Analysis of molecular determinants of affinity and relative efficacy of a series of R- and S-2-(dipropylamino)tetralins at the 5-HT1A serotonin receptor

1 Factors influencing agonist affinity and relative efficacy have been studied for the 5-HT1A serotonin receptor using membranes of CHO cells expressing the human form of the receptor and a series of R-and S-2-(dipropylamino)tetralins (nonhydroxylated and monohydroxylated (5-OH, 6-OH, 7-OH, 8-OH) species). 2 Ligand binding studies were used to determine dissociation constants for agonist binding to the 5HT(1A) receptor: (a) K-i values for agonists were determined in competition versus the binding of the agonist [H-3]-8-OH DPAT. Competition data were all fitted best by a one-binding site model. (b) K-i values for agonists were also determined in competition versus the binding of the antagonist [H-3]-NAD-199. Competition data were all fitted best by a two-binding site model, and agonist affinities for the higher (K-h) and lower affinity (K-1) sites were determined. 3 The ability of the agonists to activate the 5-HT1A receptor was determined using stimulation of [S-35]-GTPgammaS binding. Maximal effects of agonists (E-max) and their potencies (EC50) were determined from concentration/response curves for stimulation of [S-35]-GTPgammaS binding. 4 K-1/K-h determined from ligand binding assays correlated with the relative efficacy (relative Em) of agonists determined in [S-35]-GTPgammaS binding assays. There was also a correlation between K-1/K-h and K-1/EC50 for agonists determined from ligand binding and [S-35]-GTPgammaS binding assays. 5 Simulations of agonist binding and effect data were performed using the Ternary Complex Model in order to assess the use of K-1/K-h for predicting the relative efficacy of agonists. British Journal of Pharmacology (2003) 138, 1129-1139. doi: 10. 1038/sj.bjp.705085.

Agonist binding, agonist affinity and agonist efficacy at G protein-coupled receptors

Measurements of affinity and efficacy are fundamental for work on agonists both in drug discovery and in basic studies on receptors. In this review I wish to consider methods for measuring affinity and efficacy at G protein coupled receptors (GPCRs). Agonist affinity may be estimated in terms of the dissociation constant for agonist binding to a receptor using ligand binding or functional assays. It has, however, been suggested that measurements of affinity are always contaminated by efficacy so that it is impossible to separate the two parameters. Here I show that for many GPCRs, if receptor/G protein coupling is suppressed, experimental measurements of agonist affinity using ligand binding (K-obs) provide quite accurate measures of the agonist microscopic dissociation constant (K-A). Also in pharmacological functional studies, good estimates of agonist dissociation constants are possible. Efficacy can be quantitated in several ways based on functional data ( maximal effect of the agonist (E-max), ratio of agonist dissociation constant to concentration of agonist giving half maximal effect in functional assay ( K-obs/ EC50), a combined parameter EmaxKobs/EC50). Here I show that EmaxKobs/EC50 provides the best assessment of efficacy for a range of agonists across the full range of efficacy for full to partial agonists. Considerable evidence now suggests that ligand efficacy may be dependent on the pathway used to assess it. The efficacy of a ligand may, therefore, be multidimensional. It is still, however, necessary to have accurate measures of efficacy in different pathways.

Analytical potentials for triatomic molecules IX. The prediction of anharmonic force constants from potential energy surfaces based on harmonic force fields and dissociation energies for SO2 and O3

Analytical potential energy functions which are valid at all dissociation limits have been derived for the ground states of SO2 and O3. The procedure involves minimizing the errors between the observed vibrational spectra and spectra calculated by a variational procedure. Good agreement is obtained between the observed and calculated spectra for both molecules. Comparisons are made between anharmonic force fields, previously determined from the spectral data, and the force fields obtained by differentiating the derived analytical functions at the equilibrium configurations.

On defining base units in terms of fundamental constants

The definitions of the base units of the international system of units have been revised many times since the idea of such an international system was first conceived at the time of the French revolution. The objective today is to define all our units in terms of 'invariants of nature', i.e. by referencing our units to the fundamental constants of physics, or the properties of atoms, rather than the characteristics of our planet or of artefacts. This situation is reviewed, particularly in regard to finding a new definition of the kilogram to replace its present definition in terms of a prototype material artefact.

