Generic and accurate prediction of retention times in liquid chromatography by post-projection calibration

doi:10.21203/rs.3.rs-3130052/v1

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Generic and accurate prediction of retention times in liquid chromatography by post-projection calibration

https://doi.org/10.21203/rs.3.rs-3130052/v1

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Retention time predictions from molecule structures in liquid chromatography (LC) are increasingly used in MS–based targeted and untargeted analyses, providing supplementary evidence for molecule annotation and reducing experimental measurements. Nevertheless, different LC setups (e.g., differences in gradient, column, and/or mobile phase) give rise to many prediction models that can only accurately predict retention times for a specific chromatographic method (CM). Here, a generic and accurate method is present to predict retention times across different CMs, by introducing the concept of post–projection calibration. This concept builds on the direct projections of retention times between different CMs and uses 33 external calibrants to eliminate the impact of LC setups on projection accuracy. Results data shows that after calibration, the median prediction error for each CM was in all cases below 3.8%. The number of true identities ranking first among their isomeric candidates increased by 11.1 to 113.3%. This work opens up broad possibilities for coordinating retention times between different laboratories and developing extensive retention databases.

Physical sciences/Chemistry/Analytical chemistry/Mass spectrometry

Physical sciences/Chemistry/Cheminformatics

Physical sciences/Chemistry/Environmental chemistry/Environmental monitoring

Biological sciences/Structural biology/Molecular modelling

Biological sciences/Chemical biology/Computational chemistry

Retention time prediction

Reference-predicted retention time

Liquid chromatography

Data transfer

Untargeted screening

Prediction of retention time (RT) in liquid chromatography (LC) has remained an active research field over the last decade¹, to aid structural identification of unknown molecule^2–5, rapid chromatographic method (CM) optimization^6,7, and retention information transfer/harmonization among different laboratories^8–10. LC coupled to high–resolution mass spectrometry (HRMS) enables high–throughput screening of known and/or unknown molecules at low concentrations, widely applied in environmental and food analysis and in metabolomics^11–14. Identification workflows in LC–HRMS–based untargeted analysis increasingly include RT prediction steps, as it provides orthogonal evidence for mass spectra to distinguish isobaric molecules^15–17. By predicting the RTs of putative candidates and comparing them with experimental RT, the number of false–positive candidates can be significantly minimized, thereby reducing experimental measurements and economic costs. Therefore, it is crucial to accurately predict the RT on a given CM for all analytes of interest.

The common strategy for RT prediction focuses primarily on finding a relationship between structural features (e.g., theoretical molecule descriptors, fingerprints) and RT using machine–learning algorithms, usually known as quantitative structure−retention relationship (QSRR) models. QSRR models rely on RT information for numerous structures to characterize an interpretable retention mechanism and thus make accurate predictions^10,18. This strategy can predict the RT of any molecule with a known structure. For the untargeted analysis of complex samples, datasets with a broader set of examples are required to enable large–scale RT prediction as a wide variety of chemicals amenable to LC can be expected¹⁹. To the best of our knowledge, the largest experimental RT dataset at present is METLIN (http://metlin.scripps.edu) containing 80,038 molecules, which was determined on the Zorbax Extend-C18 reverse-phase (RP) column by using 0.1% formic acid in water and acetonitrile as mobile phases. This dataset has been reported multiple times for establishing structure–based models, with a median prediction error of 1.6%−6.2%^19–22. However, these models usually worked for specific LC setups, mainly due to the variance in RT between different CMs.

Many efforts have been made to enable RT data or predictive models to be transferable between different instruments and CMs to further reduce the experimental measurements for RT modeling and improve the databases’ availability. Amina et al.²³ introduced MultiConditionRT, a predictive model by QSRR approach for multiple CMs. Molecular descriptors and information describing the CM (e.g., column type, aqueous phases pH, organic modifiers and buffers) were used as independent variables, and the RTs of 78 compounds from different CMs were used as dependent variables. The RMSE of the external validation set predictions was 10.7% (2.68 min). Several linear RIs were recently used for LC–based untargeted metabolomics, showing high reproducibility for CMs with similar elution patterns^24–26. However, calibrants with simple structures or physicochemical properties (e.g., n-nitroalkanes,^27,28 alkylarylketones,²⁹ chemical labeled acids and amines²⁴) may not account for various retention behaviors from the observed or screened molecules. This would result in unexpected differences in RI between different CMs. Aalizadeh et al.¹⁰ proposed a new RI system and applied it to structure–based prediction modeling and suspect/untargeted screening. The calibrants were selected from 2123 emerging contaminants based on the maximum overlap of the RTs and chemical similarity indices, showing acceptable MS response and increased chemical diversity to generate a more comprehensive elution pattern. The RMSE of 12 external validation sets (with different LC setups) ranged from 6.1% to 14.6%.

