membrane normal is 42° in the desensitized form of the receptor. This measurement allows us to orient in part the bound ligand within the proposed receptor binding site.

Structural Alterations of Lignins in Transgenic Poplars with Depressed Cinnamyl Alcohol Dehydrogenase or Caffeic Acid O-Methyltransferase Activity Have an Opposite Impact on the Efficiency of Industrial Kraft Pulping1

We evaluated lignin profiles and pulping performances of 2-year-old transgenic poplar (Populus tremula × Populus alba) lines severely altered in the expression of caffeic acid/5-hydroxyferulic acid O-methyltransferase (COMT) or cinnamyl alcohol dehydrogenase (CAD). Transgenic poplars with CAD or COMT antisense constructs showed growth similar to control trees. CAD down-regulated poplars displayed a red coloration mainly in the outer xylem. A 90% lower COMT activity did not change lignin content but dramatically increased the frequency of guaiacyl units and resistant biphenyl linkages in lignin. This alteration severely lowered the efficiency of kraft pulping. The Klason lignin level of CAD-transformed poplars was slightly lower than that of the control. Whereas CAD down-regulation did not change the frequency of labile ether bonds or guaiacyl units in lignin, it increased the proportion of syringaldehyde and diarylpropane structures and, more importantly with regard to kraft pulping, of free phenolic groups in lignin. In the most depressed line, ASCAD21, a substantially higher content in free phenolic units facilitated lignin solubilization and fragmentation during kraft pulping. These results point the way to genetic modification of lignin structure to improve wood quality for the pulp industry.

Introduction of the transposable element Minos into the germ line of Drosophila melanogaster.

A transposon based on the transposable element Minos from Drosophila hydei was introduced into the genome of Drosophila melanogaster using transformation mediated by the Minos transposase. The transposon carries a wild-type version of the white gene (w) of Drosophila inserted into the second exon of Minos. Transformation was obtained by injecting the transposon into preblastoderm embryos that were expressing transposase either from a Hsp70-Minos fusion inserted into the genome via P-element-mediated transformation or from a coinjected plasmid carrying the Hsp70-Minos fusion. Between 1% and 6% of the fertile injected individuals gave transformed progeny. Four of the insertions were cloned and the DNA sequences flanking the transposon ends were determined. The "empty" sites corresponding to three of the insertions were amplified from the recipient strain by PCR, cloned, and sequenced. In all cases, the transposon has inserted into a TA dinucleotide and has created the characteristic TA target site duplication. In the absence of transposase, the insertions were stable in the soma and the germ line. However, in the presence of the Hsp70-Minos gene the Minos-w transposon excises, resulting in mosaic eyes and germ-line reversion to the white phenotype. Minos could be utilized as an alternative to existing systems for transposon tagging and enhancer trapping in Drosophila; it might also be of use as a germ-line transformation vector for non-Drosophila insects.

On the possibility of coherently stimulated recombination and cosmological structure generation: cosmological consequences.

Given a specific physical mechanism for instabilities during cosmological recombination discussed in an earlier paper, we examine the nonlinear growth of density structures to form fractal-like structural patterns out to the horizon scale at that epoch (approximately 200 Mpc today). A model for such fractal patterns is presented. Such effects could explain observed large-scale structure patterns and the formation of objects at high z, while keeping microwave background anisotropies at the observed minimal levels. We also discuss possible microwave background implications of such a transition and note a potentially observable spectral signature at lambda approximately 0.18 mm as well as a weak line near the peak in the microwave background.