A better global resolution function and a novel iterative stochastic search method for optimization of high-performance liquid chromatographic separation

HPLC optimization strategy consists of four elements; experimental design, retention modeling, quality criteria function, and optimum search method. In this paper we present a simple, superior alternative to general classes of classical resolution functions (S function) and a novel optimum search algorithm (iterative stochastic search, ISS) for HPLC optimization. Comparison of S with general classes of resolution-based quality criteria functions (Rs, Rp, and Rmin) shows superior features such as correct assessment of favorable separation conditions, preservation of peak pair contributions, elimination of arbitrary cut-off values, and a unique capability to interpret absolute significance of function values through a simple inequality. The proposed ISS algorithm is more robust than standard methods and it is easily applicable to hyperdimensional optimization. ISS also shows clear advantages in its ability to correctly identify the global optimum (instead of local optimum), with higher precision, with more efficient use of computation cycles, and with easier implementation. Successful application of S and ISS to HPLC optimization was demonstrated in the separation of representative functionalities (sugars, alcohols, and organic acids) present in microbial fermentations. Both the optimal and pathological (worst) conditions were successfully predicted and experimentally verified.     

Systematic optimisation of high-performance liquid chromatographic separation by varying the temperature, gradient, and stationary phase

Optimisation of the separation of a synthetic drug mixture by HPLC is performed by changing both continuous variables, i.e. mobile phase composition and temperature, and categorical variables, here the stationary phase. The retention of solutes is described on the basis of a general linear model in which the different columns are modelled by indicator variables. From the solute-specific retention models the global separation optimum is evaluated on the basis of multidimensional window diagrams using relative retentions of all peak pairs as the figure-of-merit.     

“PRISMA” Model for Computer-Aided HPLC Mobile Phase Optimization Based on an Automatic Peak Identification Approach

Abstract

The tripartite “PRISMA” optimization model, as part of the “PRISMA” system, includes all possible solvent combinations between 1–4 solvents, with a possible fifth one as modifier. The solvent composition is characterized by the solvent strength (S_T) and the selectivity points (P_S).

At a constant S_T the correlation between the P_S and the retention data (horizontal function) can be described by a quadratic function. For constant P_S the solvent strengths and retention data correlate (vertical function) with a logarithmic function. These correlations are used to formulate a mathematical model for the dependence of retention times (capacity factor) on the mobile phase composition. Unknown compounds are estimated in the mathematical model from a sequence of standard chromatograms after having identified individual peaks by an automatic procedure. Only retention times, relative peak areas, and information about the mobile phase compositions are required as input for the identification approach. The approach involves a combination of statistical methods which exploit both the basic properties of retention data and the mathematical relation between retention data, selectivity points, and solvent strength as derived from the “PRISMA” model. Diagnostic information for checking the identification is generated as a by-product. The mathematical model completed by the estimated constants predicts the expected retention times for each possible mobile phase combination. Peak start and peak end times are predicted in a way similar to the retention times, once the identification has been performed. The most important aspects of a chromatogram can thus be predicted for arbitrary mobile phases.

The separation quality of predicted chromatograms is assessed by the chromatographic response function (CRF). The optimal mobile phase combination is that which theoretically generates the chromatogram with the maximal CRF value. This optimal composition is found by a simple mathematical procedure, which maximises the CRF in dependence upon the mobile phase combination. The optimum found is a local one if the starting set of chromatograms contains no variation of the solvent strength, and a global one if, in the set of starting chromatograms, the solvent strength is varied in a suitable way. Recommendations for the starting position are given.

Twelve measurements are necessary for a local optimum, and 15 for the global one. To increase the accuracy, six measurements at three different solvent strength levels are proposed. Generally the highest and the lowest solvent strength level differ by ±(5)% from the middle level.

This strategy is also relevant when modifiers are used in constant amounts. The chromatographic behavior of substances to be separated can be predicted with 1% accuracy from correlations of k' values and selectivity points. Based on these relationships, an automatical mobile phase optimization strategy for isocratic separations is suggested with the “PRISMA” model.     

Computer-assisted method development and optimization in high-performance liquid chromatography

This paper reports the use of DryLab, a computer simulation software package, to assist in the development and optimization of a reversed-phase high-performance liquid chromatographic (HPLC) method for the separation of a model drug candidate and its degradation products. Prior to the optimization process, columns with various bonded phases are evaluated for their chromatographic performance using the sample of interest. Simultaneous optimization of two separation variables and the use of resolution maps to predict the optimal conditions are illustrated. Options to optimize column conditions (column length and flow-rate) to further reduce run time are briefly discussed. The accuracy of DryLab-predicted retention times and resolution is compared with experimental values. The DryLab software used in this study provided satisfactory predictions for the selected model, with average errors of less than 3.5 and 11.8% for retention time and resolution, respectively.     

