A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

T cell-mediated and non-specific inflammatory mechanisms contribute to the skin pathology of HPV 16 E6E7 transgenic mice

One of three lines of mice transgenic for the E6 and E7 genes of human papillomavirus type 16 (HPV16) expressed from an alpha A-crystallin promoter also expresses the transgene ectopically in the skin. This line, designated alpha ACE6E7#19, develops skin disease from 3 months of age, characterised by epidermal hyperplasia and eventual skin loss. Administration of complete Freund's adjuvant (CFA) to alpha ACE6E7#19 mice, but not to nontransgenic littermate controls, induced local epidermal hyperplasia which was histologically similar to the spontaneously arising skin pathology. Local application of 2,4-dinitrochlorobenzene (DNCB) to DNCB-sensitised aACE6E7#19 mice, but not DNCB-sensitised controls, also induced hyperplasia. Treatment with cyclosporin A (CsA) or systemic depletion of CD4+ cells significantly reduced the incidence of skin disease. These data suggest that local inflammation, and cytokines produced by T helper cells, contribute to the induction of hyperplastic skin disease in alpha ACE6E7#19 mice. Spontaneous skin disease with similar histological appearance, frequency, age of onset and severity in alpha ACE6E7#19 mice was observed in scid-/- aACE6E7#19 mice, despite immune paresis. Antigen-specific immune responses and T-cell cytokines a re therefore not necessary for the induction of skin disease. We propose that epidermal hyperplasia associated with HPV16 E6 and E7 expression in skin is accelerated by local secretion of pro-inflammatory cytokines, whose production can be enhanced by activated CD4+ T cells.

A novel stable inhibitor of endopeptidases EC 3.4.24.15 and 3.4.24.16 potentiates bradykinin-induced hypotension

We have developed a novel inhibitor of the metalloendopeptidases EC 3.4.24.15 (EP24.15) and EC 3.4.24.16 (EP24.16), N-[1-(R, S)-carboxy-3-phenylpropyl]-Ala-Aib-Tyr-p-aminobenzoate (JA2), in which alpha-aminoisobutyric acid (Aib) is substituted for an alanine in a well-described but unstable inhibitor, cFP-AAY-pAB. This substitution increases the resistance of the inhibitor to degradation without altering potency. In the present study, we investigated the effects of JA2 (5 mg/kg) on the responses of mean arterial pressure to bradykinin, angiotensin I, and angiotensin II in conscious rabbits. The depressor responses to both low (10 ng/kg) and high (100 ng/kg) doses of bradykinin were increased 7.0 +/- 2.7-fold and 1.5 +/- 0.3-fold, respectively, during the 30 minutes after JA2 administration (mean+/-SEM, n=8). Bradykinin potentiation was undiminished 4 hours after JA2 injection. In contrast, the hypertensive effects of angiotensins I and II were unaltered, indicating that the bradykinin-potentiating effects were not due to angiotensin-converting enzyme inhibition. These data suggest that JA2 is not only a potent and specific inhibitor of EP24.15 and EP24.16 but is also stable in vivo. Furthermore, the potentiation of bradykinin-induced hypotension by JA2 suggests for the first time a role for one or both of these peptidases in the metabolism of bradykinin in the circulation.

Conformational selection of inhibitors and substrates by proteolytic enzymes: Implications for drug design and polypeptide processing

Inhibitors of proteolytic enzymes (proteases) are emerging as prospective treatments for diseases such as AIDS and viral infections, cancers, inflammatory disorders, and Alzheimer's disease. Generic approaches to the design of protease inhibitors are limited by the unpredictability of interactions between, and structural changes to, inhibitor and protease during binding. A computer analysis of superimposed crystal structures for 266 small molecule inhibitors bound to 48 proteases (16 aspartic, 17 serine, 8 cysteine, and 7 metallo) provides the first conclusive proof that inhibitors, including substrate analogues, commonly bind in an extended beta-strand conformation at the active sites of all these proteases. Representative superimposed structures are shown for (a) multiple inhibitors bound to a protease of each class, (b) single inhibitors each bound to multiple proteases, and (c) conformationally constrained inhibitors bound to proteases. Thus inhibitor/substrate conformation, rather than sequence/composition alone, influences protease recognition, and this has profound implications for inhibitor design. This conclusion is supported by NMR, CD, and binding studies for HIV-1 protease inhibitors/ substrates which, when preorganized in an extended conformation, have significantly higher protease affinity. Recognition is dependent upon conformational equilibria since helical and turn peptide conformations are not processed by proteases. Conformational selection explains the resistance of folded/structured regions of proteins to proteolytic degradation, the susceptibility of denatured proteins to processing, and the higher affinity of conformationally constrained 'extended' inhibitors/substrates for proteases. Other approaches to extended inhibitor conformations should similarly lead to high-affinity binding to a protease.

