Analysis of peak asymmetry in chromatography

The knowledge of the symmetry of chromatographic peaks is extremely important regarding the digital signal processing. The significant deviation of the peak shape from the symmetrical peak makes hardly possible the acquisition of chromatographic signal information, such as the retention time, the peak area, the peak width at half peak height, the peak overlapping, etc. In the literature one can find many methods for the determination of the asymmetry factor. For example it is suitable to calculate the skewness from the third central moment. However in case of noisy baseline the value of the skewness oscillates highly depending on the number of points used for the mathematical calculation. In this work a new method is presented for the determination peak shape asymmetry. We order mathematical function to the chromatographic peaks by fitting, and then symmetrical curve is generated with the same peak maximum position and height, the peak width is fitted. The difference of the two functions is constituted and areas of the data differences are calculated, which are really characteristics of the peak asymmetry. Correlation between the area of the difference signal and the asymmetry factor is established. The method was applied for different types of chromatographic peak shapes and the results were interpreted.     

On the equations describing chromatographic peaks and the problem of the deconvolution of overlapped peaks

The problem of the appropriate choice of the function that describes a chromatographic peak is examined in combination with the deconvolution of overlapped peaks by means of the non-linear least-squares method. It is shown that the majority of the functions proposed in the literature to describe chromatographic peaks are not suitable for this purpose. Only the polynomial modified Gaussian function can describe almost every peak but it is mathematically incorrect unless it is redefined properly. Two new functions are proposed and discussed. It is also shown that the deconvolution of an overlapping peak can be done with high accuracy using a non-linear least-squares procedure, like Microsoft Solver, but this target is attained only if we use as fitted parameters the position of the peak maximum and the peak area (or height) of every component in the unresolved chromatographic peak. In case we use as fitted parameters all the parameters that describe each single peak enclosed in the multi-component peak, then Solver leads to better fits, which though do not correspond to the best deconvolution of the peak. Finally, it is found that Solver gives much better results than those of modern methods, like the immune and genetic algorithms.     

Preserving the chromatographic integrity of high-speed supercritical fluid chromatography separations using time-of-flight mass spectrometry

The advantage of high-speed time-of-flight-mass spectrometry (TOF-MS) detection for ultrafast qualitative supercritical fluid chromatography/mass spectrometry (SFC/MS) applications allows the superior resolving power of SFC to be exploited in high-throughput analysis. A chromatographic comparison of quadrupole MS and TOF-MS shows high-speed TOF total ion current data point sampling to be more indicative of fast SFC separations and corresponding short (1-2 s) baseline peak widths. Results shown for analysis of a six-compound mixture with two peaks eluting at 0.86 and 0.89 min exhibit >50% resolution by high-speed TOF data sampling, whereas the same peaks appear to coelute using quadrupole MS data sampling. Additionally, a marked improvement in the peak baseline widths is afforded by fast TOF data acquisition of 0.1 s/spectrum, resulting in a reduction in the baseline width, 1.6 s, of sulfanilamide in a four-compound mixture that is more than 2-fold greater than that achieved at the slower data acquisition of 0.5 s/spectrum. The resulting increase in resolution and improved peak shapes allow automatic integration routines to perform more effectively. For most classes of compounds amenable to high performance liquid chromatography, including druglike species, steroids, and polymers, the union of SFC with TOF-MS provides the maximum density of chemical information per unit time available with any high-speed chromatographic/mass spectrometric method.     

Rapid characterization of anthocyanins in red raspberry fruit by high-performance liquid chromatography coupled to single quadrupole mass spectrometry

This paper describes the results of a comparison of four peak functions in describing real chromatographic peaks. They are the empirically transformed Gaussian, polynomial modified Gaussian, generalized exponentially modified Gaussian and hybrid function of Gaussian and truncated exponential functions. Real chromatographic peaks of different shapes (fronting. symmetric, and tailing) are obtained by various separation conditions of reversed-phase liquid chromatography. They are then fitted to the peak functions via the Marquardt-Levenberg algorithm, a nonlinear least-squares curve-fitting procedure, by Microsoft Solver. The qualities of the fits are evaluated by the sum of the squares of the residuals. It is concluded in the study that the empirically transformed Gaussian function offers the highest flexibility (best fits) to all shapes of chromatographic peaks, including extremely asymmetric tailing peaks with a peak asymmetry of up to 8. The flexibility of this function should improve our ability to process chromatographic peaks such as deconvolution of overlapped peaks and smoothing noisy peaks for the determination of statistical moments.     

