Combining Pharmacokinetics and Vibrational Spectroscopy: MCR-ALS Hard-and-Soft Modelling of Drug Uptake In Vitro Using Tailored Kinetic Constraints

Raman microspectroscopy is a label-free technique which is very suited for the investigation of pharmacokinetics of cellular uptake, mechanisms of interaction, and efficacies of drugs in vitro. However, the complexity of the spectra makes the identification of spectral patterns associated with the drug and subsequent cellular responses difficult. Indeed, multivariate methods that relate spectral features to the inoculation time do not normally take into account the kinetics involved, and important theoretical information which could assist in the elucidation of the relevant spectral signatures is excluded. Here, we propose the integration of kinetic equations in the modelling of drug uptake and subsequent cellular responses using Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) and tailored kinetic constraints, based on a system of ordinary differential equations. Advantages of and challenges to the methodology were evaluated using simulated Raman spectral data sets and real Raman spectra acquired from A549 and Calu-1 human lung cells inoculated with doxorubicin, in vitro. The results suggest a dependency of the outcome on the system of equations used, and the importance of the temporal resolution of the data set to enable the use of complex equations. Nevertheless, the use of tailored kinetic constraints during MCR-ALS allowed a more comprehensive modelling of the system, enabling the elucidation of not only the time-dependent concentration profiles and spectral features of the drug binding and cellular responses, but also an accurate computation of the kinetic constants.