A further approach for RT prediction is to project known RTs from one CM onto another. The initial strategy involves building a library based on the relationship between the isocratic retention factor (k) and solvent composition (φ), thus estimating RTs for gradient CMs^8,30. However, this approach requires that the mobile phase, column, and column temperature are the same as those used in the isocratic method, thus limiting the applicability of this strategy. Stanstrup et al.⁹ introduced a direct RT projection approach that uses known RTs of overlapping molecules on both CMs to yield a non–linear function, i.e., an RT projection model. This model allows for RT transfer between the two CMs, that is, by knowing the RT of a molecule on one CM, the RT of that molecule on the other CM can be predicted. These predictions are extremely accurate over alternative methods, with a median prediction error of less than 3.7%. For the metabolomics community, such approaches had been used to share the RTs observed in publicly available databases and the RTs predicted by QSRR models with other CMs/laboratories^9,19–22,31. Predicted–experimental projections can predict the RT of known structure on any CM, while larger prediction errors were expected in contrast to traditional QSRR models and experimental–experimental projections due to the propagation of projection error itself and the inherent prediction error. The accuracy of projections also depended on the overlapping molecules used for model training (i.e., training points)^21,32 and the similarity of elution pattern between input and output CMs⁹. Insufficient overlapping molecules may be unable to quantify a relationship of RTs between the two CMs, resulting in poor accuracy of predicted RTs. In addition, differences in molecule elution order caused by specific LC setups (e.g., gradients, columns, mobile phases, etc.) limited the projectability of a given CM³¹.

This work presents a new strategy to accurately transfer experimental and predicted RTs between different CMs by introducing an external calibration step into projections. 33 molecules were used as calibrants to build a projection model and a reference–projection model for a given CM. The reference–predicted RT (rpRT) derived from the reference–projection model, enables propagating/calibrating the error of predicted RT caused by specific LC setups. We focused on the projection errors before and after calibration with different LC setups. The effect of similarity in elution pattern between input and reference–input CMs and the number of calibrants on post–projection calibration was analyzed. Further, we tested the ability to transfer predicted RT from QSRR models and filter/rank putative isomeric candidates.

Workflow overview. The objective is to make accurate RT predictions for a given CM using publicly available datasets from other CMs. The post–projection calibration method is developed to calibrate the effect of LC setups on these predictions. The workflow is shown schematically in Fig. 1. In the first step, a multiple CMs–based retention time (MCMRT) database was developed. This database includes > 9000 experimental RTs for 343 molecules with a high diversity of chemical structures and 30 CMs with different LC setups. A total of 33 molecules are selected from the database based on their retention behaviors and used as calibrants.

In the second step, the experimental RTs of the calibrants from a publicly available dataset (i.e., input CM) and a given CM (i.e., output CM) are used to generate a projection model. This public dataset is also used to train a QSRR model for molecules whose experimental RT was not recorded in the dataset. If there is no experimental RT for all calibrants in the dataset, the predicted RTs by the QSRR model are used to replace the missing values. With the projection model, the dataset's experimental RTs and the QSRR model's predicted RTs can be transferred onto the given CM.

In the final step, a reference–input CM is selected based on its similarity with the input CM in the elution pattern. The reference–input and output CMs are used to determine the RTs of 33 calibrants. The reference–projection model is generated using the experimental RTs of 33 calibrants on the reference–input and output CMs. In untargeted analysis, the RTs of putative candidates for an unknown identity observed on the output CM are predicted with the projection model, based on their experimental RTs in the dataset or predicted RTs by the QSRR model. The reference–projection model yields a reference–predicted RT (rpRT) for the observed unknown identity. The rpRT can be used instead of experimental RT to compare with predicted RT. This method can calibrate the projection error caused by LC setups, enabling accurate RT data transferring among a wider range of CMs, and improving annotation of unknown molecules.

