Predicting the uniqueness of single non-negative profiles estimated by multivariate curve resolution methods.

In many kinds of chemical data, one or more species are unknown and the only efficient way to identify and/or quantify them is by mathematical resolution of the mixture spectra. The major problem with such mathematical decompositions is the possibility of obtaining a range of feasible solutions instead of a unique solution due to insufficient prior information about the system under study. However, even with the minimal non-negativity assumptions, there may be some levels of uniqueness, i.e., full/partial/fractional, in the results of the bilinear decomposition of chemical data which is very important to detect. In this study, a procedure is proposed to predict the uniqueness of the resolved non-negative profiles obtained by MCR-ALS (or analogous methods like NMF, EFA, SIMPLISMA, ITTFA, HELP, etc.). This uniqueness prediction is based on the data-based uniqueness (DBU) theorem and the general rule of uniqueness (GRU) presented in previous studies. The proposed procedure is easy to implement, has no additional computational cost, and is general for different systems with any number of components. Several simulated and experimental datasets containing different numbers of components were used to examine and evaluate the proposed procedure.

Effects of the Pentapeptide P33 on Memory and Synaptic Plasticity in APP/PS1 Transgenic Mice: A Novel Mechanism Presenting the Protein Fe65 as a Target.

Regulated intramembrane proteolysis (RIP) of the amyloid precursor protein (APP) leads to the formation of fragments, among which the intracellular domain of APP (AICD) was also identified to be a causative of early pathological events. AICD-counteracting proteins, such as Fe65, may serve as alternative therapeutic targets of Alzheimer's disease (AD). The detection of elevated levels of Fe65 in the brains of both human patients and APP transgenic mice may further strengthen the hypothesis that influencing the interaction between Fe65 and APP may have a beneficial effect on the course of AD. Based on a PXP motif, proven to bind to the WW domain of Fe65, a new pentapeptide was designed and tested. The impedimental effect of P33 on the production of beta amyloid (Aß) (soluble fraction and aggregated plaques) and on the typical features of the AD pathology (decreased dendritic spine density, synaptic markers, elevated inflammatory reactions) was also demonstrated. Significant enhancements of both learning ability and memory function were observed in a Morris water maze paradigm. The results led us to formulate the theory that P33 acts by altering the conformation of Fe65 via binding to its WW domain, consequently hindering any interactions between Fe65 and key members involved in APP processing.

Duality based direct resolution of unique profiles using zero concentration region information.

Self Modeling Curve Resolution (SMCR) is a class of techniques concerned with estimating pure profiles underlying a set of measurements on chemical systems. In general, the estimated profiles are ambiguous (non-unique) except if some special conditions fulfilled. Implementing the adequate information can reduce the so-called rotational ambiguity effectively, and in the most desirable cases lead to the unique solution. Therefore, studies on circumstances resulting in unique solution are of particular importance. The conditions of unique solution can particularly be studied based on duality principle. In bilinear chemical (e.g., spectroscopic) data matrix, there is a natural duality between its row and column vector spaces using minimal constraints (non-negativity of concentrations and absorbances). In this article, the conditions of the unique solution according to duality concept and using zero concentration region information is intended to show. A simulated dataset of three components and an experimental system with synthetic mixtures containing three amino acids tyrosine, phenylalanine and tryptophan are analyzed. It is shown that in the presence of sufficient information, the reliable unique solution is obtained that is valuable in analytical qualification and for quantitative verification analysis.

Local Rank Deficiency Caused Problems in Analyzing Chemical Data.

Multivariate curve resolution (MCR) is a powerful methodology for analyzing chemical data in different application fields such as pharmaceutical analysis, agriculture, food chemistry, environment, and industrial and clinical chemistry. However, MCR results are often complicated by rotational ambiguity, meaning that there is a range of feasible solutions that fulfill the constraints and explain equally well the observed experimental data. Constraints determine the properties of resolved profiles in MCR methods by enforcing different assumptions on data. The applied constraints on chemical data sets should be derived from the physical nature and prior knowledge of the system under study. Therefore, the reliability of the constraints in order to get accurate results is a critical aspect that should be considered by analytical chemists who use MCR methods. Local rank information plays a key role in the curve resolution of multicomponent chemical systems. Applying the local rank constraint can reduce the extent of rotational ambiguity considerably, and in some cases, unique solutions can be achieved. Local rank exploratory methods like Evolving Factor Analysis (EFA) method provide local rank maps in order to obtain the presence pattern of components on the main assumption that the number of components in each window is equal to its rank. It is shown in this work that the local rank is a mathematical concept that may not be in concordance with chemical information. Thus, applying the local rank constraint for restricting the rotational ambiguity in MCR methods can lead to incorrect solutions! This problem is due to "local rank deficiency", which is introduced in this contribution.