Prediction of peak shape as a function of retention in reversed-phase liquid chromatography

Optimisation of the resolution of multicomponent samples in HPLC is usually carried out by changing the elution conditions and considering the variation in retention of the analytes, to which a standard peak shape is assigned. However, the change in peak shape with the composition of the mobile phase can ruin the optimisation process, yielding unexpected overlaps in the experimental chromatograms for the predicted optimum, especially for complex mixtures. The possibility of modelling peak shape, in addition to peak position, is therefore attractive. A simple modified-Gaussian model with a parabolic variance, which is a function of conventional experimental parameters: retention time (tR), peak height (H0), standard deviation at the peak maximum (sigma0), and left (A) and right (B) halfwidths, is proposed. The model is a simplification of a previous equation proposed in our laboratory. Linear and parabolic relationships were found between the peak shape parameters (sigma0), A and B) and tR, with a mean relative error of 1-5% in most cases. This error was partially due to variations in peak position and shape among injections, which in some cases were above 2%. Correlations between (sigma0, A and B) and the retention time, which is easily modelled as a function of mobile phase composition, allowed a simple and reliable prediction of chromatographic peaks. A parameter that depends on the slopes of the linear relationships for A and B versus tR is also proposed to evaluate column efficiency. The modified-Gaussian model was used to describe the peaks of six diuretics of diverse acid-base behaviour and polarity, which were eluted with 15 mobile phases where the composition was varied between 30 and 50% (v/v) acetonitrile and the pH between 3 and 7.     

HPLC of nucleotides. II. General methods and their development for analysis and preparative separation. An approach to selectivity control

In order to develop efficient separation methods for nucleotides according to their size and heterocyclic composition, the application of ion-exchange, reverse-phase, and normal-phase adsorption HPLC has been studied. The comparative investigation of retention power and selectivity of various packings (non-polar bonded-phase and amino silicas) in relation to nucleotide length and composition yields data which enable suitable packings to be selected and a method of preparing the new packing for a particular separation problem to be formulated. Thus a new anion exchanger with high selectivity and dynamic mass transfer has been prepared for fractionation of large oligonucleotides. The effect of the eluent pH and composition (organic modifier, salt) on retention, selectivity, and resolution in ion-exchange and reverse-phase HPLC has been studied. The optimum separation conditions comprise elution with oppositely directed gradients of the salt and the modifier, use of a precolumn packing that provides the best protection for the main column without loss of its efficiency, and the optimum gradient program for the desired retention of the component of interest. The relation between loading and sample concentration has been studied and the system for gradient elution improved. Our work shows that two-dimensional separation is the most reliable and informative method for preparation of homogeneous oligonucleotides. The hydrophobic-pair ion-exchange mechanism is proposed for ion-pair chromatography. Protected and partially deblocked oligonucleotides, chemically synthesized for genetic engineering studies, have been separated with high selectivity by adsorption (normal-phase) HPLC which is efficient for gradient elution with isohydric eluents. The analysis of a monomeric composition of nano-(pico-) molar amounts of oligonucleotides has been developed; the procedure involves microcolumn digestion of the oligonucleotides with immobilized enzymes followed by microcolumn separation of the nucleoside-mononucleotide mixture. Also, a new slurry method for packing stable HPLC columns with a tightly consolidated, nonshrinkable bed of particles has been developed.     

Overpressured layer chromatography in comparison with thin-layer and high-performance liquid chromatography for the determination of coumarins with reference to the composition of the mobile phase

The retention behaviour of fifteen closely related coumarins in normal-phase overpressured layer chromatography (OPLC) was studied with the aim of comparing the retentions with those in normal-phase thin-layer chromatography (TLC) and high-performance liquid chromatography (HPLC) when optimization of the mobile phase was carried out according to the PRISMA system. The mobile phase optimization was carried out on TLC plates in unsaturated chambers. The resulting mobile phases were transposed to off-line, non-equilibrated OPLC and further to HPLC. The retention in TLC was measured at 37 selectivity points and in OPLC and HPLC at 13 points. Capacity factors (k′) and separation factors () were calculated in order to study the retention behaviour in the different systems. Two- and three-dimensional evaluations of k′ against selectivity points showed similar retention behaviours for the coumarins in TLC, OPLC and HPLC. The values for TLC, OPLC and HPLC showed similar patterns in the three-dimensional evaluations. The retention behaviour at different solvent strengths was also examined. According to quadratic regression, k′ showed a dependence on the change in solvent strength. OPLC, which can be considered as a “planar column” technique, and TLC are closely related methods, whereas HPLC shows a different behaviour in the elution process with regard to solvent strength.     

