A Practical Excel Tool to Support the Development of Comprehensive 2D-LC Separations

Two-dimensional liquid chromatography (2D-LC) is regarded as an important strategy to improve chromatographic performance. This technique increases peak capacity and selectivity, while keeping analysis time reasonable (1). There are different ways to combine two chromatographic dimensions. Some are simple (such as heart-cutting), others are moderately complex (such as multiple heart-cutting or selective comprehensive) and some are more advanced (such as full comprehensive two-dimensional liquid chromatography, which is defined as LCxLC).Among these methods, LCxLC provides much more information than the others (2). It is especially useful for very complex mixtures containing many substances. However, to get the best results from LCxLC, the conditions in both dimensions must be carefully adjusted (3,4). This is because combining two chromatographic dimensions introduces many constraints. In LCxLC, many parameters are closely connected (5). For example, changing the flow rate of the mobile phase in the first dimension affects efficiency, peak capacity, dilution and pressure, which is expected. However, it also impacts sampling time, gradient time, dilution and peak capacity in the second dimension, which is less obvious. Interestingly, the impact of changing flow rate depends on the column geometry in both dimensions. A decrease in flow rate can either improve or reduce the overall performance, depending on the 2D-LC setup. To correctly evaluate the impact of any parameters (in the first dimension, second dimension, or the interface), it is essential to use an Excel spreadsheet that combines all the chromatographic equations.

We have developed a free Excel-based calculator to help researchers entering the field of comprehensive two-dimensional liquid chromatography (LC×LC) with confidence. The calculator has three main parts, as shown in Figure 1 highlighting Characterization, Optimization, and Visualization. The calculator can be downloaded directly from the following website: https://farma-unites.unige.ch/en/rudaz-lab/tools/2d-lc-smart-calculator.

The first part of the tool focuses on the characterization of the LC×LC system. This step is essential, as it is necessary to know key system parameters such as extra-column variance (¹σ²_ext, ²σ²_ext), time offset (¹t_offset, ²t_offset), system pressure (²ΔP_system) and gradient delay volume (¹V_D, ²V_D). These parameters have a strong impact on the overall performance of an LC×LC setup and must be considered when optimizing analysis conditions. In addition to entering these system-specific values, the user has to choose the chromatographic mode for the first dimension as hydrophilic interaction liquid chromatography (HILIC) or reversed phase liquid chromatography (RPLC). The second dimension has to be performed in RPLC. The user must also select the type of molecules to be analyzed (either small molecules or peptides). Based on this input, the calculator will recommend two different experimental gradients in each dimension. These two gradients have to be realized practically on the sample analyzed by the user, in order to determine the optimal gradient composition ranges (initial and final mobile phase compositions) for both dimensions.

The second part of the tool is dedicated to the optimization of the two dimensional liquid chromatography (2D-LC) setup. As shown in Figure 2, this Excel spreadsheet contains many parameters, but helpful comments have been added to each cell so that the user can easily understand what information is needed. To begin, the user must enter some general information about the sample, including the type of molecules, average molecular weight, and sample diluent. Next, the user provides the first dimension (¹D) conditions, including the separation mode, column dimensions, system characteristics and mobile phase conditions. Based on these data, the calculator estimates key parameters for the first dimension (6), such as effective peak capacity, dilution factor, and total pressure and injection volume. The interfacing conditions must also be entered. This includes (i) the sampling rate (number of cuts per 6σ peak width), which allows to calculate the sampling time (total analysis time available in the second dimension), (ii) the split factor between the two dimensions (it is obviously possible to have no split), and (iii) the possibility of solvent dilution between the two dimensions using either a make-up solvent or active solvent modulation (ASM). Next, the user enters the same type of information for the second dimension (²D) as previously for ¹D, which also provides the key parameters in ²D. volume (7,8). Once all values are entered, the tool automatically calculates and simulates the following performance indicators for the selected LC×LC conditions:

• Effective peak capacity (an estimate of the overall separation power of the 2D system)
• Sample dilution factor (the degree of dilution the sample experiences from injection to detection)
• Number of runs required in the second dimension (based on the total analysis time and sampling conditions)
• Required solvent dilution factor (this accounts for solvent compatibility between the two dimensions, especially when using a make-up pump or ASM.

