A complementary mobile phase approach based on the peak count concept oriented to the full resolution of complex mixtures

Situations of minimal resolution are often found in liquid chromatography, when samples that contain a large number of compounds, or highly similar in terms of structure and/or polarity, are analysed. This makes full resolution with a single separation condition (e.g., mobile phase, gradient or column) unfeasible. In this work, the optimisation of the resolution of such samples in reversed-phase liquid chromatography is approached using two or more isocratic mobile phases with a complementary resolution behaviour (complementary mobile phases, CMPs). Each mobile phase is dedicated to the separation of a group of compounds. The CMPs are selected in such a way that, when the separation is considered globally, all the compounds in the sample are satisfactorily resolved. The search of optimal CMPs can be carried out through a comprehensive examination of the mobile phases in a selected domain. The computation time of this search has been reported to be substantially reduced by application of a genetic algorithm with local search (LOGA). A much simpler approach is here described, which is accessible to non-experts in programming, and offers solutions of the same quality as LOGA, with a similar computation time. The approach makes a sequential search of CMPs based on the peak count concept, which is the number of peaks exceeding a pre-established resolution threshold. The new approach is described using as test sample a mixture of 30 probe compounds, 23 of them with an ionisable character, and the pH and organic solvent contents as experimental factors.     

A Novel Quality Criteria for Optimization of Chromatographic Multicomponent Separations

This study presents a Chromatographic Optimization Function (COF) to optimize chromatographic separation conditions. The COF proposed herein provides several advantages over conventional COFs, including the ability to eliminate the ambiguous selection of the weighting factors and easily obtain the acceptable or maximum resolution in the shortest separation time. The parameters used to construct this COF are in the form of sigmoidal functions to reduce the weight of the response for less acceptable conditions and to filter out undesired situations. In addition, resolution between peaks, length of separation time, and number of peaks separated are used as parameters for constructing the proposed COF. Closely examining the performance of the COF for both simulated and experimental chromatographic separations reveals an adequate correlation with human judgment and, also, creates no problems in selecting weighting factors.     

The statistical overlap theory of chromatography using power law (fractal) statistics

The chromatographic dimensionality was recently proposed as a measure of retention time spacing based on a power law (fractal) distribution. Using this model, a statistical overlap theory (SOT) for chromatographic peaks is developed that estimates the number of peak maxima as a function of the chromatographic dimension, saturation and scale. Power law models exhibit a threshold region whereby below a critical saturation value no loss of peak maxima due to peak fusion occurs as saturation increases. At moderate saturation, behavior is similar to the random (Poisson) peak model. At still higher saturation, the power law model shows loss of peaks nearly independent of the scale and dimension of the model. The physicochemical meaning of the power law scale parameter is discussed and shown to be equal to the Boltzmann-weighted free energy of transfer over the scale limits. The scale is discussed. Small scale range (small β) is shown to generate more uniform chromatograms. Large scale range chromatograms (large β) are shown to give occasional large excursions of retention times; this is a property of power laws where "wild" behavior is noted to occasionally occur. Both cases are shown to be useful depending on the chromatographic saturation. A scale-invariant model of the SOT shows very simple relationships between the fraction of peak maxima and the saturation, peak width and number of theoretical plates. These equations provide much insight into separations which follow power law statistics.     

Optimization by orthogonal array design of ion-pair HPLC separation of the enzymatic hydrolysis products of yeast RNA

<正>The separation of enzymatic hydrolysis products of yeast RNA by ion-pair HPLC was studied.A modified chromatographic response function(MCRF) was proposed to appraise the effectiveness of chromatographic separation.This function takes the number of peaks,resolution and the retention time of the last peak into consideration.It shows advantages for optimization of HPLC separation of complex mixtures.An orthogonal array design was used to separate the hydrolysate of yeast RNA and the optimal chromatographic conditions were obtained.     

A component tracking algorithm for accelerated and improved liquid chromatography-mass spectrometry method development

A method for tracking of sample components during liquid chromatography-mass spectrometry (LC-MS) method development has been proposed. The method manages to, fully automatically and without user intervention, find the chromatographic peaks in the data sets, discriminate them to sample components and track them when the separation conditions have been changed. The algorithm utilises the resolution obtained from all considered data sets and has the ability to discriminate the non informative parts. The technique has a great sensitivity even in cases where a majority of the tracked components cannot easily be spotted by means of traditional total ion chromatogram (TIC) or base peak chromatogram (BPC) representations. The method was tested on an experimental sample using six different columns and an average of 79% of the suggested sample components could be successfully tracked at a minimum area of 0.05% of the main component in the sample. 66 components with 79-92% of the total suggested component area were able to be tracked between all data sets. The method could be used to rapidly investigate selectivity during different types of separation conditions.     