Parametric studies of matched filters to enhance the signal-to-noise ratios of LC-MS-MS peaks

Chromatographic parameters of reference signals employed in matched filter methods have been studied using numerical experiments to improve the signal-to-noise (S/N) ratios of small liquid chromatography (LC) peaks obtained with electrospray tandem mass spectrometers (MS-MS). These parameters include the width, shape, and S/N ratios of chromatographic peaks used as the reference signal profiles. Our results show the effect of reference peak widths on improving the S/N ratio of chromatographic peaks; the influence of reference peak shapes is negligible. To verify simulation results, various reference signals, including analyte peaks of high concentration standards, internal standard peaks, and artificial Gaussian peaks of different widths, have been employed to enhance signal peaks on real liquid chromatography-tandem mass spectrometry (LC-MS-MS) chromatograms via matched filter methods. Our experimental results demonstrate that the S/N ratio enhancement of chromatographic peaks agree with the simulation predictions. These findings, therefore, suggest that regardless of peak shape, a well-smooth peak with a width close to that of the analyte peak is an adequate reference signal, when matched filter methods are used to improve LC-MS-MS chromatograms. Nevertheless, all methods processed LC-MS-MS peaks in this study do not achieve the ideal improvement ratios estimated with simulation results. We attribute this deficiency to spike-like noise, which have considerable low frequency components riding on LC-MS-MS chromatograms. Matched filtering, which works as a low-pass filter in the frequency domain, cannot effectively eliminate low frequency flicker noise contributed by these spikes. In addition, simple median filtering does not provide adequate improvement despite being able to smooth out most spikes in the chromatograms.     

色谱工作站采样时间的迭代计算

采用迭代计算确定色谱工作站采样时间,建立了连续变速采样的方法。方法具有采样点数少,节省内存空间,数据处理速度快及误差小的优点,可用于恒温及等梯度洗脱分析。     

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.     

Inner chromatogram projection (ICP) for resolution of GC-MS data with embedded chromatographic peaks

The chromatographic peak located inside another peak in the time direction is called an embedded or inner peak in contradistinction with the embedding peak, which is called an outer peak. The chemical components corresponding to inner and outer peaks are called inner and outer components, respectively. This special case of co-eluting chromatograms was investigated using chemometric approaches taking GC-MS as an example. A novel method, named inner chromatogram projection (ICP), for resolution of GC-MS data with embedded chromatographic peaks is derived. Orthogonal projection resolution is first utilized to obtain the chromatographic profile of the inner component. Projection of the two-way data matrix columnwise-normalized along the time direction to the normalized profile of the inner component found is subsequently performed to find the selective m/z points, if they exist, which represent the chromatogram of the outer component by itself. With the profiles obtained, the mass spectra can easily be found by means of a least-squares procedure. The results for both simulated data and real samples demonstrate that the proposed method is capable of achieving satisfactory resolution performance not affected by the shapes of chromatograms and the relative positions of the components involved.     

基于无基底扣除的数据趋势累积谱峰检测算法

谱峰的检测分析在色谱技术研究中具有十分重要的作用,但在色谱数据采集、传输的过程中,不同程度的噪声干扰给谱峰检测带来了极大的困难.目前传统的谱峰检测算法普遍通过基底扣除的方式对谱峰的形态进行预定义,将谱峰分为单峰、重叠峰等多个种类.针对不同种类的谱峰采用不同的检测方法,这就导致了传统的谱峰检测算法具有高复杂度、低自动化程...     

Sampling frequency,response times and embedded signal filtration in fast,high efficiency liquid chromatography: A tutorial

With increasingly efficient columns, eluite peaks are increasingly narrower. To take full advantage of this, choice of the detector response time and the data acquisition rate a.k.a. detector sampling frequency, have become increasingly important. In this work, we revisit the concept of data sampling from the theorem variously attributed to Whittaker, Nyquist, Kotelnikov, and Shannon. Focusing on time scales relevant to the current practice of high performance liquid chromatography (HPLC) and optical absorbance detection (the most commonly used method), even for very narrow simulated peaks Fourier transformation shows that theoretical minimum sampling frequency is still relatively low (<10 Hz). However, this consideration alone may not be adequate for real chromatograms when an appreciable amount of noise is present. Further, depending on the instrument, the manufacturer's choice of a particular data bunching/integration/response time condition may be integrally coupled to the sampling frequency. In any case, the exact nature of signal filtration often occurs in a manner neither transparent to nor controllable by the user. Using fast chromatography on a state-of-the-art column (38,000 plates), we evaluate the responses produced by different present generation instruments, each with their unique black box digital filters. We show that the common wisdom of sampling 20 points per peak can be inadequate for high efficiency columns and that the sampling frequency and response choices do affect the peak shape. If the sampling frequency is too low or response time is too large, the observed peak shapes will not remain as narrow as they really are – this is especially true for high efficiency and high speed separations. It is shown that both sampling frequency and digital filtering affect the retention time, noise amplitude, peak shape and width in a complex fashion. We show how a square-wave driven light emitting diode source can reveal the nature of the embedded filter. We discuss time uncertainties related to the choice of sampling frequency. Finally, we suggest steps to obtain optimum results from a given system.     

