Response surface methodology (RSM) as a tool for optimization in analytical chemistry

A review about the application of response surface methodology (RSM) in the optimization of analytical methods is presented. The theoretical principles of RSM and steps for its application are described to introduce readers to this multivariate statistical technique. Symmetrical experimental designs (three-level factorial, Box-Behnken, central composite, and Doehlert designs) are compared in terms of characteristics and efficiency. Furthermore, recent references of their uses in analytical chemistry are presented. Multiple response optimization applying desirability functions in RSM and the use of artificial neural networks for modeling are also discussed.     

Optimization of a liquid chromatography ion mobility-mass spectrometry method for untargeted metabolomics using experimental design and multivariate data analysis

High-resolution mass spectrometry coupled with pattern recognition techniques is an established tool to perform comprehensive metabolite profiling of biological datasets. This paves the way for new, powerful and innovative diagnostic approaches in the post-genomic era and molecular medicine. However, interpreting untargeted metabolomic data requires robust, reproducible and reliable analytical methods to translate results into biologically relevant and actionable knowledge. The analyses of biological samples were developed based on ultra-high performance liquid chromatography (UHPLC) coupled to ion mobility - mass spectrometry (IM-MS). A strategy for optimizing the analytical conditions for untargeted UHPLC-IM-MS methods is proposed using an experimental design approach. Optimization experiments were conducted through a screening process designed to identify the factors that have significant effects on the selected responses (total number of peaks and number of reliable peaks). For this purpose, full and fractional factorial designs were used while partial least squares regression was used for experimental design modeling and optimization of parameter values. The total number of peaks yielded the best predictive model and is used for optimization of parameters setting.     

试验设计与优化方法

本文介绍了作者所在研究小组多年来在试验优化方法方面的研究工作，内容涉及正交试验设计、单纯形优化法、均匀设计法、回归正交设计和模糊正交设计、人工神经网络等多种试验优化设计方法的应用，优化效果的综合评价，多种试验优化设计方法的综合应用等     

Application of Experimental Design Methodologies in the Enantioseparation of Pharmaceuticals by Capillary Electrophoresis: A Review

Chirality is one of the major issues in pharmaceutical research and industry. Capillary electrophoresis (CE) is an interesting alternative to the more frequently used chromatographic techniques in the enantioseparation of pharmaceuticals, and is used for the determination of enantiomeric ratio, enantiomeric purity, and in pharmacokinetic studies. Traditionally, optimization of CE methods is performed using a univariate one factor at a time (OFAT) approach; however, this strategy does not allow for the evaluation of interactions between experimental factors, which may result in ineffective method development and optimization. In the last two decades, Design of Experiments (DoE) has been frequently employed to better understand the multidimensional effects and interactions of the input factors on the output responses of analytical CE methods. DoE can be divided into two types: screening and optimization designs. Furthermore, using Quality by Design (QbD) methodology to develop CE-based enantioselective techniques is becoming increasingly popular. The review presents the current use of DoE methodologies in CE-based enantioresolution method development and provides an overview of DoE applications in the optimization and validation of CE enantioselective procedures in the last 25 years. Moreover, a critical perspective on how different DoE strategies can aid in the optimization of enantioseparation procedures is presented.     

Statistical designs and response surface techniques for the optimization of chromatographic systems

This paper describes fundamentals and applications of multivariate statistical techniques for the optimization of chromatographic systems. The surface response methodologies: central composite design, Doehlert matrix and Box-Behnken design are discussed and applications of these techniques for optimization of sample preparation steps (extractions) and determination of experimental conditions for chromatographic separations are presented. The use of mixture design for optimization of mobile phases is also related. An optimization example involving a real separation process is exhaustively described. A discussion about model validation is presented. Some applications of other multivariate techniques for optimization of chromatographic methods are also summarized.     

Chemometric tools in electroanalytical chemistry: Methods for optimization based on factorial design and response surface methodology

The aim of this paper is to give a brief overview of chemometric techniques based on factorial designs and response surface methodologies used in the optimization of electroanalytical methods. Chemometric techniques have several important advantages over one-way optimization for analytical applications, including a relatively low cost, a reduced number of experiments, and possibilities to evaluate interactions among variables. These techniques also enable the selection of optimal experimental conditions, helping to avoid trivial mistakes during optimization. Despite these facts, chemometric techniques have rarely been applied to electroanalytical data, especially in comparison with their use in spectroscopy. The application of chemometric methods in electroanalytical chemistry has been mostly used for solving overlapping signals, multivariate calibration methods, model identification and optimization of analytical procedures. This review is focused on the latter applications and overviews the role of full or fractional factorial designs (first-order designs), as well as second-order designs, such as central composite, Doehlert and Box-Behnken designs, for optimization of electroanalytical methods. A discussion of chemometric-related advantages is also given for stripping analyses, flow injection systems with amperometric detection, differential pulse voltammetry, square wave voltammetry and electrochemical sensor preparation.     

