Resolution of Overlapping Chromatographic Peaks Using a Genetic Algorithm

ABSTRACT

A genetic algorithm for resolution of overlapping chromatographic peaks (GAROCP) using real-number coding, non-uniform mutation and arithmetical crossover methods is described in this paper. It was applied to resolution of highly overlapped multicomponent high-performance liquid chromatographic peaks by fitting experimental chromatogram to the exponentially modified Gaussian (EMG) model. The genetic algorithm was used to find the minimum of fitting error to optimize the parameters in the EMG functions which determine the shape and area of each peak. The applicability of the method was investigated with both simulated signals calculated by EMG functions and experimental multicomponent overlapping chromatograms.     

Resolution of multicomponent overlapped peaks A comparison of several curve resolution methods

Several curve resolution methods were compared in their performance of identification and quantification of overlapping peaks. These resolution methods are heuristic evolving latent projections (HELP), sub-window factor analysis (SFA), and orthogonal projection resolution (OPR). In this paper, HELP, SFA and OPR with the rank map produced by evolving factor analysis (EFA) or fixed size moving window-evolving factor analysis (FSMW-EFA) were applied to the simulated and experimental data. The resolved results were compared qualitatively and quantitatively. In addition, the further comparison was carried out with the results obtained from multivariate curve resolution-alternate least square (MCR-ALS) by using the initial estimates provided by EFA.     

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。     

联用色谱数据的局部分辨

提出了一种对二维数据严重重叠峰中待测组份进行分辨的新方法：子窗口分析法（ｓｕｂｗｉｎｄｏｗ ａｎａｌｙｓｉｓ，ＳＡ）。该方法充分利用重叠区信息，成功地解析出严重重叠峰中待测组份的光谱，进而利用正交投影求得待测组份色谱曲线．这种对二维数据进行局部分辨的方法，降低了对色谱分离条件的要求，可直接应用于未知组份的定性定量分析。     

正交投影用于一维重叠色谱峰分辨及背景扣除

对于两组份色谱重叠峰体系,当以小组份色谱峰作为干扰时,本文利用正交投影方法,通过构造正交投影矩阵,利用原始信号及其投影与背景之间的内在关系来确定真实背景,从而将背景干扰予以扣除,使含背景干扰的一维重叠色谱峰得以分辨。模拟研究表明,对于两组份色谱峰重叠体系当以小色谱峰为干扰时本文方法具有很好的分辨效果,对于完全重叠峰,即使其峰分离度为零能得到满意的结果。     

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.     

直观推导式演进特征投影法解析多环芳烃的重叠色谱峰

用高效液相色谱法(HPLC)测定多环芳烃时,因芴、苊和菲,茚(1,2,3-cd)芘和苯并(g,h,i)苝的色谱峰严重重叠而影响测定结果。本研究用高效液相色谱-二极管阵列检测器(DAD)和荧光检测器(FLD)测定多环芳烃,在激发波长λex=230nm,发射波长λem=300～500nm范围内采集重叠峰的HPLC-FLD二维色谱数据,再用直观推导式演进特征投影法(HELP)解析它们的重叠色谱峰,分辨结果令人满意。该方法对重叠组分的分辨下限为0.02mg/L。结果表明,用二维色谱荧光数据解析色谱重叠峰,灵敏度更高,可用于环境样品中多环芳烃的测定。     

Determining orthogonal and similar chromatographic systems from the injection of mixtures in liquid chromatography-diode array detection and the interpretation of correlation coefficients color maps

Generic orthogonal chromatographic systems might be helpful tools as potential starting points in the development of methods to separate impurities and the active substance in drugs with unknown impurity profiles. The orthogonality of 38 chromatographic systems was evaluated from weighted-average-linkage dendrograms and color maps, both based on the correlation coefficients between the retention factors on the different systems. On each chromatographic system, 68 drug substances were injected as mixtures of three or four components to increase the throughput. The (overlapping) peaks were identified and resolved with a peak purity algorithm, orthogonal projection approach (OPA). The visualization techniques applied allowed a simple evaluation of orthogonal and (groups of) similar systems.     

