Periodic or Bounded Solutions of Carathéodory Systems of Ordinary Differential Equations

In this paper we extend the guiding function approach to show that there are periodic or bounded solutions for first order systems of ordinary differential equations of the form x1 =f(t,x), a.e. epsilon[a,b], where f satisfies the Caratheodory conditions. Our results generalize recent ones of Mawhin and Ward.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

A master equation model for bimolecular reaction via multi-well isomerization intermediates

A reversible linear master equation model is presented for pressure- and temperature-dependent bimolecular reactions proceeding via multiple long-lived intermediates. This kinetic treatment, which applies when the reactions are measured under pseudo-first-order conditions, facilitates accurate and efficient simulation of the time dependence of the populations of reactants, intermediate species and products. Detailed exploratory calculations have been carried out to demonstrate the capabilities of the approach, with applications to the bimolecular association reaction C3H6 + H reversible arrow C3H7 and the bimolecular chemical activation reaction C2H2 +(CH2)-C-1--> C3H3+H. The efficiency of the method can be dramatically enhanced through use of a diffusion approximation to the master equation, and a methodology for exploiting the sparse structure of the resulting rate matrix is established.

Kinetic analysis of vascular marker distribution in perfused rat livers after regeneration following partial hepatectomy

Background/Aims: Liver clearance models are based on information (or assumptions) on solute distribution kinetics within the microvasculatory system, The aim was to study albumin distribution kinetics in regenerated livers and in livers of normal adult rats, Methods: A novel mathematical model was used to evaluate the distribution space and the transit time dispersion of albumin in livers following regeneration after a two-thirds hepatectomy compared to livers of normal adult rats. Outflow curves of albumin measured after bolus injection in single-pass perfused rat livers were analyzed by correcting for the influence of catheters and fitting a long-tailed function to the data. Results: The curves were well described by the proposed model. The distribution volume and the transit time dispersion of albumin observed in the partial hepatectomy group were not significantly different from livers of normal adult rats. Conclusions: These findings suggest that the distribution space and the transit time dispersion of albumin (CV2) is relatively constant irrespective of the presence of rapid and extensive repair. This invariance of CV2 implies, as a first approximation, a similar degree of intrasinusoidal mixing, The finding that a sum of two (instead of one) inverse Gaussian densities is an appropriate empirical function to describe the outflow curve of vascular indicators has consequences for an improved prediction of hepatic solute extraction.

Refining the risk-benefit equation for thrombolysis: How to identity the low risk patient before administering thrombolytic therapy

In view of the relative risk of intracranial haemorrhage and major bleeding with thrombolytic therapy, it is important ro identify as early as possible the low risk patient who may not have a net clinical benefit from thrombolysis in the setting of acute myocardial infarction. An analysis of 5434 hospital-treated patients with myocardial infarction in the Perth MONICA study showed that age below 60 and absence of previous infarction or diabetes, shock, pulmonary oedema, cardiac arrest and Q-wave or left bundle branch block on the initial ECG identified a large group of patients with a 28 day mortality of only 1%, and one year mortality of only 2%. Identification of baseline risk in this way helps refine the risk-benefit equation for thrombolytic therapy, and may help avoid unnecessary use of thrombolysis in those unlikely to benefit.

Saturation mutagenesis of the beta subunit of the human granulocyte-macrophage colony-stimulating factor receptor shows clustering of constitutive mutations, activation of ERK MAP kinase and STAT pathways, and differential beta subunit tyrosine phosphoryl

The high-affinity receptors for human granulocyte-macrophage colony-stimulating factor (GM-CSF), interleukin-1 (IL-3), and IL-5 are heterodimeric complexes consisting of cytokine-specific alpha subunits and a common signal-transducing beta subunit (h beta c). We have previously demonstrated the oncogenic potential of this group of receptors by identifying constitutively activating point mutations in the extracellular and transmembrane domains of h beta c. We report here a comprehensive screen of the entire h beta c molecule that has led to the identification of additional constitutive point mutations by virtue of their ability to confer factor independence on murine FDC-P1 cells. These mutations were clustered exclusively in a central region of h beta c that encompasses the extracellular membrane-proximal domain, transmembrane domain, and membrane-proximal region of the cytoplasmic domain. Interestingly, most h beta c mutants exhibited cell type-specific constitutive activity, with only two transmembrane domain mutants able to confer factor independence on both murine FDC-P1 and BAF-B03 cells. Examination of the biochemical properties of these mutants in FDC-P1 cells indicated that MAP kinase (ERK1/2), STAT, and JAK2 signaling molecules were constitutively activated. In contrast, only some of the mutant beta subunits were constitutively tyrosine phosphorylated. Taken together; these results highlight key regions involved in h beta c activation, dissociate h beta c tyrosine phosphorylation from MAP kinase and STAT activation, and suggest the involvement of distinct mechanisms by which proliferative signals can be generated by h beta c. (C) 1998 by The American Society of Hematology.

