Homologous Lens Research Articles

Generalized torsion for hyperbolic 3‐manifold groups with arbitrary large rank

AbstractLet be a group and a non‐trivial element in . If some non‐empty finite product of conjugates of equals to the trivial element, then is called a generalized torsion element. To the best of our knowledge, we have no hyperbolic 3‐manifold groups with generalized torsion elements whose rank is explicitly known to be greater than two. The aim of this short note is to demonstrate that for a given integer there are infinitely many closed hyperbolic 3‐manifolds which enjoy the property: (i) the Heegaard genus of is , (ii) the rank of is , and (ii) has a generalized torsion element. Furthermore, we may choose as homology lens spaces and so that the order of the generalized torsion element is arbitrarily large.

Replica exchange molecular dynamics simulations reveal self-association sites in M-crystallin caused by mutations provide insights of cataract

Crystallins are ubiquitous, however, prevalence is seen in eye lens. Eye lens crystallins are long-lived and structural intactness is required for maintaining lens transparency and protein solubility. Mutations in crystallins often lead to cataract. In this study, we performed mutations at specific sites of M-crystallin, a close homologue of eye lens crystallin and studied by using replica exchange molecular dynamics simulation with generalized Born implicit solvent model. Mutations were made on the Ca2+ binding residues (K34D and S77D) and in the hydrophobic core (W45R) which is known to cause congenital cataract in homologous γD-crystallin. The chosen mutations caused large motion of the N-terminal Greek key, concomitantly broke the interlocking Greek keys interactions and perturbed the compact core resulting in several folded and partially unfolded states. Partially unfolded states exposed large hydrophobic patches that could act as precursors for self-aggregation. Accumulation of such aggregates is the potential cause of cataract in homologous eye lens crystallins.

Some arithmetic properties of the CWL invariant

To derive information about rational homology 3-spheres via the Casson–Walker–Lescop (CWL) invariant λ, this paper focuses on the fractional part of the invariant, completes the determination of the fractional parts of λ for homology lens spaces, shows that the fractional part is an invariant of the linking forms mod Z for homology lens spaces and gives a complete set of invariants derived from λ to classify the linking forms mod Z.

Reidemeister torsion and lens surgeries on knots in homology 3-spheres II

We introduce the norm and the order of a polynomial and of a homology lens space. We calculate the norm of the cyclotomic polynomials, and apply it to lens surgery problem for a knot whose Alexander polynomial is the same as an iterated torus knot.

Reidemeister torsion and lens surgeries on knots in homology 3-spheres I

We introduce the norm and the order of a polynomial and of a homology lens space. We calculate the norm of the cyclotomic polynomials, and apply it to lens surgery problem for a knot whose Alexander polynomial is the same as an iterated torus knot.

Homology lens spaces in topological 4-manifolds

For a closed $4$-manifold $X^4$ and closed $3$-manifold $M^3$ we investigate the smallest integer $n$ (perhaps $n=\infty$) such that $M^3$ embeds in $\#_nX^4$, the connected sum of $n$ copies of $X^4$. It is proven that any lens space (or homology lens space) embeds topologically locally flatly in $\#_2({\mathbf C}P^2\#\ \overline {{\mathbf C}P}^2)$, in $\#_4 S^2\times S^2$ and in $\#_8 \mathbf{C}P^2$.

Flat connection contribution to topology changing amplitudes in an ensemble of seifert fibered homology spheres

The Fintushel-Stern pseudofree orbifolds are exploited to construct wave functions of universes created as a result of the interaction of cones on lens spaces. We also study the problem of the definition of topology changing amplitudes for tunneling topology changes, described by cobordisms with Seifert fibered homology sphere boundaries. It is demonstrated that such topology changes are accompanied by creation or annihilation of the lens spaces. The topology-changing amplitude calculations are carried out in the stationary phase approximation for Kodama wave functions. In this approximation the changing amplitudes factorize and they are expressed by means of Chern-Simons invariants of flat connections over Seifert fibered homology spheres and lens spaces.

Homology lens spaces and Dehn surgery on homology spheres

A homology lens space is a closed 3-manifold with ℤ-homology groups isomorphic to those of a lens space. A useful theorem found in [Fu] states that a homology lens space $M^3$ may be obtained by an (n/1)-Dehn surgery on a homology 3-sphere if and only if

Surgery formulae for Casson's invariant and extensions to homology lens spaces.

