Topological Homology Research Articles

The Geometry of Projective, Injective, and Flat Banach Modules

In this paper, we prove general facts on metrically and topologically projective, injective, and flat Banach modules. We prove theorems pointing to the close connection between metric, topological Banach homology and the geometry of Banach spaces. For example, in geometric terms we give a complete description of projective, injective, and flat annihilator modules. We also show that for an algebra with the geometric structure of an - or -space all its homologically trivial modules possess the Dunford–Pettis property.

MPC1-like Is a Placental Mammal-specific Mitochondrial Pyruvate Carrier Subunit Expressed in Postmeiotic Male Germ Cells

Selective transport of pyruvate across the inner mitochondrial membrane by the mitochondrial pyruvate carrier (MPC) is a fundamental step that couples cytosolic and mitochondrial metabolism. The recent molecular identification of the MPC complex has revealed two interacting subunits, MPC1 and MPC2. Although in yeast, an additional subunit, MPC3, can functionally replace MPC2, no alternative MPC subunits have been described in higher eukaryotes. Here, we report for the first time the existence of a novel MPC subunit termed MPC1-like (MPC1L), which is present uniquely in placental mammals. MPC1L shares high sequence, structural, and topological homology with MPC1. In addition, we provide several lines of evidence to show that MPC1L is functionally equivalent to MPC1: 1) when co-expressed with MPC2, it rescues pyruvate import in a MPC-deleted yeast strain; 2) in mammalian cells, it can associate with MPC2 to form a functional carrier as assessed by bioluminescence resonance energy transfer; 3) in MPC1 depleted mouse embryonic fibroblasts, MPC1L rescues the loss of pyruvate-driven respiration and stabilizes MPC2 expression; and 4) MPC1- and MPC1L-mediated pyruvate imports show similar efficiency. However, we show that MPC1L has a highly specific expression pattern and is localized almost exclusively in testis and more specifically in postmeiotic spermatids and sperm cells. This is in marked contrast to MPC1/MPC2, which are ubiquitously expressed throughout the organism. To date, the biological importance of this alternative MPC complex during spermatogenesis in placental mammals remains unknown. Nevertheless, these findings open up new avenues for investigating the structure-function relationship within the MPC complex.

Nonconcordant links with homology cobordant zero-framed surgery manifolds

We use topological surgery in dimension four to give sufficient conditions for the zero framed surgery manifold of a 3-component link to be homology cobordant to the 3-torus, which arises from zero framed surgery on the Borromean rings, via a topological homology cobordism preserving the homotopy classes of the meridians. This enables us to give new examples of 3-component links with unknotted components and vanishing pairwise linking numbers, such that any two of these links have homology cobordant zero surgeries in the above sense, but the zero surgery manifolds are not homeomorphic. Moreover the links are not concordant to one another, and in fact they can be chosen to be height n but not height n+1 symmetric grope concordant, for each n which is at least three.