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.     

The reproducible acquisition of comparative liquid chromatography/tandem mass spectrometry data from complex biological samples

An in-depth study of the reproducibility of data acquired for comparative proteomics analysis using a prototype two-stage heated laminar flow chamber fitted to a commercial high-performance liquid chromatography/tandem mass spectrometry (HPLC/MS/MS) instrument was undertaken. The study is based on 24 replicate samples from four independent membrane preparations derived from two matched breast cancer cell lines. Variation and reproducibility in the data were evaluated at several levels highlighting the relative efficiency and variability of the acquisition routines used. Specifically, variation in the number and relative intensities of chromatographic peaks eluted from the LC column, precursor ion selection and sequence identification were evaluated. On average, approximately 6500 chromatographic peaks were generated for each acquisition with a corresponding coefficient of variance (CV) of less than 20%. Precursor ion selection and sequence identification averaged 1380 and 780 events per acquisition sample, respectively, with corresponding CVs of less than 10% for each. The reproducibility in the precursor ion selection was typically better than 60% between similar replicates. Using protein and peptide internal standards, it was found that the CV in retention time across the gradient between two acquisition pairs was typically less than 5%, whereas the average intensity ratio was 1.0 (expected) with a CV approaching 20%. An evaluation of the intensity ratios calculated from endogenous peptide sequences, identified across the acquisition set, indicated a CV of approximately 30%. Similarly, the CV associated with the top 1000 peptides indicated a mean and median of 28.4 and 26.95%. For a given acquisition pair it was also found that approximately 11% of the chromatographic peaks eluting from the column were linked to a sequence or identified. For these experiments, less than 10% of the peak pairs had absolute ratios greater than 2.0 and of those only approximately 10% had sequences linked to them. For each matched acquisition set on average 406 proteins were identified with a CV of less than 10%. Of the proteins that were identified approximately 30% had at least one predicted trans-membrane domain, indicating a four-fold increase over a crude homogenate sample with only minor enrichment. During these experiments it was found that the interface did not significantly alter the relative charge state distribution of ions, nor did it introduce significant interference from background ions. The interface was capable of 24-hour acquisition cycles.     

Chromatographic quantitation using fractions of the peak areas

Quantitative chromatographic analysis is liable to errors due to peak asymmetry because the uncertainty in the detected position of the end of the peak tail decreases the reliability of the computed peak area. This dependence may be a severe drawback whenever peaks of different areas must be compared, as in the case of calibration curves. A new approach to overcome the uncertainties of area calculation due to peak asymmetry is reported in this paper. The approach consists of calculating only the area included between the start and the maximum of the chromatographic peak. Simulated and experimental chromatographic data were used in this study. Both the peak start-to-peak maximum area (SMA) and the start-to-end or total area (TA) were calculated and the quantitative results were compared. Within the scope of this work it is concluded that the SMA yields calibration curves that are more linear and have intercepts closer to zero than the calibration curves obtained using the TA.     

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.     

Peak clustering in two-dimensional gas chromatography with mass spectrometric detection based on theoretical calculation of two-dimensional peak shapes: the 2DAid approach

A method is presented to facilitate the non-target analysis of data obtained in temperature-programmed comprehensive two-dimensional (2D) gas chromatography coupled to time-of-flight mass spectrometry (GC×GC-ToF-MS). One main difficulty of GC×GC data analysis is that each peak is usually modulated several times and therefore appears as a series of peaks (or peaklets) in the one-dimensionally recorded data. The proposed method, 2DAid, uses basic chromatographic laws to calculate the theoretical shape of a 2D peak (a cluster of peaklets originating from the same analyte) in order to define the area in which the peaklets of each individual compound can be expected to show up. Based on analyte-identity information obtained by means of mass spectral library searching, the individual peaklets are then combined into a single 2D peak. The method is applied, amongst others, to a complex mixture containing 362 analytes. It is demonstrated that the 2D peak shapes can be accurately predicted and that clustering and further processing can reduce the final peak list to a manageable size.     

