Constrained least squares methods for estimating reaction rate constants from spectroscopic data

Model errors, experimental errors and instrumental noise influence the accuracy of reaction rate constant estimates obtained from spectral data recorded in time during a chemical reaction. In order to improve the accuracy, which can be divided into the precision and bias of reaction rate constant estimates, constraints can be used within the estimation procedure. The impact of different constraints on the accuracy of reaction rate constant estimates has been investigated using classical curve resolution (CCR). Different types of constraints can be used in CCR. For example, if pure spectra of reacting absorbing species are known in advance, this knowledge can be used explicitly. Also, the fact that pure spectra of reacting absorbing species are non-negative is a constraint that can be used in CCR. Experimental data have been obtained from UV-vis spectra taken in time of a biochemical reaction. From the experimental data, reaction rate constants and pure spectra were estimated with and without implementation of constraints in CCR. Because only the precision of reaction rate constant estimates could be investigated using the experimental data, simulations were set up that were similar to the experimental data in order to additionally investigate the bias of reaction rate constant estimates. From the results of the simulated data it is concluded that the use of constraints does not result self-evidently in an improvement in the accuracy of rate constant estimates. Guidelines for using constraints are given.