Theory of peak capacity in gradient elution

Peak capacity is the best measure of the performance of a gradient separation. In this paper, the theory of peak capacity for the standard operating conditions of reversed-phase and ion-exchange chromatography is outlined. The influence of the operating conditions on the peak capacity of a separation are discussed. Finally, bandspreading phenomena in gradient chromatography are analyzed.     

Implications of column peak capacity on the separation of complex peptide mixtures in single- and two-dimensional high-performance liquid chromatography

Column peak capacity was utilized as a measure of column efficiency for gradient elution conditions. Peak capacity was evaluated experimentally for reversed-phase (RP) and cation-exchange high-performance liquid chromatography (HPLC) columns, and compared to the values predicted from RP-HPLC gradient theory. The model was found to be useful for the prediction of peak capacity and productivity in single- and two-dimensional (2D) chromatography. Both theoretical prediction and experimental data suggest that the number of peaks separated in HPLC reaches an upper limit, despite using highly efficient columns or very shallow gradients. The practical peak capacity value is about several hundred for state-of-the-art RP-HPLC columns. Doubling the column length (efficiency) improves the peak capacity by only 40%, and proportionally increases both the separation time and the backpressure. Similarly, extremely shallow gradients have a positive effect on the peak capacity, but analysis becomes unacceptably long. The model predicts that a 2D-HPLC peak capacity of 15,000 can be achieved in 8 h using multiple fraction collection in the first dimension followed by fast RP-HPLC gradients employing short, but efficient columns in the second dimension.     

用反相液相色谱分离多肽时峰容量与色谱柱长度关系的研究

在蛋白质组学研究中,多肽混合物的有效分离对蛋白质鉴定和蛋白质之间相互作用的研究起着决定性的影响。基于此,用反相液相色谱研究了在两个不同长度的色谱柱上分离多肽混合物时色谱柱长度与峰容量的关系,同时考察了梯度洗脱时间对峰容量和峰宽的影响。实验结果表明,色谱柱长度对峰容量有显著的影响,而延长梯度洗脱时间不仅可以增加峰容量,而且可以增加峰宽。这说明用毛细管液相色谱 串联质谱联用方法对多肽混合物进行分离鉴定时,采用较长的色谱柱和较长的梯度洗脱时间有利于对更多的多肽进行分析鉴定。     

二维液相色谱-质谱联用分离中药复方葛根芩连汤中的有效成分

建立了二维液相色谱-质谱联用方法分离中药复方葛根芩连汤的成分。以CN柱作第一维色谱柱,水和甲醇梯度洗脱分离;以ODS柱作第二维色谱柱,20 mmol/L乙酸铵缓冲液和乙腈梯度洗脱分离;质谱检测采用电喷雾电离/大气压化学电离（ESI/APCI）复合离子源,正负离子扫描。实验结果表明搭建的二维液相色谱的峰容量显著高于一维色谱,分离效率得到了明显的提高。以第一维色谱的第3个流分为例,对其二维分离进行仔细分析,发现质谱比紫外光谱检测到的组分多,质谱中采用负离子模式比正离子模式检测到的组分多。表明搭建的二维液相色谱-质谱分离平台分离效果好,提高了液相色谱的峰容量和分离效率。该方法操作简便,可作为中药等复杂体系分离分析的有效手段。     

The impact of sampling time on peak capacity and analysis speed in on-line comprehensive two-dimensional liquid chromatography

Comprehensive two-dimensional liquid chromatography (2DLC) offers a number of practical advantages over optimized one-dimensional LC in peak capacity and thus in resolving power. The traditional “product rule” for overall peak capacity for a 2DLC system significantly overestimates peak capacity because it neglects under-sampling of the first dimension separation. Here we expand on previous work by more closely examining the effects of the first dimension peak capacity and gradient time, and the second dimension cycle times on the overall peak capacity of the 2DLC system. We also examine the effects of re-equilibration time on under-sampling as measured by the under-sampling factor and the influence of molecular type (peptide vs. small molecule) on peak capacity. We show that in fast 2D separations (less than 1 h), the second dimension is more important than the first dimension in determining overall peak capacity and conclude that extreme measures to enhance the first dimension peak capacity are usually unwarranted. We also examine the influence of sample types (small molecules vs. peptides) on second dimension peak capacity and peak capacity production rates, and how the sample type influences optimum second dimension gradient and re-equilibration times.     

