PLS analysis of distance matrices to detect nonlinear relationships between biological potency and molecular properties.

Although the statistical method of partial least squares (PLS) is widely used for the analysis of the relationship between molecular properties and biological potency, it is recognized that PLS detects only linear relationships. We tested two types of properties: simulated univariate data and electrostatic molecular field as a function of Hammett sigma constants. In both cases we compared relationships in which the function is linear, asymptotic, or rises to an optimum and then falls. We found that PLS analysis of the matrix of the distances between every pair of compounds detects all three types of relationships with the same quality of cross-validation. The successful application of the method requires that the distance matrices be constructed such that each contains only information about one property (for example, the electrostatic field around the functional group of interest). Carbo and Hodgkin similarities perform less well than distances.