Róbert Rajkó

Computation of the range (band boundaries) of feasible solutions and measure of the rotational ambiguity in self-modeling/multivariate curve resolution

Nowadays self-modeling/multivariate curve resolution algorithms have become very popular in chemometrics, i.e. for evaluating analytical chemical measurements. The developments split into two directions: (1) finding band solution and (2) finding unique solution. For band solutions the task is to find the band boundaries of the feasible regions. The size of the range calculated in this way can be considered as the measure of the rotational ambiguity. In this paper the developed methods are compared and some theoretical and practical considerations are given according to the improper and proper calculations.

Preparation of a Solid Dispersion by a Dropping Method to Improve the Rate of Dissolution of Meloxicam

Application of a solid dispersion system is one of the methods used to increase the bioavailability of poorly water-soluble drugs. Adaptation of the dropping method from the chemical industry as a formulation procedure may help the scaling-up process and simplify the formulation of poorly water-soluble compounds. Meloxicam (ME), a nonsteroidal anti-inflammatory drug that is poorly soluble in water, and polyethylene glycol (PEG) 4000, a water-soluble carrier, were formulated by using a dropping method in an attempt to improve the dissolution of ME. Pure ME and physical mixtures and tablets of ME–PEG 4000 (1:3 ratio) were compared as regards their dissolution with samples formulated by the dropping method. The results revealed that the round particles (solid drops) exhibited a higher dissolution rate than those of the physical mixtures, tablets, and pure ME. Self-modeling curve resolution (SMCR) as a chemometric method was used to evaluate X-ray powder diffractometry (XRPD) data. The results demonstrated the presence of a new crystalline phase in the solid dispersion, which can help the fast and quantitative dissolution from the solid drops. The round particles can be adapted to individual therapy by using a distributor.

Investigation of the equality constraint effect on the reduction of the rotational ambiguity in three-component system using a novel grid search method

The obtained results by soft modeling multivariate curve resolution methods often are not unique and are questionable because of rotational ambiguity. It means a range of feasible solutions equally fit experimental data and fulfill the constraints. Regarding to chemometric literature, a survey of useful constraints for the reduction of the rotational ambiguity is a big challenge for chemometrician. It is worth to study the effects of applying constraints on the reduction of rotational ambiguity, since it can help us to choose the useful constraints in order to impose in multivariate curve resolution methods for analyzing data sets. In this work, we have investigated the effect of equality constraint on decreasing of the rotational ambiguity. For calculation of all feasible solutions corresponding with known spectrum, a novel systematic grid search method based on Species-based Particle Swarm Optimization is proposed in a three-component system.

A review of recent methods for the determination of ranges of feasible solutions resulting from soft modelling analyses of multivariate data

Soft modelling or multivariate curve resolution (MCR) are well-known methodologies for the analysis of multivariate data in many different application fields. Results obtained by soft modelling methods are very likely impaired by rotational and scaling ambiguities, i.e. a full range of feasible solutions can describe the data equally well while fulfilling the constraints of the system. These issues are severely limiting the applicability of these methods and therefore, they can be considered as the most challenging ones. The purpose of the current review is to describe and critically compare the available methods that attempt at determining the range of ambiguity for the case of 3-component systems. Theoretical and practical aspects are discussed, based on a collection of simulated examples containing noise-free and noisy data sets as well as an experimental example.

Conditional Fisher's exact test as a selection criterion for pair-correlation method. Type I and Type II errors

Abstract The pair-correlation method (PCM) has been developed recently for discrimination between two variables. PCM can be used to identify the decisive (fundamental, basic) factor from among correlated variables even in cases when all other statistical criteria fail to indicate significant difference. These decisions are needed frequently in QSAR studies and/or chemical model building. The conditional Fishers exact test, based on testing significance in the 2×2 contingency tables is a suitable selection criterion for PCM. The test statistic provides a probabilistic aid for accepting the hypothesis of significant differences between two factors, which are almost equally correlated with the response (dependent variable). Differentiating between factors can lead to alternative models at any arbitrary significance level. The power function of the test statistic has also been deduced theoretically. A similar derivation was undertaken for the description of the influence of Type I (false-positive conclusion, error of the first kind) and Type II (false-negative conclusion, error of the second kind) errors. The appropriate decision is indicated from the low probability levels of both false conclusions.

Study of the effects of drugs on the structures of sucrose esters and the effects of solid-state interactions on drug release

Sucrose esters (SEs) have a wide range of hydrophilic-lipophilic balance (HLB) values (1-16), and hence can be applied as surfactants, or as solubility or penetration enhancers. In general, SEs are used in hot-melt technology, because of their low melting points, but literature data are not available on the effects of active agents on the structures of SEs and the possible solid-state interactions. In this study, drug-SE products were prepared by melt technology and investigated by differential scanning calorimetry (DSC), X-ray powder diffraction (XRPD), rheological measurements and dissolution tests. The model drugs meloxicam and diclofenac sodium and three SEs with different polarities (P1670, S970 and B370) were chosen for the preparation of the products. The DSC and XRPD results revealed that the structures of the SEs were rearranged, with a decrease in the degree of crystallinity. The dissolved drug molecules broke down the structures of the SEs, but were not built into the crystalline phase of the carrier. The dissolution of the drugs was influenced by the different HLB values and gel-forming behaviour of the SEs, and also by the polarity of the drug and the interactions between the drug and the SEs.

