Introduction to a Biological Systems Science

Biological systems analysis and biodynamic modelling of physiological and biological interrelationships in human body and mammal

3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations

The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs

A cloud physics investigation utilizing Skylab data

There are no author-identified significant results in this report

Geometric Sensitivity of a Pinhole Collimator

Geometric sensitivity for single photon emission computerized tomography (SPECT) is given by a double integral over the detection plane. It would be useful to be able to explicitly evaluate this quantity. This paper shows that the inner integral can be evaluated in the situation where there is no gamma ray penetration of the material surrounding the pinhole aperature. This is done by converting the integral to an integral in the complex plane and using Cauchy’s theorem to replace it by one which can be evaluated in terms of elliptic functions

Lower-order ODEs to determine new twisting type N Einstein spaces via CR geometry

In the search for vacuum solutions, with or without a cosmological constant, of the Einstein field equations of Petrov type N with twisting principal null directions, the CR structures to describe the parameter space for a congruence of such null vectors provide a very useful tool. A work of Hill, Lewandowski and Nurowski has given a good foundation for this, reducing the field equations to a set of differential equations for two functions, one real, one complex, of three variables. Under the assumption of the existence of one Killing vector, the (infinite-dimensional) classical symmetries of those equations are determined and group-invariant solutions are considered. This results in a single ODE of the third order which may easily be reduced to one of the second order. A one-parameter class of power series solutions, g(w), of this second-order equation is realized, holomorphic in a neighborhood of the origin and behaving asymptotically as a simple quadratic function plus lower-order terms for large values of w, which constitutes new solutions of the twisting type N problem. The solution found by Leroy, and also by Nurowski, is shown to be a special case in this class. Cartan's method for determining equivalence of CR manifolds is used to show that this class is indeed much more general. In addition, for a special choice of a parameter, this ODE may be integrated once, to provide a first-order Abel equation. It can also determine new solutions to the field equations although no general solution has yet been found for it.Comment: 28 page

The asymptotic expansion of a CR invariant and Grauert tubes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46246/1/208_2005_Article_BF01446285.pd

Non-Raft AC2 Defines a cAMP Signaling Compartment That Selectively Regulates IL-6 Expression in Airway Smooth Muscle Cells

Adenylyl cyclase (AC) isoforms differ in their tissue distribution, cellular localization, regulation, and protein interactions. Most cell types express multiple AC isoforms. We hypothesized that cAMP produced by different AC isoforms regulates unique cellular responses in human bronchial smooth muscle cells (BSMC). Overexpression of AC2, AC3, or AC6 had distinct effects on forskolin (Fsk)-induced expression of a number of known cAMP-responsive genes. These data show that different AC isoforms can differentially regulate gene expression. Most notable, overexpression and activation of AC2 enhanced interleukin 6 (IL-6) expression, but overexpression of AC3 or AC6 had no effect. IL-6 production by BSMC was induced by Fsk and select G protein-coupled receptor (GPCR) agonists, though IL-6 levels did not directly correlate with global cAMP levels. Treatment with PKA selective 6-Bnz-cAMP or Epac selective 8-CPT-2Me-cAMP cAMP analogs revealed a predominant role for PKA in cAMP-mediated induction of IL-6. IL-6 promoter mutations demonstrated that AP-1 and CRE transcription sites were required for Fsk to stimulate IL-6 expression. Our present study defines an AC2 cAMP signaling compartment that specifically regulates IL-6 expression in BSMC via Epac and PKA and demonstrates that other AC isoforms are excluded from this pool

Distinctive Left-Sided Distribution of Adrenergic-Derived Cells in the Adult Mouse Heart

Adrenaline and noradrenaline are produced within the heart from neuronal and non-neuronal sources. These adrenergic hormones have profound effects on cardiovascular development and function, yet relatively little information is available about the specific tissue distribution of adrenergic cells within the adult heart. The purpose of the present study was to define the anatomical localization of cells derived from an adrenergic lineage within the adult heart. To accomplish this, we performed genetic fate-mapping experiments where mice with the cre-recombinase (Cre) gene inserted into the phenylethanolamine-n-methyltransferase (Pnmt) locus were cross-mated with homozygous Rosa26 reporter (R26R) mice. Because Pnmt serves as a marker gene for adrenergic cells, offspring from these matings express the β-galactosidase (βGAL) reporter gene in cells of an adrenergic lineage. βGAL expression was found throughout the adult mouse heart, but was predominantly (89%) located in the left atrium (LA) and ventricle (LV) (p<0.001 compared to RA and RV), where many of these cells appeared to have cardiomyocyte-like morphological and structural characteristics. The staining pattern in the LA was diffuse, but the LV free wall displayed intermittent non-random staining that extended from the apex to the base of the heart, including heavy staining of the anterior papillary muscle along its perimeter. Three-dimensional computer-aided reconstruction of XGAL+ staining revealed distribution throughout the LA and LV, with specific finger-like projections apparent near the mid and apical regions of the LV free wall. These data indicate that adrenergic-derived cells display distinctive left-sided distribution patterns in the adult mouse heart