(147g) Demonstrating Mathematical Equivalence between Partial Least Squares and the Beer-Lambert Law in Estimating Protein Concentrations with Spectroscopic Data

The pharmaceutical industry has made significant developments in upstream production through optimized cell culture and expression technologies utilizing feedback from process measurements. However, this optimization has been unmatched in downstream purification and analytical methods, partly due to lack of appropriate measurement techniques, resulting in significant manufacturing inefficiencies. These inefficiencies have motivated the development of “soft-sensor” based models, where real-time data is combined with multi-variate data analysis (MVDA), to allow for live estimation of product attributes, which in turn can be utilized to improve process operations. Partial Least Squares (PLS) is an MVDA technique that is commonly used with UV/Vis data to build models for the estimation of therapeutic protein concentration and impurity levels. The selection of UV/Vis data for this application is justified through the Beer-Lambert law, which assumes a linear relationship between protein mixture components and their UV/Vis absorbances. Existing literature has widely considered PLS and the Beer-Lambert Law as distinct modeling alternatives. However, this paper demonstrates that, in addition to being a well-established data analytics tool, the model formulation of PLS is identical to the multi-component Beer-Lambert Law model, providing a mechanistic underpinning to the selection of the technique for soft-sensor models, and inspiring potential advancements.

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.