Four-component pharmacophore model for endomorphins toward µ opioid receptor subtypes.

In the present work, a series of simulation tools were used to determine structure-activity relationships for the endomorphins (EMs) and derive µ-pharmacophore models for these peptides. Potential lowest energy conformations were determined in vacuo by systematically varying the torsional angles of the Tyr(1)-Pro(2) (ω(1)) and Pro(2)-Trp(3)/Phe(3) (ω(2)) as tuning parameters in AM1 calculations. These initial models were then exposed to aqueous conditions via molecular dynamics simulations. In aqueous solution, the simulations suggest that endomorphin conformers strongly favor the trans/trans pair of the ω(1)/ω(2) amide bonds. From two-dimensional probability distributions of the ring-to-ring distances with respect to the pharmacophoric angles for EMs, a selectivity range of µ(1) is ca. 8.3 ~ 10.5 Å for endomorphin-2 and selectivity range of µ(2) is ca. 10.5 ~ 13.0 Å for endomorphin-1 were determined. Four-component µ-pharmacophore models are proposed for EMs and are compared to the previously published δ- and κ-pharmacophore models.

On the use of hollow tube geometries for resonant ultrasound spectroscopy.

Resonant ultrasound spectroscopy (RUS) can nondestructively obtain the elastic constants of compact specimens, however many materials have hollow cross-sections and frequency analysis of such geometries is required before inclusion in the RUS methodology. Resonant mode shapes of tubes with length equal to diameter and varying ratios of tube inner to outer diameter (Λ) as well as Poisson's ratio (ν) were identified by eigenvalue analysis using a commercial finite element code. Longitudinal and shear RUS experiments were conducted on tubes with Λ varying between 0 and 0.95 and compared to the numerical results. Simulations predict that the fundamental mode transitions from pure torsion to symmetric or antisymmetric ring bending at Λ = 0.3. The frequency of the first torsion mode is invariant to Λ and unequivocal identification of this mode is obscured by overlap of bending harmonics as Λ approaches 0.95. In the context of rapid calculation of isotropic elastic constants, shear moduli were calculated from the first torsional mode and Poisson's ratio was inferred from the Demarest maps of the mode structure's dependence upon Poisson's ratio. An average shear modulus of 27.5 + 1.5 ∕ -0.6 GPa, about 5% larger than literature values for 6061 aluminum, and ν of 0.33 were inferred. Errors are attributed to tube aspect ratios slightly greater than 1 and weak material anisotropy. Existing analytical solutions for ring bending modes derived from shell approximations and for infinitely long tubes under plane strain assumptions do not adequately describe the fundamental modes for short tubes. The shear modulus can be calculated for all Λ using the existing analytical solution.

Resonant ultrasound spectroscopy of cylinders over the full range of Poisson's ratio.

Mode structure maps for freely vibrating cylinders over a range of Poisson's ratio, ν, are desirable for the design and interpretation of experiments using resonant ultrasound spectroscopy (RUS). The full range of isotropic ν (-1 to +0.5) is analyzed here using a finite element method to accommodate materials with a negative Poisson's ratio. The fundamental torsional mode has the lowest frequency provided ν is between about -0.24 and +0.5. For any ν, the torsional mode can be identified utilizing the polarization sensitivity of the shear transducers. RUS experimental results for materials with Poisson's ratio +0.3, +0.16, and -0.3 and a previous numerical study for ν = 0.33 are compared with the present analysis. Interpretation of results is easiest if the length∕diameter ratio of the cylinder is close to 1. Slight material anisotropy leads to splitting of the higher modes but not of the fundamental torsion mode.