Conotoxin TVIIA, a novel peptide from the venom of Conus tulipa - 2. Three-dimensional solution structure

The three-dimensional solution structure of conotoxin TVIIA, a 30-residue polypeptide from the venom of the piscivorous cone snail Conus tulipa, has been determined using 2D H-1 NMR spectroscopy. TVIIA contains six cysteine residues which form a 'four-loop' structural framework common to many peptides from Conus venoms including the omega-, delta-, kappa-, and mu O-conotoxins. However, TVIIA does not belong to these well-characterized pharmacological classes of conotoxins, but displays high sequence identity with conotoxin GS, a muscle sodium channel blocker from Conus geographus. Structure calculations were based on 562 interproton distance restraints inferred from NOE data, together with 18 backbone and nine side-chain torsion angle restraints derived from spin-spin coupling constants. The final family of 20 structures had mean pairwise rms differences over residues 2-27 of 0.18 +/- 0.05 Angstrom for the backbone atoms and 1.39 +/- 0.33 Angstrom for all heavy atoms. The structure consists of a triple-stranded, antiparallel beta sheet with +2x, -1 topology (residues 7-9, 16-20 and 23-27) and several beta turns. The core of the molecule is formed by three disulfide bonds which form a cystine knot motif common to many toxic and inhibitory polypeptides. The global fold, molecular shape and distribution of amino-acid sidechains in TVIIA is similar to that previously reported for conotoxin GS, and comparison with other four-loop conotoxin structures provides further indication that TVIIA and GS represent a new and distinct subgroup of this structural family. The structure of TVIIA determined in this study provides the basis for determining a structure-activity relationship for these molecules and their interaction with target receptors.

Metal-directed synthesis routes to a 16-membered tetraazamacrocycle with two pendant primary amine groups

The reaction of the bis(propane-1,3-diamine)copper(II) ion with paraformaldehyde and nitroethane in dry methanol under basic conditions produces a macrocyclic product, (cis-3,11-dimethyl-3,11-dinitro-1,5,9,13-tetraazacyclohexadecane)copper(II) perchlorate, in low yield, compared with the good yield obtained in the parallel chemistry possible even under aqueous conditions using palladium(II) as a template. The palladium complex was reduced with zinc amalgam in dilute aqueous acid to yield the metal-free 16-membered macrocyclic hexaamine, in this case re-complexed and characterised by an X-ray crystal structure as the (cis-3,11-dimethyl-1,5,9,13-tetraazacyclohexadecane-3,11-diamine)copper(II) perchlorate. The copper ion is found in a tetragonally elongated and trigonally-distorted octahedral environment, with all six of the ligand nitrogens coordinated, the two primary amine pendant groups occupying cis sites. (C) 2000 Elsevier Science S.A. All rights reserved.

Mesoionic pyridopyrimidinylium and pyridooxazinylium olates and non-mesoionic pyridopyrimidinones. Structures in the solid state, solution, and matrices

X-Ray crystal structures, C-13 NMR spectra and theoretical calculations (B3LYP/6-31G*) are reported for the mesoionic (zwitterionic) pyridopyrimidinylium- and pyridooxazinyliumolates 2a, 3a and 5a,b as well as the enol ether 11b and the enamine 11c. The 1-NH compounds like 1a, 2a and 3a exist in the mesoionic form in the crystal and in solution, but the OH tautomers such as 1b and 2b dominate in the gas phase as revealed by the Ar matrix IR spectra in conjunction with DFT calculations. All data indicate that the mesoionic compounds can be regarded as intramolecular pyridine-ketene zwitterions (cf. 16 --> 17) with a high degree of positive charge on the pyridinium nitrogen, a long pyridinium N-CO bond (ca. 1.44-1.49 Angstrom), and normal C=O double bonds (ca. 1.22 Angstrom). All mesoionic compounds exhibit a pronounced tilting of the olate C=O groups (the C=O groups formally derived from a ketene) towards the pyridinium nitrogen, giving NCO angles of 110-118 degrees. Calculations reveal a hydrogen bond with 6-CH, analogous to what is found in ketene-pyridine zwitterions and the C3O2-pyridine complex. The 2-OH tautomers of type 1b, 2b, and 11 also show a high degree of zwitterionic character as indicated by the canonical structures 11 12.

