A multi-method chemometric analysis in spectroelectrochemistry: Case study on molybdenum mono-dithiolene complexes.

Spectroelectrochemical (SEC) analyses combine spectroscopic measurements with electrochemical techniques and can provide deep insight into complex multi-component chemical reaction systems. SEC experiments typically produce large amounts of spectroscopic data. Chemometric techniques are required for the data analysis and aim at extracting the underlying pure component information. Here we analyze spectroelectrochemically gained UV-vis data from five molybdenum mono-dithiolene complexes with changing redox states. SEC enables an electrochemical control of the mixture composition which supports the application of chemometric curve resolution techniques. The factor ambiguity problem is addressed by a multi-method approach combining chemometric tools from the evolving factor analysis (EFA) and from the area of feasible solutions (AFS) methodology in combination with factor duality arguments. EFA enables a subsystem analysis. Two subsystems with three species each are identified, which belong to a reductive and to an oxidative region. A joint species is contained in both regions. A complete pure component decomposition becomes possible in a final step.

On the analysis of chromatographic biopharmaceutical data by curve resolution techniques in the framework of the area of feasible solutions.

Monitoring preparative protein chromatographic steps by in-line spectroscopic tools or fraction analytics results in medium or large sized data matrices. Multivariate Curve Resolution (MCR) serve to compute or to estimate the concentration values of the pure components only from these data matrices. However, MCR methods often suffer from an inherent solution ambiguity which underlies the factorization problem. The typical unimodality of the chromatographic profiles of pure components can support the chemometric analysis. Here we present the pure components estimation process within the framework of the area of feasible solutions, which is a systematic approach to represent the range of all possible solutions. The unimodality constraint in combination with Pareto optimization is shown to be an effective method for the pure component calculation. Applications are presented for chromatograms on a model protein mixture containing ribonuclease A, cytochrome c and lysozyme and on a two-dimensional chromatographic separation of a monoclonal antibody from its aggregate species. The root mean squared errors of the first case study are 0.0373, 0.0529 and 0.0380 g/L compared to traditional off-line analytics. The second case study illustrates the potential of recovering hidden components with MCR from off-line reference analytics.

Evaluation of the extension of rotation ambiguity associated to multivariate curve resolution solutions by the application of the MCR-BANDS method.

Multivariate Curve Resolution (MCR) methods have been widely used to resolve the spectra (instrumental responses) and concentration profiles of the unknown constituents of chemical mixtures especially when no prior information is available about the nature and composition of these mixtures. Based on the fulfillment of a bilinear model, like the multivariate extension of Beer's law, MCR solutions are affected by rotation ambiguity, which means that a range of feasible solutions can explain the observed data equally well fulfilling the same constraints. The MCR-BANDS method has been proposed to provide a measure of the extension of rotation ambiguity associated to a particular MCR feasible solution. In this work, the two extreme (maximum and minimum) feasible solutions obtained by the MCR-BANDS method are investigated and projected on to the area of feasible solution (AFS) obtained by other methods like the FACPACK method, and compared under the application of different constraints. In contrast to other methods that estimate the whole set of feasible solutions (i.e. the AFS), MCR-BANDS provides a simpler and flexible way to give an estimation of the extension of rotation ambiguity associated to a particular MCR solution (for instance using the MCR-ALS method) of systems with any number of components and under any type of constraints, in the concentration and spectral domains.

A ray casting method for the computation of the area of feasible solutions for multicomponent systems: Theory, applications and FACPACK-implementation.

Multivariate curve resolution methods suffer from the non-uniqueness of the solutions. The set of possible nonnegative solutions can be represented by the so-called Area of Feasible Solutions (AFS). The AFS for an s-component system is a bounded (s-1)-dimensional set. The numerical computation and the geometric construction of the AFS is well understood for two- and three-component systems but gets much more complicated for systems with four or even more components. This work introduces a new and robust ray casting method for the computation of the AFS for general s-component systems. The algorithm shoots rays from the origin and records the intersections of these rays with the AFS. The ray casting method is computationally fast, stable with respect to noise and is able to detect the various possible shapes of the AFS sets. The easily implementable algorithm is tested for various three- and four-component data sets.