Understanding the relative affinity and specificity of the pleckstrin homology domain of protein kinase B for inositol phosphates

Protein kinase B (PKB) is a serine/threonine kinase that plays a key role in the phosphoinositide 3-kinase (PI3K) pathway-one of the most frequently activated proliferation pathways in cancer. In this pathway, PKB is recruited to the plasma membrane by direct interaction of its pleckstrin homology (PH) domain with the inositol phosphate head-group of phosphatidylinositol 3,4,5-trisphosphate [PtdIns(3,4,5)P(3)] or phosphatidylinositol 3,4-bisphosphate [PtdIns(3,4)P(2)]. This recruitment is a critical stage in the activation of PKB, whose downstream effectors play important roles in cell survival, proliferation and growth. It is therefore of great interest to understand PKB's mode of binding, as well as its specificity and affinity for different phosphoinositides. We have used a total of 3 μs of molecular dynamics (MD) simulations to better understand the interactions of the PKB PH domain with the inositol phosphate head-groups of phosphoinositides involved in the PI3K pathway. Our computational models successfully mirror PKB's in vivo selectivity for 3-phosphorylated phosphoinositides. Furthermore, the models also help to rationalize unexpected in vitro data in which inositol 1,4,5-trisphosphate [Ins(1,4,5)P(3)] binds with a relatively high affinity to the PKB PH domain, despite its parent lipid phosphatidylinositol 4,5-bisphosphate [PtdIns(4,5)P(2)] being known not to bind in vivo. With the support of computational simulations, we propose that when not bonded to a phosphatidate tail Ins(1,4,5)P(3) binds in an orientation in which its inositol ring is flipped with respect to the 3-phosphorylated inositol phosphate ligands and its parent lipid.     

Tuning the coordination chemistry of a Cu(II) complex at high-pressure

Application of pressure on the Cu-complex CuAsp causes Jahn-Teller Cu-O bonds to be compressed, increasing the coordination environment from [4 + 1] to [4 + 2], highlighted by a discontinuity on compression of these bonding interactions.     

Semigroups of inverse quotients

We examine, in a general setting, a notion of inverse semigroup of left quotients, which we call left I-quotients. This concept has appeared, and has been used, as far back as Clifford??s seminal work describing bisimple inverse monoids in terms of their right unit subsemigroups. As a consequence of our approach, we find a straightforward way of extending Clifford??s work to bisimple inverse semigroups (a step that has previously proved to be awkward). We also put some earlier work of Gantos into a wider and clearer context, and pave the way for further progress.     

Convergence of quasi-Newton matrices generated by the symmetric rank one update

Quasi-Newton algorithms for unconstrained nonlinear minimization generate a sequence of matrices that can be considered as approximations of the objective function second derivatives. This paper gives conditions under which these approximations can be proved to converge globally to the true Hessian matrix, in the case where the Symmetric Rank One update formula is used. The rate of convergence is also examined and proven to be improving with the rate of convergence of the underlying iterates. The theory is confirmed by some numerical experiments that also show the convergence of the Hessian approximations to be substantially slower for other known quasi-Newton formulae.The work of this author was supported by the National Sciences and Engineering Research Council of Canada, and by the Information Technology Research Centre, which is funded by the Province of Ontario.     

Lax Operator for the Quantised Orthosymplectic Superalgebra Uq[osp(m|n)]

Representations of quantum superalgebras provide a natural framework in which to model supersymmetric quantum systems. Each quantum superalgebra, belonging to the class of quasi-triangular Hopf superalgebras, contains a universal R-matrix which automatically satisfies the Yang–Baxter equation. Applying the vector representation π, which acts on the vector module V, to the left-hand side of a universal R-matrix gives a Lax operator. In this article a Lax operator is constructed for the quantised orthosymplectic superalgebras U _q [osp(m|n)] for all m > 2, n ≥ 0 where n is even. This can then be used to find a solution to the Yang–Baxter equation acting on V ⊗ V ⊗ W, where W is an arbitrary U _q [osp(m|n)] module. The case W = V is studied as an example. Presented by A. Verschoren.     

New crash procedures for large systems of linear constraints

Many algorithms for solving linearly constrained optimization problems maintain sets of basic variables. The calculation of the initial basis is of great importance as it determines to a large extent the amount of computation that will then be required to solve the problem. In this paper, we suggest a number of simple methods for obtaining an initial basis and perform tests to indicate how they perform on a variety of real-life problems.