A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

A tetracycline derivative, minocycline, reduces inflammation and protects against focal cerebral ischemia with a wide therapeutic window

The only treatment of patients with acute ischemic stroke is thrombolytic therapy, which benefits only a fraction of stroke patients. Both human and experimental studies indicate that ischemic stroke involves secondary inflammation that significantly contributes to the outcome after ischemic insult. Minocycline is a semisynthetic second-generation tetracycline that exerts antiinflammatory effects that are completely separate from its antimicrobial action. Because tetracycline treatment is clinically well tolerated, we investigated whether minocycline protects against focal brain ischemia with a wide therapeutic window. Using a rat model of transient middle cerebral artery occlusion, we show that daily treatment with minocycline reduces cortical infarction volume by 76 ± 22% when the treatment is started 12 h before ischemia and by 63 ± 35% when started even 4 h after the onset of ischemia. The treatment inhibits morphological activation of microglia in the area adjacent to the infarction, inhibits induction of IL-1β-converting enzyme, and reduces cyclooxygenase-2 expression and prostaglandin E2 production. Minocycline had no effect on astrogliosis or spreading depression, a wave of ionic transients thought to contribute to enlargement of cortical infarction. Treatment with minocycline may act directly on brain cells, because cultured primary neurons were also salvaged from glutamate toxicity. Minocycline may represent a prototype of an antiinflammatory compound that provides protection against ischemic stroke and has a clinically relevant therapeutic window.

An NO derivative of ursodeoxycholic acid protects against Fas-mediated liver injury by inhibiting caspase activity

Caspases are key mediators in liver inflammation and apoptosis. In the present study we provide evidence that a nitric oxide (NO) derivative of ursodeoxycholic acid (UDCA), NCX-1000 ([2-(acetyloxy)benzoic acid 3-(nitrooxymethyl)phenyl ester]), protects against liver damage in murine models of autoimmune hepatitis induced by i.v. injection of Con A or a Fas agonistic antibody, Jo2. Con A administration causes CD4+ T lymphocytes to accumulate in the liver and up-regulates FasL expression, resulting in FasL-mediated cytotoxicity. Cotreating mice with NCX-1000, but not with UDCA, protected against liver damage induced by Con A and Jo2, inhibited IL-1β, IL-18, and IFN-γ release and caspase 3, 8, and 9 activation. Studies on HepG2 cells demonstrated that NCX-1000, but not UDCA, directly prevented multiple caspase activation induced by Jo2. Incubating HepG2 cells with NCX-1000 resulted in intracellular NO formation and a DTT-reversible inhibition of proapoptotic caspases, suggesting that cysteine S-nitrosylation was the main mechanism responsible for caspase inhibition. Collectively, these data suggest that NCX-1000 protects against T helper 1-mediated liver injury by inhibiting both the proapoptotic and the proinflammatory branches of the caspase superfamily.

Selective binding of perfringolysin O derivative to cholesterol-rich membrane microdomains (rafts)

There is increasing evidence that sphingolipid- and cholesterol-rich microdomains (rafts) exist in the plasma membrane. Specific proteins assemble in these membrane domains and play a role in signal transduction and many other cellular events. Cholesterol depletion causes disassembly of the raft-associated proteins, suggesting an essential role of cholesterol in the structural maintenance and function of rafts. However, no tool has been available for the detection and monitoring of raft cholesterol in living cells. Here we show that a protease-nicked and biotinylated derivative (BCθ) of perfringolysin O (θ-toxin) binds selectively to cholesterol-rich microdomains of intact cells, the domains that fulfill the criteria of rafts. We fractionated the homogenates of nontreated and Triton X-100-treated platelets after incubation with BCθ on a sucrose gradient. BCθ was predominantly localized in the floating low-density fractions (FLDF) where cholesterol, sphingomyelin, and Src family kinases are enriched. Immunoelectron microscopy demonstrated that BCθ binds to a subpopulation of vesicles in FLDF. Depletion of 35% cholesterol from platelets with cyclodextrin, which accompanied 76% reduction in cholesterol from FLDF, almost completely abolished BCθ binding to FLDF. The staining patterns of BCθ and filipin in human epidermoid carcinoma A431 cells with and without cholesterol depletion suggest that BCθ binds to specific membrane domains on the cell surface, whereas filipin binding is indiscriminate to cell cholesterol. Furthermore, BCθ binding does not cause any damage to cell membranes, indicating that BCθ is a useful probe for the detection of membrane rafts in living cells.