Net analyte signal as a deconvolution-oriented resolution criterion in the optimisation of chromatographic techniques

The performance of two multivariate calibration measurements, multivariate selectivity (SEL(s)) and scalar net analyte signal (scalar NAS), as chromatographic objective functions (COFs), was investigated. Since both assessments are straightforwardly related to the quantification of analytes in the presence of interferents, they were expected to confer new features in the optimisation of compound resolution, not present in conventional assessments. These capabilities are especially interesting in situations of low resolution, where peak deconvolution becomes an attractive alternative. For comparison purposes, chromatographic resolution (R(s)) and peak purity (p(s)) were used as reference COFs. In order to correlate COFs with the probability of deconvolution error, an artificial peak crossing was used to generate 73 different peak arrangements, which were deconvolved using three different methods. SEL(s) exhibited the best correlation, which allowed predicting properly the risk of obtaining inaccurate deconvolutions. The optimisation of a poorly resolved mixture of 16 aromatic compounds by reversed-phase liquid chromatography with methanol-water and acetonitrile-water mobile phases was examined to investigate the differences in performance among the resolution criteria. In situations like these, SEL(s) tends to consider acceptable mobile phase compositions with partial coelution, which permits however the deconvolution with low errors. In contrast, p(s) selects compositions where the resolution of some compounds is sacrificed to enhance the separation of others. Scalar NAS was not so favourable as expected, since it depends on sampling frequency and peak widening. SEL(s) was not affected by these factors.     

Influence of the peak height distribution on separation performances: Discrimination factor and effective peak capacity

Summary A new index of performance of the chromatographic separation between two adjacent peaks, the discrimination factor, d₀, is defined. It is normalized between 0 and 1 and is directly and easily determined from the chromatogram. It does not depend on any assumption regarding peak shape, except that the peak profiles of individual sample components have a single mode. Its value depends on the relative heights of the two peaks as well as on their separation. The separation power of a chromatographic system is classically measured by its peak capacity, defined on the basis of constant resolution between adjacent peaks. A previously developed statistical theory of the composition of mixtures makes it possible to extend the concept of peak capacity by taking into account the peak height distribution in typical average chromatograms. A new parameter, the effective peak capacity, is defined for this purpose on the basis of a constant discrimination factor between adjacent peaks. It allows to take into account the distribution of peak heights in statistical theories of the evaluation of complex chromatograms and in the measurement of the limit of determination in quantitative analysis. The characteristics of the two new parameters, the discrimination factor and effective peak capacity, are discussed and compared with those of their classical homologs, resolution and peak capacity, in the case of gaussian component peaks of equal widths.     

Metrics of separation performance in chromatography. Part 1. Definitions and application to static analyses

Earlier introduced metrics of separation performance are described in a systematic way. After providing the definitions of the metrics suitable for a broad variety of applications, the study focuses on static analyses (isothermal GC, isocratic LC, etc.) and their general separation performance. Statistically expected number of resolved (adequately separated) single-component peaks is treated as the ultimate metric of general separation performance of chromatographic analysis. That number depends on the peak capacity of the analysis and the number of components in a test mixture. The peak capacity, in turn, depends on the separation capacity of a column and the lowest separation required by the data-analysis system for resolving poorly separated peaks. The separation capacity is a special case of a broader metric of the separation measure which is a function of column efficiency, solute separability, and the level of the solute interaction with a column stationary phase. The formulae for theoretical prediction of all these metrics for arbitrary pairs of peaks in static analyses are derived. To provide a better insight into the basic metrics of the separation performance, additional metrics such as the solute discrimination (relative difference in solute velocities), utilization of separability (solute discrimination per unit of their separability), specific separation (the separation per unit of separability), and others are defined and found for static analyses.     

Resolution of the Embedded Chromatographic Peaks by Modified Orthogonal Projection Resolution and Entropy Maximization Method

ABSTRACT

The embedded chromatographic peaks usually can not be completely resolved by conventional multivariate resolution methods. The resolution condition of a certain component in two-way data is first reviewed. A modified orthogonal projection resolution (OPR) algorithm and new entropy maximization (EM) method are then proposed to resolve embedded chromatographic peaks in this paper. The modified OPR algorithm performs more precisely than conventional orthogonal projection resolution algorithm in resolving the chromatography of minor peak. The entropy criterion defined on the differential chromatography could obtain an approximate solution in resolution of the major chromatographic peak. Simulated and real data show that the modified OPR and entropy maximization (EM) methods perform well in solving the embedded problem.     

