Verification of statistical-overlap theory in micellar electrokinetic chromatography

The limited peak capacity of neutral compounds in micellar electrokinetic chromatography (MEKC) causes peak overlap in a simple 38-compound sample that is predicted by statistical-overlap theory (SOT). The low-concentration sample was prepared in-house from several compound classes to span the entire migration-time range and was resolved partially in a pH=7 phosphate buffer containing 50 mM sodium dodecyl sulfate. Peaks, singlets, doublets, and other multiplets were identified on the basis of known migration times and were counted at 13 voltages spanning 4 – 26 kV. These numbers agreed well with predictions of a simple SOT based on the assumption of an inhomogeneous Poisson distribution of migration times. Because the dispersion theory of MEKC is simple, the standard deviations of single-component peaks were modeled theoretically. As part of a new way to implement SOT, probability distributions of the numbers of peaks, singlets, and so on, were computed by Monte Carlo simulation. These distributions contain all theoretical information on peak multiplicity predictable by SOT and were used to evaluate the agreement between experiment and theory. The peak capacity of MEKC was calculated numerically and substituted into the simplest equations in SOT, affirming that peak overlap arises from limited peak capacity.     

Influence of column radial heterogeneity on peak fronting in linear chromatography.

Using numerical calculations of elution peak profiles, an explanation of the fronting behavior of elution peaks in linear chromatography was found in certain radial distributions of the mobile phase flow velocity and local bed efficiency. Fronting peaks are observed only if the flow velocity is higher in the wall region than in the center part of the column and the local efficiency is lower near the wall than in the center. By contrast, tailing or symmetrical peaks are observed if only the flow velocity or the local efficiency are radially heterogeneous. The degree of peak fronting increases with increasing amplitude of the radial distributions. The influence of the radial heterogeneity of the flow velocity on the degree of peak fronting is more severe for high than for low efficiency columns. An equation is suggested to correlate peak fronting behavior for columns of different efficiencies and a procedure proposed for the estimation of the radial distributions of the flow velocity and the local efficiency by analyzing some characteristics of asymmetric peaks.     

Application of wavelet transforms and an approximate deconvolution method for the resolution of noisy overlapped peaks in DNA capillary electrophoresis

A new procedure for resolving noisy overlapped peaks in DNA separations by capillary electrophoresis (CE) is developed. The procedure combines both a wavelet-based denoising method that effectively denoises the signal and a novel approximate deconvolution technique that resolves the fragment peaks and improves the ability to separate highly overlapped peaks early in the electrophoresis process. Different kinds of overlapped peaks with and without noise simulated by computer as well as some DNA experimental electropherograms were submitted to the new procedure. A second order differential operator with variable coefficients is applied to the entire electrophoresis signal at any given time and approximate deconvolutions of the individual Gaussian peaks are performed. The operator incorporates the effect of the superposition and gives exact annihilation in the neighborhood of each peak. Overlapped peaks with a resolution higher than 0.46 can be resolved directly. Also, the method can determine the peak components of signals with a signal to noise ratio higher than 1.4     

Predicting chance infrared spectroscopic matching frequencies

Identification by spectroscopic matching is important in commercial and forensic analysis. The occurrence of chance matches of target infrared spectra is investigated by intercomparison within a spectral database of approximately 50 000 materials. While the frequency of chance matches varies substantially with the material of interest, a simple binomial model gave predictions up to seven orders of magnitude too low for a 6-peak match, while hypergeometric probabilities improved the prediction to within one order of magnitude of observation. It was necessary to take account of both the effective number of possible peak positions, and the distribution of number of peaks within spectra, to obtain reasonable predictions. Simple truncation of the number of positions, coupled with assumed distributions of number of peaks based on observed parameters for a small sample from the database, gave predictions within a factor of two of observation; the predictions were essentially exact given a large sample estimate of the mean peak incidence probability. The implications for confirmatory analysis are discussed with particular reference to the detection of veterinary drug residues.     