Optimization of a multisolvent composition in RP-HPLC: Convenient criterion for preliminary search for the best eluent strength

Summary Interpretive methods are very commonly used to direct the search for the optimum solvent composition. For multisolvent systems, the composition search space is often reduced to one straight line (ternary systems with two organic modifiers), three straight lines (three ternary systems with each possible pair of the organic modifiers of the tetrahedron) — or a plane delimited by a triangle (quaternary systems inside the solvent tetrahedron). In each case, the space is restricted by binary compositions of equal solvent strength, in such a way that through it, the analysis time remains approximately constant. This restricted space is defined without taking into account any selectivity criterion between peaks, and consequently, if a given pair of peaks is badly resolved with the considered binary solvents, the probability of any mixture of them improving the peak selectivity will be very low. The ability to calculate the retention models in a binary solvent system from two linear gradient runs, allows the prediction of the selectivity for each pair of solutes into each binary solvent system (ACN/Water, MeOH/Water, THF/Water) from six preliminary linear gradient runs, and then, to determine and eliminate all the sets of isoeluotropic binary compositions that will offer little hope of giving useful separation conditions with multisolvent systems and, at the same time, to select the most promising set of binary compositions. The selectivity and the total time of the chromatogram are the two parameters that are considered for this search. When several possiblities are found, priority is given to the simplest solvent system (binary rather than ternary and ternary rather than quaternary). Reducing the number of preliminary experiments and improving the accuracy of the predicted optimum are the two objectives of this approach. Its practical interest is discussed by comparing the results obtained for an illustrative separation to those obtained with another existing method.     

Capillary electrochromatography-mass spectrometry for the separation and identification of isomeric polyaromatic hydrocarbon DNA adducts derived from in vitro reactions

Capillary electrochromatography (CEC) is an emerging technique that combines features of both micro-capillary high-performance liquid chromatography (microHPLC) and capillary electrophoresis (CE). This separation technique possesses high speed and the efficiency of an electro-driven system, while the selectivity and sample loadability compare to those of a packed capillary LC column. Since the separation mechanism is based on that of HPLC, the concept of isoeluotropic strength and selectivity of solvents as well as the on-column focusing techniques for sample introduction used in LC can be applied in CEC. This article examines some of these features of CEC in the context of our own experiences with the technique. More specifically, emphasis is placed on applications of CEC to the analysis of DNA adducts of polyaromatic hydrocarbons by coupling CEC to mass spectrometry. It is shown that, with proper selection of mixed organic modifiers in the mobile phase, i.e. ternary and quaternary mobile phases, complex DNA adduct mixtures derived from in vitro reactions can be separated isocratically with improved selectivity and much greater speed than by HPLC. Additionally, the speed of the analysis is further enhanced by employing a step gradient. Furthermore, CEC may be easily coupled to mass spectrometry such that the characterization of each isolated component from the mixtures is performed on-line with the separation. By using on-column focusing, the sample loadability onto a CEC column is improved.     

Designing polymer matrix for microchip-based double-stranded DNA capillary electrophoresis

An optimization strategy for ternary solvent-strength gradient elution RP chromatography is described in which a two-dimensional model of gradient time (2 levels) against ternary proportions of organic modifiers (4 levels) was constructed. From the resolution surface the optimum ratio of organic modifiers could be selected. Excellent retention time and acceptable peak width and resolution simulations were obtained. The separation could be further optimized from the same input data by using a standard one-dimensional model in order to optimize for gradient slope, duration and shape. Excellent retention time and acceptable peak width and resolution simulations were obtained (< 1, 2 and 6% error, respectively).     

