Nonlinear dependence of biological activity on hydrophobic character: the bilinear model

Abstract

In homologous series of compounds biological activity is linearly dependent on hydrophobic character until a cut-off point is reached where this linear relationship changes to a nonlinear relationship: biological activity increases with increase of hydrophobic character, reaches a maximum and then decreases with further increase of hydrophobic character. Drug transport in biological systems is determined by the rate constants of transfer of the drug through aqueous and organic compartments. In simple in vitro systems the rate constant k1 of transport of a drug from an aqueous phase into an organic phase and the rate constant k2 of the reverse process can be described as functions of the partition coefficient P: log k1 = log P - log (beta P + 1) + c and log k2 = - log (beta P + 1) + c. Observed and calculated k1 and k2 values are used to simulate drug transport in different multicompartment systems. Based on the McFarland probability model a new model for the quantitative description of the dependence of biological activity on hydrophobic character, called bilinear model, log 1/C = a log P - b log (beta P + 1) + C, has been derived recently: unsymmetrical curves with linear ascending and descending sides and a parabolic part within the range of optimal lipophilicity result from this model. The bilinear model is applied to experimental data of drug absorption, drug distribution and drug activity in biological systems. A comparison of the parabolic model and the bilinear model shows that in nearly all cases a better fit of the data results from the bilinear model.