King Crickets, Raspy Crickets and Weta, Their Wings, Their Fossil Relatives

Topographic homology conjectures (= THCs) in fore- and hind wing venation of extant king crickets, raspy crickets and weta are re-evaluated. Based on the premises that topological homology is established so that the amount of transformation that has to be assumed to explain differences between patterns is minimized, a new set of THCs (= STHC), based on morphological data on the species cf. mexicanus de Saussure, 1859: 209, laudatum Johns, 1997, ornata Willemse, 1963, cf. bicornis Karny, 1929a, pinguipes? Rentz in Morton & Rentz, 1983, pinguipes Rentz in Morton & Rentz, 1983, an undetermined species, punctipennis Walker, 1869, and rufovaria Kirby, 1888, is elaborated. Among other transformations, the occurrence of a re-routing of MP along CuA (i.e., the basal M CuA stem splits into MA and MP CuA, instead of into MA MP and CuA) is demonstrated for pinguipes, punctipennis, and rufovaria. Concurrently, intra-specific variability in forewing venation is appreciated for laudatum, ornata, cf. bicornis, pinguipes, punctipennis, and rufovaria. A cladotypic-compliant nomenclatural scheme is elaborated based on the proposed THCs. The taxon Agryllacris nom.-dis.typ. nov. is defined based on the character state ‘in forewing, CuA CuPaα with two distal branches only’; the taxon Tagryllacris nom.-dis.-typ. nov. is defined based on the character state ‘in forewing, M CuA splits into MA and MP CuA’; the taxon Etagryllacris nom.-dis.-typ. nov. is defined based on the character state ‘in forewing, CuA CuPaα keep fused’; the taxon Metagryllacris nom. nov, dis. Zeuner, 1939, typ. nov. is defined based on the character state ‘in forewing, MA fused with R at wing base’. Based on new data, the species †perfecta Sharov, 1968 is identified as a member of the taxon Agryllacris, and the fossil species †megaptera Gorochov, 1987a, isimplicis Gorochov, 1987a, †elongata Gorochov, 1987a, †madygenioides Gorochov, 1987a, †perlonga Gorochov, 1987a, and † devexa Gorochov, 1987a are considered as junior synonyms of †perfecta. The nomenclatural treatment is extended to the unrelated taxon †Bintoniellidae nom. Handlirsch, 1938, dis. Sharov, 1968, typ. nov, defined based on the character state ‘in forewing, no distinct base of CuPaα diverging from CuPa (and fusing with CuA or M CuA)’. Belonging to this taxon, the species †primaria Sharov, 1968 is considered as a junior synonym † triassica Sharov, 1968:168.A consequence of the assignment of †perfecta to Agryllacris is that this group stems in the Triassic, at least, i.e., ca 170 million years earlier than previously assumed. As a result, the loss of the complex ‘tettigonid-gryllid-like’ (i.e., Grylloptera) stridulatory apparatus is no longer needed to account for the morphology of king crickets, raspy crickets and weta forewing. Finally, a refinement of the concept of parallelism is proposed based on transformations observed in the taxa Agryllacris and Bintoniellidae, and on their polarity and frequency of occurrence. The concept of parallelism is narrowed down, those of atavism and reversal discussed, and the concepts of iteronatism, cryptoparallelism, and pronatism proposed.

Comparative studies on the histology and ultrastructure of the siphons of two species of Tellinidae (Mollusca: Bivalvia) from Brazil

Despite the great importance of the siphons for infaunal bivalves, only a few studies have examined their tissues using histology techniques or scanning electron microscopy. In the present study, the siphons of Tellina lineata Turton, 1819 and Macoma biota Arruda & Domaneschi, 2005 were investigated. The siphon walls are composed by a series of muscle sheets of longitudinal ("L"), circular ("C") and radial ("R") fibers, with a clear pattern common to both species: there is a main median longitudinal layer (Lm), and two peripheral circular layers, one inner (Ci) and one outer (Co), near the epithelia. A median circular layer (Cm) separates an internal (Lmi) from an outer (Lmo) median longitudinal layer. Further, the Co is split by a thin outer longitudinal layer (Lo), forming Coi and Coo layers, the former being obliquely oriented. Thin radial fibers (R) delimit clear packages of Lmi and Lmo fibers. In each siphon, there are six longitudinal nerve cords, running within the Lmi layer, adjacent to the Cm. The inhalant and exhalant siphons of M. biota are very similar in structure, but the Lmo of the exhalant siphon is almost twice as thick as its Lmi, while in the inhalant siphon these layers have similar thicknesses; the Coi is very thick, especially in the exhalant siphon. The inhalant siphon of T. lineata is very similar to that of M. biota, differing only with respect to the thickness of the Coi, which in the former species is not as well developed as in the latter. The Lmo of the exhalant siphon of T. lineata is by far the most developed layer, with the Lmi represented only by uniseriate small cells; in the vicinities of the nerve cords, the Cm is split in two layers. The epithelia of both siphons of M. biota and T. lineata bear ciliated receptors, which were difficult to observe as they were frequently covered with mucus. It was possible to observe that cilia are present in both species, differing in length and in the number per receptor between the inhalant and exhalant siphons, and between the species. Detailed comparisons among the siphons of M. biota and T. lineata and other bivalve species are very difficult, because of at least two reasons. First, each investigator has used different methods to prepare and observe the siphons through histological sections; and second, different nomenclatural schemes are used to describe the musculature of the siphons, causing confusion when the same layers are compared among different species. In order to unify the nomenclature of tissue layers of the bivalve siphons, we now propose a scheme to name these layers based on topological homology.