Software for Microprocessor Controlled HPLC: Peak Area Integration

Abstract

Programs are described for determination of peak areas and peak retention times from the chromatographic data obtained by a dual-microprocessor data handling microcomputer (DHC). The programs provide the necessary equipment testing and calibration routines for an accurate reproduction of a recorded chromatogram, and they are written to be merged with the data acquisition programs to provide a true “real-time” integrator. The integration is performed with baseline stabilization and automatic peak splitting. These features make the integrator applicable to gradient elution chromatography, as well as for the integration of complex chromatograms with overlapping peaks. The integrated chromatogram can be displayed with the limits of integration for each peak. Results of peak area integration of simple and complex chromatograms demonstrate satisfactorily accurate and consistant results that are independent of chromatographic conditions and shape of the peaks.     

Evaluation of analyte protectants to improve gas chromatographic analysis of pesticides

A common problem in gas chromatography (GC) applications is the analyte losses and/or peak tailing due to undesired interactions with active sites in the inlet and column. Analytes that give poor peak shapes or degrade have higher detection limits, are more difficult to identify and integrate, and are more prone to interferences than stable analytes that give narrow peaks. For susceptible analytes, significant peak quality improvements are obtained when matrix components are present because they fill active sites, thus reducing analyte interactions. This phenomenon is called "matrix-induced chromatographic response enhancement." Several approaches have been proposed to minimize peak distortion phenomena and compensate for matrix-induced effects, which is especially important for accurate quantitation, but each approach has serious limitations for routine multi-pesticide analysis. In this study, we demonstrate the feasibility of using "analyte protectants" to provide a more convenient and effective solution to the problem than other approaches developed thus far. The protecting agents are added to extracts and matrix-free standards alike to provide the chromatographic enhancement effect even for the most susceptible analytes in a very dirty GC system. In this study, we evaluated 93 different compounds to find the most suitable ones for improving chromatographic quality of the signal. Because hydrogen bonding has been shown to be an important factor in analyte interactions with active sites, we mainly focused on additives with strong hydrogen bonding capabilities. Dramatic peak enhancements were achieved using compounds containing multiple hydroxy groups, such as sugars and sugar derivatives, and gulonolactone appears to be the most effective protecting agent for the most pesticides that we tested. The benefits of using analyte protectants versus alternative procedures for overcoming matrix-induced effects in quantitation include: (a) simpler procedure; (b) easier integration of peaks; (c) lower detection limits; (d) better quantitation; (e) less maintenance of the GC inlet; and (e) lower cost. However, long-term influences on the performance of the chromatographic system have yet to be established.     

Modulation-induced error in comprehensive two-dimensional gas chromatographic separations

There is a fundamental difference between data collected in comprehensive two-dimensional gas chromatographic (GCxGC) separations and data collected by one-dimensional GC techniques (or heart-cut GC techniques). This difference can be ascribed to the fact that GCxGC generates multiple sub-peaks for each analyte, as opposed to other GC techniques that generate only a single chromatographic peak for each analyte. In order to calculate the total signal for the analyte, the most commonly used approach is to consider the cumulative area that results from the integration of each sub-peak. Alternately, the data may be considered using higher order techniques such as the generalized rank annihilation method (GRAM). Regardless of the approach, the potential errors are expected to be greater for trace analytes where the sub-peaks are close to the limit of detection (LOD). This error is also expected to be compounded with phase-induced error, a phenomenon foreign to the measurement of single peaks. Here these sources of error are investigated for the first time using both the traditional integration-based approach and GRAM analysis. The use of simulated data permits the sources of error to be controlled and independently evaluated in a manner not possible with real data. The results of this study show that the error introduced by the modulation process is at worst 1% for analyte signals with a base peak height of 10xLOD and either approach to quantitation is used. Errors due to phase shifting are shown to be of greater concern, especially for trace analytes with only one or two visible sub-peaks. In this case, the error could be as great as 6.4% for symmetrical peaks when a conventional integration approach is used. This is contrasted by GRAM which provides a much more precise result, at worst 1.8% and 0.6% when the modulation ratio (MR) is 1.5 or 3.0, respectively for symmetrical peaks. The data show that for analyses demanding high precision, a MR of 3 should be targeted as a minimum, especially if multivariate techniques are to be used so as to maintain data density in the primary dimension. For rapid screening techniques where precision is not as critical lower MR values can be tolerated. When integration is used, if there are 4-5 visible sub-peaks included for a symmetrical peak at MR=3.0, the data will be reasonably free from phase-shift-induced errors or a negative bias. At MR=1.5, at least 3 sub-peaks must be included for a symmetrical peak. The proposed guidelines should be equally relevant to LCxLC and other similar techniques.     

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.