Time-resolved QSAR: an approach to PLS modelling of three-way biological data

This paper outlines a novel approach to the analysis of three-way Y-data in quantitative structure–activity relationship (QSAR) modelling. The new method represents a modification of an existing approach for multivariate modelling of batch process data. It is based on unfolding the three-way Y-matrix into a two-way matrix according to a sequential order of an external variable. In QSAR, time, pH, or temperature at which the biological data were gathered, are conceivably such external variables. Thus, unfolding can be done differently depending on the objective of the investigation, thereby shifting the focus of the QSAR analysis. The ensuing multivariate data analysis uses two levels of modelling. (1) On the lower (observation) level a projections to latent structures (PLS) model is developed between the unfolded biological data and the external variable. This model will identify compounds with biological data being sensitive to changes in the external variable (like time, pH, or temperature). (2) The scores of the lower level model are then re-arranged to enable the upper (QSAR) level model. In this model, a battery of structure descriptors (X) is related to the Y-matrix of scores of the lower level model. As an example, a series of 35 compounds and their anti-microbial activity towards the bacterial strain Escherichia coli CCM2260 is used. This biological activity has been determined at different times (2 to 10 h) and pH-values (pH 5.6 to 8.0).