Conserved quantities and the formation of black holes in the Brans-Dicke theory of gravitation

In Part I, we construct a symmetric stress-energy-momentum pseudo-tensor for the gravitational fields of Brans-Dicke theory, and use this to establish rigorously conserved integral expressions for energy-momentum Pⁱ and angular momentum J^ik. Application of the two-dimensional surface integrals to the exact static spherical vacuum solution of Brans leads to an identification of our conserved mass with the active gravitational mass. Application to the distant fields of an arbitrary stationary source reveals that Pⁱ and J^ik have the same physical interpretation as in general relativity. For gravitational waves whose wavelength is small on the scale of the background radius of curvature, averaging over several wavelengths in the Brill-Hartle-Isaacson manner produces a stress-energy-momentum tensor for gravitational radiation which may be used to calculate the changes in Pⁱ and J^ik of their source.

In Part II, we develop strong evidence in favor of a conjecture by Penrose--that, in the Brans-Dicke theory, relativistic gravitational collapse in three dimensions produce black holes identical to those of general relativity. After pointing out that any black hole solution of general relativity also satisfies Brans-Dicke theory, we establish the Schwarzschild and Kerr geometries as the only possible spherical and axially symmetric black hole exteriors, respectively. Also, we show that a Schwarzschild geometry is necessarily formed in the collapse of an uncharged sphere.

Appendices discuss relationships among relativistic gravity theories and an example of a theory in which black holes do not exist.

New conserved vorticity integrals for moving surfaces in multi-dimensional fluid flow

For inviscid fluid flow in any n-dimensional Riemannian manifold, new conserved vorticity integrals generalizing helicity, enstrophy, and entropy circulation are derived for lower-dimensional surfaces that move along fluid streamlines. Conditions are determined for which the integrals yield constants of motion for the fluid. In the case when an inviscid fluid is isentropic, these new constants of motion generalize Kelvin’s circulation theorem from closed loops to closed surfaces of any dimension.

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

Conserved aspartic acids are essential for the enzymic activity of the WecA protein initiating the biosynthesis of O-specific lipopolysaccharide and enterobacterial common antigen in Escherichia coli

The integral membrane protein WecA mediates the transfer of N-acetylglucosamine (GlcNAc) 1-phosphate to undecaprenyl phosphate (Und-P) with the formation of a phosphodiester bond. Bacteria employ this reaction during the biosynthesis of enterobacterial common antigen as well as of many O-specific lipopolysaccharides (LPSs). Alignment of a number of prokaryotic and eukaryotic WecA-homologous sequences identified a number of conserved aspartic acid (D) residues in putative cytoplasmic loops II and III of the inner-membrane protein. Site-directed mutagenesis was used to study the role of the conserved residues D90, D91 (loop II), D156 and D159 (loop III). As controls, D35, D94 and D276 were also mutagenized. The resulting WecA derivatives were assessed for function by complementation analysis of O-antigen biosynthesis, by the ability to incorporate radiolabelled precursor to a biosynthetic intermediate, by detection of the terminal GlcNAc residue in LPS and by a tunicamycin competition assay. It was concluded from these analyses that the conserved aspartic acid residues are functionally important, but also that they participate differently in the transfer reaction. Based on these results it is proposed that D90 and D91 are important in forwarding the reaction product to the next biosynthetic step, while D156 and D159 are a part of the catalytic site of the enzyme.

Conserved amino acid residues found in a predicted cytosolic domain of the lipopolysaccharide biosynthetic protein WecA are implicated in the recognition of UDP-N-acetylglucosamine

WecA, an integral membrane protein that belongs to a family of polyisoprenyl phosphate N-acetylhexosamine-1-phosphate transferases, is required for the biosynthesis of O-specific LPS and enterobacterial common antigen in Escherichia coli and other enteric bacteria. WecA functions as an UDP-N-acetylglucosamine (GlcNAc):undecaprenyl-phosphate GlcNAc-1-phosphate transferase. A conserved short sequence motif (His-Ile-His-His; HIHH) and a conserved arginine were identified in WecA at positions 279-282 and 265, respectively. This region is located within a predicted cytosolic segment common to all bacterial homologues of WecA. Both HIHH279-282 and the Arg265 are reminiscent of the HIGH motif (His-Ile-Gly-His) and a nearby upstream lysine, which contribute to the three-dimensional architecture of the nucleotide-binding site among various enzymes displaying nucleotidyltransferase activity. Thus, it was hypothesized that these residues may play a role in the interaction of WecA with UDP-GlcNAc. Replacement of the entire HIHH motif by site-directed mutagenesis produced a protein that, when expressed in the E. coli wecA mutant MV501, did not complement the synthesis of O7 LPS. Membrane extracts containing the mutated protein failed to transfer UDP-GlcNAc into a lipid-rich fraction and to bind the UDP-GlcNAc analogue tunicamycin. Similar results were obtained by individually replacing the first histidine (H279) of the HIHH motif as well as the Arg265 residue. The functional importance of these residues is underscored by the high level of conservation of H279 and Arg265 among bacterial WecA homologues that utilize several different UDP-N-acetylhexosamine substrates.