Definition and detection of data-based uniqueness in evaluating bilinear (two-way) chemical measurements

Multivariate curve resolution methods, frequently used in analyzing bilinear data sets, result in ambiguous decomposition in general. Implementing the adequate constraints may lead to reduce the so-called rotational ambiguity drastically, and in the most favorable cases to the unique solution. However, in some special cases, non-negativity constraint as minimal information of the system is a sufficient condition to resolve profiles uniquely. Although, several studies on exploring the uniqueness of the bilinear non-negatively constrained multivariate curve resolution methods have been made in the literature, it has still remained a mysterious question. In 1995, Manne published his profile-based theorems giving the necessary and sufficient conditions of the unique resolution. In this study, a new term, i.e., data-based uniqueness is defined and investigated in details, and a general procedure is suggested for detection of uniquely recovered profile(s) on the basis of data set structure in the abstract space. Close inspection of Borgen plots of these data sets leads to realize the comprehensive information of local rank, and these argumentations furnish a basis for data-based uniqueness theorem. The reported phenomenon and its exploration is a new stage (it can be said fundament) in understanding and describing the bilinear (matrix-type) chemical data in general. Our proposed detection tool is restricted to three-component systems because of the visual limitations of the Borgen plot, but the theorem is universal for systems with more than three components. A recently published experimental four-component system is used for illustrating this theorem in the case of systems with more than three components.

Newer developments on self-modeling curve resolution implementing equality and unimodality constraints.

Analytical self-modeling curve resolution (SMCR) methods resolve data sets to a range of feasible solutions using only non-negative constraints. The Lawton-Sylvestre method was the first direct method to analyze a two-component system. It was generalized as a Borgen plot for determining the feasible regions in three-component systems. It seems that a geometrical view is required for considering curve resolution methods, because the complicated (only algebraic) conceptions caused a stop in the general study of Borgens work for 20 years. Rajkó and István revised and elucidated the principles of existing theory in SMCR methods and subsequently introduced computational geometry tools for developing an algorithm to draw Borgen plots in three-component systems. These developments are theoretical inventions and the formulations are not always able to be given in close form or regularized formalism, especially for geometric descriptions, that is why several algorithms should have been developed and provided for even the theoretical deductions and determinations. In this study, analytical SMCR methods are revised and described using simple concepts. The details of a drawing algorithm for a developmental type of Borgen plot are given. Additionally, for the first time in the literature, equality and unimodality constraints are successfully implemented in the Lawton-Sylvestre method. To this end, a new state-of-the-art procedure is proposed to impose equality constraint in Borgen plots. Two- and three-component HPLC-DAD data set were simulated and analyzed by the new analytical curve resolution methods with and without additional constraints. Detailed descriptions and explanations are given based on the obtained abstract spaces.

Additional knowledge for determining and interpreting feasible band boundaries in self-modeling/multivariate curve resolution of two-component systems

Recently Taulers mcrbands Matlab script and Maeders grid method were used by Abdollahi et al. to calculate the elements of transformation matrix for obtaining feasible band boundaries in multivariate curve resolution of a two-component system. Neither method is analytical, instead they are iterative. For long time it is well-known that Lawton and Sylvestres approach can provide the feasible band boundaries analytically and non-iteratively. In this paper, firstly in the literature, the clear relationship is given between Lawton and Sylvestres approach and Taulers approach (as well as Maeders approach). It was found that all approaches are identical for noiseless or moderately noisy two-component systems and, it was illustrated by figures and tables provided in Supplementary Material.

Protein Array Based Interactome Analysis of Amyloid-β Indicates an Inhibition of Protein Translation

Oligomeric amyloid-β is currently of interest in amyloid-β mediated toxicity and the pathogenesis of Alzheimers disease. Mapping the amyloid-β interaction partners could help to discover novel pathways in disease pathogenesis. To discover the amyloid-β interaction partners, we applied a protein array with more than 8100 unique recombinantly expressed human proteins. We identified 324 proteins as potential interactors of oligomeric amyloid-β. The Gene Ontology functional analysis of these proteins showed that oligomeric amyloid-β bound to multiple proteins with diverse functions both from extra and intracellular localizations. This undiscriminating binding phenotype indicates that multiple protein interactions mediate the toxicity of the oligomeric amyloid-β. The most highly impacted cellular system was the protein translation machinery. Oligomeric amyloid-β could bind to altogether 24 proteins involved in translation initiation and elongation. The binding of amyloid-β to purified rat hippocampal ribosomes validated the protein array results. More importantly, in vitro translation assays showed that the oligomeric amyloid-β had a concentration dependent inhibitory activity on translation. Our results indicate that the inhibited protein synthesis is one of the pathways that can be involved in the amyloid-beta induced neurotoxicity.