Modelling the gas chromatographic separation of multicomponent samples on a system of three open-tubular columns coupled in series

A procedure was developed for modelling the gas chromatographic separation on a system of columns coupled in series. This procedure can be used for computer based optimization of lengths and order of serially coupled columns at isothermal conditions. The sample component retention factors and column resistances needed for the model can easily be measured on each individual column. The proposed procedure was verified by analyzing a 52 component hydrocarbon mixture on three columns of different polarity coupled in series by various column orders. Good agreement between experimental and calculated retention data was found. The procedure is also well suited for optimization of the chromatographic selectivity by coupling columns with different selectivity in series.Dedicated to Professor Dr. h.c. mult. J.F.K. Huber on the occasion of his 70th birthday     

Optimizing separations in reversed-phase liquid chromatography by varying pH and solvent composition

Summary An interpretive optimization procedure in which pH can be one of the variables is presented with the emphasis on optimizing separations. When varying the pH in reversed-phase liquid chromatography the retention of ionogenic solutes will change. Thus, the selectivity between ionogenic and neutral solutes or between ionogenic solutes mutually can be optimized. However, pH also greatly affects the efficiency (plate count) and peak shape (asymmetry). Optimum selectivity (i.e. large differences in retention times) may be observed under conditions where peaks are broad and asymmetrical. Thus, it is essential to simultaneously consider retention, peak width and peak shape and their effects on separation (effective resolution) in pH-optimization studies. A procedure in which this is done is presented and applied to optimizing the separation of a synthetic mixture of selected pharmaceuticals. After initial experiments to establish the parameter space (boundaries for pH and binary methanol — water composition), twelve experiments are performed according to a 3×4 experimental design. At each loaction the retention, peak height, peak area and peak symmetry are recorded for each solute. These data are then used to build models for each of the four characteristics and for each solute. From this set of models the response surface, describing the quality of separation as a function of pH and composition, can be calculated. A variety of optimization criteria (quantifying quality of separation) can be used. The optimum corresponds to the highest point on the response surface.     

A simple procedure for the rapid optimization of reversed-phase separations with ternary mobile phase mixtures

Summary A simple rapid procedure is described for estimating optimum compositions of ternary mobile phase mixtures for the separation of samples by reversed-phase liquid chromatography (RPLC). Retention data in two iso-eluotropic binary mobile phase mixtures (mixtures with equal retention times) are required to initiate the procedure. The logarithm of the capacity factor is assumed to vary linearly with the composition of isoeluotropic ternary mixtures formed by mixing the two limiting binaries. Using the product of resolution factors of adjacent peaks as the criterion, an optimum ternary composition is then calculated. After a chromatogram has been obtained with the predicted optimum ternary mobile phase, the procedure is repeated until no further improvement can be achieved. Examples of the application of the present procedure are described to illustrate its effectiveness.     

基于石墨化炭黑预涂覆技术的色谱柱制备和性能评价

采用石墨化炭黑(GCB)预涂覆技术对白酒分析专用色谱柱(LZP-930)的制备方法进行了优化,详细考察了所制备的色谱柱(LZP-930G)的性能参数,并对LZP-930G色谱柱的保留行为进行了评价,探讨了GCB对LZP-930G色谱柱性能的影响。研究发现,LZP-930G色谱柱的柱效、惰性、稳定性和极性均得到了明显提高,从而改善了酸类和醇类组分的分离选择性和色谱峰峰形,实现了白酒中53种易挥发和半挥发性微量组分的同时分离,且各组分的保留时间和峰面积的相对标准偏差分别小于0.63%和4.51%(n=5)。表明GCB预涂覆技术能够用于高性能白酒分析色谱柱的制备方法。     

Peptide nucleic acid and amino acid modified peptide nucleic acid analysis by capillary zone electrophoresis

A rapid, high resolution, and low sample consumption CZE method is developed for peptide nucleic acid (PNA) analysis for the first time. 30% v/v acetonitrile in PNA sample and 20% v/v acetonitrile in 50 mM borax‐boric acid (pH 8.7) as BGE were employed after optimization. The calibration curves were linear for PNA concentration ranging from 1 to 50 μmol/L. LOD and LOQ of PNA were 0.2 and 1.0 μmol/L, respectively. Since the commercially available reagent gives rise to huge PNA peak and an apparent impurity peak, the purity of PNA was evaluated to be about 81.4% by CZE method, obviously lower than the supplier's purity value of 99.9% evaluated by RP–HPLC, and also lower than 94.8% determined with RP–HPLC by our research group. The CZE method takes only 5 min, needs only 90 nL PNA, much less than 20 min and 20 μL PNA in RP–HPLC method. Moreover, the CZE method is applicable for the analysis of glutamic acid modified and lysine modified PNAs, they show different migration time with their corresponding complementary PNAs. Our results show CZE provides a new choice for PNA and modified PNA analysis, also their purity or quality evaluation.     

