Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

Genetic, structural, and molecular insights into the function of ras of complex proteins domains

Ras of complex proteins (ROC) domains were identified in 2003 as GTP binding modules in large multidomain proteins from Dictyostelium discoideum. Research into the function of these domains exploded with their identification in a number of proteins linked to human disease, including leucine-rich repeat kinase 2 (LRRK2) and death-associated protein kinase 1 (DAPK1) in Parkinson’s disease and cancer, respectively. This surge in research has resulted in a growing body of data revealing the role that ROC domains play in regulating protein function and signaling pathways. In this review, recent advances in the structural informa- tion available for proteins containing ROC domains, along with insights into enzymatic function and the integration of ROC domains as molecular switches in a cellular and organismal context, are explored.

Pathogenic Parkinson’s disease mutations across the functional domains of LRRK2 alter the autophagic/lysosomal response to starvation

LRRK2 is one of the most important genetic contributors to Parkinson’s disease (PD). Point mutations in this gene cause an autosomal dominant form of PD, but to date no cellular phenotype has been consis- tently linked with mutations in each of the functional domains (ROC, COR and Kinase) of the protein product of this gene. In this study, primary fibroblasts from individuals carrying pathogenic mutations in the three central domains of LRRK2 were assessed for alterations in the autophagy/lysosomal pathway using a combination of biochemical and cellular approaches. Mutations in all three domains resulted in alterations in markers for autophagy/lysosomal function compared to wild type cells. These data high- light the autophagy and lysosomal pathways as read outs for pathogenic LRRK2 function and as a marker for disease, and provide insight into the mechanisms linking LRRK2 function and mutations.

Common components of risk and uncertainty attitudes across contexts and domains: Evidence from 30 countries

Attitudes towards risk and uncertainty have been indicated to be highly context-dependent, and to be sensitive to the measurement technique employed. We present data collected in controlled experiments with 2,939 subjects in 30 countries measuring risk and uncertainty attitudes through incentivized measures as well as survey questions. Our data show clearly that measures correlate not only within decision contexts or measurement methods, but also across contexts and methods. This points to the existence of one underlying “risk preference”, which influences attitudes independently of the measurement method or choice domain. We furthermore find that answers to a general and a financial survey question correlate with incentivized lottery choices in most countries. Incentivized and survey measures also correlate significantly between countries. This opens the possibility to conduct cultural comparisons on risk attitudes using survey instruments.

The application of a domains based analysis to family processes: implications for assessment and therapy

Social domains are classes of interpersonal processes each with distinct procedural rules underpinning mutual understanding, emotion regulation and action. We describe the features of three domains of family life – safety, attachment and discipline/expectation – and contrast them with exploratory processes in terms of the emotions expressed, the role of certainty versus uncertainty, and the degree of hierarchy in an interaction. We argue that everything that people say and do in family life carries information about the type of interaction they are engaged in – that is, the domain. However, sometimes what they say or how they behave does not make the domain clear, or participants in the social interactions are not in the same domain (there is a domain mismatch). This may result in misunderstandings, irresolvable arguments or distress. We describe how it is possible to identify domains and judge whether they are clear and unclear, and matched and mismatched, in observed family interactions and in accounts of family processes. This then provides a focus for treatment and helps to define criteria for evaluating outcomes.

Syk and Src family kinases regulate C-type lectin receptor 2 (CLEC-2)-mediated clustering of podoplanin and platelet adhesion to lymphatic endothelial cells

The interaction of C-type lectin receptor 2 (CLEC-2) on platelets with Podoplanin on lymphatic endothelial cells initiates platelet signaling events that are necessary for prevention of blood-lymph mixing during development. In the present study, we show that CLEC-2 signaling via Src family and Syk tyrosine kinases promotes platelet adhesion to primary mouse lymphatic endothelial cells at low shear. Using supported lipid bilayers containing mobile Podoplanin, we further show that activation of Src and Syk in platelets promotes clustering of CLEC-2 and Podoplanin. Clusters of CLEC-2-bound Podoplanin migrate rapidly to the center of the platelet to form a single structure. Fluorescence lifetime imaging demonstrates that molecules within these clusters are within 10 nm of one another and that the clusters are disrupted by inhibition of Src and Syk family kinases. CLEC-2 clusters are also seen in platelets adhered to immobilized Podoplanin using direct stochastic optical reconstruction microscopy. These findings provide mechanistic insight by which CLEC-2 signaling promotes adhesion to Podoplanin and regulation of Podoplanin signaling, thereby contributing to lymphatic vasculature development.

