Nonlinear structure-activity relations

In a similar way, hydride transfer reactions in alkane/alkene transformations depend in a nonlinear fashion upon the varying concentration of acid sites. Post et al. [50] showed elegantly that the rates of these bimolecular reactions depend upon the square of the concentration of the acid sites, while the rates of the monomolecular reactions (protolytic cracking [51]) were linearly dependent on the proton concentration. This suggests that similar effects can also be expected in more complex organic transformations, where less thoroughly developed structure-activity relations exist. 

Fig. 6.11 Stereo views of the two forms of 6-XXI (FNBH), upper, tetragonal form exhibiting nonlinear optical activity lower, inactive monoclinic form, showing the presence of cen-trosymmetrically related dimers of crystallographically independent molecules. The tetragonal structure appears particularly complex because of the presence of 16 molecules in the unit cell, aU of which are shown. When viewed in stereo individual molecules, and the relationships between them, may be discerned.

Kim, K.H. (1992c). 3D Quantitative Structure-Activity Relationships Nonlinear Dependence Described Directly from 3D Structures Using a Comparative Molecular Field Analysis (CoMFA) Approach. Quant.Struct.-Act.Relat., 11, 309-317. 

Martin H) has written a perceptive analysis of the possible ways in which an ionized species may behave in various models and contribute to or be responsible for a given activity. QSAR studies that have dealt with ion-pair partitioning include a study of fibrinolytics ( ) and the effect of benzoic acids on the K ion flux in mollusk neurons ( ). Schaper (10) recently reanalyzed a large number of absorption studies to include terms for the absorption of ionized species. Because specific values were not available for log Pj, he let the relation between log Pi and log P be a parameter in a nonlinear regression analysis. In most cases he used the approximation that the difference between the two values is a constant in a given series. This same assumption was made in the earlier studies (, ) Our work suggests that the pKa of an acid can influence this differential (see below). The influence of structure on the log P of protonated bases or quaternary ammonium compounds is much more complex (11,12) and points out the desirability of being able to easily measure these values. 

PCM modeling aims to find an empirical relation (a PCM equation or model) that describes the interaction activities of the biopolymer-molecule pairs as accurate as possible. To this end, various linear and nonlinear correlation methods can be used. Nonlinear methods have hitherto been used to only a limited extent. The method of prime choice has been partial least-squares projection to latent structures (PLS), which has been found to work very satisfactorily in PCM. PCA is also an important data-preprocessing tool in PCM modeling. Modeling includes statistical model-validation techniques such as cross validation, external prediction, and variable-selection and signal-correction methods to obtain statistically valid models. (For general overviews of modeling methods see [10]). 

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