Algebraic Bol loops

In this paper, we study the category of algebraic Bol loops over an algebraically closed field of definition. On the one hand, we apply techniques from the theory of algebraic groups in order to prove structural theorems for this category. On the other hand, we present some examples showing that these loops lack some nice properties of algebraic groups; for example, we construct local algebraic Bol loops which are not birationally equivalent to global algebraic loops.

Special identities for Bol algebras

Bol algebras appear as the tangent algebra of Bol loops. A (left) Bol algebra is a vector space equipped with a binary operation [a, b] and a ternary operation {a, b, c} that satisfy five defining identities. If A is a left or right alternative algebra then A(b) is a Bol algebra, where [a, b] := ab - ba is the commutator and {a, b, c} := < b, c, a > is the Jordan associator. A special identity is an identity satisfied by Ab for all right alternative algebras A, but not satisfied by the free Bol algebra. We show that there are no special identities of degree <= 7, but there are special identities of degree 8. We obtain all the special identities of degree 8 in partition six-two. (C) 2011 Elsevier Inc. All rights reserved.

ON SOME GENERALIZATIONS OF GROUPS WITH TRIALITY

In the present paper we generalize the concept of groups with triality and apply it to the theory of the Moufang, Bol and Bruck loops. Such generalizations allow us to reduce certain problems from the loop theory to problems in the theory of groups.

Modelling bluetooth and fusing with loops

The invited presentation was delivered at Queensland Department of Main Roads, Brisbane Australia, 17th June 2013

Proteolytic activation of Chlamydia trachomatis HTRA is mediated by PDZ1 domain interactions with protease domain loops L3 and LC and beta strand β5

Chlamydia trachomatis is a bacterial pathogen responsible for one of the most prevalent sexually transmitted infections worldwide. Its unique development cycle has limited our understanding of its pathogenic mechanisms. However, CtHtrA has recently been identified as a potential C. trachomatis virulence factor. CtHtrA is a tightly regulated quality control protein with a monomeric structural unit comprised of a chymotrypsin-like protease domain and two PDZ domains. Activation of proteolytic activity relies on the C-terminus of the substrate allosterically binding to the PDZ1 domain, which triggers subsequent conformational change and oligomerization of the protein into 24-mers enabling proteolysis. This activation is mediated by a cascade of precise structural arrangements, but the specific CtHtrA residues and structural elements required to facilitate activation are unknown. Using in vitro analysis guided by homology modeling, we show that the mutation of residues Arg362 and Arg224, predicted to disrupt the interaction between the CtHtrA PDZ1 domain and loop L3, and between loop L3 and loop LD, respectively, are critical for the activation of proteolytic activity. We also demonstrate that mutation to residues Arg299 and Lys160, predicted to disrupt PDZ1 domain interactions with protease loop LC and strand β5, are also able to influence proteolysis, implying their involvement in the CtHtrA mechanism of activation. This is the first investigation of protease loop LC and strand β5 with respect to their potential interactions with the PDZ1 domain. Given their high level of conservation in bacterial HtrA, these structural elements may be equally significant in the activation mechanism of DegP and other HtrA family members.

Bluetooth vehicle trajectory by fusing Bluetooth and loops : motorway travel time statistics

Loop detectors are widely used on the motorway networks where they provide point speed and traffic volumes. Models have been proposed for temporal and spatial generalization of speed for average travel time estimation. Advancement in technology provides complementary data sources such as Bluetooth MAC Scanner (BMS), detecting the MAC ID of the Bluetooth devices transported by the traveller. Matching the data from two BMS stations provides individual vehicle travel time. Generally, on the motorways loops are closely spaced, whereas BMS are placed few kilometres apart. In this research, we fuse BMSs and loops data to define the trajectories of the Bluetooth vehicles. The trajectories are utilised to estimate the travel time statistics between any two points along the motorway. The proposed model is tested using simulation and validated with real data from Pacific motorway, Brisbane. Comparing the model with the linear interpolation based trajectory provides significant improvements.

Conformational analysis of small disulfide loops. Spectroscopic and theoretical studies on a synthetic cyclic tetrapeptide containing cystine

The conformational analysis of the synthetic peptide Boc-Cys-Pro-Val-Cys-NHMe has been carried out, as a model for small disulfide loops, in biologically active polypeptides. 'H NMR studies (270 MHz) establish that the Val(3) and Cys(4) NH groups are solvent shielded, while 13C studies establish an all-trans peptide backbone. Circular dichroism and Raman spectroscopy provide evidence for a right-handed twist of the disulfide bond. Analysis of the vicinal (JaB)c oupling constants for the two Cys residues establishes that XI - *60° for Cys(4), while some flexibility is suggested at Cys( 1). Conformational energy calculations, imposing intramolecular hydrogen bonding constraints, favor a P-turn (type I) structure with Pro(2)-Va1(3) as the corner residues. Theoretical and spectroscopic results are consistent with the presence of a transannular 4 - 1 hydrogen bond between Cys( 1) CO and Cys(4) NH groups, with the Val NH being sterically shielded from the solvent environment.

