Recovery of Rate Constants from Rank Deficient Kinetic Data: Comparison of MCR Approaches

Abstract

Measurement of rate constants of various processes is crucial both for research and for industrial design. It is typically done by fitting kinetic models to experimental data, which are mostly multivariate nowadays. These data often bear ill properties like noise and/or rank deficiency, which may ruin the relevance of the obtained results. In the present work we tested the ability of three well defined multivariate curve resolution approaches (model-free MCR-ALS, model-based MCR-ALS and full-matrix non-linear least square fit) to recover rate constants from simple simulated kinetic data when the spectra of components are almost linearly dependent. Model-free estimation of concentrations produced incorrect estimates. Model-based analysis was possible, but the quality of estimates of rate constants and convergence were strongly degraded by rank deficiency. Full-matrix non-linear least square fit displayed the best results both with respect to accuracy of the estimates and calculation performance. It proved its known value of the method of choice. The quality of the estimates depended strongly on the ratio between the rate constants: cases with highly similar and highly dissimilar rate constants were more problematic. The reasons of poor convergence of ALS algorithms and sources of bias in the estimates of rate constants are discussed.