Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Restricted structural gene polymorphism in the Mycobacterium tuberculosis complex indicates evolutionarily recent global dissemination

One-third of humans are infected with Mycobacterium tuberculosis, the causative agent of tuberculosis. Sequence analysis of two megabases in 26 structural genes or loci in strains recovered globally discovered a striking reduction of silent nucleotide substitutions compared with other human bacterial pathogens. The lack of neutral mutations in structural genes indicates that M. tuberculosis is evolutionarily young and has recently spread globally. Species diversity is largely caused by rapidly evolving insertion sequences, which means that mobile element movement is a fundamental process generating genomic variation in this pathogen. Three genetic groups of M. tuberculosis were identified based on two polymorphisms that occur at high frequency in the genes encoding catalase-peroxidase and the A subunit of gyrase. Group 1 organisms are evolutionarily old and allied with M. bovis, the cause of bovine tuberculosis. A subset of several distinct insertion sequence IS6110 subtypes of this genetic group have IS6110 integrated at the identical chromosomal insertion site, located between dnaA and dnaN in the region containing the origin of replication. Remarkably, study of ≈6,000 isolates from patients in Houston and the New York City area discovered that 47 of 48 relatively large case clusters were caused by genotypic group 1 and 2 but not group 3 organisms. The observation that the newly emergent group 3 organisms are associated with sporadic rather than clustered cases suggests that the pathogen is evolving toward a state of reduced transmissability or virulence.

Specific atomic groups and RNA helix geometry in acceptor stem recognition by a tRNA synthetase

Oligonucleotides that recapitulate the acceptor stems of tRNAs are substrates for aminoacylation by many tRNA synthetases in vitro, even though these substrates are missing the anticodon trinucleotides of the genetic code. In the case of tRNAAla a single acceptor stem G⋅U base pair at position 3·70 is essential, based on experiments where the wobble pair has been replaced by alternatives such as I⋅U, G⋅C, and A⋅U, among others. These experiments led to the conclusion that the minor-groove free 2-amino group (of guanosine) of the G⋅U wobble pair is essential for charging. Moreover, alanine-inserting tRNAs (amber suppressors) that replace G⋅U with mismatches such as G⋅A and C⋅A are partially active in vivo and can support growth of an Escherichia coli tRNAAla knockout strain, leading to the hypothesis that a helix irregularity and nucleotide functionalities are important for recognition. Herein we investigate the charging in vitro of oligonucleotide and full-length tRNA substrates that contain mismatches at the position of the G⋅U pair. Although most of these substrates have undetectable activity, G⋅A and C⋅A variants retain some activity, which is, nevertheless, reduced by at least 100-fold. Thus, the in vivo assays are much less sensitive to large changes in aminoacylation kinetic efficiency of 3·70 variants than is the in vitro assay system. Although these functional data do not clarify all of the details, it is now clear that specific atomic groups are substantially more important in determining kinetic efficiency than is a helical distortion. By implication, the activity of mutant tRNAs measured in the in vivo assays appears to be more dependent on factors other than aminoacylation kinetic efficiency.

Geometry of circular vectors and pattern recognition of shape of a boundary

This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.

Preferential exclusion of sucrose from recombinant interleukin-1 receptor antagonist: Role in restricted conformational mobility and compaction of native state

Understanding the mechanism for sucrose-induced protein stabilization is important in many diverse fields, ranging from biochemistry and environmental physiology to pharmaceutical science. Timasheff and Lee [Lee, J. C. & Timasheff, S. N. (1981) J. Biol. Chem. 256, 7193–7201] have established that thermodynamic stabilization of proteins by sucrose is due to preferential exclusion of the sugar from the protein’s surface, which increases protein chemical potential. The current study measures the preferential exclusion of 1 M sucrose from a protein drug, recombinant interleukin 1 receptor antagonist (rhIL-1ra). It is proposed that the degree of preferential exclusion and increase in chemical potential are directly proportional to the protein surface area and that, hence, the system will favor the protein state with the smallest surface area. This mechanism explains the observed sucrose-induced restriction of rhIL-1ra conformational fluctuations, which were studied by hydrogen–deuterium exchange and cysteine reactivity measurements. Furthermore, infrared spectroscopy of rhlL-1ra suggested that a more ordered native conformation is induced by sucrose. Electron paramagnetic resonance spectroscopy demonstrated that in the presence of sucrose, spin-labeled cysteine 116 becomes more buried in the protein’s interior and that the hydrodynamic diameter of the protein is reduced. The preferential exclusion of sucrose from the protein and the resulting shift in the equilibrium between protein states toward the most compact conformation account for sucrose-induced effects on rhIL-1ra.

