Hard‐modelled trilinear decomposition (HTD) for an enhanced kinetic multicomponent analysis

Abstract

We present a novel approach for kinetic, spectral and chromatographic resolution of trilinear data sets acquired from slow chemical reaction processes via repeated chromatographic analysis with diode array detection. The method is based on fitting rate constants of distinct chemical model reactions (hard-modelled, integrated rate laws) by a Newton±Gauss±Levenberg/Marquardt (NGL/M) optimization in combination with principal component analysis (PCA) and/or evolving factor analysis (EFA), both known as powerful methods from bilinear data analysis. We call our method hard-modelled trilinear decomposition (HTD). Compared with classical bilinear hard-modelled kinetic data analysis, the additional chromatographic resolution leads to two major advantages: (1) the differentiation of indistinguishable rate laws, as they can occur in consecutive first-order reactions; and (2) the circumvention of many problems due to rank deficiencies in the kinetic concentration profiles. In this paper we present the theoretical background of the algorithm and discuss selected chemical rate laws.

Systematic prediction of linear dependencies in the concentration profiles and implications on the kinetic hard-modelling of spectroscopic data

“…In this contribution, we do not consider the kinetic analysis of tri-linear data -strategy (5) -as this has been discussed in literature as a special case of strategy (1), leading to full spectral resolution due to an additional dimension of resolution [18]. If strategy (1) is used, the method optionally includes the calculation of the linear combinations of the true pure component spectra, i.e.…”

“…5) Perform a tri-linear experiment and treat the linear dependencies, for example, with strategy (1) [18] Complete spectral resolution due to an additional dimension of resolution, e.g. chromatography.…”

“…if some concentration profiles are linearly dependent, the pseudo-inverse and thus the pure component spectra cannot be directly computed. In such cases, there are at least five different strategies, as described in Table 1, to treat rank deficiency problems in the concentration matrix and to allow the fitting of pure component spectra [18].…”

Model-based approaches to investigate the interactions between unmodified gold nanoparticles and DNA strands

“…Recording the excitation-emission matrices for multiple samples or a single sample during a process, provides a three-way data array. To analyze the three-way data, based on its numerical properties, some multi-way techniques can be used [35][36][37][38]. Because of the rank deficiency of the data as a result of fluorescence resonance energy transfer (FRET) between the two fluorophores in the hybridized form, Tucker3 is the preferred multi-way method for this purpose.…”

Non‐negativity constraints for elimination of multiple solutions in fitting of multivariate kinetic models to spectroscopic data

“…This represents a significant time saving for users of multivariate kinetic fitting. Alternatively, the ambiguity problem in kinetic fitting can also be solved by extending the kinetic analysis to three-way methods by adding one more additional measurement modes using hyphenated techniques [30]. In this case, more complex experimental procedures are required and more time is needed for the analysis of the data.…”