Benefits of statistical molecular design, covariance analysis, and reference models in QSAR: a case study on acetylcholinesterase

Scientific disciplines such as medicinal- and environmental chemistry, pharmacology, and toxicology deal with the questions related to the effects small organic compounds exhort on biological targets and the compounds’ physicochemical properties responsible for these effects. A common strategy in this endeavor is to establish structure–activity relationships (SARs). The aim of this work was to illustrate benefits of performing a statistical molecular design (SMD) and proper statistical analysis of the molecules’ properties before SAR and quantitative structure–activity relationship (QSAR) analysis. Our SMD followed by synthesis yielded a set of inhibitors of the enzyme acetylcholinesterase (AChE) that had very few inherent dependencies between the substructures in the molecules. If such dependencies exist, they cause severe errors in SAR interpretation and predictions by QSAR-models, and leave a set of molecules less suitable for future decision-making. In our study, SAR- and QSAR models could show which molecular sub-structures and physicochemical features that were advantageous for the AChE inhibition. Finally, the QSAR model was used for the prediction of the inhibition of AChE by an external prediction set of molecules. The accuracy of these predictions was asserted by statistical significance tests and by comparisons to simple but relevant reference models. Electronic supplementary material The online version of this article (doi:10.1007/s10822-014-9808-1) contains supplementary material, which is available to authorized users.

°C. The resulting mixture was stirred for 40 min before being evaporated to dryness under reduced pressure and used immediately as described above without purification.
General procedure 2: reaction of amines and alkyl halides. K2CO3 (2.50 equiv) was added to a solution of the relevant amine (2.50-2.60 mmol, 1.00 equiv) and alkyl halide (1.05 equiv) in acetonitrile (10 mL) and the resulting suspension was refluxed for 24 h. After being allowed to attain rt, sat. aq. NaHCO3 (5 mL) was added to the mixture, the layers were separated, and the water phase was extracted with CH2Cl2 (2×10 mL). The combined organic phases were dried (Na2SO4) and concentrated under reduced pressure. The crude residue was purified by column chromatography on silica gel (EtOAc:MeOH 5:1).

General procedure 3: removal of Boc groups.
A HCl solution (4.0 M in diethyl ether, 6 ml) was added to the relevant carbamate (0.22-0.40 mmol, 1 equiv) dissolved in EtOH (4 mL). The mixture was stirred at rt for 10 h before being made basic by addition of sat. aq. NaHCO3, and extracted with CHCl3 (3×10 mL). The combined organic layers were dried (Na2SO4) and concentrated under reduced pressure. The residue was dissolved in MeOH, adjusted to pH 5 using 10% aqueous HCl solution, and the resulting solution was purified by preparative HPLC (MeCN/water 10  60%, 20 mL/min over 30 min).

AChE inhibition assay
Recombinant Homo sapiens AChE was expressed according to previously described methods [6,7]. The enzymatic activity was measured using the Ellman assay [8]

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Statistical analysis of QSAR model and reference models The predicted pIC50 resulting of all four test sets from the QSAR model and reference models were tested for the probability that they were drawn from a normal distribution using the Anderson-Darling (AD) test [10] at a confidence limit of 95% (p=0.05) implemented in Excel [11,12]. Average and median pIC50 values were obviously not normally distributed and was excluded from the significance testing. The AD-test result are given in the table above and show that the predicted pIC50 for Set1-2 resulting from the QSAR model and reference models LogP, vdW and PLS were normally distributed. So were the predictions for Set3 from the QSAR and LogP models, but no predictions for Set4. Predicted pIC50 were compared to measured pIC50 values via a one-tailed F-test (comparing variances) and a paired students t-test (comparing means) and critical values based on prediction molecules minus one (n-1) degrees of freedom. If F < Fcrit or t < tcrit there is a no difference between the models' predictions and the measured pIC50 in terms of variance and median, respectively. The conclusion regarding pIC50 based on both F-and t-tests was that the QSAR-models' predictions was generally statistically not different from the measured pIC50 (calculated F or t smaller critical value), while the reference models were significantly different from measured pIC50 (calculated F or t was larger critical value). Non-parametric Kolmogorov-Smirnov (KS) [13,14] and Mann-Whitney (MW) U-test [15,16] tests were performed on Set3-4 (Set1 and Set2 contained too few data points), which generally had non-normally distributed predictions and the results showed that the only significant similarity was between the QSAR models' prediction and the measured pIC50 for Set3-4 and for Nearest neighbor for Set3. The reference models average and median was tested with the KS and MW tests and resulted in a p of 0.000, indicating that average and median are insufficient predictors of pIC50. S19