Spectrum of a Feinberg-Zee random hopping matrix

This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya, and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the unit disc almost surely. It also obtains an analogous result for a more general class of random matrices whose spectra contain a hole around the origin. The presence of the hole forces substantial changes to the analysis.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Rhinocetin, a venom-derived integrin-specific antagonist inhibits collagen-induced platelet and endothelial cell functions

Snaclecs are small non-enzymatic proteins present in viper venoms reported to modulate haemostasis of victims through effects on platelets, vascular endothelial and smooth muscle cells. In this study, we have isolated and functionally characterised a snaclec which we named rhinocetin from the venom of West African gaboon viper, Bitis gabonica rhinoceros. Rhinocetin was shown to comprise α and β chains with the molecular masses of 13.5 and 13kDa respectively. Sequence and immunoblot analysis of rhinocetin confirmed this to be a novel snaclec. Rhinocetin inhibited collagen-stimulated activation of human platelets in dose dependent manner, but displayed no inhibitory effects on glycoprotein VI (collagen receptor) selective agonist, CRP-XL-, ADP- or thrombin-induced platelet activation. Rhinocetin antagonised the binding of monoclonal antibodies against the α2 subunit of integrin α2β1 to platelets and coimmunoprecipitation analysis confirmed integrin α2β1 as a target for this venom protein. Rhinocetin inhibited a range of collagen induced platelet functions such as fibrinogen binding, calcium mobilisation, granule secretion, aggregation and thrombus formation. It also inhibited integrin α2β1 dependent functions of human endothelial cells. Together, our data suggest rhinocetin to be a modulator of integrin α2β1 function and thus may provide valuable insights into the role of this integrin in physiological and pathophysiological scenarios including haemostasis, thrombosis and envenomation.

A matrix iteration for dynamic network summaries

We propose a new algorithm for summarizing properties of large-scale time-evolving networks. This type of data, recording connections that come and go over time, is being generated in many modern applications, including telecommunications and on-line human social behavior. The algorithm computes a dynamic measure of how well pairs of nodes can communicate by taking account of routes through the network that respect the arrow of time. We take the conventional approach of downweighting for length (messages become corrupted as they are passed along) and add the novel feature of downweighting for age (messages go out of date). This allows us to generalize widely used Katz-style centrality measures that have proved popular in network science to the case of dynamic networks sampled at non-uniform points in time. We illustrate the new approach on synthetic and real data.

Protein kinase B is regulated in platelets by the collagen receptor glycoprotein VI

Phosphoinositide 3-kinase (PI3K) is a critical component of the signaling pathways that control the activation of platelets. Here we have examined the regulation of protein kinase B (PKB), a downstream effector of PI3K, by the platelet collagen receptor glycoprotein (GP) VI and thrombin receptors. Stimulation of platelets with collagen or convulxin (a selective GPVI agonist) resulted in PI3K-dependent, and aggregation independent, Ser(473) and Thr(308) phosphorylation of PKBalpha, which results in PKB activation. This was accompanied by translocation of PKB to cell membranes. The phosphoinositide-dependent kinase PDK1 is known to phosphorylate PKBalpha on Thr(308), although the identity of the kinase responsible for Ser(473) phosphorylation is less clear. One candidate that has been implicated as being responsible for Ser(473) phosphorylation, either directly or indirectly, is the integrin-linked kinase (ILK). In this study we have examined the interactions of PKB, PDK1, and ILK in resting and stimulated platelets. We demonstrate that in platelets PKB is physically associated with PDK1 and ILK. Furthermore, the association of PDK1 and ILK increases upon platelet stimulation. It would therefore appear that formation of a tertiary complex between PDK1, ILK, and PKB may be necessary for phosphorylation of PKB. These observations indicate that PKB participates in cell signaling downstream of the platelet collagen receptor GPVI. The role of PKB in collagen- and thrombin-stimulated platelets remains to be determined.

Collagen, convulxin, and thrombin stimulate aggregation-independent tyrosine phosphorylation of CD31 in platelets. Evidence for the involvement of Src family kinases

Platelet endothelial cell adhesion molecule-1 (CD31) is a 130-kDa glycoprotein receptor present on the surface of platelets, neutrophils, monocytes, certain T-lymphocytes, and vascular endothelial cells. CD31 is involved in adhesion and signal transduction and is implicated in the regulation of a number of cellular processes. These include transendothelial migration of leukocytes, integrin regulation, and T-cell function, although its function in platelets remains unclear. In this study, we demonstrate the ability of the platelet agonists collagen, convulxin, and thrombin to induce tyrosine phosphorylation of CD31. Furthermore, we show that this event is independent of platelet aggregation and secretion and is accompanied by an increase in surface expression of CD31. A kinase capable of phosphorylating CD31 was detected in CD31 immunoprecipitates, and its activity was increased following activation of platelets. CD31 tyrosine phosphorylation was reduced or abolished by the Src family kinase inhibitor PP2, suggesting a role for these enzymes. In accordance with this, each of the Src family members expressed in platelets, namely Fyn, Lyn, Src, Yes, and Hck, was shown to co-immunoprecipitate with CD31. The involvement of Src family kinases in this process was confirmed through the study of mouse platelets deficient in Fyn.