Species analysis of metallothionein isoforms in human brain cytosols by use of capillary electrophoresis hyphenated to inductively coupled plasma-sector field mass spectrometry

A new approach for the speciation of metallothioneins (MT) in human brain cytosols is described. The analysis is performed by application of a newly developed coupling of capillary electrophoresis (CE) with inductively coupled plasma-sector field mass spectrometry (ICP-SFMS). Isoforms of metallothioneins are separated from 30-100 microliter sample volumes by CE and the elements Cu, Zn, Cd, and S are detected by use of ICP-SFMS. The extraction of cytosols is the first step in the analytical procedure. Tissue samples from human brain are homogenized in a buffer solution and submitted to ultra-centrifugation. The supernatant is defatted and the cytosol pre-treatment is optimized for CE separation by matrix reduction. The buffer concentration and pH used for capillary electrophoretic separation of metallothionein from rabbit liver were optimized. CE with ICP-MS detection is compared to UV detection. In the electropherograms obtained from the cytosols three peaks can be assigned to MT-1, MT-2, and MT-3. As an additional method, size-exclusion chromatography (SEC) is applied. Fractions from an SEC separation of the cytosol are collected, concentrated, and then injected into the CE. The detection of sulfur by ICP-SFMS (medium resolution mode) and quantification by isotope dilution have also been investigated as a new method for the quantification of MT isoforms. The analytical procedure developed has been used for the first time in comparative studies of the distributions of MT-1, MT-2, and MT-3 in brain samples taken from patients with Alzheimer's disease and from a control group.     

Separation of Compounds in Traditional Chinese Medicines Using Comprehensive Two Dimensional Chromatography

Traditional Chinese medicine is an invaluable treasure of the Chinese nationalities. Thousands of natural species that are of pharmaceutical importance have been accumulated. Most of them are plants. Traditional Chinese medicines generally are of unusual complexity. Even a single medicinal material may contain hundreds of compounds. Since these compounds play cooperative roles pharmacologically, it is essential to analyze all compounds as a whole. It is also important for quality controls in each step of productions, such as raw material collection, processing, and manufacturing. A comprehensive two-dimensional separation system coupling capillary high performance liquid chromatography with fast capillary electrophoresis (μ-HPLC-CE) is developed to provide a powerful means to separate such complex samples. In the first dimensional separation, a home-packed micro-HPLC column was used to reduce the consultation of sample injection and avoid sample dilution. The second dimensional analysis was carried out by micellar electrokinetic chromatography(MEKC) considering the fact that most compounds in Chinese medicine are neutrals. In order to achieve high-speed separation^ theory of fast MEKC was extensively studied. Models of the fast MEKC migration behaviors were established. Relationships of theoretical plates vs. electric field strength and column length were derived. It is concluded that maintaining certain column length and applying high-voltage at the ends of the capillary simultaneously are the key points to achieving fast MEKC separation. A pulse-contacting interface was developed for the 2-D μ-HPLC-CE system. CE sampling was carried out in an instant contact of HPLC and CE columns in an optimized timing program. During the short contact period, a certain fraction of HPLC effluent was introduced into the CE capillary. Injection efficiency for such an interface was up to 81%. Relative standard deviation (RSD) of migration times and peak heights for 100 consecutive MEKC. separation were 3.0% and 1.8%, respectively. With this novel 2-D μ-HPLC-CE system, some traditional Chinese medicines were analyzed and hundreds of peaks were observed. For liquorice, over 110 components were fairly resolved. More than 250 peaks were obtained for a compound mixture of Cheng-Qi-Tang. The peak capacity of this novel comprehensive 2-D HPLC-CE system was estimated to be about 2400 in 80 min.     