Force constants and dipole‐moment derivatives of molecules from perturbed Hartree–Fock calculations

General expressions for the force constants and dipole‐moment derivatives of molecules are derived, and the problems arising in their practical application are reviewed. Great emphasis is placed on the use of the Hartree–Fock function as an approximate wavefunction, and a number of its properties are discussed and re‐emphasised. The main content of this paper is the development of a perturbed Hartree–Fock theory that makes possible the direct calculation of force constants and dipole‐moment derivatives from SCF–MO wavefunctions. Essentially the theory yields ∂ϕi / ∂RJα, the derivative of an MO with respect to a nuclear coordinate.

The calculation of force constants and normal coordinates IV: XH4 and XH3 molecules

Normal coordinate calculations of XH4 and XH3 molecules are reviewed and discussed. It is shown that for most of these molecules the true values of the force constants in the most General Harmonic Force Field can be uniquely determined only by making use of vibration-rotation interaction constants. It is emphasized that without these extra data the GFF is not determined. The results are compared with various model force fields for these molecules.

Microwave spectra and centrifugal distortion constants of oxetane

The microwave spectra of oxetane (trimethylene oxide) and its three symmetrically deuterated isotopic species have been observed on a Hewlett-Packard microwave spectrometer from 26.5 to 40 GHz. For the parent species, the β-d2 and the αα′-d4 species, about 300 lines have been assigned for each molecule, and for the d6 species more than 600 lines have been assigned. The assignments range from v = 0 to v = 5 in the puckering vibration; although they are mostly Q transitions, either 3 or 4 R transitions have been observed for each vibrational state. The spectra have been interpreted using an effective rotational hamiltonian for each vibrational state, including five quartic distortion constants according to Watson's formulation, and a variable number of sextic distortion constants; in general, the lines are fitted to about ± 10 kHz. The distortion constants show an anomalous zig-zag dependence on the puckering vibrational quantum number, similar to that first observed for the rotational constants by Gwinn and coworkers. This is interpreted according to a simple modification of the standard theory of centrifugal distortion, involving the double minimum potential function in the puckering coordinate.

Force constants and dipole moment derivatives of molecules from perturbed Hartree-Fock calculations II. Applications to limited basis set SCF-MO wavefunctions

The perturbed Hartree–Fock theory developed in the preceding paper is applied to LiH, BH, and HF, using limited basis‐set SCF–MO wavefunctions derived by previous workers. The calculated values for the force constant ke and the dipole‐moment derivative μ(1) are (experimental values in parentheses): LiH, ke  =  1.618(1.026)mdyn/Å,μ(1)  =  −18.77(−2.0±0.3)D/ÅBH,ke  =  5.199(3.032)mdyn/Å,μ(1)  =  −1.03(−)D/Å;HF,ke  =  12.90(9.651)mdyn/Å,μ(1)  =  −2.15(+1.50)D/Å. The values of the force on the proton were calculated exactly and according to the Hellmann–Feynman theorem in each case, and the discrepancies show that none of the wavefunctions used are close to the Hartree–Fock limit, so that the large errors in ke and μ(1) are not surprising. However no difficulties arose in the perturbed Hartree–Fock calculation, so that the application of the theory to more accurate wavefunctions appears quite feasible.

The calculation of force constants and normal co-ordinates II: methyl fluoride

The mathematical difficulties which can arise in the force constant refinement procedure for calculating force constants and normal co-ordinates are described and discussed. The method has been applied to the methyl fluoride molecule, using an electronic computer. The best values of the twelve force constants in the most general harmonic potential field were obtained to fit twenty-two independently observed experimental data, these being the six vibration frequencies, three Coriolis zeta constants and two centrifugal stretching constants DJ and DJK, for both CH3F and CD3F. The calculations have been repeated both with and without anharmonicity corrections to the vibration frequencies. All the experimental data were weighted according to the reliability of the observations, and the corresponding standard errors and correlation coefficients of the force constants have been deduced. The final force constants are discussed briefly, and compared with previous treatments, particularly with a recent Urey-Bradley treatment for this molecule.