NCX-1000, a NO-releasing derivative of ursodeoxycholic acid, selectively delivers NO to the liver and protects against development of portal hypertension

Portal hypertension resulting from increased intrahepatic resistance is a common complication of chronic liver diseases and a leading cause of death in patients with liver cirrhosis, a scarring process of the liver that includes components of both increased fibrogenesis and wound contraction. A reduced production of nitric oxide (NO) resulting from an impaired enzymatic function of endothelial NO synthase and an increased contraction of hepatic stellate cells (HSCs) have been demonstrated to contribute to high intrahepatic resistance in the cirrhotic liver. 2-(Acetyloxy) benzoic acid 3-(nitrooxymethyl) phenyl ester (NCX-1000) is a chemical entity obtained by adding an NO-releasing moiety to ursodeoxycholic acid (UDCA), a compound that is selectively metabolized by hepatocytes. In this study we have examined the effect of NCX-1000 and UDCA on liver fibrosis and portal hypertension induced by i.p. injection of carbon tetrachloride in rats. Our results demonstrated that although both treatments reduced liver collagen deposition, NCX-1000, but not UDCA, prevented ascite formation and reduced intrahepatic resistance in carbon tetrachloride-treated rats as measured by assessing portal perfusion pressure. In contrast to UDCA, NCX-1000 inhibited HSC contraction and exerted a relaxing effect similar to the NO donor S-nitroso-N-acetylpenicillamine. HSCs were able to metabolize NCX-1000 and release nitrite/nitrate in cell supernatants. In aggregate these data indicate that NCX-1000, releasing NO into the liver microcirculation, may provide a novel therapy for the treatment of patients with portal hypertension.

Microsatellite instability in childhood rhabdomyosarcoma is locus specific and correlates with fractional allelic loss.

Replication errors (RERs) were initially identified in hereditary nonpolyposis colon cancer and other tumors of Lynch syndrome II. Mutations in genes involved in mismatch repair give rise to a mutator phenotype, resulting in RERs. The mutator phenotype is thought to predispose to malignant transformation. Here we show that in the embryonal form of childhood rhabdomyosarcoma, RERs also occur, but in contrast to hereditary nonpolyposis colon cancer, only a subset of the microsatellite loci analyzed show RERs. The occurrence of RERs is strongly correlated with increased fractional allelic loss (P < 0.001), suggesting that the occurrence of RERs is a secondary phenomenon in rhabdomyosarcoma. Coincidental loss of genes involved in mismatch repair, possibly due to their proximity to tumor suppressor genes involved in tumor progression of embryonal form of childhood rhabdomyosarcoma, could explain the observed phenomenon.

Molecular evidence that the asexual industrial fungus Trichoderma reesei is a clonal derivative of the ascomycete Hypocrea jecorina.