A Künneth formula in topological homology and its applications to the simplicial cohomology of l1(Z+k)

We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex ${\cal X}$ of Banach spaces and continuous boundary maps $d_n$ with closed ranges and prove that $H^n({\cal X}') \cong H_n({

X-ray Structure of Isoaspartyl Dipeptidase from E. coli : A Dinuclear Zinc Peptidase Evolved from Amidohydrolases

l-aspartyl and l-asparaginyl residues in proteins spontaneously undergo intra-residue rearrangements forming isoaspartyl/β-aspartyl residues linked through their side-chain β-carboxyl group with the following amino acid. In order to avoid accumulation of isoaspartyl dipeptides left over from protein degradation, some bacteria have developed specialized isoaspartyl/β-aspartyl zinc dipeptidases sequentially unrelated to other peptidases, which also poorly degrade α-aspartyl dipeptides. We have expressed and crystallized the 390 amino acid residue isoaspartyl dipeptidase (IadA) from E. coli , and have determined its crystal structure in the absence and presence of the phosphinic inhibitor Asp-Ψ[PO 2CH 2]-LeuOH. This structure reveals an octameric particle of 422 symmetry, with each polypeptide chain organized in a (αβ) 8 TIM-like barrel catalytic domain attached to a U-shaped β-sandwich domain. At the C termini of the β-strands of the β-barrel, the two catalytic zinc ions are surrounded by four His, a bridging carbamylated Lys and an Asp residue, which seems to act as a proton shuttle. A large β-hairpin loop protruding from the (αβ) 8 barrel is disordered in the free peptidase, but forms a flap that stoppers the barrel entrance to the active center upon binding of the dipeptide mimic. This isoaspartyl dipeptidase shows strong topological homology with the α-subunit of the binickel-containing ureases, the dinuclear zinc dihydroorotases, hydantoinases and phosphotriesterases, and the mononuclear adenosine and cytosine deaminases, which all are catalyzing hydrolytic reactions at carbon or phosphorous centers. Thus, nature has adapted an existing fold with catalytic tools suitable for hydrolysis of amide bonds to the binding requirements of a peptidase.

Implication of SAR of male medfly attractants in insect olfaction

Medfly ( Ceratitis capitata ) males are strongly attracted by different compounds, not described as pheromones. The best attractants reported are (+)- f -copaene, a sesquiterpene of natural source and ( m )-ceralure-B1, a non-natural iodinated cyclohexane ester. Although their origin, atomic composition, chemical and physical properties are rather different, they show similar attraction to medflies. The question of why these compounds, act behaviorally in the same way, has been never addressed in research papers. We show here for the first time that these compounds have quite similar stereochemistry, water accessible surfaces, certain local dipole moments and, to some extent, similar octanol/water partition coefficient (log P ). When seven carbons, one oxygen and one iodine belonging to ( m )-ceralure-B1 are selectively chosen based on topological homology with (+)- f -copaene and are overlaid with nine corresponding carbons of (+)- f -copaene, the RMS is 0.367 Å. This represents a high degree of steric resemblance. Local dipole moments and charges are similar in those regions where the molecules show topological homologies. Thus, we hypothesize that these two molecules could interact with the same male medfly's odorant receptor(s). The implications of this result in future research in insect olfaction is discussed.

Identification of an alpha-helical epitope region on the PM/Scl-100 autoantigen with structural homology to a region on the heterochromatin p25beta autoantigen using immobilized overlapping synthetic peptides.

The polymyositis-scleroderma overlap syndrome (PM/Scl) autoantigen is a nucleolar multiprotein particle, presumably participating in the maturation of 5.8S rRNAs. The major target antigens of this particle are two polypeptides with apparent molecular masses of 100 and 75 kDa. In this study we identified the major linear epitopes along the PM/Scl-100 protein sequence by probing overlapping oligopeptides with anti-PM/Scl autoantisera. A major epitope region was identified between amino acids 231 and 245 of the PM/Scl-100 polypeptide. Mutational analysis of the corresponding peptide LDVPPALADFIHQQR by glycine-walk followed by immunodetection of the resulting peptides indicated that amino acids 234, 237, 240, and 241 of the PM/Scl-100 autoantigen are essential for binding of the corresponding antibodies. These results allow us to propose a local alpha-helical secondary structure for the PM/Scl-100 major epitope region. A homology search with the peptide LDVPPALADFIHQQR against the Swiss-Model three-dimensional database reveals some topological homology of the PM/Scl-100 major epitope region with the heterochromatin modifier protein p25beta, a known autoantigen recognized by antibodies from a subset of scleroderma patients.

