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.

Tyrosine phosphorylation of the Fc receptor gamma-chain in collagen-stimulated platelets.

Stimulation of platelets by the extracellular matrix protein collagen leads to activation of a tyrosine kinase-dependent mechanism resulting in secretion and aggregation. Tyrosine phosphorylation of the tyrosine kinase Syk and phospholipase Cgamma2 are early events in collagen-induced activation. We recently proposed that collagen-signaling in platelets involves a receptor or a receptor-associated protein containing an immunoreceptor tyrosine-based activation motif (ITAM) enabling interaction with Syk. In this report we show that collagen stimulation of platelets causes rapid tyrosine phosphorylation of the ITAM containing Fc receptor gamma-chain and that this is precipitated by the tandem Src homology 2 (SH2) domains of Syk expressed as a fusion protein. In addition we demonstrate an association between the Fc receptor gamma-chain with endogenous Syk in collagen-stimulated platelets. The Fc receptor gamma-chain undergoes tyrosine phosphorylation in platelets stimulated by a collagen-related peptide which does not bind the integrin alpha2beta1 and by the lectin wheat germ agglutinin. In contrast, cross-linking of the platelet low affinity receptor for immune complexes, FcgammaRIIA, or stimulation by thrombin does not induce phosphorylation of the Fc receptor gamma-chain. The present results provide a molecular basis for collagen activation of platelets which is independent of the integrin alpha2beta1 and involves phosphorylation of the Fc receptor gamma-chain, its association with Syk and subsequent phosphorylation of phospholipase Cgamma2. Collagen is the first example of a nonimmune receptor stimulus to signal through a pathway closely related to signaling by immune receptors.

On the quantum mechanical scattering statistics of many particles

The probability of a quantum particle being detected in a given solid angle is determined by the S-matrix. The explanation of this fact in time-dependent scattering theory is often linked to the quantum flux, since the quantum flux integrated against a (detector-) surface and over a time interval can be viewed as the probability that the particle crosses this surface within the given time interval. Regarding many particle scattering, however, this argument is no longer valid, as each particle arrives at the detector at its own random time. While various treatments of this problem can be envisaged, here we present a straightforward Bohmian analysis of many particle potential scattering from which the S-matrix probability emerges in the limit of large distances.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

SANS/WANS time-resolving neutron scattering studies of polymer phase transitions using NIMROD

We use new neutron scattering instrumentation to follow in a single quantitative time-resolving experiment, the three key scales of structural development which accompany the crystallisation of synthetic polymers. These length scales span 3 orders of magnitude of the scattering vector. The study of polymer crystallisation dates back to the pioneering experiments of Keller and others who discovered the chain-folded nature of the thin lamellae crystals which are normally found in synthetic polymers. The inherent connectivity of polymers makes their crystallisation a multiscale transformation. Much understanding has developed over the intervening fifty years but the process has remained something of a mystery. There are three key length scales. The chain folded lamellar thickness is ~ 10nm, the crystal unit cell is ~ 1nm and the detail of the chain conformation is ~ 0.1nm. In previous work these length scales have been addressed using different instrumention or were coupled using compromised geometries. More recently researchers have attempted to exploit coupled time-resolved small-angle and wide-angle x-ray experiments. These turned out to be challenging experiments much related to the challenge of placing the scattering intensity on an absolute scale. However, they did stimulate the possibility of new phenomena in the very early stages of crystallisation. Although there is now considerable doubt on such experiments, they drew attention to the basic question as to the process of crystallisation in long chain molecules. We have used NIMROD on the second target station at ISIS to follow all three length scales in a time-resolving manner for poly(e-caprolactone). The technique can provide a single set of data from 0.01 to 100Å-1 on the same vertical scale. We present the results using a multiple scale model of the crystallisation process in polymers to analyse the results.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.