Uncountably many quasi-isometry classes of groups of type FPFP

Previously one of the authors constructed uncountable families of groups of type $FP$ and of $n$-dimensional Poincar\'e duality groups for each $n\geq 4$. We strengthen these results by showing that these groups comprise uncountably many quasi-isometry classes. We deduce that for each $n\geq 4$ there are uncountably many quasi-isometry classes of acyclic $n$-manifolds admitting free cocompact properly discontinuous discrete group actions.Comment: Version 2: minor corrections made, theorems now numbered by sectio

Coherence for elementary amenable groups

We prove that for an elementary amenable group, coherence of the group, homological coherence of the group, and coherence of the integral group ring are all equivalent. This generalises a result of Bieri and Strebel for finitely generated soluble groups

Variation in the organization and subunit composition of the mammalian pyruvate dehydrogenase complex E2/E3BP core assembly

The final version of this article is available at the link below.Crucial to glucose homoeostasis in humans, the hPDC (human pyruvate dehydrogenase complex) is a massive molecular machine comprising multiple copies of three distinct enzymes (E1–E3) and an accessory subunit, E3BP (E3-binding protein). Its icosahedral E2/E3BP 60-meric ‘core’ provides the central structural and mechanistic framework ensuring favourable E1 and E3 positioning and enzyme co-operativity. Current core models indicate either a 48E2+12E3BP or a 40E2+20E3BP subunit composition. In the present study, we demonstrate clear differences in subunit content and organization between the recombinant hPDC core (rhPDC; 40E2+20E3BP), generated under defined conditions where E3BP is produced in excess, and its native bovine (48E2+12E3BP) counterpart. The results of the present study provide a rational basis for resolving apparent differences between previous models, both obtained using rhE2/E3BP core assemblies where no account was taken of relative E2 and E3BP expression levels. Mathematical modelling predicts that an ‘average’ 48E2+12E3BP core arrangement allows maximum flexibility in assembly, while providing the appropriate balance of bound E1 and E3 enzymes for optimal catalytic efficiency and regulatory fine-tuning. We also show that the rhE2/E3BP and bovine E2/E3BP cores bind E3s with a 2:1 stoichiometry, and propose that mammalian PDC comprises a heterogeneous population of assemblies incorporating a network of E3 (and possibly E1) cross-bridges above the core surface.This work was partly supported by EPSRC (under grants GR/R99393/01 and EP/C015452/1)

Classifying spaces for proper actions of locally finite groups

For each finite ordinal n and each locally-finite group G of cardinality aleph n, we construct an (n+1)-dimensional model for the classifying space for proper G-actions. We use this complex to obtain information about the cohomology of G with free coefficients. Our techniques also give information about the location of large free abelian groups within Kropholler's hierarchy