The MCMRT database. Three primary purposes of developing the MCMRT database are: ⅰ) selecting appropriate calibrants, ⅱ) providing concrete examples to demonstrate the limited applicability of the projection approach, and ⅲ) studying the capability of post–projection calibration approach. First, we selected 343 molecules from various chemical classes and obtained their standard materials from suppliers. Then we acquired their RT data on 30 different CMs via RPLC/ESI–HRMS. Details of RT data acquisition were provided in “Methods”. These molecules covered broad ranges of octanol/water partition coefficient values (log K_ow −8.1 to 11.6) and molecular weights (89–1449 Da), enabling to cover the entirety RT range in RPLC and mass–related properties, e.g., including both positive and negative modes and six representative adducts in ESI–MS (Fig. 2a). In terms of chemical classes, they covered 11 ClassyFire’ groups (superclass level)³³, including benzenoids (27.7%), organic acids and derivatives compounds (20.4%), organoheterocyclic compounds (18.7%), lipids and lipid-like molecules (9.9%), phenylpropanoids and polyketides (7.6%), organohalogen compounds (7.3%), organic oxygen compounds (3.5%), organosulfur compounds (1.2%), organic nitrogen compounds (1.2%), organophosphorus compounds (1.2%) and other compounds (1.5%). Notably, the METLIN database (80,038 molecules) covered seven superclasses, and MCMRT also included these classes, except nucleosides and nucleotides¹⁹. Furthermore, the organohalogen compounds (e.g., perfluorinated and polyfluoroorganic compounds) and organosulfur compounds contained in MCMRT were not observed in METLIN. Diverse element compositions (C, H, O, N, P, S, Cl, Br, F and I) indicated that these molecules have a wide range of physiochemical properties (Fig. 2b). These results demonstrated that the molecules in MCMRT are highly diverse and representative of chemical structures. Detailed information, including molecular formula, molecular weight, log K_ow, polarity response, chemical class, etc., can be found in Supplementary Table S1.

The 30 CMs covered six C₁₈ columns with different specifications (50–150 × 2.1–4.6 mm, 1.7–5 µm), six mobile phase compositions with different buffers (acidic, ammonium, mixed and semi–mixed), nine running times (10–100 min), seven gradient profiles (single or multiple gradients), five flow rates (constant or variable flow rate, 0.2–1 mL/min), and three column temperatures (30, 40 and 45°C). More details about the instrumental and chromatographic conditions are described in Supplementary Table S2. From these CMs (marked as CM 01–CM 30, Fig. 2c), many pairs of CMs with only one different chromatographic parameter can be found. For example, the only C₁₈ column between CM 04 and CM 05, the only mobile phase composition between CM 03 and CM 30, the only running time between CM 01 and CM 13, and the only gradient profile between CM 09 and CM 10 were different. We used such CMs to study the effect of a single chromatographic parameter on elution pattern, as the hypothesis behind reliable RT projections is that the molecule elution order is largely conserved⁹.

As a result, a total of 9,018 experimental RT values from 30 CMs were included in the MCMRT, of which 249 molecules had experimental RT values on all CMs, i.e., they overlapped between these CMs. About 16 to 69 molecules were not analyzed or undetectable on different CMs mainly because their preferred adducts showed low ionization efficiency. Figure 2c shows the distribution of experimental RTs across the 30 CMs for all molecules in MCMRT. These RTs were evenly distributed within each CM running time, indicating that these molecules can demonstrate the entirety RT range in LC and have no obvious preference for specific RT ranges. The experimental RT values are available in Supplementary Table S3.