Optimization score ranges from 0 to 10 (a score calculated using a multi-criteria response function, based on the Derringer’s desirability function). This value provides an overall indication of the quality of the current 2D-LC setup: a higher score means better optimized conditions.

If the goal is to optimize rather than just simulate, the spreadsheet includes a built-in macro. When activated, this macro automatically calculates all values of the key parameters mentioned above across a wide range of combinations, including the ¹D-column length, ¹D-flow rate, sampling rate and split factor. Based on these calculations, the calculator identifies and suggests the optimal values for each of these parameters. In addition, the tool offers a visualization of the optimization process using Pareto plots (9). This graphical approach focuses on two key performance indicators: peak capacity and sample dilution factor, which are the most relevant ones when optimizing a 2D-LC setup. On the Pareto diagram, each point represents a unique set of conditions (about 1,000 combinations are shown). The x-axis shows the peak capacity while the y-axis shows the sample dilution factor. The most desirable results appear on the right side of the graph. The user can give priority to sensitivity over peak capacity (bottom right), or the opposite (top right), or a compromise between the two (middle right). The visualization includes three graphs. The first graph on the left displays all possible sets of parameters and the six different colors differentiate data for six ¹D-column lengths, allowing to select the best one. Then, the middle graph displays all possible sets of parameters with the optimal column length selected at the previous stage. The five different colors differentiate data for five sampling rates, allowing to select the best one. Finally, the right graph displays all possible sets of parameters with the selected column length and sampling rate. The ten different colors differentiate data for ten 1D-flow-rates, allowing to select the best one. If the user chooses to evaluate the split factor between the first and second dimensions, the third graph includes four data points per flow rate, corresponding to values of 1, 2, 3, and 5 for the split factor. On the y-axis (dilution factor), the lowest point always corresponds to the lowest split factor (which would be 1), and the highest point corresponds to the highest split factor (which would be 5). This makes it easier to select the most appropriate splitting conditions.

The third part of the calculator is the visualization tool. This Python-based tool is bundled as a standalone executable application that can be launched directly from Excel, without requiring installation of a Python interpreter. Figure 3 shows the window used to visualize 2D-LC chromatograms. To begin, the user must load an Excel file that contains the raw chromatographic data. The data should be contained in a single sheet with only two columns: time (in min) in the first column and intensity in the second. The user must also enter the sampling time, also known as cycle time or modulation time, which corresponds to the total analysis time in the second dimension. It is also possible to subtract a blank signal by selecting a region in the ¹D chromatogram where no peaks are present. After loading the data, the user can choose among four ways to display the results. The first is a 2D contour plot, which is the standard and most common way to visualize 2D data, as shown in Figure 3. The user can also choose whether the x and y axes represent ¹D or ²D retention times. The second option is a 3D contour plot that includes both ¹D and ²D retention times, as well as peak intensity on the z-axis. The third option shows an overlay of all the ²D chromatograms, which can be useful to identify abnormal events during the analysis. Finally, the fourth option displays the raw data as a time versus intensity plot, exactly as it appears in the original Excel file. In all visualization types, the user can easily adjust the scales and color settings to better observe specific features.

In conclusion, this Excel-based tool is an excellent way to help users understanding the fundamentals of comprehensive 2D-LC. Thanks to its user-friendly interface, and clear instructions, beginners can gain confidence and quickly learn how any parameters affect the overall performance of their 2D-LC setup. At the same time, the tool offers powerful optimization and visualization capabilities that makes it also useful for more experienced users. Indeed, advanced simulations, embedded macro, and multi-criteria scoring functions allow for detailed analysis and fine-tuning of method parameters. The integrated visualization options, including Pareto plots and 2D/3D chromatograms, further support method development and result interpretation. In the end, this tool is a practical solution to guide method optimization in 2D-LC.

References

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