Doehlert matrix: a chemometric tool for analytical chemistry-review

A review of the use of the Doehlert matrix as a chemometric tool for the optimization of methods in analytical chemistry and other sciences is presented. The theoretical principles of Doehlert designs are described, including the coded values for the use of this matrix involving two, three, four and five variables. The advantages of this matrix in comparison with other response surface designs, such as central composite and Box-Behnken, designs are discussed. Finally, 57 references concerning the application of Doehlert matrices in the optimization of procedures involving spectroanalytical, electroanalytical and chromatographic techniques are considered.     

Pareto-optimal front as a tool to study the behaviour of experimental factors in multi-response analytical procedures

This work presents a methodology to analyse the behaviour of an analytical procedure, above all when optimization of the procedure is needed. The methodology starts by the design of an experiment suitable to fit response surfaces to some analytical responses of interest in the problem being studied. Then, a pareto-optimal front is estimated that accounts for the optimal possibly trading-off solutions among the responses. The analysis of the behaviour of the optimal values of the response surfaces and the experimental conditions that provide these values allows going deeply into the analytical procedure.     

Ab initio and indo molecular orbital calculations of the geometries and electronic structures of substituted sulfines

Molecular orbital calculations are presented for the parent sulfine and some mono-and dihalogensubstituted sulfines, using ab initio and INDO methods. A partial geometry optimization was performed for nine different sulfines. Charge distributions, potential surfaces and dipole moments were calculated from the wave functions of the optimized geometries. Cis-trans interconversion barriers and electronic spectra are also given. The atomic charges of the S and O atoms are insensitive to substitutions at carbon, and substituents greatly influence the potential in the environment of the molecule. The implications of the results for the chemical behavior of sulfine derivates are briefly discussed and compared with experimental data.     

An appraisal of experimental designs: Application to enantioselective capillary electromigration techniques

Enantioresolution processes are vital tools for investigating the enantioselectivities of chiral compounds. An analyst resolves to optimize enantioresolution conditions once they are determined. Generally, optimization is conducted by a one-factor-at-a-time (OFAT) approach. Although this approach may determine an adequate condition for the method, it does not often allow the estimation of the real optimum condition. Experimental designs are conducive for the optimization of enantioresolution methods via capillary electromigration techniques (CETs). They can efficiently extract information from the behavior of a method and enable the estimation of the real optimum condition. Furthermore, the application of the analytical quality by design (AQbD) approach to the development of CET-based enantioselective methods is a trend. This article (i) offers an overview of the application of experimental designs to the development of enantioselective methods from 2015 to mid-2020, (ii) reveals the experimental designs that are presently employed in CET-based enantioresolutions, and (iii) offers a critical point of view on how the different experimental designs can aid the optimization of enantioresolution processes by considering the method parameters.     

Diastereoselective synthesis of a novel phosphinic peptide as ACE inhibitor: Fragment-based design approach

In medicinal chemistry for the purpose of lead optimization, hit selection of new isofunctional chemotypes are crucial for the success of identifying novel chemical entities of increased potency. Using fragment-based design approach with the N-selective inhibitor RXP407, a novel phosphinic peptide scaffold that consisted of modified RXP407 fragments was generated. The presented synthetic route is straightforward and produces the desired product Z-RXP407 in moderate yield. The (S,R,S,S)-Z-RXP407 analog has been evaluated for the C- and N-domain constructs of angiotensin-converting enzyme. The potency of this analog has been much lower compared to the parent compound RXP407, providing thus valuable insights regarding further design based on structure–activity relationships.     

Flow injection system for hydrolysable tannin determination

A flow injection system was proposed to evaluate the transient product of a colorimetric reaction between hydrolysable tannin and potassium iodate (KIO₃) solution. The system optimization was accomplished by using statistical methods based on experimental design. Flow rate of KIO₃ solution, sample volume, carrier flow rate, and reaction coil were the selected factors for evaluation. On screening step, complete factorial 2⁴ was used and two levels for each selected factor were studied. For the optimization phase, a centered face composite design 2² + star was employed to evaluate sample volume and flow rate of KIO₃ solution, which were the factors identified in the screening phase as having more influence on the absorbance signal. After optimization, the proposed system was compared with batch determination. Some characteristics, such as analytical frequency, reagent consumption and chemical residues generation presented better results by the use of the proposed system if compared with batch method. The system presented good repeatability with standard deviation lower than 3%, for n = 10, linearity (R² = 0.9974) for tannic acid standard, analytical frequency of 15 injections h^− 1 and limit of quantification of 24 mg L^− 1 of tannic acid. Good results were obtained when the proposed system was applied to hydrolysable tannin determination in Stryphnodendron barbatimão, Eucalyptus citriodora and Phyllanthus niruri, samples of plants commonly used in popular medicine.     