The calibrants. The calibrants were also used to select an appropriate reference–input CM, which has high similarity in elution pattern with the input CM. Therefore, the selection of calibrants included the following considerations: 1) they can be detected by LC/ESI–MS; 2) they can cover the entire RT range in RPLC; 3) they can account for the effect of LC setups on molecule elution order. The latter two features enable the calibrants to demonstrate the overall elution pattern for various CMs, i.e., by knowing the RTs of calibrants on input and reference–input CMs, the similarity in elution pattern between the two CMs can be estimated. Based on the third consideration, cluster analysis of the RT matrix in MCMRT was performed using self–organizing mapping neural network (SOM) technology^34,35, to characterize the retention behavior with different LC setups for the 343 molecules. These molecules were classified into 25 groups with different RT distributions, and each group exhibited similar retention behavior (Fig. 3a). From each group, at least one molecule was selected as a calibrant. The set of calibrants ultimately contained 33 molecules (Fig. 3b). It can be seen from Fig. 3, the elution patterns demonstrated by 33 calibrants and 343 molecules were highly consistent. For example, their R² of experimental RTs between CM 24 and CM 26 (the two least similar CMs) only differed by 3.3% (0.651 vs. 0.673, Figs. 3a–b). These results indicate that the calibrants could determine the CM similarity in the elution pattern. The details for retention behavior classification and calibrants selection were provided in “Methods”. The chemical information for calibrants and the group of retention behavior for all molecules are available in Supplementary Table S3.

Before using calibrants for post–projection calibration, the differences in elution patterns caused by specific LC setups were also analyzed. From Fig. 3c, CMs with similar C₁₈ column specifications gave not only the general conservative molecule elution order but also consistent RT values, with an R² of 0.992 for 33 calibrants and a maximum difference in RT of 1.68 min. Nevertheless, differences in RT were observed for some molecules on the CMs with different C₁₈ column specifications (Figs. 3d–e), especially when the mobile phases are acidic, resulting in the reduction of R² to 0.968 (Fig. 3f). For CMs with different flow rates, the elution order is largely conservative with an R² of higher than 0.973, although the RT values changed for some molecules (Fig. 3g). We also found that the greater the difference in running time between CMs, the lower the R² between RTs and the greater the difference in RT for most molecules (Figs. 3h–i). For example, the RTs between CM 02 (15 min) and CM 12 (45 min) yielded an R² of 0.937 and a maximum RT difference of 11.6 min (Fig. 3h). In contrast, that between CM 01 (10 min) and CM 16 (100 min) yielded an R² of 0.924 and a maximum RT difference of 64.8 min (Fig. 3i). Such differences in RT indicated the importance of using an RT data set on a specific CM for training QSRR models and the necessity of predicting RTs on different CMs. Mobile phase composition negatively affects molecule elution order, as the RT differences vary for many more molecules. This is because the additives may change the pH value and ionic strength of solvents, which would change the retention behavior of many molecules by protonation, deprotonation or ionic interaction. Specifically, similar mobile phases yielded the R² of 0.936–0.979 (Figs. 3j–m). The mixed and semi–mixed buffers, mixed and acidic buffers, and mixed and ammonium buffers yielded the R² of 0.903, 0.904 and 0.899 (Figs. 3n–p). The lowest R² of 0.752 was observed between ammonium and acidic buffers (Fig. 3q). In addition, the CM similarity will be further reduced when there are many differences in LC setups. For example, CM 24 and CM 26 yield the R² of 0.651 with different C₁₈ columns, running times, flow rates and mobile phase compositions (Figs. 3a–b).

Post–projection calibration improves experimental-experimental projections. With the MCMRT database, we first studied the effect of specific LC setups on RT projection using experimental–experimental projections (Supplementary Tables S4–6). CMs 03, 22 and 28 with different mobile phases were used as input CMs, respectively. For each input CM, the remaining 29 CMs were used as output CMs respectively (see Methods for details). The distribution of the relative projection error for each output CM is shown in Figs. 4a, g, i. The projection errors varied depending on the running time and mobile phase composition of each output CM. Thus, these output CMs were divided into four groups: CMsA, B, C and D, respectively. CMsA and B contained CMs with the same mobile phase composition as the input CM whereas CMsC and D contained CMs with different mobile phase compositions from the input CM. CMsA and C contained short CMs (< 45 min), whereas CMsB and D contained long CMs (≥ 45 min). Using CM 03 as input CM, the median error across all projections in CMsA and B were 0.9 and 1.5%, which were smaller than that in CMsC and D (3.5 and 8.1%, Fig. 4a). Consistently, similar results were also obtained using CM 22 and CM 28 as input CMs. Specifically, using CM 22 as input CM, the median error across all projections in CMsA, B, C and D was 1.0, 3.4, 5.7 and 7.1%, respectively. There was no output CM in CMsB when using CM 28 as input CM, and the median error across all projections in CMsA, C and D was 1.3, 5.6 and 9.0%, respectively (Fig. 4i). These results demonstrated that the experimental–experimental projections allow the RT transfer between two CMs with the same mobile phases and short running time, showing very high accuracy (median error < 1.8%). Slight differences in the C18 column, gradient, flow rate and column temperature hardly increased these errors. However, a long running time could increase the median error to 3.4%, e.g., CM 16, with a running time of 100 min. Yet, different mobile phase compositions further declined the projection accuracy³¹. The median error was between 5.4 and 14.3%.