The relationship of the important cellulase producing asexual fungus Trichoderma reesei to its putative teleomorphic (sexual) ancestor Hypocrea jecorina and other species of the Trichoderma sect. Longibrachiatum was studied by PCR-fingerprinting and sequence analyses of the nuclear ribosomal DNA region containing the internal transcribed spacers (ITS-1 and ITS-2) and the 5.8S rRNA gene. The differences in the corresponding ITS sequences allowed a grouping of anamorphic (asexual) species of Trichoderma sect. Longibrachiatum into Trichoderma longibrachiatum, Trichoderma pseudokoningii, and Trichoderma reesei. The sexual species Hypocrea schweinitzii and H. jecorina were also clearly separated from each other. H. jecorina and T. reesei exhibited identical sequences, suggesting close relatedness or even species identity. Intraspecific and interspecific variation in the PCR-fingerprinting patterns supported the differentiation of species based on ITS sequences, the grouping of the strains, and the assignment of these strains to individual species. The variations between T. reesei and H. jecorina were at the same order of magnitude as found between all strains of H. jecorina, but much lower than the observed interspecific variations. Identical ITS sequences and the high similarity of PCR-fingerprinting patterns indicate a very close relationship between T. reesei and H. jecorina, whereas differences of the ITS sequences and the PCR-fingerprinting patterns show a clear phylogenetic distance between T. reesei/H. jecorina and T. longibrachiatum. T. reesei is considered to be an asexual, clonal line derived from a population of the tropical ascomycete H. jecorina.

Cellular mechanisms for the formation of a soluble form derivative of T-cell receptor alpha chain by suppressor T cells.

Upon stimulation with anti-CD3, suppressor T-cell (Ts) hybridomas and homologous transfectants of T-cell receptor a (TCRalpha) cDNA in the T-cell hybridoma formed a 55-kDa TCRalpha chain derivative that bound both the monoclonal anti-TCRalpha chain and polyclonal antibodies against glycosylation inhibiting factor (GIF). The peptide is a subunit of antigen-specific suppressor T-cell factor (TsF), and is considered to be a posttranslationally-formed conjugate of TCRalpha chain with GIF peptide. The TCRalpha derivative is synthesized by the transfectant after stimulation with anti-CD3, and not derived from TCR present on the cell surface. Stimulation of the stable homologous transfectants with anti-CD3 induced translocation of the 13-kDa GIF peptide into endoplasmic reticulum (ER). When a helper Ts hybridoma or a stable transfectant of the same TCRalpha cDNA in a helper cell-derived TCRalpha- clone was stimulated with anti-CD3, translocation of GIF peptide was not detected, and these cells failed to secrete a TCRalpha derivative. However, further transfection of a chimeric cDNA encoding a procalcitonin-GIF fusion protein into the helper cell-derived stable transfectant of TCRalpha cDNA resulted in translocation of the GIF protein and formation of bioactive 55-kDa GIF. The results indicated that translocation of GIF peptide through ER is unique for Ts cells, and that this process is essential for the formation/secretion of the soluble form derivative of TCRalpha chain by T cells.

Cytotoxic analogs of luteinizing hormone-releasing hormone containing doxorubicin or 2-pyrrolinodoxorubicin, a derivative 500-1000 times more potent.

Doxorubicin (DOX) and its daunosamine-modified derivative, 2-pyrrolino-DOX, which is 500-1000 times more active than DOX, were incorporated into agonistic and antagonistic analogs of luteinizing hormone-releasing hormone (LH-RH). The conjugation of DOX with LH-RH analogs was performed by using N-(9-fluorenylmethoxycarbonyl)-DOX-14-O-hemiglutarate, a dicarboxylic acid ester derivative of DOX. Coupling this derivative covalently to the epsilon-amino group of the D-Lys side chain of agonist [D-Lys6]LH-RH or antagonistic analog AC-D-Nal(2)-D-Phe(4Cl)-D-Pal(3)-Ser-Tyr-D-Lys-Leu-Arg-Pro-D-Ala-NH 2 [where Nal(2) = 3-(2-naphthyl)alanine, Pal(3) = 3-(3-pyridyl)alanine, and Phe(4CI) = 4-chlorophenylalanine] was followed by the removal of the 9-fluorenylmethoxycarbonyl protective group to yield cytotoxic derivatives of LH-RH analogs containing DOX. From these DOX containing LH-RH hybrids, intensely potent analogs with daunosamine-modified derivatives of DOX can be readily formed. Thus, cytotoxic LH-RH agonist containing DOX (AN-152) can be converted in a 66% yield by a reaction with a 30-fold excess of 4-iodobutyraldehyde in N,N-dimethylformamide into a derivative having 2-pyrrolino-DOX (AN-207). Hybrid molecules AN-152 and AN-207 fully preserve the cytotoxic activity of their radicals, DOX or 2-pyrrolino-DOX, respectively, in vitro, and also retain the high binding affinity of the peptide hormone portion of the conjugates to rat pituitary receptors for LH-RH. These highly potent cytotoxic analogs of LH-RH were designed as targeted anti-cancer agents for the treatment of various tumors that possess receptors for the carrier peptide. Initial in vivo studies show that the hybrid molecules are much less toxic than the respective cytotoxic radicals incorporated and significantly more active in inhibiting tumor growth.

