Lower bounds for the first eigenvalue of the magnetic Laplacian

We consider a Riemannian cylinder endowed with a closed potential 1-form A and study the magnetic Laplacian with magnetic Neumann boundary conditions associated with those data. We establish a sharp lower bound for the first eigenvalue and show that the equality characterizes the situation where the metric is a product. We then look at the case of a planar domain bounded by two closed curves and obtain an explicit lower bound in terms of the geometry of the domain. We finally discuss sharpness of this last estimate.Comment: Replaces in part arXiv:1611.0193

Analysis of translocation-competent secretory proteins by HDX-MS

Protein folding is an intricate and precise process in living cells. Most exported proteins evade cytoplasmic folding, become targeted to the membrane, and then trafficked into/across membranes. Their targeting and translocation-competent states are nonnatively folded. However, once they reach the appropriate cellular compartment, they can fold to their native states. The nonnative states of preproteins remain structurally poorly characterized since increased disorder, protein sizes, aggregation propensity, and the observation timescale are often limiting factors for typical structural approaches such as X-ray crystallography and NMR. Here, we present an alternative approach for the in vitro analysis of nonfolded translocation-competent protein states and their comparison with their native states. We make use of hydrogen/deuterium exchange coupled with mass spectrometry (HDX-MS), a method based on differentiated isotope exchange rates in structured vs unstructured protein states/regions, and highly dynamic vs more rigid regions. We present a complete structural characterization pipeline, starting from the preparation of the polypeptides to data analysis and interpretation. Proteolysis and mass spectrometric conditions for the analysis of the labeled proteins are discussed, followed by the analysis and interpretation of HDX-MS data. We highlight the suitability of HDX-MS for identifying short structured regions within otherwise highly flexible protein states, as illustrated by an exported protein example, experimentally tested in our lab. Finally, we discuss statistical analysis in comparative HDX-MS. The protocol is applicable to any protein and protein size, exhibiting slow or fast loss of translocation competence. It could be easily adapted to more complex assemblies, such as the interaction of chaperones with nonnative protein states.status: publishe

Probing the Conformational Dynamics of Affinity-Enhanced T Cell Receptor Variants upon Binding the Peptide-Bound Major Histocompatibility Complex by Hydrogen/Deuterium Exchange Mass Spectrometry.

Binding of the T cell receptor (TCR) to its cognate, peptide antigen-loaded major histocompatibility complex (pMHC) is a key interaction for triggering T cell activation and ultimately elimination of the target cell. Despite the importance of this interaction for cellular immunity, a comprehensive molecular understanding of TCR specificity and affinity is lacking. We conducted hydrogen/deuterium exchange mass spectrometry (HDX-MS) analyses of individual affinity-enhanced TCR variants and clinically relevant pMHC class I molecules (HLA-A*0201/NY-ESO-1 <sub>157-165</sub> ) to investigate the causality between increased binding affinity and conformational dynamics in TCR-pMHC complexes. Differential HDX-MS analyses of TCR variants revealed that mutations for affinity enhancement in TCR CDRs altered the conformational response of TCR to pMHC ligation. Improved pMHC binding affinity was in general observed to correlate with greater differences in HDX upon pMHC binding in modified TCR CDR loops, thereby providing new insights into the TCR-pMHC interaction. Furthermore, a specific point mutation in the β-CDR3 loop of the NY-ESO-1 TCR associated with a substantial increase in binding affinity resulted in a substantial change in pMHC binding kinetics (i.e., very slow k <sub>on</sub> , revealed by the detection of EX1 HDX kinetics), thus providing experimental evidence for a slow induced-fit binding mode. We also examined the conformational impact of pMHC binding on an unrelated TRAV12-2 gene-encoded TCR directed against the immunodominant MART-1 <sub>26-35</sub> cancer antigen restricted by HLA-A*0201. Our findings provide a molecular basis for the observed TRAV12-2 gene bias in natural CD8 <sup>+</sup> T cell-based immune responses against the MART-1 antigen, with potential implications for general ligand discrimination and TCR cross-reactivity processes