Expression of the collagen receptor glycoprotein VI during megakaryocyte differentiation

This study examined the expression of the platelet collagen receptor glycoprotein VI (GPVI) in megakaryocyte cell lines and primary megakaryocytes by reverse transcriptase-polymerase chain reaction and by flow cytometry and ligand blotting using the snake venom toxin convulxin. Expression of GPVI is increased in the megakaryoblastic cell lines HEL and CMK on differentiation with the phorbol ester phorbol 12-myristate 13-acetate (PMA), along with the Fc receptor gamma-chain (FcR gamma-chain). The increase in GPVI expression is associated with marked potentiation of tyrosine phosphorylation and Ca(++) elevation in response to convulxin. Syk, linker for activated T cells, and phospholipase C gamma 2 (PLC gamma 2) are among the proteins tyrosine phosphorylated on convulxin stimulation in PMA-differentiated HEL cells. Studies on primary murine megakaryocytes grown in vitro confirmed that GPVI is up-regulated in parallel with functional activation, assessed by measurement of [Ca(++)](i), during differentiation. The results demonstrate that expression of GPVI is up-regulated along with the FcR gamma-chain during differentiation of megakaryocytes. (Blood. 2000;96:2740-2745)

Collagen or collagen-related peptide cause (Ca2+)i elevation and increased tyrosine phosphorylation in human megakaryocytes.

Since megakaryocytes are the cellular precursors of platelets we have investigated whether they share responses to platelet agonists, in particular collagen. Although previous studies have reported responses to thrombin in non-human megakaryocytes, through studies of single cell calcium responses and protein tyrosine-phosphorylation we demonstrate for the first time that both isolated human megakaryocytes and CD41/61-positive megakaryocytes derived in culture from CD34+ cells share responses to the platelet agonists collagen, collagen-related peptide and thrombin. The responses to either collagen or CRP were seen only in the most mature megakaryocytes and not in megakaryocyte-like cell lines, suggesting that the response to collagen is a characteristic developed late during megakaryocyte differentiation. These primary cells offer the opportunity to use many molecular and cellular techniques to study and manipulate signalling events in response to platelet receptor agonists, which cannot be performed in the small, anucleate platelet itself.

The p85 subunit of phosphatidylinositol 3-kinase associates with the Fc receptor gamma-chain and linker for activitor of T cells (LAT) in platelets stimulated by collagen and convulxin.

There is extensive evidence to show that phosphatidylinositol 3-kinase plays an important role in signaling by the immune family of receptors, which has recently been extended to include the platelet collagen receptor, glycoprotein VI. In this report we present two potential mechanisms for the regulation of this enzyme on stimulation of platelets by collagen. We show that on stimulation with collagen, the regulatory subunit of phosphatidylinositol 3-kinase associates with the tyrosine-phosphorylated form of the adapter protein linker for activator of T Cells (LAT) and the tyrosine-phosphorylated immunoreceptor tyrosine-based activation motif of the Fc receptor gamma-chain (a component of the collagen receptor complex that includes glycoprotein VI). The associations of the Fc receptor gamma-chain and LAT with p85 are rapid and supported by the Src-homology 2 domains of the regulatory subunit. We did not obtain evidence to support previous observations that the regulatory subunit of phosphatidylinositol 3-kinase is regulated through association with the tyrosine kinase Syk. The present results provide a molecular basis for the regulation of the p85/110 form of phosphatidylinositol 3-kinase by GPVI, the collagen receptor that underlies activation.

Glycoprotein VI is the collagen receptor in platelets which underlies tyrosine phosphorylation of the Fc receptor gamma-chain.

We have recently shown that collagen activates platelets through a pathway dependent on the Fc receptor gamma-chain and the tyrosine kinase Syk. We report here that the Fc receptor gamma-chain and the candidate collagen receptor glycoprotein VI (GPVI) co-associate. Furthermore, cross-linking GPVI stimulates a similar pattern of tyrosine phosphorylation to that stimulated by collagen, including tyrosine phosphorylation of Fc receptor gamma-chain. These results support a model where GPVI couples collagen-stimulation of platelets to phosphorylation of the Fc receptor gamma-chain leading to activation of Syk and phospholipase Cgamma2.

The Fc receptor gamma-chain and the tyrosine kinase Syk are essential for activation of mouse platelets by collagen.

Activation of mouse platelets by collagen is associated with tyrosine phosphorylation of multiple proteins including the Fc receptor gamma-chain, the tyrosine kinase Syk and phospholipase Cgamma2, suggesting that collagen signals in a manner similar to that of immune receptors. This hypothesis has been tested using platelets from mice lacking the Fc receptor gamma-chain or Syk. Tyrosine phosphorylation of Syk and phospholipase Cgamma2 by collagen stimulation is absent in mice lacking the Fc receptor gamma-chain. Tyrosine phosphorylation of phospholipase Cgamma2 by collagen stimulation is also absent in mice platelets which lack Syk, although phosphorylation of the Fc receptor gamma-chain is maintained. In contrast, tyrosine phosphorylation of platelet proteins by the G protein-coupled receptor agonist thrombin is maintained in mouse platelets deficient in Fc receptor gamma-chain or Syk. The absence of Fc receptor gamma-chain or Syk is accompanied by a loss of secretion and aggregation responses in collagen- but not thrombin-stimulated platelets. These observations provide the first direct evidence of an essential role for the immunoreceptor tyrosine-based activation motif (ITAM) in signalling by a non-immune receptor stimulus.