Implementation of the Separation Quality Factor (SQF) in Chromatography Data Systems for Automated Method Evaluation

The Automated Sepration Quality Factor (SQF) calculation was applied to two chromatographically demanding applications. The first one involves the ion-pair reversed-phase liquid chromatographic separation of a complex oligonucleotide mixture, where different gradient profiles and gradient times were compared. The second application focuses on the reversed-phase liquid chromatography analysis of lipid nanoparticle (LNP) components under various gradient conditions and stationary phases. In both examples, SQF provided a more comprehensive assessment of chromatographic performance than conventional single-parameter descriptors and enabled objective ranking of chromatographic conditions.

Introduction

The evaluation of chromatographic separation quality has been a central topic since the early development of modern chromatography. Historically, chromatographers have relied on a range of performance descriptors, including theoretical plate number, plate height, peak capacity, resolution, peak-to-valley ratio, and various peak shape metrics, to characterize the effectiveness of a separation.1–5 These classical parameters have provided valuable insight into specific aspects of chromatographic performance, such as column efficiency, selectivity, and retention, and remain essential tools in routine method development and system suitability testing. However, none of these metrics alone provides a complete description of the overall quality of a chromatographic separation.

Among the traditional descriptors, resolution (Rs) has become the most widely accepted measure of separation quality, because it directly reflects the degree of separation between adjacent peaks and incorporates retention, selectivity, and efficiency into a single parameter.3 Nevertheless, resolution is inherently a pairwise metric and therefore only describes the separation between two neighboring peaks. In complex chromatograms containing numerous analytes, the critical resolution often fails to reflect the overall quality of the entire separation space. A chromatogram may exhibit an acceptable critical Rs value, while still suffering from poor peak distribution, inefficient use of the elution window, or unfavorable peak elution patterns.

To overcome some of these limitations, alternative chromatographic response functions and optimization criteria have been proposed. These include critical resolution, peak counting approaches, simplex-based optimization functions, elution window utilization concepts, and composite objective functions that combine separation efficiency with analysis time.^6–11 Such approaches have proven valuable for automated method development and chromatographic optimization, but they typically emphasize only selected aspects of chromatographic performance and often lack universal applicability across different separation modes and applications.

Over the past decade, increasing attention has been paid to the global distribution of peaks across the chromatographic window especially for complex samples (i.e., peptide mapping, oligo-mapping, proteomic and lipidomic applications). Uniformly distributed peaks are generally considered desirable, because they maximize the effective use of chromatographic space, improve the probability of resolving unknown impurities or degradation products, and enhance method robustness. Consequently, concepts such as predictive elution window stretching and shifting (PEWS²), chromatographic dimensionality, and peak spacing-based descriptors have been introduced to characterize the organization of peaks beyond simple pairwise resolution measurements.^6,7

Recently, we introduced a universal SQF as a normalized and dimensionless metric designed to provide a more comprehensive assessment of chromatographic separations. SQF combines multiple independent descriptors, including kinetic efficiency, peak symmetry, peak distribution uniformity, elution window utilization, and the so-called critical peak order, into a single quality score ranging from 0 to 1.^12–14 By integrating these complementary attributes through a geometric mean approach (eq. 1), SQF provides a more holistic representation of chromatographic quality than conventional single-parameter metrics.^13–15

where η is normalized efficiency, S is normalized average peak symmetry, DU_cv is peak distribution uniformity based on the coefficient of variation, We is elution window utilization, and CPO_min is critical peak order.^13–15

One of the key advantages of SQF is that it evaluates characteristics that are frequently overlooked in traditional chromatographic assessments. For example, it rewards efficient use of the chromatographic time domain, penalizes asymmetric peaks, considers the relative positioning of critical peak pairs, and accounts for the uniformity of peak distribution across the separation window. As a result, SQF can distinguish between chromatograms that exhibit similar critical resolution values but differ substantially in overall separation quality and robustness. The practical benefits of SQF have been demonstrated for applications such as column screening, mobile-phase optimization, impurity profiling, and stability-indicating methods.15 Because SQF is dimensionless and normalized, it facilitates objective comparison of chromatograms obtained under different operating conditions and supports data-driven decision-making during method optimization.¹³

The SQF approach is compatible with automated chromatographic evaluation. All submetrics rely on routinely calculated chromatographic parameters such as retention times, peak widths, tailing factors, and resolution values that are readily available in modern chromatography software, here referred to as chromatography data systems (CDS). Consequently, SQF can serve not only as a descriptor but also as a practical optimization target for automated workflows.