Tityus discrepans scorpion venom activates platelets through GPVI and a novel Src-dependent signaling pathway

In humans and other mammals, Tityus discrepans (Td) scorpion envenomation produces a variety of systemic effects including respiratory distress, a generalized inflammatory reaction, modulation of blood pressure, fibrin formation, and platelet activation. For many of these effects, the venom components and underlying mechanisms are not known. In the present study, we demonstrate that Td venom (TdV) stimulates integrin αIIbβ3-dependent aggregation of washed human and mouse platelets downstream of Src kinase activation. The pattern of increase in tyrosine phosphorylation induced by TdV in human platelets is similar to that induced by the collagen receptor GPVI, and includes FcR γ-chain, Syk, and PLC γ 2. Confirmation of GPVI activation by TdV was achieved by expression of human GPVI in chicken DT40 B cells and use of a reporter assay. To our surprise, TdV was able to activate mouse platelets deficient in the GPVI-FcR γ-chain complex through a pathway that was also dependent on Src kinases. TdV therefore activates platelets through GPVI and a second, as yet unidentified Src kinase-dependent pathway.

CLEC-2 is not required for platelet aggregation at arteriolar shear

The C-type lectin receptor CLEC-2 is expressed primarily on the surface of platelets, where it is present as a dimer, and is found at low level on a subpopulation of other hematopoietic cells, including mouse neutrophils [1–4] Clustering of CLEC-2 by the snake venom toxin rhodocytin, specific antibodies or its endogenous ligand, podoplanin, elicits powerful activation of platelets through a pathway that is similar to that used by the collagen receptor glycoprotein VI (GPVI) [4–6]. The cytosolic tail of CLEC-2 contains a conserved YxxL sequence preceded by three upstream acidic amino acid residues, which together form a novel motif known as a hemITAM. Ligand engagement induces tyrosine phosphorylation of the hemITAM sequence providing docking sites for the tandem-SH2 domains of the tyrosine kinase Syk across a CLEC-2 receptor dimer [3]. Tyrosine phosphorylation of Syk by Src family kinases and through autophosphorylation leads to stimulation of a downstream signaling cascade that culminates in activation of phospholipase C γ2 (PLCγ2) [4,6]. Recently, CLEC-2 has been proposed to play a major role in supporting activation of platelets at arteriolar rates of flow [1]. Injection of a CLEC-2 antibody into mice causes a sustained depletion of the C-type lectin receptor from the platelet surface [1]. The CLEC-2-depleted platelets were unresponsive to rhodocytin but underwent normal aggregation and secretion responses after stimulation of other platelet receptors, including GPVI [1]. In contrast, there was a marked decrease in aggregate formation relative to controls when CLEC-2-depleted blood was flowed at arteriolar rates of shear over collagen (1000 s−1 and 1700 s−1) [1]. Furthermore, antibody treatment significantly increased tail bleeding times and mice were unable to occlude their vessels after ferric chloride injury [1]. These data provide evidence for a critical role for CLEC-2 in supporting platelet aggregation at arteriolar rates of flow. The underlying mechanism is unclear as platelets do not express podoplanin, the only known endogenous ligand of CLEC-2. In the present study, we have investigated the role of CLEC-2 in platelet aggregation and thrombus formation using platelets from a novel mutant mouse model that lacks functional CLEC-2.

CLEC-2 activates Syk through dimerization

The C-type lectin receptor CLEC-2 activates platelets through Src and Syk tyrosine kinases, leading to tyrosine phosphorylation of downstream adapter proteins and effector enzymes, including phospholipase-C gamma2. Signaling is initiated through phosphorylation of a single conserved tyrosine located in a YxxL sequence in the CLEC-2 cytosolic tail. The signaling pathway used by CLEC-2 shares many similarities with that used by receptors that have 1 or more copies of an immunoreceptor tyrosine-based activation motif, defined by the sequence Yxx(L/I)x(6-12)Yxx(L/I), in their cytosolic tails or associated receptor chains. Phosphorylation of the conserved immunoreceptor tyrosine-based activation motif tyrosines promotes Syk binding and activation through binding of the Syk tandem SH2 domains. In this report, we present evidence using peptide pull-down studies, surface plasmon resonance, quantitative Western blotting, tryptophan fluorescence measurements, and competition experiments that Syk activation by CLEC-2 is mediated by the cross-linking through the tandem SH2 domains with a stoichiometry of 2:1. In support of this model, cross-linking and electron microscopy demonstrate that CLEC-2 is present as a dimer in resting platelets and converted to larger complexes on activation. This is a unique mode of activation of Syk by a single YxxL-containing receptor.

