Quantum cohomology and the Satake isomorphism

We prove that the geometric Satake correspondence admits quantum corrections for minuscule Grassmannians of Dynkin types $A$ and $D$. We find, as a corollary, that the quantum connection of a spinor variety $OG(n,2n)$ can be obtained as the half-spinorial representation of that of the quadric $Q_{2n-2}$. We view the (quantum) cohomology of these Grassmannians as endowed simultaneously with two structures, one of a module over the algebra of symmetric functions, and the other, of a module over the Langlands dual Lie algebra, and investigate the interaction between the two. In particular, we study primitive classes $y$ in the cohomology of a minuscule Grassmannian $G/P$ that are characterized by the condition that the operator of cup product by $y$ is in the image of the Lie algebra action. Our main result states that quantum correction preserves primitivity. We provide a quantum counterpart to a result obtained by V. Ginzburg in the classical setting by giving explicit formulas for the quantum corrections to homogeneous primitive elements

B cell responses to a peptide epitope. VI. The kinetics of antigen recognition modulates B cell-mediated recruitment of T helper subsets

The ability of Ag-primed B cells to recruit distinct Th subsets was examined using two analogous synthetic peptides, G41CT3 and G28CT3, as model Ags. With sequence differences at only two positions, these peptides were identical both with respect to fine specificity of Abs induced and ability to prime T cells. Lymph node cell populations primed with peptide G41CT3, when challenged with the homologous Ag, yielded predominantly Th2 cytokines. In contrast, a challenge with the heterologous Ag, G28CT3, resulted in a markedly increased production of Th1 cytokines. These distinctions derived from altered APC function of Ag-primed B cells due to differential kinetics of recognition of the two Ags by surface Ig receptors, as confirmed by binding studies with a panel of anti-G41CT3 mAbs. A concentration-dependent circular dichroism study revealed differences in the nature of intermolecular associations for these two peptides. Furthermore, the on-rate of peptide G28CT3 binding to Ab also increased with increasing peptide concentration, implying a dependence on intermolecular interactions. This, in turn, correlated well with the ability of peptide G28CT3 to preferentially activate either Th1 or Th2 cells. Thus, the relative proportion of Th1 vs Th2 cells recruited by Ag-primed B cells is governed by the on-rate of Ag binding to surface Ig receptors, with higher on-rates promoting Th1 recruitment. Further, even subtle changes in solution behavior of an Ag can markedly influence the kinetics of recognition by B cells

2-[2-(Hydroxy­meth­yl)phen­yl]-1-(1-naphth­yl)ethanol

The mol­ecular conformation of the title compound, C19H18O2, is stabilized by an intra­molecular O—H—O hydrogen bond. In addition, inter­molecular O—H—O inter­actions link the mol­ecules into zigzag chains running along the c axis

Schubert complexes and degeneracy loci

Given a generic map between flagged vector bundles on a Cohen-Macaulay variety, we construct maximal Cohen-Macaulay modules with linear resolutions supported on the Schubert-type degeneracy loci. The linear resolution is provided by the Schubert complex, which is the main tool introduced and studied in this paper. These complexes extend the Schubert functors of Kra\'skiewicz and Pragacz, and were motivated by the fact that Schur complexes resolve maximal Cohen-Macaulay modules supported on determinantal varieties. The resulting formula in K-theory provides a "linear approximation" of the structure sheaf of the degeneracy locus, which can be used to recover a formula due to Fulton.Comment: 23 pages, uses tabmac.sty; v2: corrected typos and added reference

B cell responses to a peptide epitope. X. Epitope selection in a primary response is thermodynamically regulated

We examine the etiological basis of hierarchical immunodominance of B cell epitopes on a multideterminant Ag. A model T-dependant immunogen, containing a single immunodominant B cell epitope, was used. The primary IgM response to this peptide included Abs directed against diverse determinants presented by the peptide. Interestingly, affinity of individual monomeric IgM Abs segregated around epitope recognized and was independent of their clonal origins. Furthermore, affinity of Abs directed against the immunodominant epitope were markedly higher than that of the alternate specificities. These studies suggested that the affinity of an epitope-specific primary response, and variations therein, may be determined by the chemical composition of epitope. This inference was supported by thermodynamic analyses of monomer IgM binding to Ag, which revealed that this interaction occurs at the expense of unfavorable entropy changes. Permissible binding required compensation by net enthalpic changes. Finally, the correlation between chemical composition of an epitope, the resultant affinity of the early primary humoral response, and its eventual influence on relative immunogenicity could be experimentally verified. This was achieved by examining the effect of various amino-terminal substitutions on immunogenicity of a, hitherto cryptic, amino-terminal determinant. Such experiments permitted delineation of a hierarchy of individual amino acid residues based on their influence; which correlated well with calculated Gibbs-free energy changes that individual residue side chains were expected to contribute in a binding interaction. Thus, maturation of a T-dependant humoral response is initiated by a step that is under thermodynamic control

