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Biomedical subjects

H Kubinyi

Publications and source records attributed to H Kubinyi.

At least 19 recordsLinked to original sources
PubMed1979

Lipophilicity and biological acitivity. Drug transport and drug distribution in model systems and in biological systems.

Different equilibrium and non-equilibrium models are used to simulate drug transport and drug distribution. The percentage of absorbed drug, the rate constants of drug absorption and the drug concentrations in the different compartments of the models can be described quantitatively by the bilinear model, e.g., log ci = a log P-b log (betaP + 1) + c. A nearly perfect fit is obtained for the simulated data from this model. Drug absorption and distribution in biological systems can be explained and described by the model-derived equations. Examples from the literature include buccal absorption, gastric and intestinal in situ and in vitro absorption, colonic absorption, renal clearance, and absorption through the skin and the blood-brain barrier; in all those cases the bilinear model gives an excellent fit of the experimental data. Combination of the pH-partition theory with the bilinear model leads to a simple quantitative model for the precise description of the relationships between lipophilicity, degree of ionization, and absorption, distribution and biological activity of drugs.

Absorption↗
PubMed1979

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

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.

Acids↗
PubMed1978

Drug partitioning: relationships between forward and reverse rate constants and partition coefficient.

The rate constant, k1, of drug transport from an aqueous phase to an organic phase and the rate constant, k2, of the reverse process can be described as functions of the partition coefficient, P:logk1 = log P-log (betaP + 1) + c' and logk2 = -log (betaP + 1) + c'. In a homologous series, where log P is a simple function of the number of CH2 groups, log k1 and log k2 also can be described as functions of the number of CH2 groups. The relationships between these equations and current physicochemical models of drug absorption are discussed.

Kinetics↗
PubMed1978

Quantitative structure-activity relationships. VI. Non-linear dependence of biological activity on hydrophobic character: calculation procedures for bilinear model.

The bilinear model, log 1/C = a log P--b log (betaP + 1) + c, is a new model for the qunatitative description of non-linear relationships between hydrophobic character and biological activity. In contrast to the parabolic Hansch model the bilinear model considers the particular effect that a linear relationship exists between lipophilicity and biological activity up to a point where this linear relationship breaks down to a non-linear relationship. Two different calculation procedures for the bilinear mode, a stepwise iteration method and the Taylor series iteration method, are explained and demonstrated with examples. The bilinear model and the parabolic Hansch model are compared by means of the statistical parameters r, s and F, by a partial F test and by an analysis of the residuals obtained with both models.

Mathematics↗
PubMed1977

Quantitative structure--activity relationships. 7. The bilinear model, a new model for nonlinear dependence of biological activity on hydrophobic character.

The bilinear model, log 1/C =a log P-b log (betaP+1) +C, a new model for nonlinear dependence of biological activity on hydrophobic character, is applied to 57 data sets of biological activity values in homologous series. From a comparison of the statistical parameters and the residuals obtained with the bilinear model and the parabolic model, the superiority of the bilinear model for a precise quantitative description of both linear and nonlinear parts of sturcture-activity relationships can be derived; the bilinear model explains the particular effect that in homologous series the relationship between biological activity and hydrophobic character is strictly linear for the lower members, while for higher members this relationship is nonlinear.

Animals↗
PubMed1977

Quantitative structure-activity relationships. V. A simple simple algorithm for Fujita-Ban and Free-Wilson analyses.

For quantitative structure-activity analyses a simple algorithm for the calculation of de novo group contributions by Fujita-Ban analysis is given. This algorithm corresponds in all details to a computer program for linear multiple regression analysis. However, the transformation of the original matrix to the normal equations matrix is easily achieved without a computer. The normal equations matrix can be solved with a modern desk calculator being equipped with a matrix ROM. Two examples are given to explain the algorithm; the calculation of all important statistical parameters is illustrated. As for quantitative structure-activity analyses this algorithm can be applied as well for the calculation of other additive parameters, such as pi from log P-values or omega from equilibrium constants.

Electronic Data Processing↗
PubMed1976

Quantitative structure-activity relationships. 1. The modified Free-Wilson approach.

The relationships between the linear free energy related Hansch model and the mathematical models of Free-Wilson and Bocek-Kopecký are reviewed and discuss. Some examples are given to illustrate the theoretically derived relationships and to demonstrate scope and limitations of each mathematical model. The modified Free-Wilson approach is shown to be completely equivalent to a nonparabolic Hansch approach; it can be used to study additivity or nonadditivity of group contributions and to control and improve the fitting of Hansch equations. The Bocek-Kopecký approach is related to the parabolic form of the Hansch approach; its practial use is limited by the great number of variables involved.

Animals↗
PubMed1976

Quantitative structure-activity relationships. 2. A mixed approach, based on Hansch and Free-Wilson Analysis.

Based on the theoretical and numerical equivalence of Hansch's linear multiple regression model and the modified Free-Wilson model a mixed approach is developed. The mixed approach is a combination of both models which makes use of the advantages of each model and widens the applicability of Hansch and Free-Wilson analysis. The Free-Wilson approach now is applicable also in the case of parabolic dependence of biological activity on a particular physical property, e.g., log P or pi. A rational explanation is given for the use of dummy variables in Hansch equations and the derivation of Hansch correlations for de novo group contributions obtained from Free-Wilson analysis. Some examples illustrate the mixed approach and demonstrate its usefulness to establish biologically meaningful structure-activity relationships.

Animals↗
PubMed1976

Quantitative structure-activity relationships. 3.1 A comparison of different Free-Wilson models.

The Fujita-Ban model and the classical Free-Wilson model are shown to be linearly related: the de novo group contributions obtained by one model are linear transformations of those obtained by the other model. An example is given to illustrate this linear dependence. The Fujita-Ban model is characterized by a number of advantages as compared with the classical Free-Wilson model: no transformation of the structural matrix and no symmetry equations are necessary; all group contributions are based on an arbitrarily chosen reference compound, preferably the unsubstituted compound; the constant term, which is the theoretically predicted activity value of the reference compound, and the values of the group contributions are not markedly influenced by addition or elimination of a compound; the problem of linear dependence (the singularity problem) sometimes can be circumvented by preparation of a contracted matrix; if the unsubstituted compound is chosen as reference compound, the group contributions are numerically equivalent to Hansch-derived group contributions; therefore, the Hansch approach and the Fujita-Ban model can be combined to a mixed approach. Taking all these facts into consideration, the Frujita-Ban model is recommended as the most suitable approach for the calculation of de novo group contributions.

Mathematics↗
PubMed1976

Quantitative structure-activity relationships. IV. Non-linear dependence of biological activity on hydrophobic character: a new model.

A new model is derived for the dependence of biological activity on hydrophobic character from a simple hypothetical system. Unlike the parabolic Hansch model this model can explain the peculiar effect that for homologous series of compounds the logarithms of biological activities of the lower homologs are linearly dependent on hydrophobic character, while for the higher homologs the relationship between biological activities and hydrophobic character changes to a parabola. Although these relationships are known and several appropriate models were proposed, the bilinear model presented in this paper is the first which can be described by a simple and generally valid equation: log 1/C = a log P--b log (beta - P + 1) + c While the parameters a, b and c can be calculated by linear multiple regression analysis, the non-linear term beta must be derived by a stepwise iteration process or ty Taylor series iteration. Examples are given for comparison of the bilinear model and the parabolic Hansch model.

Biological Transport↗