Separation and first structure elucidation of Cremophor EL-components by hyphenated capillary electrophoresis and delayed extraction-matrix assisted laser desorption/ionization-time of flight-mass spectrometry

The polyethoxylated heterogeneous components of the so far poorly characterized nonionic emulsifier Cremophor EL (polyoxyl 35 castor oil) (CrEL) were fractionated by cyclodextrin-modified micellar electrokinetic capillary chromatography (CD-MEKC). Due to the low UV absorbance of most of the CrEL-components an indirect UV detection was used with phenobarbital-sodium as background absorber. For a precise assignment of the resulting peaks to the corresponding components capillary electrophoresis (CE) had to be combined with delayed extraction-matrix assisted laser desorption/ionization-time of flight-mass spectrometry (DE-MALDI-TOF-MS) as detection system. For this purpose, the fractionating robot Probot was employed which enables both the on-line fractionation of the CE eluate on a MALDI target during the electrophoretic separation and the simultaneous dosage of the MALDI matrix solution. The applied CrEL amount was optimized by varying the CE injection parameters time, pressure and concentration of the sample in order to obtain homologue peak series of sufficient intensity without decreasing the separation efficiency. Evaluation of the mass spectra was performed by comparing the residue masses of the homologue peak series with the calculated residue masses of potential CrEL-components. However, the high number of polyethoxylated components leads to overlapping of homologue peak series with isobaric residue masses. These isobaric interferences were detected by a high mass accuracy of the measurements (obtained by internal calibration with polyethylene glycol (PEG) 1000 and by means of the residue mass plot, the newly developed evaluation method. The combination of these techniques allowed the first detailed structure analysis of the CrEL-components showing glycerol polyoxyethylene (POE) monoricinoleate and POE monoricinoleate to be the two main components of the emulsifier. Furthermore, the coupling of CE with DE-MALDI-TOF-MS is generally applicable to the fractionation and identification of polymers.     

CE analysis of the acidic organelles of a single cell

The properties of organelles within a cell have been shown to be highly heterogeneous. Until now, it has been unclear just how much of this heterogeneity is endemic to the organelle subpopulations themselves and how much is actually due to stochastic cellular noise. An attractive approach for investigating the origins of heterogeneity among the organelles of a single cell is CE with LIF detection (CE-LIF). As a proof of principle, in this report we optimize and use a single cell CE-LIF method to investigate the properties of endocytic (acidic) organelles. Our results show that the properties of individual acidic organelles containing Alexa Fluor 488 Dextran suggest that there are two groups of CCRF-CEM cells: a group with a high dextran content per cell, and a group with a low dextran content per cell. Furthermore, the individual organelle measurements of the single cells allow us to compare in each group the distributions of doxorubicin content per acidic organelle and electrophoretic mobilities of these organelles.     

Single- and multi-channel detection for generalized quantitative analysis in cases of unresolved chromatographic peaks

Computerized quantification of components under overlapping chromatographic peaks is done by calibration of chromatograms against component mixtures. For conventional (single-channel) detectors, the limitations of earlier methods based on ordinary multiple regression, can be circumvented by data reduction with the aid of principal component analysis with the partial least-squares approach. Simulation studies show that the method can be applied even when there is severe peak overlap, unstable baseline, noisy chromatograms or non-linear detector response. Advantages in the quantification of fused peaks by means of multichannel detectors are outlined. Present limitations on the quantitative evaluation of several overlapping component peaks from a single spectro-chromatogram by means of the partial least-squares method combined with multiple regression on the pure component spectra, are discussed with respect to practical high-performance liquid chromatography.     

