The Unitary Gas and its Symmetry Properties

The physics of atomic quantum gases is currently taking advantage of a powerful tool, the possibility to fully adjust the interaction strength between atoms using a magnetically controlled Feshbach resonance. For fermions with two internal states, formally two opposite spin states, this allows to prepare long lived strongly interacting three-dimensional gases and to study the BEC-BCS crossover. Of particular interest along the BEC-BCS crossover is the so-called unitary gas, where the atomic interaction potential between the opposite spin states has virtually an infinite scattering length and a zero range. This unitary gas is the main subject of the present chapter: It has fascinating symmetry properties, from a simple scaling invariance, to a more subtle dynamical symmetry in an isotropic harmonic trap, which is linked to a separability of the N-body problem in hyperspherical coordinates. Other analytical results, valid over the whole BEC-BCS crossover, are presented, establishing a connection between three recently measured quantities, the tail of the momentum distribution, the short range part of the pair distribution function and the mean number of closed channel molecules.Comment: 63 pages, 8 figures. Contribution to the Springer Lecture Notes in Physics "BEC-BCS Crossover and the Unitary Fermi gas" edited by Wilhelm Zwerger. Revised version correcting a few typo

Mouse Chromosome 3

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46995/1/335_2004_Article_BF00648421.pd

Epitope specificity determines cross-protection of a SIT-induced IgG4 antibody

The calcium-binding 2EF-hand protein Phl p 7 from timothy grass pollen is a highly cross-reactive pollen pan-allergen that can induce severe clinical symptoms in allergic patients. Recently, a human monoclonal Phl p 7-specific IgG4 antibody (mAb102.1F10) was isolated from a patient who had received grass pollen-specific immunotherapy (SIT).We studied epitope specificity, cross-reactivity, affinity and cross-protection of mAb102.1F10 towards homologous calcium-binding pollen allergens. Sequence comparisons and molecular modelling studies were performed with ClustalW and SPADE, respectively. Surface plasmon resonance measurements were done with purified recombinant allergens. Binding and cross-reactivity of patients’ IgE and mAb102.1F10 to calcium-binding allergens and peptides thereof was studied with quantitative RAST-based methods, in ELISA, basophil activation and IgE-facilitated allergen presentation experiments. Allergens from Timothy grass (Phl p 7), Alder (Aln g 4), Birch (Bet v 4), Turnip rape (Bra r 1), Lamb′s quarter (Che a 3) and Olive (Ole e 3, Ole e 8) showed high sequence similarity and cross-reacted with allergic patients’ IgE. mAb102.1F10 bound the C-terminal portion of Phl p 7 in a calcium-dependent manner. It cross-reacted with high affinity with Ole e 3 whereas binding and affinity to the other allergens was low. mAb102.1F10 showed limited inhibition of patients’ IgE binding and basophil activation. Sequence comparison and surface exposure calculations identified three amino acids likely to be responsible for limited cross-reactivity.Our results demonstrate that a small number of amino acid differences among cross-reactive allergens can reduce the affinity of binding by a SIT-induced IgG and thus limit cross-protection