Article Surgery formulae for Casson's invariant and extensions to homology lens spaces. was published on March 1, 1990 in the journal Journal für die reine und angewandte Mathematik (volume 1990, issue 405).

Simply connected 4-manifolds of second betti number 1 bounded by homology lens spaces

Simply connected 4-manifolds of second betti number 1 bounded by homology lens spaces

Human T-cell mediated response to homologous lens antigen

T-Cell response to a suspension of homologous whole lens antigen was investigated in three groups; (1) adults with normal eyes; (2) patients with mature and hypermature cataract with an intact lens capsule; and (3) patients, who had had extracapsular cataract surgery or lens injury, some of whom had clinical evidence of severe lens-induced inflammation. The results show that sensitized T-cells occur only in some patients in the third group. To our knowledge, this is the first direct evidence of a difference in the response to T-cells to lens antigen released from mature and hypermature lenses, and to lens antigen exposed by lens injury or extracapsular cataract surgery. The test may be useful to confirm clinical suspicion of delayed hypersensitivity to lens antigen in patients with severe sterile purulent inflammation or milder delayed sterile non-purulent inflammation following lens injury or extracapsular surgery, in the absence of histological proof.

Crystallins during Xenopus laevis free lens formation.

The ontogeny and localization of crystallins during free lens development (i.e. lens development without the optic vesicle) were investigated in Xenopus laevis using the indirect immunofluorescence staining method with an antiserum raised against homologous total lens soluble proteins. Since the developing free lenses pass through stages similar to those of the lenses regenerated from the inner cell layer of the outer cornea following lentectomy in the same species Freeman's classification was used to identify the stages of free lens development. The first appearance of a positive reaction occurred at early stage IV in a number of cells in an area where future lens fibre cells would develop. With further differentiation of the free lens more and more cells in the fibre area started to show a positive reaction and the first positive reaction in the epithelium was observed late in stage V. Histological examination revealed that a fully differentiated free lens and a normally developed lens are similar but that the free lens is smaller.

The immune response to homologous lens crystallin. I. Antibody production after lens injury.

Using a sensitive radioimmunoassay to homologous mouse alpha-crystallin, it was established that autoantibodies are produced to this self constituent in mice after rupture of the lens capsule by needling. Antibody to lens crystallin was detected within 4 days of lens rupture and persisted for 24 days, suggesting that these mice are not tolerant to alpha-crystallin at the B cell level. However, T cells from mice immunized with homologous crystallin cannot be stimulated to proliferate by either homologous or heterologous crystallin. On the other hand, lymphocytes from mice immunized with bovine alpha-crystallin can be stimulated to proliferate to bovine crystallin, but not to either unfractionated mouse crystallin (MC) or purified mouse alpha-crystallin. At the level of detection, therefore, T cells appear to be tolerant to homologous alpha-crystallin, but not to heterologous alpha-crystallin. LPS resulting from bacterial contamination after needling was ruled out as a necessity for antibody production because antibody to mouse alpha-crystallin was produced after sterile lens rupture with a laser. However, LPS and poly A:U did enhance the antibody response to alpha-crystallin. These data suggest that T cells, but not B cells, are tolerant to homologous crystallin and that antibody results from circumvention of specific helper T cell requirements for antibody synthesis. The implications of these findings for tolerance and autoimmune uveitis are discussed.

The immune response to homologous lens crystallin. II. A model of ocular inflammation involving eye injuries at separate times.

The immune response to homologous lens crystallin. II. A model of ocular inflammation involving eye injuries at separate times.