Analytical solution and meaning of feasible regions in two-component three-way arrays.

Although many efforts have been directed to the development of approximation methods for determining the extent of feasible regions in two- and three-way data sets; analytical determination (i.e. using only finite-step direct calculation(s) instead of the less exact numerical ones) of feasible regions in three-way arrays has remained unexplored. In this contribution, an analytical solution of trilinear decomposition is introduced which can be considered as a new direct method for the resolution of three-way two-component systems. The proposed analytical calculation method is applied to the full rank three-way data array and arrays with rank overlap (a type of rank deficiency) loadings in a mode. Close inspections of the analytically calculated feasible regions of rank deficient cases help us to make clearer the information gathered from multi-way problems frequently emerged in physics, chemistry, biology, agricultural, environmental and clinical sciences, etc. These examinations can also help to answer, e.g., the following practical question: "Is two-component three-way data with proportional loading in a mode actually a three-way data array?" By the aid of the additional information resulted from the investigated feasible regions of two-component three-way data arrays with proportional profile in a mode, reasons for the inadequacy of the seemingly trilinear data treatment methods published in the literature (e.g., U-PLS/RBL-LD that was used for extraction of quantitative and qualitative information reported by Olivieri et al. (Anal. Chem. 82 (2010) 4510-4519)) could be completely understood.

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.

Fitting-free curve resolution of spectroscopic data: Chemometric and physical chemical viewpoints.

In this paper the authors have investigated spectroscopic data analysis according to a recent development, i.e. the Direct Inversion in the Spectral Subspace (DISS) procedure. DISS is a supervised curve resolution technique, consequently it can be used once the spectra of the potential pure components are known and the experimental spectrum of a chemical mixture is also presented; hence the task is to determine the composition of the unknown chemical mixture. In this paper, the original algorithm of DISS is re-examined and some further critical reasoning and essential developments are provided, including the detailed explanations of the constrained minimization task based on Lagrange multiplier regularization approach. The main conclusion is that the regularization used for DISS is needed because of the possible shifted spectra effect instead of collinearity; and this new property, i.e. treating the mild shifted spectra effect, of DISS can be considered as its main scientific advantage.

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 Borgen's 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.

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.

Functional changes in transcriptomes of the prefrontal cortex and hippocampus in a mouse model of anxiety.

Anxiety is a multi-etiology disorder influenced by both genetic background and environment. To study the impact of a genetic predisposition, we developed a novel mouse model of anxiety using a combination of crossbreeding and behavioral selection. Comparison of the transcriptomes from the prefrontal cortex and hippocampus of anxious and control mice revealed that the numbers of significantly up- and down-regulated genes were modest, comprising approximately 2% of the tested genes. Functional analysis of the significantly altered gene sets showed that functional groups such as nervous system development, behavior, glial cell differentiation and synaptic transmission were significantly enriched among the up-regulated genes, whereas functional groups such as potassium ion transport, Wnt signaling and neuropeptidergic signaling were significantly enriched among the down-regulated genes. Many of the identified genes and functional groups have been previously linked to the molecular biology of anxiety, while several others, such as transthyretin, vasoactive intestinal polypeptide and various potassium ion channels, are novel or not as well described in this context. Supporting the gene expression data, we also found increased excitability in the hippocampi of anxious mice, which can be a phenotypic result of decreased potassium channel density. Our transcriptome screen showed that the initiation and/or effect of anxiety involve multiple pathways and cellular processes. The identified novel genes and pathways could be involved in the molecular pathogenesis of anxiety and provide potential targets for further drug development.

Protein array based interactome analysis of amyloid-ß indicates an inhibition of protein translation.