Resolution of the essential constituents of Ramulus cinnamomi by an evolving chemometric approach

The analysis of complex mixtures, such as those of traditional Chinese medicine (TCM), is difficult by conventional methods of analysis. Chemometric methods provide a new way to solve such problems. Subwindow factor analysis (SFA) paired with the evolving window orthogonal projection (EWOP) method, has been used as a new evolving approach to the resolution of volatile components of Ramulus cinnamomi (RC). Compared with conventional chromatographic analysis, the chromatographic separation conditions necessary are greatly mitigated in our approach, yet the accuracy of qualitative and quantitative results is improved, because the measured data matrix has been resolved into chromatograms and mass spectra of the chemical components. Our method is, moreover, friendly to use and easy to program. Experimental results show the efficiency and convenience of the proposed approach. Forty-seven of the seventy-eight separated constituents in an essential oil, accounting for 89.55% of the sample, were identified by mass spectroscopy (MS).     

Liquid exclusion adsorption chromatography, a new technique for isocratic separation of nonionic surfactants. III. Two-dimensional separation of fatty alcohol ethoxylates

In this paper, a novel procedure for qualitative and quantitative analysis of the two-dimensional data obtained from GC-MS is investigated to determine chemical components of essential oils in Cortex Cinnamomi from four different producing areas. A new method named iterative optimization procedure (IOP) specially used to resolve embedded peaks is also developed. With the help of IOP and other chemometric techniques, such as heuristic evolving latent projections, evolving factor analysis, sub-window factor analysis and orthogonal projection resolution, and etc., the detection of the purity of chromatographic peaks can be first addressed, and then the overlapping peaks are resolved into the pure chromatogram and mass spectrum of each component. The similarity searches in the MS database are finally conducted to qualitatively determine the chemical components. The results obtained showed that the accuracy of qualitative and quantitative analysis could be greatly enhanced by chemometric resolution methods. The chemometric resolution techniques upon the two-dimensional data can be quite promising tools for the analysis of the complex samples like traditional Chinese medicine.     

Translation Modification Iteration for Resolution and Quantification of Overlapping Chromatographic Peaks

A novel algorithm, translation modification iteration (TMI), is proposed for resolving overlapping chromatographic peaks. By this method, a series of similar peaks are obtained from the initial construction of single component peaks and approach the profiles of real single component peaks by iteration. Both simulated and experimental data are investigated with TMI, consequently overlapping peaks can be resolved into reasonable single component peaks easily and efficiently. Quantitative analysis is also successfully achieved in both simulated and experimental data, and the quantitative results obtained from TMI are superior to those obtained from perpendicular drop (PD) and tangent skim (TS) methods. Without too much time devoted to the procedure, TMI is a simple and practicable method for resolution and quantification of overlapping chromatographic peaks.

     

径向基函数神经网络用于重叠色谱峰解析

 在高斯基径向基函数神经网络 (RBFNN)学习算法中引入了鲁棒性和随机全局寻优的两阶段遗传算法 :结构学习和参数优化。通过两阶段学习算法的交替使用 ,使网络具有结构自学习和参数优化的能力 ,而后将网络应用于组分数未知的重叠色谱峰解析。该方法具有不需人为干预 ,可自动确定网络结构即组分数的优点 ;并且解析精度较高 ,适用于多组分重叠色谱峰的解析 ;对完全重叠色谱峰也具有良好的解析能力。     

Linear Modulated Stochastic Resonance Algorithm Applied to Determination of Thidiazuron Residue in Water Using Stochastic Resonance

Abstract

The newly proposed linear modulated stochastic resonance algorithm (LSRA) was used to amplify and detect the weak chromatographic peaks of thidiazuron. The output chromatographic peak is often distorted when using the traditional stochastic resonance algorithm because of the existence of strong noise. In LSRA, the distortion of the output peak can be corrected by introducing a linear force into the nonlinear system. A two‐step optimization method was proposed to give attention to both the signal‐to‐noise ratio and the peak shape of output signal. The weak chromatographic peaks of thidiazuron can be amplified significantly and the distortion of the output peaks can be corrected using LSRA. The algorithm was used to detect thidiazuron residue in water with solid phase extraction‐high performance liquid chromatography. The limit of detection and limit of quantification were improved to 2.5 ng/l and 10 ng/l, respectively.     