GPVI potentiation of platelet activation by thrombin and adhesion molecules independent of Src kinases and Syk.

We show that Syk is critical for lamellipodia formation on a range of immobilized proteins but that this can be overcome by addition of thrombin. Further, we reveal a novel role for GPVI in supporting thrombin-induced activation, independent of Syk and Src kinases.

Involvement of Src kinases and PLCgamma2 in clot retraction.

The integrin alpha(IIb)beta(3) plays a critical role in mediating clot retraction by platelets which is important in vivo in consolidating thrombus formation. Actin-myosin interaction is essential for clot retraction. In the present study, we demonstrate that the structurally distinct Src kinase inhibitors, PP2 and PD173952, significantly reduced the rate of clot retraction, but did not prevent it reaching completion. This effect was accompanied by abolition of alpha(IIb)beta(3)-dependent protein tyrosine phosphorylation, including PLCgamma2. A role for PLCgamma2 in mediating clot retraction was demonstrated using PLCgamma2-deficient murine platelets. Furthermore, platelet adhesion to fibrinogen leads to MLC phosphorylation through a pathway that is inhibited by PP2 and by the PLC inhibitor, U73122. These results demonstrate a partial role for Src kinase-dependent activation of PLCgamma2 and MLC phosphorylation in mediating clot retraction downstream of integrin alpha(IIb)beta(3).

Comparison of CLEC-2 and GPVI signaling in platelets: the role of adaptor proteins

GPVI activates platelets through an ITAM pathway by activation of Src and Syk kinases leading to activation of PLCy2. CLEC-2 has been shown to activate platelets using an ITAM-like sequence in its cytoplasmic tail that is also dependent on Src and Syk kinases, but shows a partial rather than an absolute dependence on adapter SLP-76 for activation of PLCy2. The aim of this thesis is to understand some of the key differences in these signalling pathways. GPVI is in complex with FcRwhich contains the ITAM sequence (Yxx(L/I)x6−12Yxx(L/I)). These two tyrosines provide a docking site for the tandem-SH2 domains of Syk. In this thesis I show that CLEC-2 signalling through Syk is mediated by phosphorylation of the CLEC-2 YxxL sequence, receptor dimerisation and cross-linking by the Syk SH2 domains. I also show that the differential requirement for SLP-76 is not mediated by Gads. Both signalling pathways also show partial dependency for LAT. I also show that a novel protein, G6f, is not able to substitute for LAT in this signalling pathway and also exclude the LAT-family proteins PAG, LIME, LAX and NTAL as potential LAT replacements in platelet activation by GPVI. These results extend our understanding of platelet activation by CLEC-2.

Platelet adhesion to podoplanin under flow is mediated by the receptor CLEC-2 and stabilised by Src/Syk-dependent platelet signalling

Platelet-specific deletion of CLEC-2, which signals through Src and Syk kinases, or global deletion of its ligand podoplanin results in blood-filled lymphatics during mouse development. Platelet-specific Syk deficiency phenocopies this defect, indicating that platelet activation is required for lymphatic development. In the present study, we investigated whether CLEC-2-podoplanin interactions could support platelet arrest from blood flow and whether platelet signalling is required for stable platelet adhesion to lymphatic endothelial cells (LECs) and recombinant podoplanin under flow. Perfusion of human or mouse blood over human LEC monolayers led to platelet adhesion and aggregation. Following αIIbβ3 blockade, individual platelets still adhered. Platelet binding occurred at venous but not arterial shear rates. There was no adhesion using CLEC-2-deficient blood or to vascular endothelial cells (which lack podoplanin). Perfusion of human blood over human Fc-podoplanin (hFcPDPN) in the presence of monoclonal antibody IV.3 to block FcγRIIA receptors led to platelet arrest at similar shear rates to those used on LECs. Src and Syk inhibitors significantly reduced global adhesion of human or mouse platelets to LECs and hFcPDPN. A similar result was seen using Syk-deficient mouse platelets. Reduced platelet adhesion was due to a decrease in the stability of binding. In conclusion, our data reveal that CLEC-2 is an adhesive receptor that supports platelet arrest to podoplanin under venous shear. Src/Syk-dependent signalling stabilises platelet adhesion to podoplanin, providing a possible molecular mechanism contributing to the lymphatic defects of Syk-deficient mice.