(147g) Demonstrating Mathematical Equivalence between Partial Least Squares and the Beer-Lambert Law in Estimating Protein Concentrations with Spectroscopic Data
AIChE Annual Meeting
Monday, November 14, 2022 - 2:30pm to 2:50pm
This work provides a derivation of the PLS formulation and coefficient equations and demonstrates that their structure is identical to the multi-component Beer-Lambert Law and its molar absorptivity values. To this end, artificial data was generated for a protein mixture of Immunoglobulin G (IgG), Bovine Serum Albumin (BSA), and Lysozyme over concentration ranges of 0 to 20 g/L using the Beer-Lambert model, with PLS models generated from the model-made data. The PLS model coefficients were subsequently compared to the molar absorptivity values used in the Beer-Lambert Law model, with an RMSE of 0.010 g/L demonstrating the equivalency between the two coefficient sets. Finally, experimental UV/Vis absorbance data for BSA and Lysozyme proteins using a Tecan plate reader was recorded. PLS analysis of the data and comparison of the produced model coefficients to the literature values for BSA and Lysozyme absorptivity was conducted, with a percent difference of 6.7% and 23% respectively, the latter of which was attributed to the interaction between the BSA and Lys resulting in higher absorptivity values.
The main objective of this work is to clarify how PLS and the Beer-Lambert Law are discussed and related to one another, in research of soft-sensors for biotherapeutics. The decision to use PLS for soft-sensor models is often framed as primarily a data analysis method selection issue, based on previous literature. Moreover, use of PLS versus the Beer-Lambert Law is often posited as distinct analysis methods to choose between. This work demonstrates that the Beer-Lambert Law and PLS are solving the same model formulation in the soft-sensor model applications outlined, providing a distinct mechanistic backing to the selection of PLS and further attributable meaning to the produced model coefficients.