Variational principles and the shift in the front speed due to a cutoff

We apply variational principles to reaction-diffusion equations in order to predict, for a general reaction term, the sign of the shift in the front speed due to a cutoff. We develop an improved variational principle to obtain the shift in the front speed for a wide range of reaction terms, and the theoretical results so obtained are in excellent agreement with numerical solutions. This work proves that variational principles are an optimal framework to deal with fronts propagating into unstable and metastable states under cutoff

Segregation and pursuit waves in activator-inhibitor systems

We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison with the corresponding Rinzel-Keller model for the usually studied case of self-diffusion is performed

Hyper-Activation of pp60(Src) Limits Nitric Oxide Signaling by Increasing Asymmetric Dimethylarginine Levels During Acute Lung Injury

The molecular mechanisms by which the endothelial barrier becomes compromised during lipopolysaccharide (LPS) mediated acute lung injury (ALI) are still unresolved. We have previously reported that the disruption of the endothelial barrier is due, at least in part, to the uncoupling of endothelial nitric oxide synthase (eNOS) and increased peroxynitrite-mediated nitration of RhoA. The purpose of this study was to elucidate the molecular mechanisms by which LPS induces eNOS uncoupling during ALI. Exposure of pulmonary endothelial cells (PAEC) to LPS increased pp60Src activity and this correlated with an increase in nitric oxide (NO) production, but also an increase in NOS derived superoxide, peroxynitrite formation and 3-nitrotyrosine (3-NT) levels. These effects could be simulated by the over-expression of a constitutively active pp60Src (Y527FSrc) mutant and attenuated by over-expression of dominant negative pp60Src mutant or reducing pp60Src expression. LPS induces both RhoA nitration and endothelial barrier disruption and these events were attenuated when pp60Src expression was reduced. Endothelial NOS uncoupling correlated with an increase in the levels of asymmetric dimethylarginine (ADMA) in both LPS exposed and Y527FSrc over-expressing PAEC. The effects in PAEC were also recapitulated when we transiently over-expressed Y527FSrc in the mouse lung. Finally, we found that the pp60Src-mediated decrease in DDAH activity was mediated by the phosphorylation of DDAH II at Y207 and that a Y207F mutant DDAH II was resistant to pp60Src-mediated inhibition. We conclude that pp60Src can directly inhibit DDAH II and this is involved in the increased ADMA levels that enhance eNOS uncoupling during the development of ALI

Cell Surface Transglutaminase Promotes RhoA Activation via Integrin Clustering and Suppression of the Src–p190RhoGAP Signaling Pathway

Tissue transglutaminase (tTG) is a multifunctional protein that serves as cross-linking enzyme and integrin-binding adhesion coreceptor for fibronectin on the cell surface. Previous work showed activation of small GTPase RhoA via enzymatic transamidation by cytoplasmic tTG. Here, we report an alternative nonenzymatic mechanism of RhoA activation by cell surface tTG. Direct engagement of surface tTG with specific antibody or the fibronectin fragment containing modules I(6)II(1,2)I(7-9) increases RhoA-GTP levels. Integrin-dependent signaling to RhoA and its downstream target Rho-associated coiled-coil containing serine/threonine protein kinase (ROCK) is amplified by surface tTG. tTG expression on the cell surface elevates RhoA-GTP levels in nonadherent and adherent cells, delays maximal RhoA activation upon cell adhesion to fibronectin and accelerates a rise in RhoA activity after binding soluble integrin ligands. These data indicate that surface tTG induces integrin clustering regardless of integrin–ligand interactions. This notion is supported by visualization of integrin clusters, increased susceptibility of integrins to chemical cross-linking, and biochemical detection of large integrin complexes in cells expressing tTG. In turn, integrin aggregation by surface tTG inhibits Src kinase activity and decreases activation of the Src substrate p190RhoGAP. Moreover, pharmacological inhibition of Src kinase reveals inactivation of Src signaling as the primary cause of elevated RhoA activity in cells expressing tTG. Together, these findings show that surface tTG amplifies integrin-mediated signaling to RhoA/ROCK via integrin clustering and down-regulation of the Src–p190RhoGAP regulatory pathway

Variational principles and the shift in the front speed due to a cutoff

We apply variational principles to reaction-diffusion equations in order to predict, for a general reaction term, the sign of the shift in the front speed due to a cutoff. We develop an improved variational principle to obtain the shift in the front speed for a wide range of reaction terms, and the theoretical results so obtained are in excellent agreement with numerical solutions. This work proves that variational principles are an optimal framework to deal with fronts propagating into unstable and metastable states under cutoff

Homogenization of a reaction-diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains

A reaction–diffusion system modeling concrete corrosion in sewer pipes is discussed. The system is coupled, semi-linear, and partially dissipative. It is defined on a locally periodic perforated domain with nonlinear Robin-type boundary conditions at water–air and solid–water interfaces. Asymptotic homogenization techniques are applied to obtain upscaled reaction–diffusion models together with explicit formulae for the effective transport and reaction coefficients. It is shown that the averaged system contains additional terms appearing due to the deviation of the assumed geometry from a purely periodic distribution of perforations for two relevant parameter regimes: (a) all diffusion coefficients are of order of O(1) and (b) all diffusion coefficients are of order of O (e^2) except the one for H2S(g) which is of order of O(1). In case (a) a set of macroscopic equations is obtained, while in case (b) a two-scale reaction–diffusion system is derived that captures the interplay between microstructural reaction effects and the macroscopic transport

Segregation and pursuit waves in activator-inhibitor systems

We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison with the corresponding Rinzel-Keller model for the usually studied case of self-diffusion is performed

Transglutaminase-mediated oligomerization of the fibrin(ogen) αC domains promotes integrin-dependent cell adhesion and signaling

Interactions of endothelial cells with fibrin(ogen) are implicated in inflammation, angiogenesis, and wound healing. Cross-linking of the fibrinogen αC domains with factor XIIIa generates ordered αC oligomers mimicking polymeric arrangement of the αC domains in fibrin. These oligomers and those prepared with tissue transglutaminase were used to establish a mechanism of the αC domain–mediated interaction of fibrin with endothelial cells. Cell adhesion and chemical cross-linking experiments revealed that oligomerization of the αC domains by both transglutaminases significantly increases their RGD (arginyl–glycyl–aspartate)–dependent interaction with endothelial αVβ3 and to a lesser extent with αVβ5 and α5β1 integrins. The oligomerization promotes integrin clustering, thereby increasing cell adhesion, spreading, formation of prominent peripheral focal contacts, and integrin-mediated activation of focal adhesion kinase (FAK) and extracellular signal-regulated kinase (ERK) signaling pathways. The enhanced integrin clustering is likely caused by ordered juxtaposition of RGD-containing integrin-binding sites upon oligomerization of the αC domains and increased affinity of these domains for integrins. Our findings provide new insights into the mechanism of the αC domain–mediated interaction of endothelial cells with fibrin and imply its potential involvement in cell migration. They also suggest a new role for transglutaminases in regulation of integrin-mediated adhesion and signaling via covalent modification of integrin ligands