Next, we demonstrated the calibration of projected errors with the proposed post–projection calibration approach (Supplementary Tables S4–6). CMs 07, 24 and 27 were used as reference–input CMs for input CMs 03, 22 and 28, respectively (see Methods for details). The distribution of the relative calibrated error for each output CM is shown in Figs. 4d, h, j. The median error for an output CM can be as low as 0.3% and was, in all cases, below 3.8%. The median error across all predictions in CMsA, B, C and D was reduced by 25.6, 60.5, 83.2 and 79.5%, respectively, in contrast to those before calibration. These results indicated that the error from the projection itself could be calibrated by using rpRT instead of experimental RT. The post–projection calibration method improves the RT transfer between CMs with significant differences in LC setups, e.g., long running times and different mobile phase compositions. We demonstrated that after calibration the number of molecules with an RT error high than 10% was, in all cases, below 7.3% (N = 22), while before calibration it can be as high as 71.7% (N = 218).

Then, we studied the effect of reference–input CMs on post–projection calibration (Supplementary Table S4). Five CMs were used as reference–input CMs for input CM 03, respectively. They were CM 01 with R² (i.e., of RTs between input and reference–input CMs for calibrants) = 0.923, CM 18 with R² = 0.981, CM 15 with R² = 0.990, CM 05 with R² = 0.993 and CM 07 with R² = 0.998. The distribution of the relative projection error before and after calibration for each output is shown Figs. 4a–f. The results demonstrated that the similarity in molecule elution order between input and reference–input CMs determines the accuracy of the calibration. Specifically, the median error across all predictions for all output CMs was 4.7% (Fig. 4a). After calibration, this error was decreased by -22.1, 31.4, 64.0, 52.0 and 75.6% using CM 01 (Fig. 4b), CM 18 (Fig. 4f), CM 15 (Fig. 4e), CM 05 (Fig. 4c) and CM 07 (Fig. 4d) as reference–input CMs, respectively. All output CMs observed a consistent conclusion that the calibration accuracy increased with the increase of R² from 0.923 to 0.998. Because CM 01 is slightly similar to the input CM 03, most calibrations had an error greater than that after calibration, especially for the CMs in CMsA and B. These results indicated that using reference–input CMs that are highly similar to the input CM had extremely high accuracy for calibration, e.g., CMs 05, 07 and 15, with a median error of less than 3.8% in all cases.

We also demonstrated that the number of molecules used for model training determines the projection and calibration accuracy (Fig. 4k and Supplementary Table S7). Specifically, as the number of calibrants increased from 33 to 151, the median error across all predictions in CMsA, B, C and D was reduced by 19.8, 22.2, 39.3 and 40.6%. After calibration, they were reduced by 11.4, 7.4, 10.3 and 29.9%. The median error after calibration for an output CM was in all cases below 3.8%, indicating that a small number of calibrants can achieve high accuracy for post–projection calibration. For sets A and B containing the same number of calibrants, the projection errors for each output CM varied; the median error before calibration using set A was smaller than that using set B, while after calibration, the median error using set A was greater than that using set B. It can be contributed to that the difference in the retention behavior of molecules in set B is smaller than that in set A, resulting in overfitting for projection models. However, smaller differences in the retention behavior of molecules in set B had higher similarity in calibrant elution order between input and reference–input CMs (R² = 0.998), resulting in good calibration in contrast to set A (R² = 0.993). In order to reduce experimental costs and demonstrate the overall elution pattern for a CM, 33 molecules in set A were accepted as calibrants.