Oligomeric amyloid-ß is currently of interest in amyloid-ß mediated toxicity and the pathogenesis of Alzheimer's disease. Mapping the amyloid-ß interaction partners could help to discover novel pathways in disease pathogenesis. To discover the amyloid-ß 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-ß. The Gene Ontology functional analysis of these proteins showed that oligomeric amyloid-ß 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-ß. The most highly impacted cellular system was the protein translation machinery. Oligomeric amyloid-ß could bind to altogether 24 proteins involved in translation initiation and elongation. The binding of amyloid-ß to purified rat hippocampal ribosomes validated the protein array results. More importantly, in vitro translation assays showed that the oligomeric amyloid-ß 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.

Formulation optimization of sustained-release ammonio methacrylate copolymer microspheres. Effects of log p and concentration of polar cosolvents, and role of the drug/copolymer ratio.

The objectives of this work were the formulation optimization of the preparation process parameters and to evaluate spray-dried sustained-release microspheres using ammonio methacrylate copolymer (AMC) as a polymer matrix. The effects of log P and the concentrations of the cosolvents (acetone, methyl ethyl ketone and n-butyl acetate) and different drug/copolymer ratios as independent variables on the physicochemical parameters (the W1/O emulsion viscosity, the microsphere production yield, the average particle size, the encapsulation efficiency) and the cumulative in vitro drug release as dependent variables were studied. The optimization was carried out on the basis of the 33 factorial design study. The optimization process results showed that addition of polar cosolvents proved effective, linear relationships were observed between the independent and the dependent variables. The best conditions were achieved by microspheres prepared by using a low/medium cosolvent log P, cosolvent concentration of 25-50% v/v and a drug/copolymer ratio of 1:16. The microspheres ensured sustained release with Nernst and Baker-Lonsdale release profiles.

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

Recently Tauler's mcrbands Matlab script and Maeder's 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 Sylvestre's 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 Sylvestre's approach and Tauler's approach (as well as Maeder's 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.

Quantum chemical characterization of Abraham solvation parameters for gas-liquid chromatographic stationary phases.

Quantum chemical based investigation is presented on the Abraham solvation parameters for 23 molecular (non-polymeric) GLC stationary phases. PM6 semiempirical calculations combined with conductor-like screening model (COSMO) have been utilized. Comprehensive search for an optimal model was carried out, based on best subset selection from 86 variables considered. A unified quantitative structure-property relationship model has been developed for all five Abraham parameters reported. The selected set of five structure-driven descriptors was subjected to statistical analyses, and was shown to be useful for stationary phase classification.

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.

Self-modeling curve resolution method applied for the evaluation of dissolution testing data: a case study of meloxicam-mannitol binary systems.

This paper introduces some chemometric methods, i.e., self-modeling curve resolution (SMCR), multivariate curve resolution-alternating least squares (MCR-ALS) and parallel factor analysis (PARAFAC and PARAFAC2), which are used to evaluate in vitro dissolution testing data detected by a UV-vis spectrophotometer on meloxicam-mannitol binary systems. These systems were chosen because of their relative simplicity to apply as part of the validation process illustrating the effectiveness of the developed and applied chemometric method. The paper illustrates the failure of PARAFAC methods used before for pharmaceutical data evaluations as well, and we suggest application of the feasible band form given by SMCR as a more general procedure. Steps to improve the dissolution behavior of drugs have become among the most interesting aspects of pharmaceutical technology, and our results show that a larger particle size of meloxicam is advantageous for dissolution. Instead of the use of only one characteristic wavelength, appropriate chemometric methods can furnish more information from dissolution testing data, i.e., the individual dissolution rate profiles and the individual spectra for all the components can be obtained without resorting to any separation techniques such as HPLC.

Theoretical characterization of gas-liquid chromatographic stationary phases with quantum chemical descriptors.

Quantitative structure-property relationship (QSPR) solvent model has been developed for the McReynolds constants (prototypical solutes) on 36 gas-liquid chromatographic stationary phases. PM6 semiempirical quantum chemical calculations combined with conductor-like screening model (COSMO) has been utilized. From 276 descriptors considered, forward stepwise variable selection, followed by best subset selection, yielded linear regression models containing six purely quantum chemical and two hybrid, topologically based descriptors. Internal (leave-one-out and bootstrap) as well as external validation methods confirmed the predictive power of these structure-driven models across all 10 McReynolds constants, with 40 Kováts-index units overall root-mean-square prediction error estimate.

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.