1-[3-(4-Chloro­phen­yl)isoquinolin-1-yl]-3,5-diphenyl-1H-pyrazole

The title compound, C30H20ClN3, is composed of a diaryl-substituted pyrazole ring connected to an aryl-substituted isoquinoline ring system with a dihedral angle of 65.1 (1)° between the pyrazole ring and the isoquinoline ring system. The 3-phenyl and 4-phenyl substitutents are twisted by 8.1 (1) and 43.0 (1)°, respectively, with respect to the pyrazole ring. The chloro­phenyl ring and the isoquinoline ring system are twisted by 21.2 (1)° with respect to each other

B cell responses to a peptide epitope. V. Kinetic regulation of repertoire discrimination and antibody optimization for epitope

The influence of imposing various conformational constraints on immune responses to a model epitope within a synthetic peptide immunogen was examined in mice. Although overall immunogenicity was affected, the model epitope (sequence DPAF) remained the predominant recognition site regardless of the conformation in which it was presented. A comparison of anti-DPAF mAbs obtained in response to two analogue peptides, PS1CT3 and CysCT3, in which the DPAF segment was either unconstrained or held within a cyclic loop, respectively, revealed a significant homology in the paratope composition. At one level a subset of anti-PS1CT3 and anti-CysCT3 mAbs was found to share a common heavy chain variable region. In addition, nucleotide sequence homology comparisons of both heavy and light chain variable regions identified the presence of anti-PS1CT3 and anti-CysCT3 mAbs that collectively appeared to derive from a common progenitor, but with nonidentical somatic mutations. Interestingly, however, no bias toward homologous Ag could be discerned on measurement of relative affinities of the mAbs for the two peptides. In contrast, mAb binding on-rates clearly discriminated between peptides representing the homologous vs the heterologous confomer of the DPAF epitope. Thus, it would appear that the kinetics of Ag recognition dominate over equilibrium binding criteria both in epitope-driven repertoire selection and Ab maturation in a humoral response

1-(3,5-Dimethyl-1H-pyrazol-1-yl)-3-phenyl­isoquinoline

The mol­ecular conformation of the title compound, C20H17N3, is stabilized by an intramolecular C—H⋯N inter­action. The crystal structure shows inter­molecular C—H⋯π inter­actions. The dihedral angle between the isoquinoline unit and the phenyl ring is 11.42 (1)° whereas the isoquinoline unit and the pendent dimethyl pryrazole unit form a dihedral angle of 50.1 (4)°. Furthermore, the angle between the mean plane of the phenyl ring and the dimethyl pyrazole unit is 47.3 (6)°

An Experimental Evaluation of Quenched Fe-Ga Alloys: Structural Magnetic and Magnetostrictive Properties

This study examines the effect of quenching on Fe100-x-Gax (x – 20 & 25) alloys. The long range of D03 ordering causes a minor variation in unit cell, which reduces peak intensity. This existence of D03, coupled with the A2 phase, leads to a decrease in magnetostriction in the quenched 25 at.% Ga alloy, which promotes D03 ordering. An Fe-Ga alloy having 20 at.% Ga that has been quenched possesses the A2 phase, the production of D03 is a first-order transition. Continuous ordering attempts to suppress D03 in 25 at. % Ga alloys were ineffective. Quenched Fe80-Ga20 alloy's saturation magnetization is larger than Fe75-Ga25 alloy. This suggests that lowering the nonmagnetic element Ga promotes saturation magnetization. The rise in material flaws and dislocations is due to the increased Ga content and higher quenching temperature. In a single-phase region, Fe80-Ga20 has the greatest magnetostriction at 85 ppm. Magnetostriction diminishes as Ga content rises to 25%, the D03 structure is responsible for this drop