Post–projection calibration improves predicted–experimental projections. Experimental–experimental projection and calibration approach enables the sharing and utilization of experimental RTs across laboratories independent of LC setups. Nevertheless, direct projection of experimental RTs between CMs can only share the RT for molecules already recorded in the data sets. We further tested the scalability of the post–projection calibration approach by using a publicly available dataset (Supplementary Tables S8) to deploy a QSRR model with an artificial neural network (ANN). This dataset contains 1,820 emerging contaminants whose RT was experimentally determined using CM 03^online. From all molecules in the dataset (except for 145 that overlapped with our 343 molecules), 75% of them (N = 1258) were randomly selected and used as a training set, whereas the remaining 25% (N = 408) were used as validation set (see Methods for detail).

Prediction results of the proposed ANN for the training and validation sets are available in Figs. 5a–b and Supplementary Tables S8. The mean and median relative errors for the validation set were 13.8 and 9.0% and the mean and median absolute errors were 0.8 and 0.6 min. In studies with the same dataset, Aalizadeh et al.¹⁸ used a genetic algorithm combined to support vector machine for modeling and reported similar performance to the ANN, with mean and median relative errors of 12.3 and 8.6%, respectively. From all molecules in MCMRT, 293 known experimental RT on CM 03^local were used as an external set to validate its generalization ability. The performance was estimated by projecting their predicted RT from CM 03^online onto CM 03^local via predicted–experimental projections and comparing with their experimental RT (see Methods for detail). The mean and median relative errors were 13.7% and 9.2%, respectively (Fig. 5c and Supplementary Tables S8). Among molecules with a large predicted error (> 2 min), the main ones were perfluorinated compounds and some compounds with high molecule weight (i.e., valinomycin, iodixanol), whose similar structures were not found in the dataset. This demonstrated the structural similarity between the training dataset and the input chemical structure affects the accuracy of predicted RTs¹⁹.

To study the effect of different predicted errors on post–projection calibration, these molecules were classified into four groups (1–4) based on their predicted error, including 206 molecules with an error less than 1 min, 51 molecules with an error between 1 and 2 min, 32 molecules with an error between 2 and 4 min, and 4 molecules with an error greater than 4 min (Fig. 5d). The median relative error for the four groups was 4.6, 16.2, 33.2 and 76.1%, respectively. Their predicted RTs were projected onto 30 local CMs in MCMRT (excluding CM 07^local used as reference–input CM). The predicted–experimental projection results before and after calibration are shown in Figs. 5e–h and Supplementary Tables S9. The relative errors across all projections varied depending on their predicted error; the median error in CMsD spanned from 10.7 and 21.6% with predicted error smaller than 2 min (groups 1 and 2, respectively) to 39.8 and 80.1% with predicted error larger than 2 min (groups 3 and 4, respectively) (Fig. 5e). Similar results were also observed for CMsA, B and C groups, as well as for their calibrations (Figs. 5f–h). Furthermore, with the similarity in elution pattern between input and output CMs decreased, the projection error in group 1 increased significantly. These results indicated that both predicted error and CM similarity determine the accuracy of predicted–experimental projections. For output CMs with different mobile phases from the input CM (Fig. 5f), statistically significant differences of mean error were observed before and after calibration for groups 1, 2 and 3 (Bonferroni test, P < 0.01, n_group1 = 2159, n_group2 = 536, n_group3 = 336). The mean error across all predictions in CMsA, B, C and D was reduced by 5.4, 6.0, 41.2 and 46.8% for molecules in group 1. The median error for an output CM was in all cases below 7.6%, while before calibration it ranged from 2.8 to 11.4%. These results demonstrated that the post–projection calibration approach enabled a more accurate transfer of predicted RTs onto slightly similar CMsC and D. No significant negative impact on projection error was observed for highly similar CMs A and B. Notably, the inherent prediction error from the QSRR model cannot be calibrated with this approach. Thus, a robust QSRR model, which enables accurate RT prediction for various molecule structures, is also required to support predicted–experimental projections.