Sample plug induced peak splitting in capillary electrophoresis studied using dual backscattered interferometry and fluorescence detection

The appearance of unexpected peaks in capillary electrophoresis (CE) is common and can lengthen the time of method development as assay conditions and experimental parameters are varied to understand and mitigate the effects of the additional peaks. Additional peaks can arise when a single-analyte zone is split into multiple zones. Understanding the underlying mechanism of these phenomena, recognizing conditions that favor its presence, and knowing how to confirm and eliminate the effect are important for efficient method optimization. In this study, we examine how the overlap of analyte zones with the sample plug can lead to peak splitting. This is explored experimentally using dual detection CE, which enables both the sample plug and analyte zones to be independently and simultaneously measured from the same detection volume. Simulations performed via COMSOL Multiphysics confirm the origin of the splitting and help guide experiments to reduce and eliminate the effect. Our findings show that this peak splitting mechanism can arise in separations of both small and large molecules but is, especially, prevalent in separations of slowly migrating macromolecules. This effect is also more prevalent when using a short length-to-detector, as is commonly found in microfluidic applications. A simple diffusion-less model is introduced to develop strategies for reducing peak splitting that avoids modifying the apparatus, such as by lengthening the separation length, which can be difficult. Decreasing the sample plug length and slowing the electroosmotic flow can both reduce this effect, which is confirmed experimentally.     

Identification and Accurate Size Characterization of Nanoparticles in Complex Media

We have developed a new method for the identification and accurate size characterization of nanoparticles (NPs) in complex media based on capillary electrokinetic (CE) separation coupled to inductively coupled plasma mass spectrometry (ICP‐MS). Through mass scanning and Gaussian fitting of electropherogram peaks, we can obtain multidimensional information on chemical compositions, size distributions, and ionic species of multiple NPs in a single run. The results are more accurate than those obtained by using conventional methods. This method provides a powerful tool for investigating polydisperse NP systems and rapid screening of NP‐containing products.     

Thermal marks as a signal processing aid for a portable capillary electropherograph

The interpretation of raw signals in capillary CE can be challenging if there are unknown peaks, or the signal is corrupt due to baseline fluctuations, EOF velocity drift, etc. Signal processing could be required before results can be interpreted. A suite of signal processing algorithms has been developed for CE data analysis, specifically for use in field experiments for the detection of nerve agents using portable CE instruments. Everything from baseline correction and electropherogram alignment to peak matching and identification is included in these programs. Baseline correction is achieved by interpolating a new baseline according to points found using all local extremes, by applying an appropriate outliers test. Irreproducible migration times are corrected by compensating for EOF drift, measured with the aid of thermal marks. Thermal marks are small disturbances in the capillary created by punctual heating that move with the velocity of EOF. Peaks in the sample electropherogram are identified using a fuzzy matching algorithm, by comparing peaks from the sample electropherogram to peaks from a reference electropherogram.     

Studies on substituted phenols by differential pulse cathodic stripping voltammetry: 1. Pentachlorophenol

A study of chlorophenols using differential pulse cathodic stripping voltammetry (dpcsv) is reported. Of the wide range of chlorophenols investigated, only pentachlorophenol and 2,3,4,6-tetrachlorophenol yield stripping peaks.For pentachlorophenol in water, two peaks are obtained at stripping potentials of –1.2 V and –1.58 V versus SCE. In methanol, pentachlorophenol shows one peak with a stripping potential at –1.6 V versus SCE.In the case of 2,3,4,6-tetrachlorophenol in water, two peaks are observed at –1.06 V and –1.6 V versus SCE, while in methanol only one peak arises at a stripping potential of –1.6 V. A procedure was developed for the determination of pentachlorophenol in natural waters.     

An automatic peak finding method for LC‐MS data using Gaussian second derivative filtering

A highly automated procedure for localising and characterising peaks in the chromatographic time domain of LC‐MS data has been developed. The work was initiated by an identified need to facilitate the detection and tracking of chromatographic peaks during method development for the analysis of impurities in pharmaceutical products. The algorithm is mainly based on a digital filter for which the settings are automatically adapted to the data set under study. The procedure was evaluated for synthetic data sets with various S/N levels, peak widths and baseline properties. It was found that even for the worst case tested with S/N=10 and a high variability in the baseline, 94% of the simulated analytical peaks could be detected without producing any false‐positive identifications. Furthermore, the number of correctly estimated peak heights and peak widths falling within a 10% error of the true values were 94 and 91%, respectively. For experimental data sets, peak height, and width estimations were more difficult, but the processed reconstructions showed an excellent agreement with the analytical signals of the raw data, and also a clearly improved visualisation in total ion‐ and base‐peak chromatograms.     

