QSAR - Hansch and Free Wilson Analyses

1 Hugo Kubinyi, - Hansch and free WilsonAnalysesHugo KubinyiGermanyE-Mail Kubinyi, GanellinProfessor ofMedicinal ChemistryUniversity College,London, UKS. L. Carney (DDT 9, 158-160 (2004)):Has there been a single development that, in your opinion, has moved the field of medicinal chemistry ahead more than any other?Robert Ganellin:I would go back to the 1960s to the work of Corwin Hansch on the impor-tance of lipophilicity.. I think that changed the way of thinking in medi-cinal chemistry.. I think that the application of physical organic chemical approaches to structure activity analysis have been very important. Hugo Kubinyi, XYBrNCH3CH3x HClmetaparalog 1/Cmetaparalog 1 Activities of meta-, para-, and meta,para- Disubstituted N,N-Dimethyl- -bromophenethylaminesHugo Kubinyi, (X)para(Y)log 1/Cobsd.

2 +Esmetalog 1 1 forHanschAnalysisXYBrNCH3CH3x HClHugo Kubinyi, forFree Wilson Analysismeta paralog 1/C meta- para-log 1/C(X) (Y) obs. FClBr IMeFClBr HClHugo Kubinyi, Wilson Analysis, Results: = (n = 22; r = ; s = ) Hansch Analyses , Results:C. Hansch and E. J. Lien, Biochem. Pharmacol. 17, 709 (1968)log 1/C = - + (n = 22; r = ; s = )A. Cammarata, J. Med. Chem. 15, 573 (1972)log 1/C = ( ) m - ( ) m + ( ) rvpara + (n = 22; r = ; s = ) Kubinyi, Equationslog 1/C = ( ) - ( ) + + ( )(n = 22; r = ; s = ; F = )log 1/C = ( ) - ( ) + + ( ) Esmeta + ( )(n = 22; r = ; s = ; F = ) free Wilson Equationlog 1/C = - ( ) [m-F] + ( ) [m-Cl] + ( ) [m-Br] + ( ) [m-I] + ( ) [m-Me] + ( ) [p-F] + ( ) [p-Cl] + ( ) [p-Br] + ( ) [p-I] + ( ) [p-Me] + ( )(n = 22; r = ; s = ; F = )Hugo Kubinyi, AnalysisMathematically exact procedure for the treatment of data with experimental errors (cf.)

3 Mean value, standard devation). Minimization of the sum of squared errors (= squared deviations between yi and ycalc) produces the best fit of the observed values to a certain analysis describes the relationship between:- independent variables xi (definition: can be determined without experimental error), and- dependent variables yi (contain experimental error).Hypothesis: there is a significant relationship (95% level) between xi and yi values: yes / noF test for overall significancet tests for individual significances in multiple Kubinyi, and Meaning of Statistical ParametersCorrelation coefficient r (relative quality of fit)r2 = 1 - 2/Syy Standard deviation s (absolute quality of fit)s2 = 2/(n - k - 1) F test (Fisher value; level of statistical significance)F = r2.

4 (n - k - 1)/(k.(1 - r2))Confidence intervals of ki ciiHugo Kubinyi, Log 1/C = ( ) - ( ) + + ( ) (n = 22; r = ; s = ; F = ; Q = ; sPRESS = )C = molar concentration values of the 95% confidence intervalsthat causes a certain regression of the coefficients andbiological effect coefficients the constant termnumber ofcompoundscorrelation coefficient r; measure of the relative quality of a model Fisher value;measure of thestatistical significancelogarithms ofreciprocal values are lipophilicity electronic the correct scaling parameter parameter constanttermstandard deviation of crossvalidationpredictions andsquared crossvalidationregression coefficient;both are measures ofinternal predictivity standard deviation s; measure of the absolute quality of a modelHugo Kubinyi, YX} y95% confidence intervals of the regression line95% confidende intervals for a new observationregression lineRegression Analysis - A Common QSAR Toolhomogeneousdata ?

5 This is notan outlier !beware ofextrapolationcausalrelationship?Hugo Kubinyi, Sies, Nature 332, 495 (1988)The Storks and the BabiesHugo Kubinyi, = - = = = = = Important is a Graphical Analysis of the Data !Hugo Kubinyi, Diagram Tells You More Than Thousand EquationsAnil K. Saxena, Quant. Relat. 14, 142-150 (1995)183 Hydrocarbons, Alcohols, Ethers, Esters, Carboxylic Acids, Amines and Ketones MR vs. 1 r = ; s = ; F = MR vs. 2 vr = ; s = ; F = log P vs. 1 r = ; s = ; F = log P vs. 2 vr = ; s = ; F = P = ( ) 1 - ( ) I + ( )(n = 183; r = ; s = ; F = 4,633)Hugo Kubinyi, P and In = 183r = = = 4,633 HydrocarbonsAlcohols, Ethers, Esters,Carboxylic Acids, Aminesand KetonesHugo Kubinyi, Activity of Homologous Aliphatic Aminesvs.

