Knots and links $L\subset S^3$ carry a wealth of data. Spanning surfaces $F$ (1- or 2-sided), $\partial F=L$, especially {\bf checkerboard} surfaces from link diagrams $D\subset S^2$, help to mine this data. This text explores the structure of these surfaces, with a focus on a gluing operation called {\bf plumbing}, or {\it Murasugi sum}. First, naive classification questions provide natural and accessible motivation for the geometric and algebraic notions of essentiality (incompressibility with $\partial$-incompressibility and $\pi_1$-injectivity, respectively). This opening narrative also scaffolds a system of hyperlinks to the usual background information, which lies out of the way in appendices and glossaries. We then extend both notions of essentiality to define geometric and algebraic {\it degrees} of essentiality, $\underset{\hookrightarrow}{\text{ess}}(F)$ and $\text{ess}(F)$. For the latter, cutting $S^3$ along $F$ and letting $\mathcal{X}$ denote the set of compressing disks for $\partial (S^3\backslash\backslash F)$ in $S^3\backslash\backslash F$, $\text{ess}(F):=\min_{X\in\mathcal{X}}|\partial X\cap L|$. Extending results of Gabai and Ozawa, we prove that plumbing respects degrees of algebraic essentiality, $\text{ess}(F_1*F_2)\geq\min_{i=1,2}\text{ess}(F_i)$, provided $F_1,F_2$ are essential. We also show by example that plumbing does not respect the condition of geometric essentiality. We ask which surfaces de-plumb uniquely. We show that, in general, essentiality is necessary but insufficient, and we give various sufficient conditions. We consider Ozawa's notion of representativity $r(F,L)$, which is defined similarly to $\text{ess}(F)$, except that $F$ is a closed surface in $S^3$ that contains $L$, rather than a surface whose boundary equals $L$. We use Menasco's crossing bubbles to describe a sort of thin position for such a closed surface, relative to a given link diagram, and we prove in the case of alternating links that $r(F,L)\leq2$. (The contents of Chapter 4, under the title Alternating links have representativity 2, are first published in Algebraic \& Geometric Topology in 2018, published by Mathematical Sciences Publishers.) We then adapt these arguments to the context of spanning surfaces, obtaining a simpler proof of a useful crossing band lemma, as well as a foundation for future attempts to better classify the spanning surfaces for a given alternating link. We adapt the operation of plumbing to the context of Khovanov homology. We prove that every homogeneously adequate Kauffman state has enhancements $X^\pm$ in distinct $j$-gradings whose traces (which we define) represent nonzero Khovanov homology classes over $\mathbb{Z}/2\mathbb{Z}$, and that this is also true over $\mathbb{Z}$ when all $A$-blocks' state surfaces are two-sided. A direct proof constructs $X^\pm$ explicitly. An alternate proof, reflecting the theorem's geometric motivation, applies our adapted plumbing operation. Finally, we describe an interpretation of Khovanov homology in terms of decorated cell decompositions of abstract, nonorientable surfaces, featuring properly embedded (1+1)-dimensional nonorientable cobordisms in (2+1)-dimensional nonorientable cobordisms. This formulation contains a planarity condition; removing this condition leads to Khovanov homology for virtual link diagrams.