Comparison of different types of stationary phases for the analysis of soy isoflavones by HPLC

Nowadays, there are new technologies in high-performance liquid chromatography columns available enabling faster and more efficient separations. In this work, we compared three different types of columns for the analysis of main soy isoflavones. The evaluated columns were a conventional reverse phase particle column, a fused-core particle column, and a monolithic column. The comparison was in terms of chromatographic parameters such as resolution, asymmetry, number of theoretical plates, variability of retention time, and peak width. The lower column pressure was provided by the monolithic column, although lower chromatographic performance was achieved. Conventional and fused-core particle columns presented similar pressure. Results also indicate that direct transfer between particle and monolithic columns is not possible requiring adjustment of conditions and a different method optimization strategy. The best chromatographic performance and separation speed were observed for the fused-core particle column. Also, the effect of sample solvent on the separation and peak shape was evaluated and indicated that monolithic column is the most affected especially when using higher concentrations of acetonitrile or ethanol. Sample solvent that showed the lowest effect on the chromatographic performance of the columns was methanol. Overall evaluation of methanol and acetonitrile as mobile phase for the separation of isoflavones indicated higher chromatographic performance of acetonitrile, although methanol may be an attractive alternative. Using acetonitrile as mobile phase resulted in faster, higher resolution, narrower, and more symmetric peaks than methanol with all columns. It also generated the lower column pressure and flatter pressure profile due to mobile phase changes, and therefore, it presents a higher potential to be explored for the development of faster separation methods.     

A new chromatographic response function for use in size-exclusion chromatography optimization strategies: Application to complex organic mixtures

A new chromatographic response function (CRF) is presented aiming at designing an optimal chromatographic separation protocol for assessing the molecular size distribution of complex organic mixtures, such as those of natural organic matter from different sources (atmospheric, aqueous, and terrestrial). This CRF can be applied to mixtures of unknown solutes, being well suited for describing separation processes of pair of peaks of highly unequal area, and also for overlapping and asymmetric peaks. The performance of the developed CRF was compared to that of an existing response function, using simulated chromatograms. The capability of the new function to qualify the resolution degree that it is attained under different chromatographic conditions was further assessed through a size-exclusion chromatography study of a variety of different organic compounds, via a two-level full factorial design. It was proved that this function is a reliable alternative to optimize simultaneously the composition of the mobile phase (pH, ionic strength, and organic modifier concentration) and the instrumental variables (flow rate).     

The dimensionality of chromatographic separations

The box-counting or capacity dimension algorithm, known from the fractal mathematics literature, is used to measure the dimensionality D of chromatographic separation techniques for any number of dimensions. It is shown that D has limit properties that match Giddings' sample dimensionality s. D values are shown to be sensitive to the uniformity of peak spacing. A number of examples are given where D is calculated for various limits in one- and two-dimensional separations and for heart-cutting separations. The use of D as a quantitative measure of multidimensional orthogonality is suggested as D, due to the scale-free nature, is not dependent on the effective separation area. The connection to statistical peak overlap theory is discussed.     

Semi-automated alignment and quantification of peaks using parallel factor analysis for comprehensive two-dimensional liquid chromatography–diode array detector data sets

Parallel factor analysis was used to quantify the relative concentrations of peaks within four-way comprehensive two dimensional liquid chromatography–diode array detector data sets. Since parallel factor analysis requires that the retention times of peaks between each injection are reproducible, a semi-automated alignment method was developed that utilizes the spectra of the compounds to independently align the peaks without the need for a reference injection. Peak alignment is achieved by shifting the optimized chromatographic component profiles from a three-way parallel factor analysis model applied to each injection. To ensure accurate shifting, components are matched up based on their spectral signature and the position of the peak in both chromatographic dimensions. The degree of shift, for each peak, is determined by calculating the distance between the median data point of the respective dimension (in either the second or first chromatographic dimension) and the maximum data point of the peak furthest from the median. All peaks that were matched to this peak are then aligned to this common retention data point. Target analyte recoveries for four simulated data sets were within 2% of 100% recovery in all cases. Two different experimental data sets were also evaluated. Precision of quantification of two spectrally similar and partially coeluting peaks present in urine was as good as or better than 4%. Good results were also obtained for a challenging analysis of phenytoin in waste water effluent, where the results of the semi-automated alignment method agreed with the reference LC–LC MS/MS method within the precision of the methods.     

Peak-splitting in reversed-phase,ion-pair high-performance liquid chromatography of sympathomimetic drugs and its probable mechanism

Summary In the determination of ephedrine using reversed-phase, ion-pair liquid chromatography, a chromatographically pure sample was observed to give three peaks under certain mobile phase conditions. The mobile phases which produced maximum peak splitting were determined for ephedrine and a number of other sympathomimetic drugs.A proposal that peak splitting was the result of the composite interplay of two discrete chromatographic mechanisms, was investigated. The results of analysis by GC/MS confirmed that each peak was due to ephedrine, however, only one of the three split peaks was found to contain ion pairs. It is postulated that peak splitting is a physical phenomenon on reversed-phase columns and the separation of these drugs by ion-pair HPLC is based on a mixed rather than a single mechanism.This study has also shown that errors can arise in ion-pair HPLC when multiple peaks are assumed to indicate heterogeneity. Interconvertible species of the same solute can give rise to these peaks.     

