The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

From ab initio quantum mechanics to molecular neurobiology: A cation–π binding site in the nicotinic receptor

The nicotinic acetylcholine receptor is the prototype ligand-gated ion channel. A number of aromatic amino acids have been identified as contributing to the agonist binding site, suggesting that cation–π interactions may be involved in binding the quaternary ammonium group of the agonist, acetylcholine. Here we show a compelling correlation between: (i) ab initio quantum mechanical predictions of cation–π binding abilities and (ii) EC50 values for acetylcholine at the receptor for a series of tryptophan derivatives that were incorporated into the receptor by using the in vivo nonsense-suppression method for unnatural amino acid incorporation. Such a correlation is seen at one, and only one, of the aromatic residues—tryptophan-149 of the α subunit. This finding indicates that, on binding, the cationic, quaternary ammonium group of acetylcholine makes van der Waals contact with the indole side chain of α tryptophan-149, providing the most precise structural information to date on this receptor. Consistent with this model, a tethered quaternary ammonium group emanating from position α149 produces a constitutively active receptor.

Energetics of the interaction between water and the helical peptide group and its role in determining helix propensities

The alanine helix provides a model system for studying the energetics of interaction between water and the helical peptide group, a possible major factor in the energetics of protein folding. Helix formation is enthalpy-driven (−1.0 kcal/mol per residue). Experimental transfer data (vapor phase to aqueous) for amides give the enthalpy of interaction with water of the amide group as ≈−11.5 kcal/mol. The enthalpy of the helical peptide hydrogen bond, computed for the gas phase by quantum mechanics, is −4.9 kcal/mol. These numbers give an enthalpy deficit for helix formation of −7.6 kcal/mol. To study this problem, we calculate the electrostatic solvation free energy (ESF) of the peptide groups in the helical and β-strand conformations, by using the delphi program and parse parameter set. Experimental data show that the ESF values of amides are almost entirely enthalpic. Two key results are: in the β-strand conformation, the ESF value of an interior alanine peptide group is −7.9 kcal/mol, substantially less than that of N-methylacetamide (−12.2 kcal/mol), and the helical peptide group is solvated with an ESF of −2.5 kcal/mol. These results reduce the enthalpy deficit to −1.5 kcal/mol, and desolvation of peptide groups through partial burial in the random coil may account for the remainder. Mutant peptides in the helical conformation show ESF differences among nonpolar amino acids that are comparable to observed helix propensity differences, but the ESF differences in the random coil conformation still must be subtracted.