In this article, we demonstrate that the calculation of the SQF can be fully automated within a CDS environment. Automated SQF determination enables objective and reproducible assessment of chromatographic performance without manual calculations, facilitates rapid ranking of chromatographic conditions during method development, supports automated column and method screening studies, and allows routine monitoring of overall separation quality during method lifecycle management. Furthermore, automated SQF reporting provides a comprehensive quality metric that complements traditional system suitability parameters.

Implementation of SQF Calculation Using Custom Fields

Modern CDSs allow performing user-defined calculations through custom fields that can operate at different hierarchical levels of chromatographic data. These calculations can be associated with individual samples, detected peaks, or complete chromatographic results, thereby enabling the automated derivation of complex performance metrics directly from routinely reported chromatographic parameters. The SQF is particularly well suited for implementation within a CDS environment because all its constituent parameters are derived from information that is routinely generated during chromatographic data processing. Retention times, peak widths, tailing factors, peak resolutions, and peak counts are standard outputs of chromatographic integration and therefore can serve as inputs for automated SQF calculations. The SQF is calculated according to eq. ^1.13,15

Implementation of this equation requires a series of intermediate calculations that combine sample-level parameters with peak- and chromatogram-level descriptors.¹³ Sample-specific values such as gradient time (t_G) and column dead time (t₀) are recorded (Figure 1) once for each injection and subsequently used in the calculation of two parameters (normalized kinetic efficiency η and elution window utilization W_e). Peak-level calculations are used to derive descriptors such as peak symmetry factors, retention-time differences, and peak counts. Chromatogram-level calculations then combine these individual parameters to determine the various SQF submetrics and ultimately the overall SQF value.

As an example, the determination of peak distribution uniformity (DU) requires the knowledge of the total number of detected peaks and their retention time distribution. The total peak count can be generated automatically from peak-level calculations and subsequently transferred to higher-level calculations for determination of DU. Similarly, the CPO metric requires automated evaluation of peak resolution and peak symmetry relationships among critical peak pairs, while η and W_e require chromatographic descriptors including tG, t0 and peak retention times (timing parameters).

Once the required calculation hierarchy has been established, all SQF submetrics and the final SQF value can be generated automatically during routine data processing without manual intervention. This approach enables consistent application of the SQF methodology across large datasets. Furthermore, performing all calculations directly within the CDS environment ensures that the calculation workflow remains fully integrated with the underlying chromatographic data, minimizing manual data handling and reducing the potential for transcription errors associated with external data processing.

Figure 1 shows an example of a sample table with gradient time and void time custom fields, while Figure 2 shows a result file including the calculated values of the metrics and the overall SQF.

Results and Discussion
Application 1: Oligonucleotides Separation by IP-RPLC

To demonstrate the applicability of automated SQF calculations to complex separations, an oligonucleotides test mixture containing homo- and heteropolymeric species ranging from approximately 20 to 100 nucleotides was investigated using ion-pair reversed-phase liquid chromatography (IP-RPLC). Oligonucleotide separations represent a particularly challenging chromatographic application because of the large number of closely eluting components, broad molecular-weight distribution, and the need to maximize resolving power across the entire chromatographic window. In such cases, conventional metrics such as critical resolution or peak capacity provide only a partial description of separation performance and may not adequately capture differences in peak spacing or elution-window utilization. Therefore, a series of gradients differing in both steepness and shapes were evaluated, and the resulting chromatograms were compared using the SQF approach.

Figure 3 shows three chromatograms together with corresponding normalized metrics obtained with linear (Figure 3a and 3b, t_G = 25 and 30 min, respectively) and concave gradient profile (Figure 3c).

