The initial value problems for quasi‐linear wave equations in two space dimensions with small data

The present paper studies the lifespan of solutions to quasi-linear wave equations in two space dimensions. We shall show a lower bound for the lifespan. We shall also show that if the non-linear term satisfies "null­condition", the equations have global solutions. Our basic idea is to solve ordinary differential equations which are constructed from wave equations

Disparate effects of adhesion and degranulation of platelets on myocardial and coronary function in postischaemic hearts

Beside the major effect of acute thrombus formation, little is known about the interaction of platelets with the coronary endothelium in an ischaemia–reperfusion situation. The present study was designed to investigate, separately, the consequences of platelet adhesion and degranulation during myocardial reperfusion. Methods: Isolated guinea pig hearts perfused with Krebs–Henseleit buffer and performing pressure–volume work were used. We infringed myocardial function by imposing ischaemia (20 min of low-flow perfusion with 1 ml/min and 10 min of global ischaemia) and reperfusion (15 min with 5 ml/min). During low-flow perfusion, the coronary endothelium was stimulated by thrombin before and during infusion of a bolus: 108 washed human platelets±the Arg–Gly–Asp (RGD) analogon lamifiban, the supernatant of 108 thrombin-stimulated platelets, fibrinogen (2 μM), lamifiban (2 μM) or Tyrode’s solution (control group). The parameter external heart work (EHW), determined pre- and postischaemically, served as criterion for recovery of myocardial function. Additionally, the formation of capillary transudate was measured during the reperfusion phase to assess coronary permeability. Coronary perfusion pressure was monitored continuously and myocardial production of lactate and consumption of pyruvate were measured. Electron microscopy of hearts was performed after platelet application to verify platelet adhesion in the coronary system. Results: Recovery of EHW by hearts without platelet application was 64±3% and was significantly reduced to 49±5% by platelet infusion (n=8 each). Infusion of supernatant of thrombin-stimulated platelets did not impair recovery of heart work. In the reperfusion phase (6th–10th min), hearts that either had received platelets or supernatant of platelets exhibited a significantly reduced production of capillary transudate (70 μl/min vs. 180 μl/min for the controls). Intracoronary bolus application of fibrinogen or lamifiban also reduced coronary leak. Coronary perfusion pressure and metabolic parameters were not statistically different between the groups at any time. Conclusions: Platelet adhesion to the coronary endothelium in a situation of myocardial ischaemia impairs cardiac recovery, whereas constituents released by platelets may have beneficial effects on the integrity of the coronary endothelium. In particular, fibrinogen seems to contribute to the permeability reducing effect, possibly by interaction with endothelial receptors recognising the RGD sequence

Inhibition of the Staphylococcus aureus c-di-AMP cyclase DacA by direct interaction with the phosphoglucosamine mutase GlmM

c-di-AMP is an important second messenger molecule that plays a pivotal role in regulating fundamental cellular processes, including osmotic and cell wall homeostasis in many Gram-positive organisms. In the opportunistic human pathogen Staphylococcus aureus, c-di-AMP is produced by the membrane-anchored DacA enzyme. Inactivation of this enzyme leads to a growth arrest under standard laboratory growth conditions and a re-sensitization of methicillin-resistant S. aureus (MRSA) strains to ß-lactam antibiotics. The gene coding for DacA is part of the conserved three-gene dacA/ybbR/glmM operon that also encodes the proposed DacA regulator YbbR and the essential phosphoglucosamine mutase GlmM, which is required for the production of glucosamine-1-phosphate, an early intermediate of peptidoglycan synthesis. These three proteins are thought to form a complex in vivo and, in this manner, help to fine-tune the cellular c-di-AMP levels. To further characterize this important regulatory complex, we conducted a comprehensive structural and functional analysis of the S. aureus DacA and GlmM enzymes by determining the structures of the S. aureus GlmM enzyme and the catalytic domain of DacA. Both proteins were found to be dimers in solution as well as in the crystal structures. Further site-directed mutagenesis, structural and enzymatic studies showed that multiple DacA dimers need to interact for enzymatic activity. We also show that DacA and GlmM form a stable complex in vitro and that S. aureus GlmM, but not Escherichia coli or Pseudomonas aeruginosa GlmM, acts as a strong inhibitor of DacA function without the requirement of any additional cellular factor. Based on Small Angle X-ray Scattering (SAXS) data, a model of the complex revealed that GlmM likely inhibits DacA by masking the active site of the cyclase and preventing higher oligomer formation. Together these results provide an important mechanistic insight into how c-di-AMP production can be regulated in the cell

Global existence for coupled systems of nonlinear wave and Klein-Gordon equations in three space dimensions

We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null condition on self-interactions between wave equations. Our condition is much weaker than the strong null condition introduced by Georgiev for this kind of coupled system. Consequently our result is applicable to certain physical systems, such as the Dirac-Klein-Gordon equations, the Dirac-Proca equations, and the Klein-Gordon-Zakharov equations.Comment: 31 pages. The final versio

Molecular imaging of inflammation and intraplaque vasa vasorum: A step forward to identification of vulnerable plaques?

Current developments in cardiovascular biology and imaging enable the noninvasive molecular evaluation of atherosclerotic vascular disease. Intraplaque neovascularization sprouting from the adventitial vasa vasorum has been identified as an independent predictor of intraplaque hemorrhage and plaque rupture. These intraplaque vasa vasorum result from angiogenesis, most likely under influence of hypoxic and inflammatory stimuli. Several molecular imaging techniques are currently available. Most experience has been obtained with molecular imaging using positron emission tomography and single photon emission computed tomography. Recently, the development of targeted contrast agents has allowed molecular imaging with magnetic resonance imaging, ultrasound and computed tomography. The present review discusses the use of these molecular imaging techniques to identify inflammation and intraplaque vasa vasorum to identify vulnerable atherosclerotic plaques at risk of rupture and thrombosis. The available literature on molecular imaging techniques and molecular targets associated with inflammation and angiogenesis is discussed, and the clinical applications of molecular cardiovascular imaging and the use of molecular techniques for local drug delivery are addressed