The Fa,b,c conjecture, I

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.

The Fa,b,c conjecture is true, II

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and subsequently two parts of the conjecture were proved. The conjecture completely determines all finite members of the family. Here we complete the proof of the conjecture by giving proofs for the remaining three parts. (c) 2006 Elsevier Inc. All rights reserved.

A role for protein kinase B beta/Akt2 in insulin-stimulated GLUT4 translocation in adipocytes

Insulin stimulates glucose uptake into muscle and fat cells by promoting the translocation of glucose transporter 4 (GLUT4) to the cell surface. Phosphatidylinositide 3-kinase (PI3K) has been implicated in this process. However, the involvement of protein kinase B (PKB)/Akt, a downstream target of PI3K in regulation of GLUT4 translocation, has been controversial. Here we report that microinjection of a PKB substrate peptide or an antibody to PKB inhibited insulin-stimulated GLUT4 translocation to the plasma membrane by 66 or 56%, respectively. We further examined the activation of PKB isoforms following treatment of cells with insulin or platelet-derived growth factor (PDGF) and found that PKB beta is preferentially expressed in both rat and 3T3-L1 adipocytes, whereas PKB alpha expression is down-regulated in 3T3-L1 adipocytes. A switch in growth factor response was also observed when 3T3-L1 fibroblasts were differentiated into adipocytes. While PDGF was more efficacious than insulin in stimulating PKB phosphorylation in fibroblasts, PDGF did not stimulate PKB beta phosphorylation to any significant extent in adipocytes, as assessed by several methods. Moreover, insulin, but not PDGF, stimulated the translocation of PKB beta to the plasma membrane and high-density microsome fractions of 3T3-L1 adipocytes. These results support a role for PKB beta in insulin-stimulated glucose transport in adipocytes.

PREDBALB/c: a system for the prediction of peptide binding to H2(d) molecules, a haplotype of the BALB/c mouse

PREDBALB/c is a computational system that predicts peptides binding to the major histocompatibility complex-2 (H2(d)) of the BALB/c mouse, an important laboratory model organism. The predictions include the complete set of H2(d) class I ( H2-K-d, H2-L-d and H2-D-d) and class II (I-E-d and I-A(d)) molecules. The prediction system utilizes quantitative matrices, which were rigorously validated using experimentally determined binders and non-binders and also by in vivo studies using viral proteins. The prediction performance of PREDBALB/c is of very high accuracy. To our knowledge, this is the first online server for the prediction of peptides binding to a complete set of major histocompatibility complex molecules in a model organism (H2(d) haplotype). PREDBALB/c is available at http://antigen.i2r.a-star.edu.sg/predBalbc/.