Effect of temperature and flow-rate on analysis of basic compounds in high-performance liquid chromatography using a reversed-phase column

The peak shape and retention of some basic probes together with a neutral reference compound were investigated as a function of temperature and flow-rate using a reversed-phase HPLC column at both pH 3.0 and pH 7.0. The retention of bases often showed an anomalous increase with temperature; retention mechanisms are complex as shown by studies of the effect of buffer cation concentration on retention. Considerable improvements in column efficiency for bases may result from operation at elevated temperature. Improvements did not seem attributable either to incidental changes in the retention factor, or (in this particular study where low sample masses were utilised) to the influence of sample load. The optimum flow-rate for highest efficiency is generally lower for basic compounds than neutrals, and due to the steepness of the Van Deemter curves obtained, high flow-rates appear to be particularly detrimental in the chromatography of basic compounds.     

Synthesis and application of molecularly imprinted polymer on selective solid-phase extraction for the determination of monosulfuron residue in soil

A novel sample clean-up procedure using molecularly imprinted polymer as the solid-phase extraction material for the determination of monosulfuron residue in soil samples has been developed. The molecularly imprinted polymer (MIP) was synthesized by non-covalent method with monosulfuron as the template. The selectivity and affinity of the MIP was evaluated by equilibrium adsorption and HPLC experiments, which demonstrated that the MIP has specific affinity for the template. The template-MIP interaction was studied by investigating the influence of different mobile phases on the retention of the template, which provided basic knowledge for the selection of the washing and elution solutions in the molecularly imprinted solid-phase extraction (MISPE) process. The study indicated that polar organic solvents with hydrogen bonding abilities have stronger eluting strength for the monosulfuron. After the MISPE procedure, a clean baseline was obtained in the HPLC quantification analysis. The recoveries of the method using the combination of MISPE and HPLC were above 93% and the R.S.D. was less than 3.2% in the soil sample determinations. Low detection limit (0.08 microg g(-1), when defined as 3 times of the noise) was also obtained in the method evaluation study.     

The determination of starting conditions for modifier optimization in reversed-phase HPLC

Summary After a brief introduction of the subject, the paper focusses on the first step in any optimization procedure: the delineation of the parameter space, wherein the global optimum is to be found. For organic modifier optimization in reversed-phase liquid chromatography it is shown that the necessary information can be derived from a single water-methanol gradient. It first yields an estimate of the total number of solutes in the sample, which is vital to define the peak capacity needed to achieve separation at a certain confidence level. Next, the gradient allows the prediction of suitable isocratic methanol binary solvents, and transfer rules formulate the iso-eluotropic composition of the common binary solvents (tetrahydrofuran and acetonitrile). Because all predictions are based on a statistical analysis of a limited data base, attention is given to the practical situation where an actual sample deviates from the average solute behaviour. Such deviations are revealed in the first isocratic run and can be used to arrive at a better estimate of solute retention.     

Chemometric analysis of comprehensive two-dimensional gas chromatography data using cryogenic modulation

The two-dimensional (2D) data structure generated under a high resolution GC×GC system with a small number of samplings taken across the first dimension is evaluated for the purpose of the application of chemometric deconvolution methods. Chemometric techniques such as generalized rank annihilation method (GRAM) place high demands on the reproducibility of chromatographic experiments. For GRAM to be employed for GC×GC data interpretation, it is critical that the separation method provides data with a bilinear structure; the peak-shape and retention times on both columns must be reproducible. With a limited number of samplings across a ¹D (first dimension) peak (e.g. four to six samplings) repeatability of the pattern of the modulated peaks (controlled by the modulation phase) becomes important in producing a bilinear data structure. Reproducibility of modulation phase can be affected by both reliability of the modulation period and reproducibility of the retention time of the peak on the first column (which arises from oven temperature and carrier flow rate stability). Evaluation of within-run and run-to-run retention time reproducibility (retention time uncertainty) on both columns, and modulation phase reproducibility using a modulated cryogenic system for a pair of overlapping components (fatty acid methyl esters) was undertaken. An investigation of the quality of data to permit quantification of each component by using GRAM deconvolution, was also conducted. Less than 4% run-to-run retention time uncertainty was obtained on column 1 and less than 9% run-to-run and within-run retention time uncertainty was obtained on column 2, where these R.S.D. measures are reported normalised to peak widths on each respective dimension. The R.S.D. of duplicate quantification results by GRAM ranged from 2 to 26% although the average quantification error using GRAM was less than 5%.