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.     

Chemometrics‐assisted chromatographic fingerprinting: An illicit methamphetamine case study

The volatile chemical constituents in complex mixtures can be analyzed using gas chromatography with mass spectrometry. This analysis allows the tentative identification of diverse impurities of an illicit methamphetamine sample. The acquired two‐dimensional data of liquid–liquid extraction was resolved by multivariate curve resolution alternating curve resolution to elucidate the embedded peaks effectively. This is the first report on the application of a curve resolution approach for chromatogram fingerprinting to identify particularly the embedded impurities of a drug of abuse. Indeed, the strong and broad peak of methamphetamine makes identifying the underlying peaks problematic and even impossible. Mathematical separation instead of conventional chromatographic approaches was performed in a way that trace components embedded in methamphetamine peak were successfully resolved. Comprehensive analysis of the chromatogram, using multivariate curve resolution, resulted in elution profiles and mass spectra for each pure compound. Impurities such as benzaldehyde, benzyl alcohol, benzene, propenyl methyl ketone, benzyl methyl ketone, amphetamine, N‐benzyl‐2‐methylaziridine, phenethylamine, N ,N ,α‐trimethylamine, phenethylamine, N ,α,α‐trimethylmethamphetamine, N‐acetylmethamphetamine, N‐formylmethamphetamine, and other chemicals were identified. A route‐specific impurity, N‐benzyl‐2‐methylaziridine, indicating a synthesis route based on ephedrine/pseudoephedrine was identified. Moreover, this is the first report on the detection of impurities such as phenethylamine, N ,α,α‐trimethylamine (a structurally related impurity), and clonitazene (as an adulterant) in an illicit methamphetamine sample.     

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.     

Multivariate curve resolution combined with gas chromatography to enhance analytical separation in complex samples: A review

This review describes the major advantages and pitfalls of iterative and non-iterative multivariate curve resolution (MCR) methods combined with gas chromatography (GC) data using literature published since 2000 and highlighting the most important combinations of GC coupled to mass spectrometry (GC–MS) and comprehensive two-dimensional gas chromatography with flame ionization detection (GC × GC-FID) and coupled to mass spectrometry (GC × GC–MS). In addition, a brief summary of some pre-processing strategies will be discussed to correct common issues in GC, such as retention time shifts and baseline/background contributions. Additionally, algorithms such as evolving factor analysis (EFA), heuristic evolving latent projection (HELP), subwindow factor analysis (SFA), multivariate curve resolution-alternating least squares (MCR-ALS), positive matrix factorization (PMF), iterative target transformation factor analysis (ITTFA) and orthogonal projection resolution (OPR) will be described in this paper. Even more, examples of applications to food chemistry, lipidomics and medicinal chemistry, as well as in essential oil research, will be shown. Lastly, a brief illustration of the MCR method hierarchy will also be presented.     

直观推导式演进特征投影法分辨枸杞类胡萝卜素的异构体

采用高效液相色谱-二极管阵列检测方法,初步分离了枸杞子中的类胡萝卜素。以乙腈-二氯甲烷(体积比为60∶40)为流动相,流速为1.0 mL/min,用C18柱从枸杞类胡萝卜素中分离出7个峰。但由于类胡萝卜素的结构多样性,尤其是顺反异构体的出现使得分离并不完全。利用所得三维数据提供的信息和化学计量学方法直观推导式演进特征投影法(HELP),对其中某些在二维色谱中被定性为单组分的峰进行解析,结果发现原来在二维色谱中被定性为单组分的峰大多是一些多组分峰。以其中第4个峰为例对其进行解析,得到了该类胡萝卜素的同分异构体色谱流出曲线及紫外光谱信息。该方法表明,化学计量学方法与现代分析手段有机结合,大大降低了此类复杂体系对色谱分离的要求,对同分异构体的分析具有一定的借鉴和指导意义。     

分解色谱重叠峰的参数契合法

本文研究了色谱重叠峰一阶导数曲线中各极值点的相对位置与重叠子峰面积比之间的关系，提出了一种模式参数契合的色谱重叠峰分解方法，它在准确性方面优于传统的垂线法，在速度方面优于模型拟合法，可用于实时快速处理。