Quenched Instationary Polymerization Systems, 6. The Direct Determination of Axial Dispersion in Size Exclusion Chromatography by Comparison of Theoretical and Ideal Peak Widths

For the direct determination of axial dispersion in size exclusion chromatography a simple method is presented which makes use of the measured and ideal peak widths. The peak width can be defined in two ways: either absolute as the difference of successive points of inflection or relative as the ratio of these points. If the absolute peak width is invariant for the number, molar mass and hyper distribution then this distribution can unambiguously be classified as Poissonian. The relative peak width for such distributions is strictly determined by the experimental parameters. It is demonstrated that axial dispersion only leads to an additive increase in the peak variances for peaks with a relative peak width smaller than 1.25. Thus, it is possible to determine directly the axial dispersion of an experimental size exclusion chromatography set‐up by the use of Poisson distributions prepared by quenched instationary polymerization techniques or any other technique leading to ideal Poisson distributions.     

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.     

System peaks in capillary zone electrophoresis of anions with negative voltage polarity and counter-electroosmotic flow

The system peaks that often appear on electropherograms in anion separation by CE with indirect spectrophotometric detection, negative voltage polarity and cathodic EOF are studied. The system peaks are shown to correspond to the zones with the changed concentration of the BGE constituents; they appear while the zone of each analyte anion passes through the outlet end of the capillary and are transported to the detector by EOF. An equation is suggested for predicting migration times of the system peaks with an error of 1%. The ratios of the system peak area to the analyte peak area are found to amount to 20%. It is shown that it is possible to avoid overlapping of the system peaks and analyte peaks by controlling the EOF velocity owing to hydrodynamic pressure. Using the mathematical simulation of CE shows that the system peaks and baseline shift can result from changing the transference numbers of the BGE ions and analyte ions at the capillary edge. The cases when the system peak may be incorrectly identified as the peak of analyte ion are considered. In order to avoid such errors, some practical recommendations are given.     

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.     

Resolution of overlapped peaks of amino acid derivatives in capillary electrophoresis using multivariate curve resolution based on alternating least squares

The application of chemometric techniques to the resolution of overlapped peaks in capillary electrophoresis (CE) is described. When a physical separation can not be completely accomplished, chemometrics might still resolve the determination of the analytes mathematically. CE with diode array detection can provide a large amount of data consisting of spectra registered over time. In this study, the capillary electrophoretic separation of 1,2-naphthoquinone-4-sulfonate derivatives of amino acids is studied. Most of the common amino acid derivatives can be separated at 30 kV in a fused-silica capillary by using a 40 mM sodium tetraborate + isopropanol (3:1 v/v) solution as background electrolyte. However, peaks of certain derivatives (Phe, His, Leu and Ile) still overlap. A multivariate curve resolution method based on an alternating least squares optimization procedure is used for the resolution of the overlapped electrophoretic peaks. The method takes advantage of spectral and electrophoretic differences of analytes to recover their pure electrophoretic and spectral profiles. In addition, each analyte in the mixture can be quantified using the corresponding standards.     

Quantitation in multianalyte overlapping peaks from capillary electrophoresis runs using artificial neural networks

The potentiality of artificial neural networks for multicomponent analysis in unresolved peaks from capillary electrophoresis (CE) is evaluated. The system chosen consists of mixtures of three ebrotidine metabolites, which cannot be successfully separated by CE. Data selected for analysis consist of UV spectra taken at the maximum of the CE peak. The most dissimilar analyte, in terms of spectral differences, is accurately quantitated in any type of mixture with an overall prediction error of 5%. Because of the strong interference of the two most overlapped compounds, a preliminary procedure for spectral data filtering based on principal component analysis is performed to improve their quantitation.