Non-Gaussianities and Preheating from N-flation and Magnetogenesis via rotating cosmic string loops

In this thesis we examine multi-field inflationary models of the early Universe. Since non-Gaussianities may allow for the possibility to discriminate between models of inflation, we compute deviations from a Gaussian spectrum of primordial perturbations by extending the delta-N formalism. We use N-flation as a concrete model; our findings show that these models are generically indistinguishable as long as the slow roll approximation is still valid. Besides computing non-Guassinities, we also investigate Preheating after multi-field inflation. Within the framework of N-flation, we find that preheating via parametric resonance is suppressed, an indication that it is the old theory of preheating that is applicable. In addition to studying non-Gaussianities and preheatng in multi-field inflationary models, we study magnetogenesis in the early universe. To this aim, we propose a mechanism to generate primordial magnetic fields via rotating cosmic string loops. Magnetic fields in the micro-Gauss range have been observed in galaxies and clusters, but their origin has remained elusive. We consider a network of strings and find that rotating cosmic string loops, which are continuously produced in such networks, are viable candidates for magnetogenesis with relevant strength and length scales, provided we use a high string tension and an efficient dynamo.

Structural Ordering of Disordered Ligand-Binding Loops of Biotin Protein Ligase into Active Conformations as a Consequence of Dehydration

Mycobacterium tuberculosis (Mtb), a dreaded pathogen, has a unique cell envelope composed of high fatty acid content that plays a crucial role in its pathogenesis. Acetyl Coenzyme A Carboxylase (ACC), an important enzyme that catalyzes the first reaction of fatty acid biosynthesis, is biotinylated by biotin acetyl-CoA carboxylase ligase (BirA). The ligand-binding loops in all known apo BirAs to date are disordered and attain an ordered structure only after undergoing a conformational change upon ligand-binding. Here, we report that dehydration of Mtb-BirA crystals traps both the apo and active conformations in its asymmetric unit, and for the first time provides structural evidence of such transformation. Recombinant Mtb-BirA was crystallized at room temperature, and diffraction data was collected at 295 K as well as at 120 K. Transfer of crystals to paraffin and paratone-N oil (cryoprotectants) prior to flash-freezing induced lattice shrinkage and enhancement in the resolution of the X-ray diffraction data. Intriguingly, the crystal lattice rearrangement due to shrinkage in the dehydrated Mtb-BirA crystals ensued structural order of otherwise flexible ligand-binding loops L4 and L8 in apo BirA. In addition, crystal dehydration resulted in a shift of similar to 3.5 angstrom in the flexible loop L6, a proline-rich loop unique to Mtb complex as well as around the L11 region. The shift in loop L11 in the C-terminal domain on dehydration emulates the action responsible for the complex formation with its protein ligand biotin carboxyl carrier protein (BCCP) domain of ACCA3. This is contrary to the involvement of loop L14 observed in Pyrococcus horikoshii BirA-BCCP complex. Another interesting feature that emerges from this dehydrated structure is that the two subunits A and B, though related by a noncrystallographic twofold symmetry, assemble into an asymmetric dimer representing the ligand-bound and ligand-free states of the protein, respectively. In-depth analyses of the sequence and the structure also provide answers to the reported lower affinities of Mtb-BirA toward ATP and biotin substrates. This dehydrated crystal structure not only provides key leads to the understanding of the structure/function relationships in the protein in the absence of any ligand-bound structure, but also demonstrates the merit of dehydration of crystals as an inimitable technique to have a glance at proteins in action.

Cystine peptides. Disulfide conformations in fourteen membered loops investigated by Raman spectroscopy and circular dichroism

NHCH3 (X = Gly 1, Ala 2, Aib 3, Leu 4 and D-Ala 5), have been investigated by Raman and circular dichroism (CD) spectroscopy. Solid state Raman spectra are consistent with β-turn conformations in all five peptides. These peptides exhibit similar conformations of the disulfide segment in the solid state with a characteristic disulfide stretching frequency at 519 ± 3 cm-1, indicative of a trans-gauche-gauche arrangement about the Cα—Cβ—S—S—Cβ—Cα bonds. The results correlate well with the solid state conformations determined by X-ray diffraction for peptides 3 and 4. CD studies in chloroform and dimethylsulfoxide establish solvent dependent conformational changes for peptides 1, 3 and 5. Disulfide chirality has been derived using the quadrant rule. CD results together with previously reported nuclear magnetic resonance (n.m.r.) data suggest a conformational coupling between the peptide backbone and the disulfide segment