Implication of post-projection calibration for isomer annotation. With predicted–experimental projection and approach, we further investigated its implication to improve the ranking of isomeric candidates and filtering false–positive candidates. This is done to simulate an expected situation in untargeted analysis with LC–HRMS where the chemical formula for an unknown identity is annotated (predicted) through a built–in software of the instrument, but the molecular structure is not known. From all the molecules in MCMRT, 136 were selected as unknown identities, with monoisotopic masses from 98 to 1449 Da and log K_ow values from − 8.1 to 9.8. We searched their chemical formulas on the websites of ChemSpider and PubChem, resulting in a total of 2343 isomeric candidates (2 − 40 in each). The RT of these candidates was predicted using the ANN model and transferred from CM 03^online to CMs 08^local, 15^local, 24^local and 26^local, respectively. CM 07^local was used as reference–input CM to derive their rpRT. Results from all predictions, projections and calibrations for these candidates are available in Supplementary Table S10.

We used a receiver operating characteristic (ROC) curve to determine the optimal error threshold (see Methods for details). Figures 6a–d show the ROC curve for each CM. The area under the curve (AUC) after calibration was in all cases above 0.72, while before calibration the AUC values ranged from 0.65 to 0.73. The best filtering error threshold was 11, 14, 15 and 8% for the four CMs. Compared to before calibration, a significant decrease in this threshold was observed for CM 24^local (25% vs. 15%). In addition, the optimal threshold in long CMs 15^local and 24^local was relatively greater than that in short CMs 08^local and 26^local. Figures 6e–f show the filtering results. The true positive candidates (TP) increased by 4 and 6 for CMs 24^local and 26^local, and their true negative candidates (TN) increased by 187 and 94, respectively. Although compared to all isomer candidates, the improved results after calibration are relatively small. However, if calibration is not carried out, these candidates (e.g., with special retention behavior on the output CM) will routinely be incorrectly identified and omitted in practical applications. It is important to note that after calibration ~ 30% of the false candidates were accepted for all CMs and ~ 25% of the true identities were incorrectly filtered for many reasons, including larger prediction errors from the ANN model and small changes in RT for these isomeric candidates using conventional LC methods.

The isomeric candidates were ranked based on their RT error before and after calibration. Figure 6g shows the ranking results for each CM. Before calibration, the number of true identities among the top 6 candidates (N_top6) ranged from 80 to 101 for all CMs, while after calibration, it was in all cases above 97 (71.9% of all identities). Especially for CM 26 ^local, the N_top1 value increased from 15 to 32 (113%). In addition, the sum of all true identity rankings was improved by 12 and 20% for CM 24^local (719th vs. 631th) and CM 26^local (848th to 676th). No significant improvements were observed for CMs 08^local and 15^local. Figure 6h shows an example of improving ranking with calibration. The correct identity, vardenafil, was ranked 2nd among 25 isomeric candidates using rpRT (15 min) to compare with predicted RT (14.6 min), while it dropped to 20th using experimental RT (10.2 min) for comparison. These results demonstrate that rpRT significantly improved the ranking of correct identities for those output CMs with different mobile phases from the input CM.

In this work, we developed a new post–projection calibration approach to support RT prediction in a wider range of CMs in LC. After calibration, more than 93.7% of molecules have an error of less than 10% for each CM. The mean and median errors across all experimental–experimental predictions were 2.6% and 1.3%, respectively. By post–projection calibration, the RTs predicted by QSRR models can be transferred onto other CMs with high accuracy. Further, predicted–experimental projections with calibration improved filtering and ranking putative isomeric candidates for different LC setups. The number of correctly filtered candidates and true identities ranking first among their isomeric candidates increased by − 0.5–15.1% and 11.1–113.3%, respectively.

The post–projection calibration approach enables the community to utilize experimental RT values from publicly available datasets for model training, and accurately share both experimental and predicted RT values onto a given CM. The given CM is no longer limited by LC setups. It is important to note that this calibration method focuses primarily on significantly improving the accuracy of RT data transmission among CMs with large differences in molecule elution order. We developed a comprehensive database (MCMRT) that contains > 9000 experimental RTs of 343 molecules with a high diversity of chemical structures. They are largely overlapped between 30 different CMs, which provides the community with a wide set of examples for modeling LC setups and associated RTs. We anticipated that with the widespread use of the calibrants in LC, the post–projection calibration would facilitate the cooperative development of more comprehensive and much broader retention databases for numerous molecules and CMs, thereby expanding the chemical coverage of molecule annotation.