Direct Chiral HPLC Method for the Simultaneous Determination of Warfarin Enantiomers and Its Impurities in Raw Material and Pharmaceutical Formulation: Application of Chemometric Protocol

Warfarin is a well-known anticoagulant agent that occurs in two enantiomers, (R)-(+)-warfarin and (S)-(?)-warfarin, in which 4-hydroxycoumarin and benzalacetone are commonly found as impurities. Due to the lack of analytical reports for the simultaneous estimation on warfarin and its impurities in bulk drug and pharmaceuticals, we aim at the simultaneous estimation and optimization of the chromatographic separation of warfarin and its related substances employing experimental design. Central composite design was employed to evaluate the influence of two independent variables (concentration of organic modifier and flow rate) on the output responses: capacity factor (k ₁), resolution of the peak (Rs _3,4), and retention time of the last peak (tR ₅), as well as to model these responses. Further, the central composite design results were combined in a multicriteria decision-making approach in order to obtain a set of optimal experimental conditions leading to the most desirable compromise between resolution and analysis time.     

How experimental design can improve the validation process. Studies in pharmaceutical analysis

A critical discussion about the possibility of improving the method validation process by means of experimental design is presented. The reported multivariate strategies concern the evaluation of the performance parameters robustness and intermediate precision, and the optimisation of bias and repeatability. In particular, accuracy and precision improvement constitutes a special subset of experimental design in which the bias and the relative standard deviation of the assay are optimised. D-optimal design was used in order to plan experiments for this aim. The analytical methods considered were capillary electrophoresis, HPLC, adsorptive stripping voltammetry and differential pulse polarography. All methods were applied to real pharmaceutical analysis problems.     

Methodology of multicriteria optimization in chemical analysis Some applications in stripping voltammetry

Multicriteria optimization, widely used in engineering, does not much used in the optimization of analytical signals. The aim of this paper is to show the usefulness of the desirability function to optimize instrumental responses obtained in instrumental analysis. The simultaneous optimization of a signal and of its variability is a generic question of interest to any chemical analyst. It is clear that the improvement of the two responses forms the basis of the validation of any analytical method, and affects all the figures of merit: accuracy (trueness and precision), capability of detection, robustness, sensitivity, etc. Furthermore, in the specific case of electroanalysis, an improvement in the signal may implicitly mean an increase of the signal in the blank, such that the “net signal” may not improve. This experimental approach (surface response methodology plus desirability) to multicriteria optimization has been applied to three cases of growing complexity. Thus, in the determination of Cu(II) by differential pulse anodic stripping voltammetry the simultaneous maximization of the peak current and minimization of its standard deviation is looked for. Whereas, in the determinations of Ni(II) and indomethacin by differential pulse adsorptive stripping voltammetry, the simultaneous maximization of the peak current and minimization of the blank signal is desired. In all the cases, the experimental conditions where the optima are found for each individual response are just opposite, so it is required to look for a certain compromise, that is achieved using the desirability function.     

A software package for the orthogonal polynomial approximation of analytical signals,including a simulation program for chromatograms and spectra

The computer package calculates the coefficients of the terms of orthogonal polynomial series used to approximate the analytical signal. Two different polynomial series (Hermite and Chebyshev) are used, depending on the number of peaks and spreading of the error of the approximation over the interval. The package is applied for data reduction and filtering of the analytical signal. Part of the package facilitates optimization in chromatography, by calculating the effect of varying chromatogram parameters on polynomial terms. Some scaling methods for the analytical signal are discussed. For testing purposes, a program that generates chromatograms is added to the computer package. The program simulates chromatographic peaks with user-defined peak parameters; noise can be added. The theoretical background is described and some results are presented.     