6 Rhinocladium beurmanni(E. J. Lien and P. H. Wang, J. Pharm. Sci. 69, 648-650 (1980))Parabolic Model, log Pr = ; s = ; F = Model and log MW termr = ; s = ; F = 1/C = log P - log ( + 1)- (n = 15; r = ; s = ; F = 7,401)Hugo Kubinyi, unicorns, beasts that exist on paper but not in reality (C. Hansch , 1973):sinus functionshyperbolic functionstangens functions(for references cf. H. Kubinyi, QSAR: Hansch Analysis and Related Approaches, VCH, Weinheim, 1993) Antitumor Activity of Glutamic Acid AmidesT. Jha et al., Ind. J. Chem. 25B, 169-174 (1986)log % ITW = (log P)2 log P 2 Ali - Ali + Es Ali i + (n = 8; r =.)

7 S = )R1SO2 NHCONHR2 HOOCHugo Kubinyi, fish 96-h LC50 (moles/L) = log Kow - , R2= <6, MW<1000log fish 96-h LC50 (millimoles/L) = - log Kow (CLOGP)n=2, R2= <6, MW<1000log fish 96-h LC50 (millimoles/L) = - log Kow (SRC)n=2, R2= <6, MW<1000log daphnid ChV (millimoles/L) = - log Kow (CLOGP)n=2, R2= <8, MW<1000log algal ChV (millimoles/L) = - log Kow (CLOGP)n=2, R2= <8, MW<1000log fish 96-h LC50 (mmoles/L) = + log Kow (CLOGP)n=3, R2= <6, MW<1000 Hugo Kubinyi, of Glycine Ester Amides to PapainC. Hansch and D. F. Calef, J. Org. Chem. 41, 1240 (1976)C. Hansch et al., Arch. Biochem. Biophys. 183, 383 (1977)XHRNOOXRlog 1/Km MR Kubinyi, 1/Km MR (MR values scaled by a factor )Hugo Kubinyi, (n = 7) ( ) r = ; s = ; F = = ; s = ; F = r = ; s = ; F = ( ), MR ( )r = ; s = ; F = ( ), r = ; s = ; F = , r = ; s = ; F = 1/Km = ( ) MR + ( ) + ( )(n = 7; r = ; s = ; F = )Mesylamides (n = 13) ( ) r = ; s = ; F = = ; s = ; F = r = ; s = ; F = ( ), MRr = ; s = ; F = ( ), r = ; s = ; F = , r = ; s =.

8 F = 1/Km = ( ) MR + ( ) + ( )(n = 13; r = ; s = ; F = )RHNOOORHNOCH3SO2 OHugo Kubinyi, Compounds (n = 20)MR ( )r = ; s = ; F = ( )r = ; s = ; F = = ; s = ; F = ( ), ( )r = ; s = ; F = , Ir = ; s = ; F = , Ir = ; s = ; F = , , Ir = ; s = ; F = 1/Km = ( ) MR + ( ) - ( ) I + ( )(n = 20; r = ; s = ; F = ) log 1/Km = ( ) + (n = 16; r = ; s = )NOOONXHHugo Kubinyi, Ki = ( ) MR2 - ( ) log ( .10MR2 + 1) - ( )log = - optimum MR2 = (n = 19; r = ; s = )log Ki = ( ) MR2 - ( ) log ( .10MR2 + 1) + ( ) MR3 + ( ) *3 - ( ) I - ( )log = - optimum MR2 = (n = 53; r = ; s = )Inhibition of Chymotrypsin by ThiophosphonatesC.

9 Silipo et al., Arch. Biochem. Biophys. 194, 552 (1979)Hugo Kubinyi, and Peripheral Activities of Clonidine AnalogsP. B. M. W. M. Timmermans et al., J. Med. Chem. 24, 502-507 (1981); J. Med. Chem. 27, 495 - 503 (1984)NNNClClHHLog Papp n-octanol / buffer pH central antihypertensive activity (molar dose that causes a 25% blood pressure decrease; anesthetized rat, application)C60 peripheral hypertensive activity (molar dose that causes a60 mm blood pressure increase; pithed rat, application)IC50 1 binding affinity to 1 receptors (replacement of prazosin)IC50 2 binding affinity to 2 receptors (replacement of clonidine)Hugo Kubinyi, Activity: Blood Pressure IncreasepC60 = ( ) pIC50 2 - (n = 21; r =.)

10 S = )Central Activity: Blood Pressure DecreasepC25 = ( ) pIC50 2 + ( ) log P - ( ) log ( P + 1) - = log Popt = (n = 21; r = ; s = )Peripheral vs. Central Action on Blood PressurepC25 = ( ) pC60 + ( ) log P - ( ) log ( P + 1) - = log Popt = (n = 21; r = ; s = )Hugo Kubinyi, of Benzylpyrimidines to DHFRNNNH2NH2 XEscherichia coli DHFR log 1/Ki app = ( ) 3,4,5 - ( ) log ( .10 3,4,5 + 1) + ( ) MR 3,5 + ( ) MR 4 + = = (n = 43; r = ; s = )Lactobacillus casei DHFR log 1/Ki app = ( ) 3,4 - ( ) log ( .10 + 1) + ( ) MR 3,4 + = - optimum = (n = 42; r = ; s = )Hugo Kubinyi, Mode of Trimethoprim to E.