The two-dimensional anharmonic oscillator I: vibration-rotation constants of fulminic acid, HCNO

The lowest-wavenumber vibration of HCNO and DCNO, ν5, is known to involve a largeamplitude low-frequency anharmonic bending of the CH bond against the CNO frame. In this paper the anomalous vibrational dependence of the observed rotational constants B(v5, l5), and of the observed l-doubling interactions, is interpreted according to a simple effective vibration-rotation Hamiltonian in which the appropriate vibrational operators are averaged in an anharmonic potential surface over the normal coordinates (Q5x, Q5y). All of the data on both isotopes are interpreted according to a single potential surface having a minimum energy at a slightly bent configuration of the HCN angle ( 170°) with a maximum at the linear configuration about 2 cm−1 higher. The other coefficients in the Hamiltonian are also interpreted in terms of the structure and the harmonic and anharmonic force fields; the substitution structure at the “hypothetical linear configuration” determined in this way gives a CH bond length of 1.060 Å, in contrast to the value 1.027 Å determined from the ground-state rotational constants. We also discuss the difficulties in rationalizing our effective Hamiltonian in terms of more fundamental theory, as well as the success and limitations of its use in practice.

The calculation of force constants and normal coordinates III: constrained force fields for the methyl halides

A method is discussed for imposing any desired constraint on the force field obtained in a force constant refinement calculation. The application of this method to force constant refinement calculations for the methyl halide molecules is reported. All available data on the vibration frequencies, Coriolis interaction constants and centrifugal stretching constants of CH3X and CD3X molecules were used in the refinements, but despite this apparent abundance of data it was found that constraints were necessary in order to obtain a unique solution to the force field. The results of unconstrained calculations, and of three different constrained calculations, are reported in this paper. The constrained models reported are a Urey—Bradley force field, a modified valence force field, and a constraint based on orbital-following bond-hybridization arguments developed in the following paper. The results are discussed, and compared with previous results for these molecules. The third of the above models is found to reproduce the observed data better than either of the first two, and additional reasons are given for preferring this solution to the force field for the methyl halide molecules.

Analytical functions for the ground state potential surfaces of C3 (X 1 Σ g+) and HCN (X 1 Σ +)

Analytic functions have been obtained to represent the potential energy surfaces of C3 and HCN in their ground electronic states. These functions closely reproduce the available data on the energy, geometry, and force constants in all stable conformations, as well as data on the various dissociation products, and ab initio calculations of the energy at other conformations. The form of the resulting surfaces are portrayed in various ways and discussed briefly.

Signs of l-doubling constants in NF3

Computed infrared band contours are presented for the two degenerate fundamentals of the NF3 molecule, using the l-resonance band contour program described by Cartwright and Mills, with values of the vibration-rotation constants determined from the microwave spectrum by Morino and co-workers. Computed contours are presented for both possible signs of the l-doubling constant, and comparison with the observed band contours leads to the conclusion that q3 = −121.4 MHz and q4 = +51.4 MHz.

The calculation of force constants and normal co-ordinates--VII Normal co-ordinates in the E species of allene

Force constant and normal co-ordinate calculations are reported for the E species vibrations of the allene molecule. Data on the fundamental vibration frequencies of allene-h4, allene-d4 and allene-1.1-d2 and on the five experimentally determined Coriolis zeta constants of C3H4 and C3D4, were used in a force constant refinement procedure. Allowing for product and sum rules this gives 21 independent data which were used to refine to the most general harmonic force field (10 parameters) with one constraint (in the absence of any constraints the refinement was not satisfactory). The results have been used to calculate the complete ζz Coriolis interaction matrix for the allene-1.1-d2 molecule, and hence to calculate the expected rotational structure of the perpendicular bending vibrations of this molecule; the good agreement obtained with the observed spectra is a check on our results.