No abstract

Use of the "jackknife" as a statistical tool for construction of both point and confidence interval estimators for parameters which are functions of regression coefficients and/or iteratively estimated parameters is described. Examples are presented demonstrating its utility in constructing estimators for log P0 and pi 0 using the parabolic and bilinear quantitative structure-activity relationship (QSAR) models relating nonlinear dependence of activity on hydrophobicity and for log [1/Ki(app)] assuming competitive enzyme inhibition.

The inhibition of dihydrofolate reductase from chicken liver and from Lactobacillus casei has been studied with 4,6-diamino-1,2-dihydro-2,2-dimethyl-1-(substituted-phenyl)-s-triazines. It was found that for the chicken enzyme, inhibitor potency for 101 triazines was correlated by the following equation: log 1/Kiapp = 0.85 sigma tau' - 1.04 log (beta X 10 sigma tau' + 1) + 0.57 sigma + 6.36. The parameter tau' indicates that for certain substituents, tau = 0. In the case of the L. casei DHFR results, meta and para derivatives could not be included in the same equation. For 38 meta-substituted compounds, it was found that log 1/Kiapp = 0.38 tau'3-0.91 log (beta X 10 tau'3 + 1) + 0.71I + 4.60 and for 32 para-substituted phenyltriazines log 1/Kiapp = 0.44 tau'4-0.65 log (beta tau'4 + 1') - 0.90 upsilon + 0.69I + 4.67. In the L. casei equation, I is an indicator variable for substituents of the type CH2ZC6H4-Y and ZCH2C6H4-Y, where Z = O, NH, S, or Se. The parameter upsilon is Charton's steric parameter, which is similar to Taft's Es. The mathematical models obtained from correlation analysis are compared with stereo color graphics models.

A quantitative structure-activity relationship (QSAR) has been formulated for the inhibition of purified E. coli dihydrofolate reductase by 23 5-(substituted benzyl)-2,4-diaminopyrimidines: log 1/C = 1.14MR'3,4,5 + 5.73; r = 0.887; s = 0.285. In this expression, MR'3,4,5 refers to the sum of MR values for X in the 3, 4 and 5 positions of the phenyl moiety. MR' signifies that the effective value of MR is limited to 0.79. Comparison of the QSAR for E. coli enzyme inhibition with that previously obtained for bovine enzyme offers the first general explanation for the great selectivity of the important antibacterial agent trimethoprim. Such QSSR promise to be of value in devising more selective drugs.

Theoretical electronic structure calculations on the thyroid hormones and analogues, as well as model hormone--receptor interactions, have been carried out. These studies (a) support the concept that the 4'-OH group is a H-bond donor to the in vivo nuclear receptor and suggest that at the receptor this OH group is trans to the 3' (distal) substituent; (b) indicate that there is an important intramolecular interaction between 3' and 4' substituents, and those 3' substituents that most favor both 4' OH orientation trans to the 3' group and a more acidic OH group substantially increase binding and biological activity; and (c) support the concept that there is a direct correlation between the conformational free energy of the aromatic rings and biological activity.