Peptide-specific cytotoxic T lymphocytes restricted by nonself major histocompatibility complex class I molecules: Reagents for tumor immunotherapy

Studies in melanoma patients have revealed that self proteins can function as targets for tumor-reactive cytotoxic T lymphocytes (CTL). One group of self proteins MAGE, BAGE, and GAGE are normally only expressed in testis and placenta, whilst another group of CTL recognized proteins are melanocyte-specific differentiation antigens. In this study we have investigated whether CTL can be raised against a ubiquitously expressed self protein, mdm-2, which is frequently overexpressed in tumors. The observation that T-cell tolerance is self major histocompatibility complex-restricted was exploited to generate CTL specific for an mdm-2 derived peptide presented by nonself major histocompatibility complex class I molecules. Thus, the allo-restricted T-cell repertoire of H-2d mice was used to isolate CTL specific for the mdm100 peptide presented by allogeneic H-2Kb class I molecules. In vitro, these CTL discriminated between transformed and normal cells, killing specifically Kb-positive melanoma and lymphoma tumors but not Kb-expressing dendritic cells. In vivo, the CTL showed antitumor activity and delayed the growth of melanoma as well as lymphoma tumors in H-2b recipient mice. These experiments show that it is possible to circumvent T-cell tolerance to ubiquitously expressed self antigens, and to target CTL responses against tumors expressing elevated levels of structurally unaltered proteins.

On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.

A homeodomain gene Ptx3 has highly restricted brain expression in mesencephalic dopaminergic neurons

The mesencephalic dopaminergic (mesDA) system regulates behavior and movement control and has been implicated in psychiatric and affective disorders. We have identified a bicoid-related homeobox gene, Ptx3, a member of the Ptx-subfamily, that is uniquely expressed in these neurons. Its expression starting at E11.5 in the developing mouse midbrain correlates with the appearance of mesDA neurons. The number of Ptx3-expressing neurons is reduced in Parkinson patients, and these neurons are absent from 6-hydroxy-dopamine-lesioned rats, an animal model for this disease. Thus, Ptx3 is a unique transcription factor marking the mesDA neurons at the exclusion of other dopaminergic neurons, and it may be involved in developmental determination of this neuronal lineage.

Molecular dynamics and free-energy calculations applied to affinity maturation in antibody 48G7

We investigated the relative free energies of hapten binding to the germ line and mature forms of the 48G7 antibody Fab fragments by applying a continuum model to structures sampled from molecular dynamics simulations in explicit solvent. Reasonable absolute and very good relative free energies were obtained. As a result of nine somatic mutations that do not contact the hapten, the affinity-matured antibody binds the hapten >104 tighter than the germ line antibody. Energetic analysis reveals that van der Waals interactions and nonpolar contributions to solvation are similar and drive the formations of both the germ line and mature antibody–hapten complexes. Affinity maturation of the 48G7 antibody therefore appears to occur through reorganization of the combining site geometry in a manner that optimizes the balance of gaining favorable electrostatic interactions with the hapten and losing those with solvent during the binding process. As reflected by lower rms fluctuations in the antibody–hapten complex, the mature complex undergoes more restricted fluctuations than the germ line complex. The dramatically increased affinity of the 48G7 antibody over its germ line precursor is thus made possible by electrostatic optimization.