Biological nitrogen fixation is accomplished in the bacterium Azotobacter vinelandii by means of three metalloenzymes: The molybdenum, vanadium, and iron-only nitrogenase. The knowledge regarding biological nitrogen fixation has come from studies on the Mo-dependent reaction. However, the V- and Fe-only-dependent reduction of nitrogen remains largely unknown. By using homology modeling techniques, the protein folds that contain the metal cluster active sites for the V- and Fe-only nitrogenases were constructed. The models uncovered similarities and differences existing among the nitrogenases regarding the identity of the amino acid residues lining pivotal structural features for the correct functioning of the proteins. These differences, could account for the differences in catalytic properties depicted by these enzymes. The quaternary structure of the dinitrogenases also differs. Such component in the Mo-nitrogenase is an α2β2 tetramer while for the V- an Fe-only nitrogenase is an α2β2δ2 hexamer. The latter enzymes are unable to reduce N2 in the absence of a functional δ subunit, yet they reduce H+ and the non-physiological substrate C2H2. Therefore, the δ subunit is essential for V- and Fe-only dependent nitrogen fixation by a mechanism that still remains unknown. In attempt to understand why the δ subunit is essential for V-dependent N2 reduction from a structural stand point, this work presents the strategy followed to clone the vnfG gene and purify its expression product, the δ subunit. The purified protein was subjected to crystallization trials and used to stabilize a histidine-tagged VFe protein that would otherwise purify with low Fe2+ content and poor H+ and C2H2 reduction activities. The VFe preparation was used to conduct substrate reduction assays to assess: i) The electron allocation patterns to each of the reduction products of the substrates C2H2, N2, N2H4, and N3−; and ii) Inhibition patterns among substrate and inhibitor of the nitrogenase reaction. This work also reports on the effect N2H4 and N3− has on the electron flux to the products of the C2H2 reduction. The work presented herein provides information with which to compare and contrast biological nitrogen fixation as catalyzed by the Mo- and V-nitrogenases from Azotobacter vinelandii.

Thesis (Ph.D.)--McMaster University, 2005. / Supervisor: Manfred Kolster. Includes bibliographical references (leaves 93-96).

<p>For the vast majority of proteins no experimental information about the three-dimensional structure is known, but only its sequence. Therefore, the easiest way to obtain some understanding of the structure and function of these proteins is by relating them to well studied proteins. This can be done by searching for homologous proteins. It is easy to identify a homologous sequence if the sequence identity is above 30%. However, if the sequence identity drops below 30% then more sophisticated methods have to be used. These methods often use evolutionary information about the sequences, which makes it possible to identify homologous sequences with a low sequence identity.</p><p>In order to build a three--dimensional model from the sequence based on a protein structure the two sequences have to be aligned. Here the aligned residues serve as a first approximation of the structure.</p><p>This thesis focuses on the development of fold recognition and alignment methods based on evolutionary information. The use of evolutionary information for both query and target proteins was shown to improve both recognition and alignments. In a benchmark of profile--profile methods it was shown that the probabilistic methods were best, although the difference between several of the methods was quite small once optimal gap-penalties were used. An artificial neural network based alignment method ProfNet was shown to be at least as good as the best profile--profile method, and by adding information from a self-organising map and predicted secondary structure we were able to further improve ProfNet.</p>

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No description available.

La connaissance de la structure tridimensionnelle (3D) des protéines est une information capitale. Néanmoins, le nombre de protéines dont la structure 3D a été déterminée expérimentalement est cent fois plus faible que le nombre de protéines connues aujourd'hui. Cet écart ne pourra pas être comblé, car les techniques expérimentales de détermination de structure (diffraction de rayons X et résonance magnétique nucléaire) sont coûteuses et lentes (un an de travail en moyenne pour une seule protéine). Un moyen d'obtenir plus rapidement la structure 3D de protéines est de la prédire par des moyens bioinformatiques. La technique de prédiction la plus précise actuellement est la modélisation par homologie. Celle-ci est basée sur la similitude de structure entre deux protéines de séquences similaires. L'étape critique de cette méthode est l'étape d'alignement entre la séquence à modéliser et une séquence similaire de structure connue. Notre travail a consisté tout d'abord en la conception d'une nouvelle méthode d'alignement pairé très fiable. Cette méthode a ensuite été incluse dans un système automatique de modélisation par homologie: la bonne qualité des structures prédites par le système trouve en partie son origine dans le programme d'alignement utilisé. Enfin, nous avons appliqué notre système de modélisation automatique à la modélisation de toutes les protéines déduites du génome d'une bactérie pathogène étudiée dans notre unité de recherche: Brucella melitensis. Cela nous a conduit à créer une banque de données structurales et fonctionnelles consacrée au génome de cette bactérie. Cette banque de données est devenue un outil de travail indispensable pour plusieurs équipes de recherche européennes qui étudient Brucella melitensis.