正交投影用于多波长色谱重叠峰分析

 将正交投影分辨 (OPR)技术用于多波长色谱重叠峰分辨 ,当色谱峰中最大重叠度小于或等于波长数时 ,用这一方法能从多波长色谱重叠峰中获得完全真解。基于双波长色谱分析 ,提出了一种新的色谱重叠峰中背景校正、组分数和纯组分信号区确定以及各组分重叠情况的分析方法 ,即双波长特征信息分析 (DWCI)。该法被成功的用于三组分双峰和双组分单峰重叠色谱的分析。     

Automated molecular weight assignment of electrospray ionization mass spectra.

Process improvements in the synthesis of therapeutic agents and their intermediates are often facilitated by identification of reaction by-products. Analysis by liquid chromatography/mass spectrometry (LC/MS) with electrospray ionization is a powerful approach for obtaining molecular weight information for these compounds. Such analyses are well suited for 'open-access' mass spectrometry using generic chromatographic conditions, provided spectral interpretation for unknown compounds is facile. We have developed a software application (MassAssign) that facilitates automated data processing and molecular weight assignment for chromatographic peaks detected by any standard ultraviolet-visible wavelength detector. The program assigns [M + H](+) ions (and thus molecular weight) in the mass spectra using predetermined criteria. This evaluation process differentiates [M + H](+) ions from other signals in a complex mass spectrum such as those resulting from chromatographic coelution or the presence of multiple species (i.e., fragment ions, singly charged ions, doubly charged ions, adduct ions, proton-bound dimers, etc.). Once the program has evaluated all ions in a mass spectrum that exceed a preset abundance threshold, MassAssign reports either a numeric value-indicating the chromatographic peak consists of a single component having the displayed molecular weight, 'MC'-indicating the peak consisted of multiple components, or 'ND'-that a molecular weight could not be determined unequivocally. The performance of the program was evaluated by comparing mass assignments made by MassAssign against manual interpretation for 55 samples analyzed by positive electrospray ionization using a generic HPLC method. Correct molecular weight assignments were obtained in 90% of the cases.     

Simple and Efficient Solution for Robustness Testing in Gradient Elution Liquid Chromatographic Methods

In this paper, an efficient way for robustness testing of gradient elution liquid chromatographic methods is proposed and tested on model mixtures comprising cilazapril, hydrochlorothiazide, and their degradation products, solutes that differ not only in polarities, but also in solubility and absorption characteristics. In general, the robustness could be tested with respect to various responses: resolution, retention factor, selectivity factor, change of detector response, etc. In chromatographic methods, the separation of the adjacent peaks is mandatory, and, consequently, the resolution is usually used as response. In isocratic elution methods, the resolution threshold depends on many factors, such as sizes of adjacent peaks, peak shapes, and asymmetry factor. At the same time, the situation is even more complex in gradient elution methods, because separation depends on a larger number of parameters, such as gradient profile, column geometry, mobile phase flow rate, column equilibration between gradient runs, etc. To ensure baseline separation, the authors propose application of separation criterion (s) as response and indirect modeling in the robustness evaluation. Examined response in this approach is represented by the difference between the retention time of the beginning of the peak and the retention time of the end of the previously eluting peak of the critical pair. Moreover, the proposed methodology included reusing experiments from the optimization phase to define a robust chromatographic region without increasing the number of experiments. It was shown that method robustness can be easily and efficiently evaluated by this methodology.     

Approaches to characterise chromatographic column performance based on global parameters accounting for peak broadening and skewness

Peak broadening and skewness are fundamental parameters in chromatography, since they affect the resolution capability of a chromatographic column. A common practice to characterise chromatographic columns is to estimate the efficiency and asymmetry factor for the peaks of one or more solutes eluted at selected experimental conditions. This has the drawback that the extra-column contributions to the peak variance and skewness make the peak shape parameters depend on the retention time. We propose and discuss here the use of several approaches that allow the estimation of global parameters (non-dependent on the retention time) to describe the column performance. The global parameters arise from different linear relationships that can be established between the peak variance, standard deviation, or half-widths with the retention time. Some of them describe exclusively the column contribution to the peak broadening, whereas others consider the extra-column effects also. The estimation of peak skewness was also possible for the approaches based on the half-widths. The proposed approaches were applied to the characterisation of different columns (Spherisorb, Zorbax SB, Zorbax Eclipse, Kromasil, Chromolith, X-Terra and Inertsil), using the chromatographic data obtained for several diuretics and basic drugs (β-blockers).