Fast, comprehensive two-dimensional liquid chromatography

The absolute need to improve the separating power of liquid chromatography, especially for multi-constituent biological samples, is becoming increasingly evident. In response, over the past few years, there has been a great deal of interest in the development of two-dimensional liquid chromatography (2DLC). Just as 1DLC is preferred to 1DGC based on its compatibility with biological materials we believe that ultimately 2DLC will be preferred to the much more highly developed 2DGC for such samples. The huge advantage of 2D chromatographic techniques over 1D methods is inherent in the tremendous potential increase in peak capacity (resolving power). This is especially true of comprehensive 2D chromatography wherein it is possible, under ideal conditions, to obtain a total peak capacity equal to the product of the peak capacities of the first and second dimension separations. However, the very long timescale (typically several hours to tens of hours) of comprehensive 2DLC is clearly its chief drawback. Recent advances in the use of higher temperatures to speed up isocratic and gradient elution liquid chromatography have been used to decrease the time needed to do the second dimension LC separation of 2DLC to about 20s for a full gradient elution run. Thus, fast, high temperature LC is becoming a very promising technique. Peak capacities of over 2000 and rates of peak capacity production of nearly 1 peak/s have been achieved. In consequence, many real samples showing more than 200 peaks with signal to noise ratios of better than 10:1 have been run in total times of under 30 min. This report is not intended to be a comprehensive review of 2DLC, but is deliberately focused on the issues involved in doing fast 2DLC by means of elevating the column temperature; however, many issues of broader applicability will be discussed.     

Comparison of hydrophilic-interaction, reversed-phase and porous graphitic carbon chromatography for glycan analysis

Hydrophilic-interaction liquid chromatography (HILIC), reversed-phase chromatography (RPC) and porous graphitic carbon (PGC) chromatography are typically applied for liquid chromatographic separations of protein N-glycans. Hence the performances of these chromatography modes for the separation of fluorescently labeled standard glycan samples (monoclonal antibody, fetuin, ribonuclease-B) covering high-mannose and a broad range of complex type glycans were investigated. In RPC the retention of sialylated glycans was enhanced by adding an ion-pairing agent to the mobile phase, resulting in improved peak shapes for sialylated glycans compared to methods recently reported in literature. For ion pairing RPC (IP-RPC) and HILIC ultra-high performance stationary phases were utilized to maximize the peak capacity and thus the resolution. But due to the shallow gradient in RPC the peak capacity was lower than on PGC. Retention times in HILIC and IP-RPC could be correlated to the monosaccharide compositions of the glycans by multiple linear regression, whereas no adequate model was obtained for PGC chromatography, indicating the significance of the three-dimensional structure of the analytes for retention in this method. Generally low correlations were observed between the chromatography methods, indicating their orthogonality. The high selectivities, as well as the commercial availability of ultra-high performance stationary phases render HILIC the chromatography method of choice for the analysis of glycans. Even though for complete characterization of complex glycan samples a combination of chromatography methods may be necessary.     

A practical approach to maximizing peak capacity by using long columns packed with pellicular stationary phases for proteomic research

Maximization of peak capacity is a very important step in developing one-dimensional separations of complex samples. In recent work, it was shown that the use of small particles in combination with the new technique of ultrahigh pressure liquid chromatography (UHPLC) was able to generate very high peak capacities. Here we show the ability of conventional HPLC instrumentation to give comparable peak capacities to those obtained in UHPLC for the important case of complex mixtures of peptides but at much lower pressures by using a 60 cm long set of columns packed with 5 microm pellicular (superficially porous) particles. We first show, in complete agreement with the well known results of the theory of isocratic separations that, when time is not limiting, the best peak capacities in gradient elution chromatography are obtained by using large particles and the longest column that can be operated at the pump's pressure limit. Two different types of 5 microm particles (superficially porous and totally porous) were compared for their efficiency in gradient chromatography of peptides. We find that the pellicular material gave about 50% higher peak capacity compared to the analogous porous material. A 60 cm column set packed with pellicular particles was made by connecting short columns in series; a peak capacity of about 460 was obtained in 4 h at room temperature. Increasing the column temperature to 70 degrees C reduced the analysis time to 2 h and further increased the peak capacity to more than 500. The number of peaks observed in the separation of bovine serum albumin tryptic peptides was greatly increased and the separation quality was significantly improved.     

Peak capacity in gradient reversed-phase liquid chromatography of biopolymers. Theoretical and practical implications for the separation of oligonucleotides

Reversed-phase ultra-performance liquid chromatography was used for biopolymer separations in isocratic and gradient mode. The gradient elution mode was employed to estimate the optimal mobile phase flow rate to obtain the best column efficiency and the peak capacity for three classes of analytes: peptides, oligonucleotides and proteins. The results indicate that the flow rate of the Van Deemter optimum for 2.1 mm I.D. columns packed with a porous 1.7 microm C18 sorbent is below 0.2 mL/min for our analytes. However, the maximum peak capacity is achieved at flow rates between 0.15 and 1.0 mL/min, depending on the molecular weight of the analyte. The isocratic separation mode was utilized to measure the dependence of the retention factor on the mobile phase composition. Constants derived from isocratic experiments were utilized in a mathematical model based on gradient theory. Column peak capacity was predicted as a function of flow rate, gradient slope and column length. Predicted peak capacity trends were compared to experimental results.     