Covariance properties and regularization of conserved currents in tetrad gravity

We discuss the properties of the gravitational energy-momentum 3-form within the tetrad formulation of general relativity theory. We derive the covariance properties of the quantities describing the energy-momentum content under Lorentz transformations of the tetrad. As an application, we consider the computation of the total energy (mass) of some exact solutions of Einstein's general relativity theory which describe compact sources with asymptotically flat spacetime geometry. As it is known, depending on the choice of tetrad frame, the formal total integral for such configurations may diverge. We propose a natural regularization method which yields finite values for the total energy-momentum of the system and demonstrate how it works on a number of explicit examples.

Degradation of Stearoyl-Coenzyme A Desaturase: Endoproteolytic Cleavage by an Integral Membrane Protease

Stearoyl-coenzyme A desaturase (SCD) is a key regulator of membrane fluidity, turns over rapidly, and represents a prototype for selective degradation of resident proteins of the endoplasmic reticulum. Using detergent-solubilized, desaturase-induced rat liver microsomes we have characterized a protease that degrades SCD. Degradation of SCD in vitro is highly selective, has a half-life of 3–4 h, and generates a 20-kDa C-terminal fragment of SCD. The N terminus of the 20-kDa fragment was identified as Phe177. The cleavage site occurs in a conserved 12-residue hydrophobic segment of SCD flanked by clusters of basic residues. The SCD protease remains associated with microsomal membranes after peripheral and lumenal proteins have been selectively removed. SCD protease is present in normal rat liver microsomes and cleaves purified SCD. We conclude that rapid turnover of SCD involves a constitutive microsomal protease with properties of an integral membrane protein.

Bit-pattern based integral attack

Integral attacks are well-known to be effective against byte-based block ciphers. In this document, we outline how to launch integral attacks against bit-based block ciphers. This new type of integral attack traces the propagation of the plaintext structure at bit-level by incorporating bit-pattern based notations. The new notation gives the attacker more details about the properties of a structure of cipher blocks. The main difference from ordinary integral attacks is that we look at the pattern the bits in a specific position in the cipher block has through the structure. The bit-pattern based integral attack is applied to Noekeon, Serpent and present reduced up to 5, 6 and 7 rounds, respectively. This includes the first attacks on Noekeon and present using integral cryptanalysis. All attacks manage to recover the full subkey of the final round.

Evaluation of novel Streptococcus pyogenes vaccine candidates incorporating multiple conserved sequences from the C-repeat region of the M-protein

A major challenge for Streptococcus pyogenes vaccine development is the identification of epitopes that confer protection from infection by multiple S. pyogenes M-types. Here we have identified and characterised the distribution of common variant sequences from individual repeat units of the C-repeat region (CRR) of M-proteins representing 77 different M-types. Three polyvalent fusion vaccine candidates (SV1, SV2 and SV3) incorporating the most common variants were subsequently expressed and purified, and demonstrated to be alpha-helical by Circular Dichroism (CD), a secondary conformational characteristic of the CRR in the M-protein. Antibodies raised against each of these constructs recognise M-proteins that vary in their CRR, and bind to the surface of multiple S. pyogenes isolates. Antibodies raised against SV1, containing five variant sequences, also kill heterologous S. pyogenes isolates in in vitro bactericidal assays. Further structural characterisation of this construct demonstrated the conformation of SV1 was stable at different pHs, and thermal unfolding of SV1 a reversible process. Our findings demonstrate that linkage of multiple variant sequences into a single recombinant construct overcomes the need to embed the variant sequences in foreign helix promoting flanking sequences for conformational stability, and demonstrates the viability of the polyvalent candidates as global S. pyogenes vaccine candidates.