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

Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's

It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed p-form with p=2n-4 on the Fano scheme of lines on a (2n-2)-dimensional hypersurface Y of degree n. We provide several definitions of this form - via the Abel-Jacobi map, via Hochschild homology, and via the linkage class, and compute it explicitly for n = 4. In the special case of a Pfaffian hypersurface Y we show that the Fano scheme is birational to a certain moduli space of sheaves on a p-dimensional Calabi--Yau variety X arising naturally in the context of homological projective duality, and that the constructed form is induced by the holomorphic volume form on X. This remains true for a general non Pfaffian hypersurface but the dual Calabi-Yau becomes non commutative.Comment: 34 pages; exposition of Hochschild homology expanded; references added; introduction re-written; some imrecisions, typos and the orbit diagram in the last section correcte

Counting matrices over finite fields with support on skew Young diagrams and complements of Rothe diagrams

We consider the problem of finding the number of matrices over a finite field with a certain rank and with support that avoids a subset of the entries. These matrices are a q-analogue of permutations with restricted positions (i.e., rook placements). For general sets of entries these numbers of matrices are not polynomials in q (Stembridge 98); however, when the set of entries is a Young diagram, the numbers, up to a power of q-1, are polynomials with nonnegative coefficients (Haglund 98). In this paper, we give a number of conditions under which these numbers are polynomials in q, or even polynomials with nonnegative integer coefficients. We extend Haglund's result to complements of skew Young diagrams, and we apply this result to the case when the set of entries is the Rothe diagram of a permutation. In particular, we give a necessary and sufficient condition on the permutation for its Rothe diagram to be the complement of a skew Young diagram up to rearrangement of rows and columns. We end by giving conjectures connecting invertible matrices whose support avoids a Rothe diagram and Poincar\'e polynomials of the strong Bruhat order.Comment: 24 pages, 9 figures, 1 tabl

Geometry of lines and degeneracy loci of morphisms of vector bundles

Corrado Segre played a leading role in the foundation of line geometry. We survey some recent results on degeneracy loci of morphisms of vector bundles where he still is of profound inspiration.Comment: 10 pages. To appear in the proceedings of the conference "Homage to Corrado Segre

Origin of spin gapless semiconductor behavior in CoFeCrGa: Theory and Experiment

Despite a plethora of materials suggested for spintronic applications, a new class of materials has emerged, namely spin gapless semiconductors (SGS), which offers potentially more advantageous properties than existing ones. These magnetic semiconductors exhibit a finite band gap for one spin channel and a closed gap for the other. Here, supported by electronic-structure calculations, we report evidence of SGS behavior in equiatomic quaternary CoFeCrGa, having a cubic Heusler (prototype LiMgPdSn) structure but exhibiting chemical disorder (DO3 structure). CoFeCrGa is found to transform from SGS to half-metallic phase under pressure, which is attributed to unique electronic-structure features. The saturation magnetization (MS) obtained at 8K agrees with the Slater-Pauling rule and the Curie temperature (TC) is found to exceed 400K. Carrier concentration (up to 250K) and electrical conductivity are observed to be nearly temperature independent, prerequisites for SGS. The anomalous Hall coefficient is estimated to be 185S/cm at 5K. Considering the SGS properties and high TC, this material appears to be promising for spintronic applications

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