Determination of the design space of the HPLC analysis of water‐soluble vitamins

Analysis of water‐soluble vitamins has been tremendously approached through the last decades. A multitude of HPLC methods have been reported with a variety of advantages/shortcomings, yet, the design space of HPLC analysis of these vitamins was not defined in any of these reports. As per the food and drug administration (FDA), implementing the quality by design approach for the analysis of commercially available mixtures is hypothesized to enhance the pharmaceutical industry via facilitating the process of analytical method development and approval. This work illustrates a multifactorial optimization of three measured plus seven calculated influential HPLC parameters on the analysis of a mixture containing seven common water‐soluble vitamins (B₁, B₂, B₆, B_12, C, PABA, and PP). These three measured parameters are gradient time, temperature, and ternary eluent composition (B1/B2) and the seven calculated parameters are flow rate, column length, column internal diameter, dwell volume, extracolumn volume, %B (start), and %B (end). The design is based on 12 experiments in which, examining of the multifactorial effects of these 3 + 7 parameters on the critical resolution and selectivity, was carried out by systematical variation of all these parameters simultaneously. The 12 basic runs were based on two different gradient time each at two different temperatures, repeated at three different ternary eluent compositions (methanol or acetonitrile or a mixture of both). Multidimensional robust regions of high critical R_s were defined and graphically verified. The optimum method was selected based on the best resolution separation in the shortest run time for a synthetic mixture, followed by application on two pharmaceutical preparations available in the market. The predicted retention times of all peaks were found to be in good match with the virtual ones. In conclusion, the presented report offers an accurate determination of the design space for critical resolution in the analysis of water‐soluble vitamins by HPLC, which would help the regulatory authorities to judge the validity of presented analytical methods for approval.     

Multiobjective Optimization Approach in Evaluation of Chromatographic Behaviour of Zolpidem Tartrate and Its Degradation Products

Multiresponse optimization methodology in combination with experimental design was employed as a powerful technique for simultaneous optimization of input variables significant for evaluation of chromatographic behaviour of zolpidem tartrate, zolpacid, oxozolpidem, zolpyridine and zolpaldehyde towards various responses. In the first stage of the investigation fractional factorial design was used to decrease the number of variables that should be studied in detail. Among examined variables, pH of the mobile phase, percentage of organic modifier and buffer concentration showed to be statistically important and were consequently optimized with central composite design and Derringer??s desirability function. Four responses were considered, the retention factors of zolpacid and zolpaldehyde (the first and last peak) and the resolutions between critical peaks. Optimal conditions included Luna C₁₈(2) analytical column (250?mm?x?4.6?mm, 5???m particle size), mobile phase consisted of methanol?C10?mM ammonium acetate (68.4:31.6, v/v, pH 5.4) and column temperature of 35???C. The flow rate of the mobile phase was 1?mL?min^?1 and the detection was performed at 254?nm. At the end, the method was successfully validated in accordance with ICH guideline and subsequently applied to the analysis of commercially available zolpidem tartrate tablets.     

生成模型在蛋白质序列设计中的应用

蛋白质是一切生命体的物质基础,是生命活动的主要承担者,参与各种生理功能的调节.设计具有特定功能的蛋白质在蛋白质工程、生物医药、材料科学等领域具有重要意义.蛋白质序列设计的目标是设计能够折叠成期望结构并具有相应功能的氨基酸序列,是所有理性蛋白质工程的核心问题,具有极其重要的研究和应用潜力.随着蛋白质序列数据的指数型增长和...     

Fenton’s reagent for kinetic determinations

The use of the Fenton’s reagent (FR) (a mixture of H₂O₂ and Fe²⁺) for the kinetic determination of individual chemical species is proposed. The possibilities of the reagent arise from the oxidant power of intermediate species generated during the slow oxidation of Fe²⁺ by H₂O₂, but very few analytical applications of the reagent can be found. The oxidation of organic compounds (known as the Fenton reaction) is in fact an induced chain reaction that proceeds to an extension which is influenced by the reaction conditions. Experimental design has been used for optimization thinking of the analytical application. The pesticide atrazine has been used as analyte to test the analytical possibilities of the FR. Partial least squares regression (PLS), applied to reaction profiles between 206 and 270 nm, was used as algorithm to make the calibration model. Atrazine concentrations ranging from 0.46 to 13.4×10⁻⁵ M have been used for calibration, and mean errors under 2.5% both for calibration and validation have been found. Other classical methods of calibration such as those using absolute values of absorbance, initial rates, etc. gave poor results in the cases considered. According to the study of interferences, the main drawback of the reagent is the lack of selectivity, but some possible ways of improving it are discussed. The method was applied for the determination of atrazine in several commercial atrazine-based pesticide preparations. In general, good results were obtained when compared with those found by gas-liquid chromatography as a reference. Recovery studies also gave satisfactory results.