Compact and subelliptic estimates for the $${\overline{\partial}}$$-Neumann operator on C2 pseudoconvex domains

In this paper, we will show that Catlin’s property (P) implies regularity for the -Neumann operator in W ¹ on C ² domains. We will also look at the subelliptic case and derive the natural generalization to C ^k domains when k ≥  2.     

Non-classical law of the iterated logarithm behaviour for trimmed sums

Summary We study the law of the iterated logarithm for the partial sum of i.i.d. random variables when the r _n largest summands are excluded, where r _n=o(log logn). This complements earlier work in which the case log log_n=O(r_n) was considered. A law of the iterated logarithm is again seen to prevail for a wide class of distributions, but for reasons quite different from previously.Research supported in part by NSF Grant DMS-8501732     

Rotational resonance NMR: separation of dipolar coupling and zero quantum relaxation

The solid state NMR technique of rotational resonance (R2) has been used extensively to measure distances approaching 5-6 A between 13C nuclei in a variety of compounds including amyloidogenic peptides and membrane proteins. The accuracy of the distance information extracted from the time-dependent spin dynamics at R2 is often limited by the accuracy with which the relevant zero-quantum lineshape parameters are estimated. Here we demonstrate that measurement of spinning frequency dependent magnetization exchange dynamics provides data from which both distance and zero-quantum relaxation parameters can be extracted independently. In addition to providing more accurate distance information, this technique allows examination of the zero-quantum lineshape, which can indicate the presence of correlated relaxation or chemical shift distributions between dipolar-coupled sites. With this approach we have separated the contribution of dipolar couplings and zero quantum relaxation to R2 exchange curves. Thus, we have significantly improved the accuracy of the measurement of the intramolecular, internuclear distances between a pair of 13C's in two model compounds (N-acetyl-D,L-valine and glycylglycine.HCl) that lie in the distance range 4.6-4.7 A.     

Enterococcal cytolysin: a novel two component peptide system that serves as a bacterial defense against eukaryotic and prokaryotic cells

The cytolysin is a novel, two-peptide lytic toxin produced by some strains of Enterococcus faecalis. It is toxic in animal models of enterococcal infection, and associated with acutely terminal outcome in human infection. The cytolysin exerts activity against a broad spectrum of cell types including a wide range of gram positive bacteria, eukaryotic cells such as human, bovine and horse erythrocytes, retinal cells, polymorphonuclear leukocytes, and human intestinal epithelial cells. The cytolysin likely originated as a bacteriocin involved with niche control in the complex microbial ecologies associated with eukaryotic hosts. However, additional anti-eukaryotic activities may have been selected for as enterococci adapted to eukaryotic cell predation in water or soil ecologies. Cytolytic activity requires two unique peptides that possess modifications characteristic of the lantibiotic bacteriocins, and these peptides are broadly similar in size to most cationic eukaryotic defensins. Expression of the cytolysin is tightly controlled by a novel mode of gene regulation in which the smaller peptide signals high-level expression of the cytolysin gene cluster. This complex regulation of cytolysin expression may have evolved to balance defense against eukaryotic predators with stealth.     

Novel PI analogues selectively block activation of the pro-survival serine/threonine kinase Akt

The synthesis from l-quebrachitol of a series of 3-deoxygenated ether lipid-type phosphatidylinositol (PI) analogues is reported, that selectively block activation of Akt and downstream substrates without affecting activation of the upstream kinase, PDK-1, or other kinases downstream of ras such as MAPK in H157 and H1703 lung cancer cells that have high levels of constitutively active Akt. The 2-hydroxyl in these compounds was deleted or alkylated with the intent to preclude metabolic degradation of these compounds by PI-specific phospholipase C (PI-PLC). PI analogues with phosphate linkers are more effective than those with carbonate linkers. Specific inhibition of Akt by these compounds validates ligand design targeted to the PH domains of crucial signaling proteins, thus providing a unique class of possible cancer therapeutics.