Beyond Single Metrics: A New Approach to Measuring LC×LC Orthogonality

In comprehensive two-dimensional liquid chromatography (LC×LC), measuring separation quality has long been a point of debate. Traditional single-metric approaches often oversimplify an inherently complex process, leaving researchers with inconsistent or even misleading results.

In a recent conversation with LCGC International, Soraya Chapel explained how she and her collaborators used multi-metric orthogonality score and open-source Python tool address these challenges. By combining multiple descriptors into a composite score, the approach reduces user bias, provides a more balanced assessment of separation space, and opens the door to more reproducible method development. Chapel also discussed their choice of reversed-phase liquid chromatography × reversed-phase liquid chromatography (RPLC×RPLC) over mixed-mode pairings, and why their sub-hour method represents a step forward for high-throughput environmental analysis.

How does the orthogonality score improve upon existing single-metric approaches for evaluating comprehensive two-dimensional liquid chromatography (LC×LC) separation quality?

There are many approaches to evaluate LC×LC separation quality from an orthogonality point of view, because separation orthogonality itself is a multifaceted concept. On paper, describing a perfectly orthogonal LC×LC separation is straightforward: peaks are evenly distributed across the entire 2D separation space, with no correlation between retention times in each dimension, no clustering, and no outliers. Conversely, in a completely non-orthogonal system, peaks align along a diagonal, reflecting strong correlation and low complementarity between the two separations.

The reality, however, is that most LC×LC separations fall somewhere in between these two extremes. They exhibit partial orthogonality: good coverage of the separation space in some regions but not in others, areas where peaks cluster together, and perhaps a few outliers scattered across the surface. This intermediate situation complicates interpretation. Should outliers be included in the effective separation space, or excluded as noise? And which of the many available metrics is best suited to make that distinction? These uncertainties explain why so many different approaches have been proposed to quantify orthogonality.

Most single-metric approaches capture only one aspect of orthogonality, whether it is space coverage, information similarity between dimensions, or peak distribution density. Each provides useful information but also comes with limitations. Metrics that emphasize coverage often overlook clustering, while correlation-based metrics underestimate sparse but relevant coverage. In practice, results vary dramatically depending on which metric is chosen, and in some cases, the same separation can appear highly orthogonal or poorly orthogonal on paper depending on the metric chosen to describe it. Relying on a single descriptor can therefore give an incomplete or even misleading picture.

Our approach addresses this challenge by combining multiple orthogonality metrics into a single composite score. To avoid redundancy, metrics are first grouped according to statistical similarity, ensuring that correlated descriptors do not dominate the result. The final orthogonality score is then calculated as an average across these groups. This strategy integrates complementary perspectives, reduces sensitivity to outliers, and provides a more robust and balanced measure of how effectively the 2D separation space is used. In our study, we implemented nine widely used orthogonality metrics (now expanded to 12 in the latest version of the tool, as described in our more recent work [1]) and grouped them according to their correlation patterns. The resulting orthogonality score is not tied to one definition of orthogonality but instead reflects the multifaceted aspect of the concept. In this way, it provides a richer, more reliable assessment of LC×LC space occupation quality than any single-metric approach.

In what ways does the integration of nine orthogonality metrics into a Python-based tool help reduce user bias in method development?

Traditionally, the evaluation of orthogonality in LC×LC has often relied on either visual inspection of separation plots or the application of a single preferred metric. Both approaches introduce subjectivity. With visual inspection, analysts inevitably make judgments influenced by prior experience or expectations, and two people might interpret the same separation quite differently. Similarly, when relying on a single metric, the choice of which one to use often comes down to habit or convenience, rather than a deliberate assessment of whether that metric captures the most relevant features of the separation. This creates room for user bias and inconsistent decision-making.

By integrating nine established orthogonality metrics into a single Python-based tool, we aimed to standardize this process. The tool automates the calculation of each metric, eliminating manual error and ensuring that the full range of orthogonality descriptors is considered. Instead of forcing users to pick one metric or rely solely on visual judgment, the tool provides a consensus score derived from a wide range of metrics. This ensures that the evaluation reflects multiple aspects of orthogonality, rather than one narrow perspective. It also removes the need for the user to choose a side and prevents overreliance on any subjective interpretation.

Another way the tool reduces bias is through transparency. Users can inspect all metrics individually, visualize how separations distribute in the 2D space, and even adjust the weighting of descriptors in the final score if they wish. This means that if a researcher prefers to emphasize a specific metric for their application, the option is still there, but the default ranking is objective, reproducible, and free from personal preference.

Finally, embedding this framework in a freely available tool makes it highly reproducible and sharable. The same dataset analyzed by different users will yield the same outputs, which is rarely the case with subjective assessments. This reproducibility is particularly important in collaborative or interdisciplinary projects, where different groups might otherwise apply different criteria when evaluating separation quality.

What considerations guided the selection of RPLC×RPLC as the optimal mode combination for this application, despite the common preference for mixed-mode pairings?

Mixed-mode pairings such as HILIC/RPLC are often considered the best choice in LC×LC because they are expected to maximize orthogonality by combining fundamentally different retention mechanisms. This assumption has been repeated so often in the literature that it can bias expectations during method development. However, our systematic evaluation of 703 possible 2D combinations, covering multiple column chemistries, pH values, and organic modifiers, showed that the most attractive option for our analyte set was, in fact, an RPLC×RPLC combination.

