多项式微分系统的不变直线的不同斜率的最大个数

本文证明了公式β（ｎ）＝σ（ｎ－１）＋１其中α（ｎ－１）是ｎ－１次多项式微分系统的不为直线的最多条数，βｎ）是ｎ次多项式微分系统的不变直线的不同斜率的最大个数。这里假设所讨论的多项式系统只有限条不变直线。     

AB5 subtilase cytotoxin inactivates the endoplasmic reticulum chaperone BiP

AB5 toxins are produced by pathogenic bacteria and consist of enzymatic A subunits that corrupt essential eukaryotic cell functions, and pentameric B subunits that mediate uptake into the target cell. AB5 toxins include the Shiga, cholera and pertussis toxins and a recently discovered fourth family, subtilase cytotoxin, which is produced by certain Shiga toxigenic strains of Escherichia coli. Here we show that the extreme cytotoxicity of this toxin for eukaryotic cells is due to a specific single-site cleavage of the essential endoplasmic reticulum chaperone BiP/GRP78. The A subunit is a subtilase-like serine protease; structural studies revealed an unusually deep active-site cleft, which accounts for its exquisite substrate specificity. A single amino-acid substitution in the BiP target site prevented cleavage, and co-expression of this resistant protein protected transfected cells against the toxin. BiP is a master regulator of endoplasmic reticulum function, and its cleavage by subtilase cytotoxin represents a previously unknown trigger for cell death.     

Human clade B serpins (ov-serpins) belong to a cohort of evolutionarily dispersed <Emphasis Type="Italic">intracellular</Emphasis> proteinase inhibitor clades that protect cells from promiscuous proteolysis

Serpins are unique among the various types of active site proteinase inhibitors because they covalently trap their targets by undergoing an irreversible conformational rearrangement. Members of the serpin superfamily are present in the three major domains of life (Bacteria, Archaea and Eukarya) as well as several eukaryotic viruses. The human genome encodes for at least 35 members that segregate evolutionarily into nine (A-I) distinct clades. Most of the human serpins are secreted and circulate in the bloodstream where they reside at critical checkpoints intersecting self-perpetuating proteolytic cascades such as those of the clotting, thrombolytic and complement systems. Unlike these circulating serpins, the clade B serpins (ov-serpins) lack signal peptides and reside primarily within cells. Most of the human clade B serpins inhibit serine and/or papain-like cysteine proteinases and protect cells from exogenous and endogenous proteinase-mediated injury. Moreover, as sequencing projects expand to the genomes of other species, it has become apparent that intracellular serpins belonging to distinct phylogenic clades are also present in the three major domains of life. As some of these serpins also guard cells against the deleterious effects of promiscuous proteolytic activity, we propose that this cytoprotective function, along with similarities in structure are common features of a cohort of intracellular serpin clades from a wide variety of species.Received 24 June 2003; received after revision 16 July 2003; accepted 5 August 2003     

The structural basis for membrane binding and pore formation by lymphocyte perforin

Natural killer cells and cytotoxic T lymphocytes accomplish the critically important function of killing virus-infected and neoplastic cells. They do this by releasing the pore-forming protein perforin and granzyme proteases from cytoplasmic granules into the cleft formed between the abutting killer and target cell membranes. Perforin, a 67-kilodalton multidomain protein, oligomerizes to form pores that deliver the pro-apoptopic granzymes into the cytosol of the target cell. The importance of perforin is highlighted by the fatal consequences of congenital perforin deficiency, with more than 50 different perforin mutations linked to familial haemophagocytic lymphohistiocytosis (type 2 FHL). Here we elucidate the mechanism of perforin pore formation by determining the X-ray crystal structure of monomeric murine perforin, together with a cryo-electron microscopy reconstruction of the entire perforin pore. Perforin is a thin 'key-shaped' molecule, comprising an amino-terminal membrane attack complex perforin-like (MACPF)/cholesterol dependent cytolysin (CDC) domain followed by an epidermal growth factor (EGF) domain that, together with the extreme carboxy-terminal sequence, forms a central shelf-like structure. A C-terminal C2 domain mediates initial, Ca(2+)-dependent membrane binding. Most unexpectedly, however, electron microscopy reveals that the orientation of the perforin MACPF domain in the pore is inside-out relative to the subunit arrangement in CDCs. These data reveal remarkable flexibility in the mechanism of action of the conserved MACPF/CDC fold and provide new insights into how related immune defence molecules such as complement proteins assemble into pores.