Familial partial epilepsy with variable foci: A new partial epilepsy syndrome with suggestion of linkage to chromosome 2

Familial partial epilepsy with variable foci (FPEVF) joins the recently recognized group of inherited partial epilepsies. We describe an Australian family with 10 individuals with partial seizures over four generations. Detailed electroclinical studies were performed on all affected and 17 clinically unaffected family members. The striking finding was that the clinical features of the seizures and interictal electroencephalographic foci differed among family members and included frontal, temporal, occipital, and centroparietal seizures. Mean age of seizure onset was 13 years (range, 0.75-43 years). Two individuals without seizures had epileptiform abnormalities on electroencephalographic studies. Penetrance of seizures was 62%. A genome-wide search failed to demonstrate definitive linkage, but a suggestion of linkage was found on chromosome 2q with a LOD score of 2.74 at recombination fraction of zero with the marker D2S133. FPEVF differs from the other inherited partial epilepsies where partial seizures in different family members are clinically similar. The inherited nature of this new syndrome may be overlooked because of relatively low penetrance and because of the variability in age at onset and electroclinical features between affected family members.

mRNA differential display of 2-amino-1-methyl-6-phenylinlidazo[4,5-b]pyridine-induced rat mammary gland tumors

The mRNA differential display technique was used to compare mRNAs between normal mammary gland and turner-derived epithelial cells from female Sprague-Dawley rat mammary gland tumors induced by the heterocyclic amine 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) and promoted by a high-fat diet (23.5% corn oil). Two genes, beta-casein and transferrin, were identified as differentially expressed. The expression of these genes was examined across a bank of rat mammary gland tumors derived from animals on a low-fat diet (5% corn oil) or the high-fat diet. Carcinomas had over a 10- and 50-fold lower expression of beta-casein and transferrin, respectively than normal mammary gland. In addition, carcinomas from animals on the high-fat diet showed on average a 5-fold higher expression of beta-casein, and transferrin than carcinomas from animals on the low-fat diet. The results indicate the process of mammary gland tumorigenesis alters the expression of certain genes in the mammary gland, and that the level of dietary fat further modulates the expression of these genes.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Increased expression of mitochondrial genes in human alcoholic brain revealed by differential display

Polymerase chain reaction (PCR)-based differential display was used to screen for alterations in gene expression in the mesolimbic system of the human alcoholic brain. Total RNA was extracted from the nucleus accumbens of five alcoholic and five control brains. A selected subpopulation of mRNA was reverse-transcribed to cDNA and amplified by PCR. A differentially expressed cDNA fragment was recovered, cloned, and sequenced. Full sequence analysis of this 467 bp fragment revealed 98.2% homology with the human mitochondrial 12S rRNA gene. Dot-blot analysis showed increased expression of this gem in nucleus accumbens and hippocampus, but not in the superior frontal cortex, primary motor cortex, caudate, and pallidus/putamen In a total of eight human alcoholic brains, compared with seven control brains. A similar increased expression was observed by dot-blot analysis, using RNA from the cerebral cortex of rats chronically treated with alcohol vapor. Hybridization of a 16S rRNA oligonucleotide probe indicated that the expression of both rRNAs genes was significantly increased in nucleus accumbens. These results indicate that chronic alcohol consumption induces alteration in expression of mitochondrial genes in selected brain regions. The altered gene expression may reflect mitochondrial dysfunction In the alcohol-affected brain.

A pore-size-dependent equation of state for multilayer adsorption in cylindrical mesopores

The chemical potential of adsorbed film inside cylindrical mesopores is dependent on the attractive interactions between the adsorbed molecules and adsorbent, the curvature of gas/adsorbed phase interface, and surface tension. A state equation of the adsorbed film is proposed to take into account the above factors. Nitrogen adsorption on model adsorbents, MCM-41, which exhibit uniform cylindrical channels, are used to verify the theoretical analysis. The proposed theory is capable of describing the important features of adsorption processes in cylindrical mesopores. According to this theory, at a given relative pressure, the smaller the pore radius is, the thicker the adsorbed film will be. The thickening of adsorbed films in the pores as the vapor pressure increases inevitably causes an increase in the interface curvature, which consequently leads to capillary condensation. Besides, this study confirmed that the interface tension depends substantially on the interface curvature in small mesopores. A quantitative relationship between the condensation pressure and the pore radius can be derived from the state equation and used to predict the pore radius from a condensation pressure, or vice versa.