This finding was not accidental but the outcome of our data-driven approach. The organic micropollutant (OMP) mixture we studied was chemically very diverse and spanned a wide polarity range. The first consideration was the measured orthogonality of each paired system. Although mixed-mode pairings may appear orthogonal in principle, our multi-metric evaluation showed that in practice, certain RPLC×RPLC combinations provided more balanced coverage of the 2D separation space for this specific analyte set. This underscores the fact that orthogonality is sample-dependent: the best combination for one sample type may not be optimal for another.

Secondly, it is important to recognize that, although highly influential, orthogonality is not the only relevant parameter when selecting two systems for pairing in LC×LC. To be successful, a 2D separation must combine high orthogonality and high peak capacity. While some mixed-mode systems did achieve high orthogonality, they suffered from drawbacks such as narrow usable elution composition range, limited retention, and poor peak shapes for certain compound classes. These factors ultimately reduced the practical 2D peak capacity. In contrast, the selected RPLC×RPLC combination, which used different organic modifiers and pH values in both dimensions, offered a complementary selectivity while maintaining good separation kinetics.

Finally, we also made some practical considerations beyond orthogonality and peak capacity. For example, we required conditions that allowed good ionization efficiency in MS and columns that could withstand elevated temperatures to speed up ²D-runs. When these constraints were applied, the RPLC×RPLC option also consistently ranked at the top of our evaluation.

In summary, the choice for RPLC×RPLC was guided not by convention but by systematic evidence. The process highlights the importance of testing assumptions in LC×LC method development: while mixed-mode pairings are often beneficial, in our case, two complementary RPLC systems proved superior by showing excellent overall performance.

How was peak capacity measured and validated for the sub-hour LC × LC method, and how does the value of 1887 compare to conventional environmental analysis workflows?

We estimated the effective 2D peak capacity of the final online RPLC x RPLC method by multiplying the respective peak capacities in each dimension, calculated based on the experimental peak widths and retention times of the first and last eluting compounds. Then, we corrected this theoretical value by accounting for both the first-dimension undersampling and the actual retention space coverage of the 2D separation using established theoretical equations (2,3). To ground this number in real experimental performance, we injected a standard mixture of 303 OMPs spiked in real wastewater effluent. Out of the 303 injected analytes, 293 were successfully detected in MS, which underscores the separation performance of the system under these conditions. To further illustrate its applicability, we also analyzed a real wastewater sample. The resulting contour plots displayed extremely complex patterns with dense, well-distributed peaks, including clusters suggestive of families of related compounds.

The significance of this result becomes clear when compared to conventional workflows for environmental analysis. In typical 1D-LC-MS approaches applied to complex mixtures such as wastewater OMPs, peak capacities rarely exceed a few hundred under routine conditions, and hours or even days are often required to reach values near 1000. For example, in the same study, we developed a 1D-LC–MS method that achieved a peak capacity of only 387 in 45 minutes. In contrast, our LC×LC method delivered a peak capacity of 1887 in the same timeframe, representing a five-fold increase in separation power.

This combination of high peak capacity and relatively short analysis time demonstrates the value of LC×LC not only for achieving deeper chemical coverage but also for enabling more efficient workflows. In environmental monitoring, where laboratories often process large numbers of samples under time and resource constraints, the ability to achieve a peak capacity close to 2000 in under an hour represents a significant step forward compared to conventional one-dimensional methods.

References

1. M. Pardon, S. Chapel, P. de Witte, D. Cabooter, Screening and optimization of online comprehensive two‑dimensional liquid chromatography conditions for the analysis of hospital wastewater, Analytical and Bioanalytical Chemistry, https://doi.org/10.1007/s00216-025-06071-z
2. G. Semard, V. Peulon-Agasse, A. Bruchet, J.-P. Bouillon, P. Cardinaël, Convex hull: A new method to determine the separation space used and to optimize operating conditions for comprehensive two-dimensional gas chromatography, Journal of Chromatography A 1217 (2010) 5449–5454. https://doi.org/10.1016/j.chroma.2010.06.048.
3. J.M. Davis, D.R. Stoll, P.W. Carr, Effect of First-Dimension Undersampling on Effective Peak Capacity in Comprehensive Two-Dimensional Separations, Anal. Chem. 80 (2008) 461–473. https://doi.org/10.1021/ac071504j.

About the Interviewee

Soraya Chapel is a Marie Skłodowska-Curie postdoctoral fellow at the University of Orléans and is currently based at Kyushu University in Fukuoka, Japan, where she works on a collaborative project focused on the development of greener multidimensional chromatographic systems using supercritical CO₂ for the study of bioactive compounds in natural products. She previously held an ATER (temporary assistant professor) position at the University of Rouen, working on PFAS analysis in post-fire samples, and completed a postdoctoral fellowship at KU Leuven, focusing on innovative multidimensional liquid chromatography approaches for profiling organic micropollutants in environmental water samples. She earned her Ph.D. in analytical chemistry from Université Claude Bernard Lyon 1 (France) in 2021, where her thesis focused on developing sub-hour online comprehensive 2D-LC methods for the separation of complex peptide and protein samples.