Bok is a pro-apoptotic Bcl-2 protein with restricted expression in reproductive tissues and heterodimerizes with selective anti-apoptotic Bcl-2 family members

In the intracellular death program, hetero- and homodimerization of different anti- and pro-apoptotic Bcl-2-related proteins are critical in the determination of cell fate. From a rat ovarian fusion cDNA library, we isolated a new pro-apoptotic Bcl-2 gene, Bcl-2-related ovarian killer (Bok). Bok had conserved Bcl-2 homology (BH) domains 1, 2, and 3 and a C-terminal transmembrane region present in other Bcl-2 proteins, but lacked the BH4 domain found only in anti-apoptotic Bcl-2 proteins. In the yeast two-hybrid system, Bok interacted strongly with some (Mcl-1, BHRF1, and Bfl-1) but not other (Bcl-2, Bcl-xL, and Bcl-w) anti-apoptotic members. This finding is in direct contrast to the ability of other pro-apoptotic members (Bax, Bak, and Bik) to interact with all of the anti-apoptotic proteins. In addition, negligible interaction was found between Bok and different pro-apoptotic members. In mammalian cells, overexpression of Bok induced apoptosis that was blocked by the baculoviral-derived cysteine protease inhibitor P35. Cell killing induced by Bok was also suppressed following coexpression with Mcl-1 and BHRF1 but not with Bcl-2, further indicating that Bok heterodimerized only with selective anti-apoptotic Bcl-2 proteins. Northern blot analysis indicated that Bok was highly expressed in the ovary, testis and uterus. In situ hybridization analysis localized Bok mRNA in granulosa cells, the cell type that underwent apoptosis during follicle atresia. Identification of Bok as a new pro-apoptotic Bcl-2 protein with restricted tissue distribution and heterodimerization properties could facilitate elucidation of apoptosis mechanisms in reproductive tissues undergoing hormone-regulated cyclic cell turnover.

Melan-A/MART-151–73 represents an immunogenic HLA-DR4-restricted epitope recognized by melanoma-reactive CD4+ T cells

The human Melan-A/MART-1 gene encodes an HLA-A2-restricted peptide epitope recognized by melanoma-reactive CD8+ cytotoxic T lymphocytes. Here we report that this gene also encodes at least one HLA-DR4-presented peptide recognized by CD4+ T cells. The Melan-A/MART-151–73 peptide was able to induce the in vitro expansion of specific CD4+ T cells derived from normal DR4+ donors or from DR4+ patients with melanoma when pulsed onto autologous dendritic cells. CD4+ responder T cells specifically produced IFN-γ in response to, and also lysed, T2.DR4 cells pulsed with the Melan-A/MART-151–73 peptide and DR4+ melanoma target cells naturally expressing the Melan-A/MART-1 gene product. Interestingly, CD4+ T cell immunoreactivity against the Melan-A/MART-151–73 peptide typically coexisted with a high frequency of anti-Melan-A/MART-127–35 reactive CD8+ T cells in freshly isolated blood harvested from HLA-A2+/DR4+ patients with melanoma. Taken together, these data support the use of this Melan-A/MART-1 DR4-restricted melanoma epitope in future immunotherapeutic trials designed to generate, augment, and quantitate specific CD4+ T cell responses against melanoma in vivo.

Crossreactive recognition of viral, self, and bacterial peptide ligands by human class I-restricted cytotoxic T lymphocyte clonotypes: Implications for molecular mimicry in autoimmune disease

The immunodominant, CD8+ cytotoxic T lymphocyte (CTL) response to the HLA-B8-restricted peptide, RAKFKQLL, located in the Epstein–Barr virus immediate-early antigen, BZLF1, is characterized by a diverse T cell receptor (TCR) repertoire. Here, we show that this diversity can be partitioned on the basis of crossreactive cytotoxicity patterns involving the recognition of a self peptide—RSKFRQIV—located in a serine/threonine kinase and a bacterial peptide—RRKYKQII—located in Staphylococcus aureus replication initiation protein. Thus CTL clones that recognized the viral, self, and bacterial peptides expressed a highly restricted αβ TCR phenotype. The CTL clones that recognized viral and self peptides were more oligoclonal, whereas clones that strictly recognized the viral peptide displayed a diverse TCR profile. Interestingly, the self and bacterial peptides equally were substantially less effective than the cognate viral peptide in sensitizing target cell lysis, and also resulted only in a weak reactivation of memory CTLs in limiting dilution assays, whereas the cognate peptide was highly immunogenic. The described crossreactions show that human antiviral, CD8+ CTL responses can be shaped by peptide ligands derived from autoantigens and environmental bacterial antigens, thereby providing a firm structural basis for molecular mimicry involving class I-restricted CTLs in the pathogenesis of autoimmune disease.