Fast gas chromatography: packed column solvating gas chromatography versus open tubular column gas chromatography

Packed capillary column solvating gas chromatography (SGC) and open tubular column gas chromatography (GC) were compared with respect to their potentials for fast separations. A recently introduced "universal" peak capacity equation was used to compare the performance of these two methods. The effects of various factors on peak capacity were investigated. Results demonstrate that retention factor and column efficiency are the main factors affecting peak capacity for fast separations. Packed columns produce both high retention factors and high selectivities. While high efficiencies and high peak capacities can be demonstrated by both techniques, open tubular column GC can surpass packed capillary column SGC in both measurements, except for the case of the analysis of simple mixtures in short analysis times, where retention factor and selectivity become important. Practical aspects such as pressure drop and sample capacity are compared for SGC and open tubular column GC. It was found that packed column SGC demonstrates higher sample capacities, but requires much higher column inlet pressures than open tubular column GC. A variety of mobile phases can be used for packed column SGC, which can provide high solvating power for large and polar compounds.     

Direct coupling of capillary electrophoresis and nuclear magnetic resonance spectroscopy for the identification of a dinucleotide

Summary In this paper, a general peak capacity expression was evaluated using columns containing various packing materials under solvating gas chromatography (SGC) conditions. Differing from column efficiency, peak capacity can describe both separation capability and speed when introducing the dead time into the peak capacity expression. Various factors that influence peak capacity in SGC are described, including particle pore size, chemical surface modification, particle size, column length, temperature, and pressure.     

The effect of elevated temperature on conventional stationary phases used in SFC

Summary The effect of elevated temperatures on conventional packed bonded-phase columns used in supercritical-fluid chromatography (SFC) has been investigated. The impact of column conditioning temperature on the capacity factor, peak width, and peak asymmetry on octadecyl and propylamino columns from five commerical suppliers is reported.     

多维液相色谱技术的进展

与一维分离模式相比,多维色谱分离技术的最大特点是可极大地提高峰容量．近几年,随着蛋白质组学的出现尤其是表达谱的开展,对分离技术提出更高的要求．多维高效液相色谱系统以其快速、高效、自动化程度高以及易与质谱等其他技术联用等优势再一次成为研究应用的热点．本文结合本课题组在多维色谱方面的工作介绍了多维色谱技术的发展及应用,重点介绍在蛋白质组学平台中的应用．     

Comprehensive two-dimensional gas chromatography: metrics,potentials, limits

Metrics for evaluation of separation performance of comprehensive two-dimensional gas chromatography (GCxGC) and for quantitative comparison of that performance with similar performance of its 1D (one-dimensional) counterparts are described. The performance improvement can be expressed via reduction in the saturation of a chromatogram or-in the case of the uniform distribution of peaks along the second dimension--via the peak capacity gain due to GCxGC. An order of magnitude peak capacity gain due to the comprehensive GCxGC is possible under optimal conditions. Optimal parameters of the second dimension column as well as the optimal operational conditions for that column and for the modulator in a comprehensive GCxGC are also presented.     

Theoretical advantages and drawbacks of on-line,multidimensional liquid chromatography using multiple columns operated in parallel

The theoretical advantages and drawbacks of using a multiple-, parallel column approach in on-line multidimensional liquid chromatography systems were investigated. Much time or peak capacity can be gained with the use of multiple parallel columns at the second-dimension while the aggregate time of separation increases only by the increment of the gradient time of the second-dimension. Multidimensional chromatographic systems are now used to perform many tasks ranging from routine, fast analyses to specialized, arduous separations. In this work, we focus on the advantages of a multiple, parallel columns approach to on-line multidimensional liquid chromatography systems. Calculations of the achievable peak capacities were made as functions of the number of columns operated in parallel. Increasing the number of second-dimension columns from one to two or three causes the largest increase in peak capacity with only a slight increase of aggregate time. We also present some practical aspects to consider when attempting multidimensional separations with multiple columns operated in parallel.     

