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

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

β1 Integrin Maintains Integrity of the Embryonic Neocortical Stem Cell Niche

IInteractions between laminins and integrin receptors hold neural stem cells in place at the ventricular surface of embryonic brain. Transient disruption leads to abnormal stem cell divisions and permanent cortical malformation

Molecular Mechanism of the Constitutive Activation of the L250Q Human Melanocortin-4 Receptor Polymorphism †

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65471/1/j.1747-0285.2006.00362.x.pd

The masterpieces of John Forbes Nash Jr.

In this set of notes I follow Nash’s four groundbreaking works on real algebraic manifolds, on isometric embeddings of Riemannian manifolds and on the continuity of solutions to parabolic equations. My aim has been to stay as close as possible to Nash’s original arguments, but at the same time present them with a more modern language and notation. Occasionally I have also provided detailed proofs of the points that Nash leaves to the reader

PKA and Epac cooperate to augment bradykinin-induced interleukin-8 release from human airway smooth muscle cells

Background: Airway smooth muscle contributes to the pathogenesis of pulmonary diseases by secreting inflammatory mediators such as interleukin-8 (IL-8). IL-8 production is in part regulated via activation of G(q)-and G(s)-coupled receptors. Here we study the role of the cyclic AMP (cAMP) effectors protein kinase A (PKA) and exchange proteins directly activated by cAMP (Epac1 and Epac2) in the bradykinin-induced IL-8 release from a human airway smooth muscle cell line and the underlying molecular mechanisms of this response.Methods: IL-8 release was assessed via ELISA under basal condition and after stimulation with bradykinin alone or in combination with fenoterol, the Epac activators 8-pCPT-2'-O-Me-cAMP and Sp-8-pCPT-2'-O-Me-cAMPS, the PKA activator 6-Bnz-cAMP and the cGMP analog 8-pCPT-2'-O-Me-cGMP. Where indicated, cells were pre-incubated with the pharmacological inhibitors Clostridium difficile toxin B-1470 (GTPases), U0126 (extracellular signal-regulated kinases ERK1/2) and Rp-8-CPT-cAMPS (PKA). The specificity of the cyclic nucleotide analogs was confirmed by measuring phosphorylation of the PKA substrate vasodilator-stimulated phosphoprotein. GTP-loading of Rap1 and Rap2 was evaluated via pull-down technique. Expression of Rap1, Rap2, Epac1 and Epac2 was assessed via western blot. Downregulation of Epac protein expression was achieved by siRNA. Unpaired or paired two-tailed Student's t test was used.Results: The beta(2)-agonist fenoterol augmented release of IL-8 by bradykinin. The PKA activator 6-Bnz-cAMP and the Epac activator 8-pCPT-2'-O-Me-cAMP significantly increased bradykinin-induced IL-8 release. The hydrolysis-resistant Epac activator Sp-8-pCPT-2'-O-Me-cAMPS mimicked the effects of 8-pCPT-2'-O-Me-cAMP, whereas the negative control 8-pCPT-2'-O-Me-cGMP did not. Fenoterol, forskolin and 6-Bnz-cAMP induced VASP phosphorylation, which was diminished by the PKA inhibitor Rp-8-CPT-cAMPS. 6-Bnz-cAMP and 8-pCPT-2'-O-Me-cAMP induced GTP-loading of Rap1, but not of Rap2. Treatment of the cells with toxin B-1470 and U0126 significantly reduced bradykinin-induced IL-8 release alone or in combination with the activators of PKA and Epac. Interestingly, inhibition of PKA by Rp-8-CPT-cAMPS and silencing of Epac1 and Epac2 expression by specific siRNAs largely decreased activation of Rap1 and the augmentation of bradykinin-induced IL-8 release by both PKA and Epac.Conclusion: Collectively, our data suggest that PKA, Epac1 and Epac2 act in concert to modulate inflammatory properties of airway smooth muscle via signaling to the Ras-like GTPase Rap1 and to ERK1/2.</p