For the vast majority of proteins no experimental information about the three-dimensional structure is known, but only its sequence. Therefore, the easiest way to obtain some understanding of the structure and function of these proteins is by relating them to well studied proteins. This can be done by searching for homologous proteins. It is easy to identify a homologous sequence if the sequence identity is above 30%. However, if the sequence identity drops below 30% then more sophisticated methods have to be used. These methods often use evolutionary information about the sequences, which makes it possible to identify homologous sequences with a low sequence identity. In order to build a three--dimensional model from the sequence based on a protein structure the two sequences have to be aligned. Here the aligned residues serve as a first approximation of the structure. This thesis focuses on the development of fold recognition and alignment methods based on evolutionary information. The use of evolutionary information for both query and target proteins was shown to improve both recognition and alignments. In a benchmark of profile--profile methods it was shown that the probabilistic methods were best, although the difference between several of the methods was quite small once optimal gap-penalties were used. An artificial neural network based alignment method ProfNet was shown to be at least as good as the best profile--profile method, and by adding information from a self-organising map and predicted secondary structure we were able to further improve ProfNet.

<p>Quantum sl_3 projectors are morphisms in Kuperberg's sl_3 spider, a diagrammatically defined category equivalent to the full pivotal subcategory of the category of (type 1) finite-dimensional representations of the quantum group U_q (sl_3 ) generated by the defining representation, which correspond to projection onto (and then inclusion from) the highest weight irreducible summand. These morphisms are interesting from a topological viewpoint as they allow the combinatorial formulation of the sl_3 tangle invariant (in which tangle components are labelled by the defining representation) to be extended to a combinatorial formulation of the invariant in which components are labelled by arbitrary finite-dimensional irreducible representations. They also allow for a combinatorial description of the SU(3) Witten-Reshetikhin-Turaev 3-manifold invariant. </p><p>There exists a categorification of the sl_3 spider, due to Morrison and Nieh, which is the natural setting for Khovanov's sl_3 link homology theory and its extension to tangles. An obvious question is whether there exist objects in this categorification which categorify the sl_3 projectors. </p><p>In this dissertation, we show that there indeed exist such "categorified projectors," constructing them as the stable limit of the complexes assigned to k-twist torus braids (suitably shifted). These complexes satisfy categorified versions of the defining relations of the (decategorified) sl_3 projectors and map to them upon taking the Grothendieck group. We use these categorified projectors to extend sl_3 Khovanov homology to a homology theory for framed links with components labeled by arbitrary finite-dimensional irreducible representations of sl_3 .</p> / Dissertation

Haemonchus contortus is a parasitic nematode that is controlled in large part by nematocidal drugs that target receptors of the parasitic nervous system. Hco-UNC-49 is a nematode GABA receptor that has a relatively low overall sequence homology to mammalian GABA receptors but is very similar to the UNC-49 receptor found in the free living nematode Caenorhabditis elegans. However, the nematode receptors do exhibit different sensitivities to GABA which may be linked to differences in the putative GABA binding domains. Mutational analysis conducted in this study identified at least one amino acid, positioned near the GABA binding domain, which may partially account for differences in nematode GABA sensitivity. In addition, positions reported to be crucial for GABA sensitivity in mammalian receptors also affect GABA sensitivity in Hco- UNC-49 suggesting that the GABA binding domains of the mammalian and nematode GABA receptors share some pharmacological similarities. However, there were some differences observed. For example, in mammalian GABAA receptors amino acids from both  and  subunits appear to be important for GABA sensitivity. For residues examined in this study, only those on the UNC-49B subunit, and not UNC-49C, appear important for GABA sensitivity. / UOIT