Geometry of circular vectors and pattern recognition of shape of a boundary

This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.

Involvement of Asn-293 in stereospecific agonist recognition and in activation of the beta 2-adrenergic receptor.

To investigate the molecular mechanism for stereospecific binding of agonists to beta 2-adrenergic receptors we used receptor models to identify potential binding sites for the beta-OH-group of the ligand, which defines the chiral center. Ser-165, located in transmembrane helix IV, and Asn-293, situated in the upper half of transmembrane helix VI, were identified as potential binding sites. Mutation of Ser-165 to Ala did not change the binding of either isoproterenol isomer as revealed after transient expression in human embryonic kidney (HEK)-293 cells. In contrast, a receptor mutant in which Asn-293 was replaced by Leu showed substantial loss of stereospecific isoproterenol binding. Adenylyl cyclase stimulation by this mutant after stable expression in CHO cells confirmed the substantial loss of stereospecificity for isoproterenol. In a series of agonists the loss of affinity in the Leu-293 mutant receptor was strongly correlated with the intrinsic activity of the compounds. Full agonists showed a 10-30-fold affinity loss, whereas partial agonists had almost the same affinity for both receptors. Stereospecific recognition of antagonists was unaltered in the Leu-293 mutant receptor. These data indicate a relationship between stereospecificity and intrinsic activity of agonists and suggest that Asn-293 is important for both properties of the agonist-receptor interaction.