Amenability of algebras of approximable operators

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson's space.Comment: 20 pages, to appear in Israel Journal of Mathematic

[NiFe]-hydrogenase maturation in vitro: analysis of the roles of the HybG and HypD accessory proteins

[NiFe]-hydrogenases (Hyd) bind a nickel-iron-based cofactor. The Fe ion of the cofactor is bound by two cyanide ligands and a single carbon monoxide ligand. Minimally six accessory proteins (HypA–HypF) are necessary for NiFe(CN)2CO cofactor biosynthesis in Escherichia coli. It has been shown that the anaerobically purified HypC–HypD–HypE scaffold complex carries the Fe(CN)2CO moiety of this cofactor. In the present study, we have purified the HybG–HypDE complex and used it to successfully reconstitute in vitro active Hyd from E. coli. HybG is a homologue of HypC that is specifically required for the maturation of Hyd-2 and also functions in the maturation of Hyd-1 of E. coli. Maturation of active Hyd-1 and Hyd-2 could be demonstrated in extracts derived from HybG- and HypD-deficient E. coli strains by adding anaerobically purified HybG–HypDE complex. In vitro maturation was dependent on ATP, carbamoylphosphate, nickel and reducing conditions. Hydrogenase maturation was prevented when the purified HybG–HypDE complex used in the maturation assay lacked a bound Fe(CN)2CO moiety. These findings demonstrate that it is possible to isolate incompletely processed intermediates on the maturation pathway and to use these to activate apo-forms of [NiFe]-hydrogenase large subunits

Nonlinear spectral calculus and super-expanders

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.Comment: Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current pape

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

The Twin-Arginine Translocation Pathway in α-Proteobacteria Is Functionally Preserved Irrespective of Genomic and Regulatory Divergence

The twin-arginine translocation (Tat) pathway exports fully folded proteins out of the cytoplasm of Gram-negative and Gram-positive bacteria. Although much progress has been made in unraveling the molecular mechanism and biochemical characterization of the Tat system, little is known concerning its functionality and biological role to confer adaptive skills, symbiosis or pathogenesis in the α-proteobacteria class. A comparative genomic analysis in the α-proteobacteria class confirmed the presence of tatA, tatB, and tatC genes in almost all genomes, but significant variations in gene synteny and rearrangements were found in the order Rickettsiales with respect to the typically described operon organization. Transcription of tat genes was confirmed for Anaplasma marginale str. St. Maries and Brucella abortus 2308, two α-proteobacteria with full and partial intracellular lifestyles, respectively. The tat genes of A. marginale are scattered throughout the genome, in contrast to the more generalized operon organization. Particularly, tatA showed an approximately 20-fold increase in mRNA levels relative to tatB and tatC. We showed Tat functionality in B. abortus 2308 for the first time, and confirmed conservation of functionality in A. marginale. We present the first experimental description of the Tat system in the Anaplasmataceae and Brucellaceae families. In particular, in A. marginale Tat functionality is conserved despite operon splitting as a consequence of genome rearrangements. Further studies will be required to understand how the proper stoichiometry of the Tat protein complex and its biological role are achieved. In addition, the predicted substrates might be the evidence of role of the Tat translocation system in the transition process from a free-living to a parasitic lifestyle in these α-proteobacteria

Transport of Folded Proteins by the Tat System

The twin-arginine protein translocation (Tat) system has been characterized in bacteria, archaea and the chloroplast thylakoidal membrane. This system is distinct from other protein transport systems with respect to two key features. Firstly, it accepts cargo proteins with an N-terminal signal peptide that carries the canonical twin-arginine motif, which is essential for transport. Second, the Tat system only accepts and translocates fully folded cargo proteins across the respective membrane. Here, we review the core essential features of folded protein transport via the bacterial Tat system, using the three-component TatABC system of Escherichia coli and the two-component TatAC systems of Bacillus subtilis as the main examples. In particular, we address features of twin-arginine signal peptides, the essential Tat components and how they assemble into different complexes, mechanistic features and energetics of Tat-dependent protein translocation, cytoplasmic chaperoning of Tat cargo proteins, and the remarkable proofreading capabilities of the Tat system. In doing so, we present the current state of our understanding of Tat-dependent protein translocation across biological membranes, which may serve as a lead for future investigations

Functional tat transport of unstructured, small, hydrophilic proteins

The twin-arginine translocation ( Tat) system is a protein translocation system that is adapted to the translocation of folded proteins across biological membranes. An understanding of the folding requirements for Tat substrates is of fundamental importance for the elucidation of the transport mechanism. We now demonstrate for the first time Tat transport for fully unstructured proteins, using signal sequence fusions to naturally unfolded FG repeats from the yeast Nsp1p nuclear pore protein. The transport of unfolded proteins becomes less efficient with increasing size, consistent with only a single interaction between the system and the substrate. Strikingly, the introduction of six residues from the hydrophobic core of a globular protein completely blocked translocation. Physiological data suggest that hydrophobic surface patches abort transport at a late stage, most likely by membrane interactions during transport. This study thus explains the observed restriction of the Tat system to folded globular proteins on a molecular level