ORIENTATION AND ANATOMICAL NOTATION IN CONODONTS

All aspects of conodont paleontology rely on the identification and description of homologous anatomical units or elements. But the current schemes of anatomical notation and terms for orientation were formulated at a time when little was known of conodont anatomy or skeletal architecture, resulting in some confusion and difficulties in their application. With improving knowledge of cono- donts, these problems are becoming increasingly acute. In an attempt to address current problems, we introduce new terms for orientation in conodonts and their elements, and a modified scheme of anatomical notation. The principal axes of the conodont body are identified as rostrocaudal, dorsoventral, and mediolateral, with opposite lateral sides designated dextral and sinistral. Anatomical notation is defined according to topological relationships between elements with reference to the principal axes of the body and takes the form of letters with numeric subscripts (e.g., P 1 ,P 2 ,S 0-S4). The ozarkodinid apparatus serves as a standard, but the Pn-Sn scheme can be applied rigorously to all taxa that are known from natural assemblages or where an hypothesis of topological homology can be inferred from secondary morphological criteria. homology as an hypothesis of similarity that is based on topo- logical relations and which contains potential phylogenetic in- formation (see Rieppel, 1994 for discussion). Topology refers to the numbers of, and the relative spatial relationships between, recognizable anatomical units. Similarity, in this context, does not mean morphological similarity of the units under consider- ation. We should also point out that homology is hierarchical, operating at different levels including genes, development, and structure. It is also contextual as illustrated by the classic ex- ample of batwings and birdwings; these structures are homolo- gous as tetrapod forelimbs but not as wings. In this paper we deal only with homology of whole elements within the conodont apparatus (not homology of the apparatus, nor homology of parts of elements).

Orientation and anatomical notation in conodonts

All aspects of conodont paleontology rely on the identification and description of homologous anatomical units or elements. But the current schemes of anatomical notation and terms for orientation were formulated at a time when little was known of conodont anatomy or skeletal architecture, resulting in some confusion and difficulties in their application. With improving knowledge of conodonts, these problems are becoming increasingly acute.In an attempt to address current problems, we introduce new terms for orientation in conodonts and their elements, and a modified scheme of anatomical notation. The principal axes of the conodont body are identified as rostrocaudal, dorsoventral, and mediolateral, with opposite lateral sides designated dextral and sinistral. Anatomical notation is defined according to topological relationships between elements with reference to the principal axes of the body and takes the form of letters with numeric subscripts (e.g., P1, P2, S0-S4). The ozarkodinid apparatus serves as a standard, but the Pn-Snscheme can be applied rigorously to all taxa that are known from natural assemblages or where an hypothesis of topological homology can be inferred from secondary morphological criteria.

On non-zero values of the central homological dimension of C*-algebras

The paper is related to the area which was recently called topological homology [3, 6, 12, 16, 4]. We consider questions associated with the central Hochschild cohomology of C*-algebras. The study of the latter was begun by J. Phillips and I. Raeburn in [9, 10], when they were investigating some problems of the theory of perturbations of C*-algebras. In [8] we obtained a description of the structure of C*-algebras with central bidimension zero: it was proved that these C*-algebras are unital and have continuous trace. In the special case of separable and a priori unital C*-algebras this statement was proved by J. Phillips and I. Raeburn in [11] with the help of a different approach. The question was raised. Which values can the central bidimension of C*-algebras take? In the present paper it is shown that, for any CCR-algebra A having at least one infinite-dimensional irreducible representation, the central bidimension and the global central homological dimension of A are greater than one. At the same time it is proved that there exist CCR-algebras which are centrally biprojective, but which have both dimensions equal to one. This situation contrasts with the state of affairs in the “traditional” theory of the Banach Hochschild cohomology. Recall [3, Ch. 5] that the bidimension and the global homological dimension of any infinite-dimensional biprojective C*-algebra are equal to two. Besides, there is no CCR-algebra of bidimension one (respectively, global homological dimension one). See [7].

Structural and topological homology between porcine intestinal and renal brush border aminopeptidase

A method for the preparation of closed, right-side-out vesicles from the brush border membrane of the kidney proximal tubules is described. The aminopeptidase known to be bound to this membrane was investigated in order to compare its properties with those already reported for the intestinal enzyme. Both are composed of a hydrophilic, cataytically active part lying on the external side of the membrane and a short hydrophobic domain probably located in the N-terminal region of one of the subunits ensuring fixation to the lipid matrix. The enzymes were also found to be chemically similar. Moreover, a quantitative immunological technique showed that they contained 6 cross-reacting determinants, consistent with a very high degree of homology. Four of these determinants were accessible in the bound form of the enzymes in the region of the active site. The other two, probably related to the junction between the hydrophilic moiety and the hydrophobic anchor were completely masked in the bound form. The remainder (6 in the intestinal and 4 in the renal enzyme), were heterologous. The accessibility of two well defined determinants in this latter group was substantialy reduced, perhaps by the proximity of the lipid and/or of other enzyme molecules.

Extension of topological homology theories to partially orderd sets.

Extension of topological homology theories to partially orderd sets.