Some homology lens spaces which bound rational homology balls

Some homology lens spaces which bound rational homology balls

The evolutionary sequence and quantities of different antigenic determinants of calf lens alpha crystallin

Immunochemieal cross-reactions between calf lens alpha crystallin and homologous proteins from different vertebrate classes were used for the study of antigenic determinants which, in the evolution of this protein, were derived from common ancestral forms. Determination of the sequence in which the different antigenic determinants evolved was based on estimation of the relative number of antigenic determinants shared by calf alpha crystallin with alpha crystallin from other vertebrate classes. For this estimation, samples of antiserum to calf lens alpha crystallin were absorbed with homologous lens proteins from each of the different vertebrate classes. The unabsorbed antiserum reacted with homologous proteins from all vertebrate classes. Each of the absorbed antisera showed a taxonomically different extent of residual cross-reaction. The species used for absorption were then ordered according to an increasing taxonomic extent of residual cross-reactions of the absorbed anti-calf antiserum, indicating a sequence of species with decreasing numbers of antigenic determinants shared with the mammalian protein. This sequence represents the increasing phylogenetic distances between the species used for absorption and the species used to produce the antiserum. This immunochemical determination showed that the phylogenetic sequence in which antigenic determinants present in the calf alpha crystallin molecule were formed, progressed from the primitive aquatic vertebrates agnatha, elasmobranchii and actinopterygii to the primitive land vertebrates and then to amphibia, reptilia, aves and mammalia. For the estimation of the relative amount (%) of determinants derived from different ancestral forms and transferred in evolution to calf alpha crystallin, 125I bound to a calf alpha crystallin immunoadsorbent after saturation with total 125I anti-calf alpha crystallin Fab fragments was compared to 125I bound to the same amounts of calf alpha crystallin after saturation with 125I Fab fragments of phylogenetically restricted specificity. Of all antigenic determinants in present-day calf alpha crystallin. approximately 42% were found also in the homologous lamprey protein. These determinants originated with the primitive agnatha which started the vertebrate subphylum 450 million years ago. Only about 15% originated with the mammalia, some 200 million years later, rellecting the slow evolutionary change of this protein molecule.

Immunopathology of the lens. II. Humoral and cellular immune responses to homologous lens antigens and their roles in ocular inflammation.

It has been possible for the first time to demonstrate antibodies to homologous lens proteins in rabbits without the addition of adjuvant. By means of immunofluorescence and immunoperoxidase methods it has been possible not only to show for the first time that homologous lens antibodies cross-react with extraocular tissues but that the cross-reacting antigens are related to the cell mitochondria, microsomes, and the proteins associated with contractile organelles. The rabbits did not produce antibodies to gamma-crystallins even when the whole lens homogenate was injected with Freund's complete adjuvant. This suggests that gamma-crystallins are non-antigenic in homologous situations, and this may be related to both B- and T-cell tolerance. Alternatively, the failure of gamma-crystallins to induce antibody production may be due to intermolecular antigenic competition with other crystallins. The presence of mycobacteria in an adjuvant is essential for an antibody response to be detectable by agar diffusion techniques. The response to homologous lens antigens, both in magnitude as well as in duration, varied in different rabbits, which suggested to us that a central control mechanism involving the immune response (Ir) genes may plan an important role. Antibodies to homologous lens proteins as detected by immunofluorescence and immunoperoxidase methods were shown to be of the IgG class. This is the first time that the kinetics of the immune response to the same homologous lens antigen in saline with or without incomplete or complete adjuvant has been examined and their relative merits compared. Systemic homologous immunisation followed by discission of the lens led to a marked Arthus type reaction in and around the lens, but a typical granulomatous phakoallergic endophthalmitis was not produced. It seems likely that the rabbit is not suitable for the production of an experimental model of this condition.

Experimental lens-induced granulomatous endophthalmitis: Preliminary histopathologic observations

An experimental lens-induced granulomatous endophthalmitis (ELGE), which histopathologically is virtually identical to the human phakoanaphylactic endophthalmitis (or lens-induced uveitis), was produced after injury to the lens in rats that had been previously sensitized to homologous lens protein in complete Freund's adjuvant. ELGE was not observed in four different groups of control animals. We believe, therefore, that this study provides direct evidence that ELGE is an immune reaction to autologous lens antigens in rats previously sensitized to homologous lens antigens.

Intravitreal Challenge of Rabbit Eyes with Live Rubella Virus and Homologous Lens Protein

Intravitreal Challenge of Rabbit Eyes with Live Rubella Virus and Homologous Lens Protein

Intravitreal Challenge of Rabbit Eyes with Live Rubella Virus and Homologous Lens Protein

Intravitreal Challenge of Rabbit Eyes with Live Rubella Virus and Homologous Lens Protein