An alpha-mercaptoacrylic acid derivative is a selective nonpeptide cell-permeable calpain inhibitor and is neuroprotective.

Overactivation of calcium-activated neutral protease (calpain) has been implicated in the pathophysiology of several degenerative conditions, including stroke, myocardial ischemia, neuromuscular degeneration, and cataract formation. Alpha-mercaptoacrylate derivatives (exemplified by PD150606), with potent and selective inhibitory actions against calpain, have been identified. PD150606 exhibits the following characteristics: (i) Ki values for mu- and m-calpains of 0.21 microM and 0.37 microM, respectively, (ii) high specificity for calpains relative to other proteases, (iii) uncompetitive inhibition with respect to substrate, and (iv) it does not shield calpain against inactivation by the active-site inhibitor trans-(epoxysuccinyl)-L-leucyl-amido-3-methylbutane, suggesting a nonactive site action for PD150606. The recombinant calcium-binding domain from each of the large or small subunits of mu-calpain was found to interact with PD150606. In low micromolar range, PD15O6O6 inhibited calpain activity in two intact cell systems. The neuroprotective effects of this class of compound were also demonstrated by the ability of PD150606 to attenuate hypoxic/hypoglycemic injury to cerebrocortical neurons in culture and excitotoxic injury to Purkinje cells in cerebellar slices.

Interaction of an alkylating camptothecin derivative with a DNA base at topoisomerase I-DNA cleavage sites.

DNA topoisomerase I (top1) is a ubiquitous nuclear enzyme. It is specifically inhibited by camptothecin, a natural product derived from the bark of the tree Camptotheca acuminata. Camptothecin and several of its derivatives are presently in clinical trial and exhibit remarkable anticancer activity. The present study is a further investigation of the molecular interactions between the drug and the enzyme-DNA complex. We utilized an alkylating camptothecin derivative, 7-chloromethyl-10,11-methylenedioxycamptothecin (7-ClMe-MDO-CPT), and compared its activity against calf thymus top1 in a DNA oligonucleotide containing a single top1 cleavage site with the activity of its nonalkylating analog, 7-ethyl-10,11-methylenedioxycamptothecin (7-Et-MDO-CPT). In the presence of top1, 7-ClMe-MDO-CPT produced a DNA fragment that migrated more slowly than the top1-cleaved DNA fragment observed with 7-Et-MDO-CPT. Top1 was unable to religate this fragment in the presence of high NaCl concentration or proteinase K at 50 degrees C. This fragment was resistant to piperidine treatment and was also formed with an oligonucleotide containing a 7-deazaguanine at the 5' terminus of the top1-cleaved DNA (base + 1). It was however cleaved by formic acid treatment followed by piperidine. These observations are consistent with alkylation of the +1 base (adenine or guanine) by 7-ClMe-MDO-CPT in the presence of top1 covalent complexes and provide direct evidence that camptothecins inhibit top1 by binding at the enzyme-DNA interface.

Estimating and forecasting generalized fractional Long memory stochastic volatility models

In recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model.