Inhibition of MHC class I-restricted antigen presentation by γ2-herpesviruses

The γ-herpesviruses, in contrast to the α- and β-herpesviruses, are not known to inhibit antigen presentation to CD8+ cytotoxic T lymphocytes (CTLs) during lytic cycle replication. However, murine γ-herpesvirus 68 causes a chronic lytic infection in CD4+ T cell-deficient mice despite the persistence of a substantial CTL response, suggesting that CTL evasion occurs. Here we show that, distinct from host protein synthesis shutoff, γ-herpesvirus 68 down-regulates surface MHC class I expression on lytically infected fibroblasts and inhibits their recognition by antigen-specific CTLs. The viral K3 gene, encoding a zinc-finger-containing protein, dramatically reduced the half-life of nascent class I molecules and the level of surface MHC class I expression and was by itself sufficient to block antigen presentation. The homologous K3 and K5 genes of the related Kaposi's sarcoma-associated virus also inhibited antigen presentation and decreased cell surface expression of HLA class I antigens. Thus it appears that an immune evasion strategy shared by at least two γ-herpesviruses allows continued lytic infection in the face of strong CTL immunity.

Region-specific differentiation of neural tube-derived neuronal restricted progenitor cells after heterotopic transplantation

Spinal cord neuronal restricted progenitor (NRP) cells, when transplanted into the neonatal anterior forebrain subventricular zone, migrate to distinct regions throughout the forebrain including the olfactory bulb, frontal cortex, and occipital cortex but not to the hippocampus. Their migration pattern and differentiation potential is distinct from anterior forebrain subventricular zone NRPs. Irrespective of their final destination, NRP cells do not differentiate into glia. Rather they synthesize neurotransmitters, acquire region-specific phenotypes, and receive synapses from host neurons after transplantation. Spinal cord NRPs express choline acetyl transferase even in regions where host neurons do not express this marker. The restricted distribution of transplanted spinal cord NRP cells and their acquisition of varied region-specific phenotypes suggest that their ultimate fate and phenotype is dictated by a combination of intrinsic properties and extrinsic cues from the host.

Identification of HLA class II-restricted determinants of Mycobacterium tuberculosis-derived proteins by using HLA-transgenic, class II-deficient mice

T helper 1 cells play a major role in protective immunity against mycobacterial pathogens. Since the antigen (Ag) specificity of CD4+ human T cells is strongly controlled by HLA class II polymorphism, the immunogenic potential of candidate Ags needs to be defined in the context of HLA polymorphism. We have taken advantage of class II-deficient (Ab0) mice, transgenic for either HLA-DRA/B1*0301 (DR3) or HLA-DQB1*0302/DQA*0301 (DQ8) alleles. In these animals, all CD4+ T cells are restricted by the HLA molecule. We reported previously that human DR3-restricted T cells frequently recognize heat shock protein (hsp)65 of Mycobacterium tuberculosis, and only a single hsp65 epitope, p1–20. DR3.Ab0 mice, immunized with bacillus Calmette–Guérin or hsp65, developed T cell responses to M. tuberculosis, and recognized the same hsp65 epitope, p1–20. Hsp65-immunized DQ8.Ab0 mice mounted a strong response to bacillus Calmette–Guérin but not to p1–20. Instead, we identified three new DQ8-restricted T cell epitopes in the regions 171–200, 311–340, and 411–440. DR3.Ab0 mice immunized with a second major M. tuberculosis protein, Ag85 (composed of 85A, 85B, and 85C), also developed T cell responses against only one determinant, 85B p51–70, that was identified in this study. Importantly, subsequent analysis of human T cell responses revealed that HLA-DR3+, Ag85-reactive individuals recognize exactly the same peptide epitope as DR3.Ab0 mice. Strikingly, both DR3-restricted T cell epitopes represent the best DR3-binding sequences in hsp65 and 85B, revealing a strong association between peptide-immunodominance and HLA binding affinity. Immunization of DR3.Ab0 with the immunodominant peptides p1–20 and p51–70 induced T cell reactivity to M. tuberculosis. Thus, for two different Ags, T cells from DR3.Ab0 mice and HLA-DR3+ humans recognize the same immunodominant determinants. Our data support the use of HLA-transgenic mice in identifying human T cell determinants for the design of new vaccines.