Information fusion via constrained principal component regression for robust quantification with incomplete calibrations.

Incomplete calibrations are encountered in many applications and hamper chemometric data analyses. Such situations arise when target analytes are embedded in a chemically complex matrix from which calibration concentrations cannot be determined with reasonable efforts. In other cases, the samples' chemical composition may fluctuate in an unpredictable way and thus cannot be comprehensively covered by calibration samples. The reason for calibration model to fail is the regression principle itself which seeks to explain measured data optimally in terms of the (potentially incomplete) calibration model but does not consider chemical meaningfulness. This study presents a novel chemometric approach which is based on experimentally feasible calibrations, i.e. concentration series of the target analytes outside the chemical matrix ('ex situ calibration'). The inherent lack-of-information is then compensated by incorporating additional knowledge in form of regression constraints. Any outside knowledge can be utilized such as literature values of concentration ranges, concentration ratios implied e.g. by stoichiometry, sum parameters to which multiple analytes need to amount to, and/or reasonable signal reconstructions. The core idea is to mitigate the regression principle's strive for the best possible explanation of measured signals toward the best possible explanation under the condition of chemical meaningfulness. As proof-of-principle application, quantitative analyses of selected compounds in microalgae cells have been chosen. After acquiring FTIR calibration spectra from concentration series of 28 analytes, an ex situ calibration model has been built via principal component regression (PCR). Since microalgae biomass is a very complex matrix, the prediction step based on such an incomplete calibration fails. However, after incorporating several regression constraints into PCR predictions, chemically impossible results are avoided as depicted in the graphical abstract. Equally important are enhancements in concentration reproducibility. For most samples in the chosen application, the errorbars were reduced by one order of magnitude. By means of this novel chemometric method, quantitative analyses have been improved so much that cell responses to chemical shifts in their culturing environment can be studied.