Optimizing separations in online comprehensive two‐dimensional liquid chromatography

Online comprehensive two‐dimensional liquid chromatography has become an attractive option for the analysis of complex nonvolatile samples found in various fields (e.g. environmental studies, food, life, and polymer sciences). Two‐dimensional liquid chromatography complements the highly popular hyphenated systems that combine liquid chromatography with mass spectrometry. Two‐dimensional liquid chromatography is also applied to the analysis of samples that are not compatible with mass spectrometry (e.g. high‐molecular‐weight polymers), providing important information on the distribution of the sample components along chemical dimensions (molecular weight, charge, lipophilicity, stereochemistry, etc.). Also, in comparison with conventional one‐dimensional liquid chromatography, two‐dimensional liquid chromatography provides a greater separation power (peak capacity). Because of the additional selectivity and higher peak capacity, the combination of two‐dimensional liquid chromatography with mass spectrometry allows for simpler mixtures of compounds to be introduced in the ion source at any given time, improving quantitative analysis by reducing matrix effects. In this review, we summarize the rationale and principles of two‐dimensional liquid chromatography experiments, describe advantages and disadvantages of combining different selectivities and discuss strategies to improve the quality of two‐dimensional liquid chromatography separations.     

Real-time control of column switching in multidimensional gas chromatography

In chromatography the separation power expressed in terms of peak capacity can be greatly enhanced by multidimensional techniques. The most important aspect of multidimensional chromatography is the precise location of the heart-cut window. Very often the reliability of this positioning is ensured by applying relatively large heart-cuts; this reduces the intrinsic selectivity offered by the technique. The best way of locating peaks in chromatography is by means of retention indices. This technique can also be used in multidimensional chromatography. A method is described whereby the heartcut window in multidimensional gas chromatography (MDGC) can be defined precisely.     

Peak capacity optimization in comprehensive two dimensional liquid chromatography: a practical approach

In this work we develop a practical approach to optimization in comprehensive two dimensional liquid chromatography (LC x LC) which incorporates the important under-sampling correction and is based on the previously developed gradient implementation of the Poppe approach to optimizing peak capacity. The Poppe method allows the determination of the column length, flow rate as well as initial and final eluent compositions that maximize the peak capacity at a given gradient time. It was assumed that gradient elution is applied in both dimensions and that various practical constraints are imposed on both the initial and final mobile phase composition in the first dimension separation. It was convenient to consider four different classes of solute sets differing in their retention properties. The major finding of this study is that the under-sampling effect is very important and causes some unexpected results including the important counter-intuitive observation that under certain conditions the optimum effective LC x LC peak capacity is obtained when the first dimension is deliberately run under sub-optimal conditions. In addition, we found that the optimum sampling rate in this study is rather slower than reported in previous studies and that it increases with longer first dimension gradient times.     

Comments on the Implementation of a Simple Peak Capacity Optimization Procedure and Comparison of Poly(styrene–divinylbenzene) and RP-18 Silica Monolithic Capillary Columns of 5-cm for the Analysis of Protein Digests

For the analysis of protein digests, the peak capacity in reversed-phase liquid chromatography is of paramount importance. A univariate method to maximize the peak capacity as developed by Wang et al. (Anal Chem 78:3406–3416, 20) has been applied and tested for a monolithic RP-18 silica capillary column. In their method, using model peptides representing a bovine serum albumin digest, the gradient time and temperature are kept constant while the flow rate and eluent strength are varied. Despite our criticism on the fixed starting conditions, a long gradient time leading to an unnecessary long analysis time and a high temperature leading to possible degradation products in the chromatogram, and the peak capacity as the only optimization parameter this fast and simple optimization strategy turns out to be applicable to capillary monolithic columns. Furthermore, the influence of the peak capacity on a second optimization parameter, the MS protein identification score, is examined. The procedure is also used to enhance the performance of two popular types of monolithic capillary LC columns (silica-C18 and poly(styrene–divinylbenzene)) of the same length for the analysis of protein digests. Comparison of both columns show that the calculated chromatographic parameters, like productivity and peak capacity, and identification score for both columns are about the same. For a more complicated nine-protein digest the performance of the silica monolith is slightly better.     

Comparison of one-dimensional and comprehensive two-dimensional separations by gas chromatography

Comprehensive two-dimensional gas chromatography (GC x GC) can reveal information on the composition of a sample in a way that cannot be done by one-dimensional GC (1D-GC). GC x GC also offers much greater control of chromatographic selectivity based on molecular structure. However, in spite of more than 15 years of claims of the ability of GC x GC to resolve an overwhelmingly larger number of peaks than 1D-GC, and in spite of the theoretically proven potential of GC x GC to have an order of magnitude larger peak capacity than 1D-GC, the peak capacity of currently practiced GC x GC does not generally exceed the peak capacity attainable from 1D-GC with the same analysis time and the same minimal detectable concentration (MDC). The methodology for comparing the peak capacity of GC x GC to 1D-GC is described. The comparison of the performance of GC x GC to 1D-GC shows that the modulator is the key bottleneck limiting the performance of existing GC x GC. To realize the full potential of GC x GC, duration of injection from a modulator into the second-dimension column should be reduced by an order of magnitude or more. Use of powerful data analysis techniques such as peak deconvolution in both dimensions can further increase resolving power of GC x GC.