A Schwarz lemma for K\"ahler affine metrics and the canonical potential of a proper convex cone

This is an account of some aspects of the geometry of K\"ahler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for K\"ahler affine metrics of Yau's Schwarz lemma for volume forms. By a theorem of Cheng and Yau there is a canonical K\"ahler affine Einstein metric on a proper convex domain, and the Schwarz lemma gives a direct proof of its uniqueness up to homothety. The potential for this metric is a function canonically associated to the cone, characterized by the property that its level sets are hyperbolic affine spheres foliating the cone. It is shown that for an $n$-dimensional cone a rescaling of the canonical potential is an $n$-normal barrier function in the sense of interior point methods for conic programming. It is explained also how to construct from the canonical potential Monge-Amp\`ere metrics of both Riemannian and Lorentzian signatures, and a mean curvature zero conical Lagrangian submanifold of the flat para-K\"ahler space.Comment: Minor corrections. References adde

Crystal structure of the CusBA heavy-metal efflux complex of Escherichia coli

Gram-negative bacteria, such as Escherichia coli, expel toxic chemicals via tripartite efflux pumps spanning both the inner and outer membranes. The three parts are: 1) a membrane fusion protein connecting 2) a substrate-binding inner membrane transporter to 3) an outer membrane-anchored channel in the periplasmic space. A crystallographic model of this tripartite efflux complex has been unavailable simply because co-crystallization of different components of the system has proven to be extremely difficult. We previously described the crystal structures of both the inner membrane transporter CusA1 and membrane fusion protein CusB2 of the CusCBA efflux system3,4 from E. coli. We here report the co-crystal structure of the CusBA efflux complex, revealing the trimeric CusA efflux pump interacts with six CusB protomers at the upper half of the periplasmic domain. These six CusB molecules form a channel extending contiguously from the top of the pump. The affinity of the CusA and CusB interaction was found to be in the micromolar range. Finally, we predicted a three-dimensional structure of the trimeric CusC outer membrane channel, and develop a model of the tripartite efflux assemblage. This CusC3-CusB6-CusA3 model presents a 750 kDa efflux complex spanning the entire bacterial cell envelope to export Cu(I)/Ag(I) ions

The copper centers of tyramine β-monooxygenase and its catalytic-site methionine variants: an X-ray absorption study

Tyramine β-monooxygenase (TBM) is a member of a family of copper monooxygenases containing two noncoupled copper centers, and includes peptidylglycine monooxygenase and dopamine β-monooxygenase. In its Cu(II) form, TBM is coordinated by two to three His residues and one to two non-His O/N ligands consistent with a [CuM(His)2(OH2)2–CuH(His)3(OH2)] formulation. Reduction to the Cu(I) state causes a change in the X-ray absorption spectroscopy (XAS) spectrum, consistent with a change to a [CuM(His)2S(Met)–CuH(His)3] environment. Lowering the pH to 4.0 results in a large increase in the intensity of the Cu(I)–S extended X-ray absorption fine structure (EXAFS) component, suggesting a tighter Cu–S bond or the coordination of an additional sulfur donor. The XAS spectra of three variants, where the CuM Met471 residue had been mutated to His, Cys, and Asp, were examined. Significant differences from the wild-type enzyme are evident in the spectra of the reduced mutants. Although the side chains of His, Cys, and Asp are expected to substitute for Met at the CuM site, the data showed identical spectra for all three reduced variants, with no evidence for coordination of residue 471. Rather, the K-edge data suggested a modest decrease in coordination number, whereas the EXAFS indicated an average of two His residues at each Cu(I) center. These data highlight the unique role of the Met residue at the CuM center, and pose interesting questions as to why replacement by the cuprophilic thiolate ligand leads to detectable activity whereas replacement by imidazole generates inactive TBM

A Novel CCR5 Mutation Common in Sooty Mangabeys Reveals SIVsmm Infection of CCR5-Null Natural Hosts and Efficient Alternative Coreceptor Use In Vivo

In contrast to HIV infection in humans and SIV in macaques, SIV infection of natural hosts including sooty mangabeys (SM) is non-pathogenic despite robust virus replication. We identified a novel SM CCR5 allele containing a two base pair deletion (Δ2) encoding a truncated molecule that is not expressed on the cell surface and does not support SIV entry in vitro. The allele was present at a 26% frequency in a large SM colony, along with 3% for a CCR5Δ24 deletion allele that also abrogates surface expression. Overall, 8% of animals were homozygous for defective CCR5 alleles and 41% were heterozygous. The mutant allele was also present in wild SM in West Africa. CD8+ and CD4+ T cells displayed a gradient of CCR5 expression across genotype groups, which was highly significant for CD8+ cells. Remarkably, the prevalence of natural SIVsmm infection was not significantly different in animals lacking functional CCR5 compared to heterozygous and homozygous wild-type animals. Furthermore, animals lacking functional CCR5 had robust plasma viral loads, which were only modestly lower than wild-type animals. SIVsmm primary isolates infected both homozygous mutant and wild-type PBMC in a CCR5-independent manner in vitro, and Envs from both CCR5-null and wild-type infected animals used CXCR6, GPR15 and GPR1 in addition to CCR5 in transfected cells. These data clearly indicate that SIVsmm relies on CCR5-independent entry pathways in SM that are homozygous for defective CCR5 alleles and, while the extent of alternative coreceptor use in SM with CCR5 wild type alleles is uncertain, strongly suggest that SIVsmm tropism and host cell targeting in vivo is defined by the distribution and use of alternative entry pathways in addition to CCR5. SIVsmm entry through alternative pathways in vivo raises the possibility of novel CCR5-negative target cells that may be more expendable than CCR5+ cells and enable the virus to replicate efficiently without causing disease in the face of extremely restricted CCR5 expression seen in SM and several other natural host species