Visual inspection of the chromatograms immediately reveals substantial differences in peak distribution across the elution window. In the chromatogram obtained with the 25 min linear gradient (Figure 3a), the majority of oligonucleotide peaks elute within a relatively narrow retention range between approximately 16 and 24 min, with several clusters of closely spaced peaks clearly visible, while the first peak is eluted very early (t_R ~ 1.5 min). In agreement with this observation, the DU value was extremely low (0.004), indicating highly nonuniform peak spacing despite the relatively good kinetic efficiency (η = 0.973) and acceptable average peak symmetry (S = 0.871). As a consequence, the overall SQF remained low (0.293), demonstrating that the choice of use of a geometric mean penalizes chromatograms featuring good overall performance, but very low performance in one metric, thereby favoring chromatograms that reach a compromise between all the five metrics.

Extending the gradient time from 25 to 30 min, while decreasing the eluent strength of the initial mobile phase composition, resulted in a noticeable improvement in overall separation quality (Figure 3b). The SQF increased from 0.293 to 0.508, primarily due to the increase in peak distribution uniformity (DU = 0.174 versus 0.004). However, the chromatogram still exhibited significant clustering, particularly in the later-eluting region where many peaks remained concentrated within a relatively narrow retention interval. Interestingly, the elution window utilization metric decreased from 0.744 to 0.436, indicating that the change of starting mobile phase composition was not efficiently translated into a better utilization of the gradient time. Similarly, the lower CPO value (0.507) suggests the presence of less favorable critical peak relationships compared with the other conditions evaluated. Although the longer linear gradient and decreased initial eluent strength improved overall separation quality, the resulting chromatogram remained suboptimal from a global separation perspective.

The most significant improvement was achieved using the concave gradient profile (Figure 3c). This chromatogram exhibits a much more uniform distribution of peaks throughout the elution window, with substantially reduced peak clustering and improved spacing between neighboring components. As a result, both DU (0.427) and W_e (0.917) reached their highest values among the tested conditions. In addition, the CPO metric increased to 0.931, indicating favorable critical peak behavior across the chromatogram. Although the kinetic efficiency (η = 0.951) was slightly lower than for the linear gradients due to lower gradient compression effects, this small decrease was offset by improvements in the distribution-related metrics, resulting in a substantially higher SQF value of 0.792.

These results highlight an important advantage of the SQF approach. If the chromatograms were compared solely based on efficiency or peak shape, only minor differences would be observed because normalized efficiency and average peak symmetry remained relatively similar for all three conditions. In contrast, SQF clearly differentiates the separations by incorporating additional descriptors. The results further demonstrate that for complex oligonucleotide separations, optimization of gradient shape may have a greater influence on overall chromatographic quality than simply increasing gradient duration. The concave gradient enabled a more effective redistribution of peaks across the available separation window, thereby producing the highest overall SQF and the best chromatogram from both an analytical and method development perspective.

Application 2: Lipid Composition Analysis in Lipid Nanoparticle Characterization

A second application was performed using a reversed-phase liquid chromatographic method for the analysis of lipid components commonly employed in lipid nanoparticle (LNP) formulations. A lipid mixture containing various ionizable lipids in addition to helper lipids (i.e., PEGylated lipids, zwitterionic lipids, and cholesterol) was screened on two different stationary phases. The chromatographic performance across three gradient conditions was evaluated to investigate the influence of column selectivity and gradient steepness on the overall separation quality. While column screening and gradient optimization are typically guided by critical pair resolution or peak-counting approaches, here we preferred to consider the automatically calculated SQF value as a multidimensional performance descriptor to compare the chromatograms obtained under different conditions.

Figure 4 shows the chromatograms obtained for the analysis of model LNP components using two different reversed-phase columns and three gradient times (t_G = 3, 4, and 5 min). The corresponding normalized separation quality metrics and SQF values are provided within each chromatogram.

For Column 1, increasing the gradient time resulted in a gradual improvement of the overall separation quality, while for Column 2 it remained essentially unchanged, suggesting limited benefit of longer methods. On Column 1 (Figure 4 a–c), the SQF increased from 0.667 at t_G = 3 min to 0.715 and 0.750 at t_G = 4 and 5 min, respectively. This trend was primarily driven by improvements in peak distribution uniformity (DU increased from 0.442 to 0.534), peak symmetry (increased from 0.851 to 0.936), and critical peak order (CPO increased from 0.551 to 0.805). At the same time, elution window utilization decreased slightly from 0.741 to 0.667, reflecting the expected reduction in gradient steepness. Nevertheless, the gains in peak spacing and critical-pair behavior outweighed the modest decrease in window utilization, resulting in progressively higher SQF values.