Multiple conformational epitopes are recognized by natural and induced immunity to the E7 protein of human papilloma virus type 16 in man

The reactivity of sera from patients with cervical cancer with the E7 protein of human papilloma virus type 16 (HPV16) was estimated using a novel non-radioactive immunoprecipitation assay and four established protein-and peptide-based immunoassays. Six of 14 sera from patients with cervical cancer and 1 of 10 sera from healthy laboratory staff showed repeated reactivity with E7 in at least one assay. Four of the 7 reactive sera were consistently reactive in more than one assay, but only one was reactive in all four assays. Following immunization with E7, 2 of 5 patients with cervical cancer had increased E7-specific reactivity, measurable in one or more assays. No single assay was particularly sensitive for E7 reactivity, or predictive of cervical cancer. Mapping of E7 reactivity to specific E7 peptides was unsuccessful, suggesting that natural or induced E7 reactivity in human serum is commonly directed to conformational epitopes of E7, These results suggest that each assay employed with is study measures a different aspect of E7 reactivity, and that various reactivities to E7 may manifest following HPV infection or immunization. This finding is of significance for monitoring of E7 immunotherapy and for serological screening for cervical cancer. Copyright (C) 2000 S.Karger, AG. Basel.

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying U-q(sl (2/1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.

The chemistry of 5-oxodihydroisoxazoles .16. A new synthesis of pyrroles, furans, thiophens and their benzo analogues

Ethyl 5-oxo-2-phenyl-2,5-dihydroisoxazole-4-carboxylate (2) was photolysed at 300 mn in the presence of phenols, enols, anilines, enamines, aryl thiols and thioenols affording enamines. Treatment of these enamines with Lewis or protic acids gives the respective benzo and five-membered ring systems.

E7 oncoprotein of human papillomavirus type 16 expressed constitutively in the epidermis has no effect on E7-specific B- or Th-repertoires or on the immune response induced or sustained after immunization with E7 protein

A line of FVB (H-2(q)) mice transgenic for the E6/E7 open reading frames of Human Papillomavirus type 16 driven from the alpha-A crystallin promoter expresses E7 mRNA in lens and skin epithelium. E7 protein is detectable in adult skin, coinciding with the development or inflammatory skin disease, which progresses to papillomata and squamous carcinomata in some mice. By examining the outcome of parenteral immunization with E7 protein, we sought to determine whether endogenous expression of E7 in skin had induced a preexisting immune outcome, i.e., specific immunity or tolerance, or whether the mice remain naive (''ignorant'') to E7. Our data show that the antibody response to defined E7 B-epitopes, the proliferative response to Th epitopes, and the delayed-type hypersensitivity (DTH) response to whole E7 did not differ between groups or young and old E6/E7 transgenic mice (likely having different degrees of lifetime exposure to E7 protein) or between E6/E7-transgenic and nontransgenic parental strain control mice. Although an E7-specific CTL response could not be induced in the H-2(q) background of these mice, incorporation of a D-b allele into the genome allowed comparison of D-b-restricted CTL responses in E6/E7 transgenic and nontransgenic mice. Experiments indicated that the E7-immunization-induced CTL response did not differ significantly between E6/E7 transgenic and nontransgenic mice. We interpret these results to indicate that in spite of expression of E7 protein in adult skin, E6/E7 transgenic mice remain immunologically naive (ignorant) of E7 epitopes presented by immunization. (C) 1997 Academic Press.

Finite element analysis of mechanical properties in discontinuously reinforced metal matrix composites with ultrafine microstructure

This investigation focused on the finite element analyses of elastic and plastic properties of aluminium/alumina composite materials with ultrafine microstructure. The commonly used unit cell model was used to predict the elastic properties. By combining the unit cell model with an indentation model, coupled with experimental indentation measurements, the plastic properties of the composites and the associated strengthening mechanism within the metal matrix material were investigated. The grain size of the matrix material was found to be an important factor influencing the mechanical properties of the composites studied. (C) 1997 Elsevier Science S.A.

Integer matrix diagonalization

We consider algorithms for computing the Smith normal form of integer matrices. A variety of different strategies have been proposed, primarily aimed at avoiding the major obstacle that occurs in such computations-explosive growth in size of intermediate entries. We present a new algorithm with excellent performance. We investigate the complexity of such computations, indicating relationships with NP-complete problems. We also describe new heuristics which perform well in practice. Wie present experimental evidence which shows our algorithm outperforming previous methods. (C) 1997 Academic Press Limited.