A similar trend was observed for Column 2 (Figure 4 d–f), although the changes were less pronounced. The SQF values remained relatively stable, varying between 0.760 and 0.775 across the studied gradient times, confirming that using longer methods was not chromatographically justified. Kinetic efficiency increased slightly with gradient duration (η = 0.887–0.918), while peak distribution uniformity remained essentially unchanged (DU ≈ 0.61). Notably, all chromatograms obtained on Column 2 achieved the maximum possible CPO score (CPO = 1.000), indicating adequate separation of the critical peak pairs. The combination of high DU and optimal CPO values contributed substantially to the consistently high SQF scores observed for this column.

Comparison of the two columns reveals that column selectivity had a larger impact on the overall separation quality than gradient steepness. Regardless of gradient time, Column 2 consistently yielded higher SQF values than Column 1. Visual inspection of the chromatograms confirms that the peaks obtained on Column 2 were more uniformly distributed across the chromatographic window and exhibited fewer critical separations. This observation is reflected by the considerably higher DU values (0.608–0.622 versus 0.442–0.534) and the maximum CPO score obtained under all conditions.

Interestingly, the kinetic efficiency values were relatively similar for all six conditions (η = 0.861–0.918), demonstrating that differences in peak width alone would not have been sufficient to distinguish the chromatographic performance of the tested conditions. Likewise, peak symmetry values varied only moderately. In contrast, the SQF metric clearly differentiated the chromatograms.

Automated Reporting of SQF Metrics

Once the SQF calculation workflow has been implemented within the CDS, the calculated parameters can be incorporated directly into customized chromatographic reports. This enables automatic reporting of both the individual SQF submetrics and the final SQF value together with the standard chromatographic results generated during data processing.

Figure 5 illustrates an example report containing conventional chromatographic peak information, including retention time, peak area, peak height, USP tailing factor, and resolution, together with SQF-related parameters derived from the custom calculations. In addition to the final SQF score, intermediate metrics such as η, S, DU, W_e, and CPO can be reported automatically for every processed chromatogram.

The ability to generate these results directly within the reporting workflow offers several advantages. First, all calculated values remain linked to the original chromatographic data and are therefore fully traceable. Second, inclusion of SQF and its individual submetrics within routine chromatographic reports provides a standardized and objective assessment of overall separation quality that can be readily reviewed, compared, and archived. This capability is particularly beneficial in regulated pharmaceutical environments, where data integrity, reproducibility, and auditability are critical requirements.

Conclusion

In the present work, we demonstrated that SQF calculations can be successfully implemented and fully automated within ea CDS using standard chromatographic outputs and custom fields. Because all required inputs are routinely generated during chromatographic data processing, no specialized external software or manual data manipulation is required. Once the calculation workflow is established, all submetrics and the final SQF value are automatically generated as part of the normal data-processing sequence.

A particularly important observation from these studies is that chromatograms exhibiting similar efficiencies or peak symmetries may differ substantially in their overall quality due to differences in peak distribution, chromatographic space utilization, or critical peak behavior. By integrating these complementary separation attributes into a single normalized score, SQF facilitates objective comparison of chromatographic conditions and reduces reliance on subjective visual inspection. This feature is especially valuable for complex separations involving large numbers of analytes, such as oligonucleotide mapping, peptide mapping, lipidomics, metabolomics, impurity profiling, and other high-information-content analyses.

Beyond method development, automated SQF calculation may also provide benefits for column screening, robustness studies, system suitability assessment, lifecycle management, and automated optimization workflows. Because the calculations are performed directly within the CDS environment, the entire process remains traceable and compliant with established data-management practices. Furthermore, this approach still allows for easy modifications of the formulas without requiring extensive changes to a rigid workflow.

Overall, the results presented here demonstrate that automated CDS-based implementation transforms SQF from a conceptual separation metric into a practical analytical tool.

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