RT acquisition for the MCMRT database. The pure standard materials for the 343 molecules were analyzed on a Vanquish UHPLC System (Thermo Fisher Scientific, USA) coupled to an Orbitrap Q–Exactive Plus mass spectrometer (Thermo Fisher Scientific, USA) using 30 different CMs. Each CM–dependent dataset was acquired within one day, with three repetitions. These CMs covered six C₁₈ columns with different manufacturers, column lengths (50–150 mm), diameters (2.1–4.6 mm) and particle sizes (1.7–5 µm). The gradients consist of single and multi–slopes with isocratic or gradient flow rates of 0.2 to 0.5 mL/min. The total running times ranged from 10 to 100 min. Among these CMs, 18 used water/methanol (90:10, v/v) as mobile phase A, 12 used water as mobile phase A, 24 used methanol as mobile phase B, and 6 used acetonitrile as mobile phase B. Different additives were considered in these mobile phases, such as 0.01% formic acid with 5 mM ammonium formate (A1B1), 0.1% formic acid with 4 mM ammonium formate (A5B5), 0.1% formic acid (A2B2), 5 mM ammonium formate (A4B4), and 5 mM ammonium acetate (A3B3). In addition, column temperatures ranging from 30 ℃ to 45 ℃ were included. A full description of LC setups for each CM can be found in Supplementary Table S2. All analyses were performed in positive and negative ionization mode using a full mass scan. The parameters were as follows: two scan ranges for 80–400 Da/350–1600 Da; resolution = 70,000; AGC target = 1e6; maximum injection time = 100 ms; sheath gas = 40; aux gas = 8; sweep gas = 1; spray voltage = 2.5 kV; heater Temp = 350 ℃; Capillary Temp = 250 ℃; RF–Lens = 60.

Retention behavior classification and calibrant selection. Molecules in the MCMRT database were classified based on their retention behavior, thereby selecting calibrants with diverse retention behaviors. Firstly, thirty RT data sets for 249 overlapping molecules were analyzed using self-organizing mapping (SOM) clustering algorithm, to characterize their retention behavior on one CM and between different CMs. These molecules were classified into 25 groups (Supplementary Table S3). Then, the remaining 86 molecules lacking RT values on certain CMs were manually classified into these groups based on the RT distribution of adjacent points. To ensure that the RT values of all calibrants can be collected on common ESI–MS based LC setups, the calibrants were selected from the molecules that have experimental RTs on all CMs. From each group, at least one molecule was selected and included in the calibrant set, comprehensively considering the RT distribution, MS response and stability. In addition, molecules with common structures were preferred as calibrants so that when the experimental RTs of all calibrants were not recorded in a given dataset, their RTs could be accurately predicted using a QSRR model. Finally, a total of 33 molecules from the MCMRT database were used as calibrants (Set A), covering generic retention behavior (i.e., their elution order largely conserved on most CMs) and special retention behavior (i.e., their elution order was easily affected by specific LC setups). The chemical information for calibrants and the group of retention behavior for all molecules are available in Supplementary Table S3.

To study the effect of different calibrants on projection and calibration results, four sets of calibrants were used to train projection and reference–projection models using CM 03 as the input CM and CM 05 as the reference–input CM. The remaining 28 CMs were used as output CMs, respectively. These sets, namely sets A, B, C and D, contain 33, 33, 61 and 151 molecules, respectively. The larger the number of molecules, the higher the density of RT distribution. Except for set B lacking eight retention behaviors, the other three sets covered all retention behaviors (i.e., 25 groups). Projection and calibration were made for all molecules in the MCMRT database. The chemical information for the four sets of calibrants is available in Supplementary Table S7.

QSRR model construction and parameters. The model construction and hyperparameter optimization was performed in MATLAB R2021b. A set of 1820 chemicals of emerging contaminants with known RT values on CM 03^online was collected from the report by Aalizadeh et al.¹⁰ They were divided into the learning (n = 1666) and test sets (n = 154), respectively, where the test set consists of molecules that overlapped with the MCMRT database. Their molecular structure data (with extension .mol) was collected from the PubChem database (https://pubchem.ncbi.nlm.nih.gov/), and a total of 1444 2D–molecular descriptors were calculated for each compound using PaDel-descriptor³⁶. An artificial neural network (ANN) based on multilayer perceptron was used to develop the QSRR model. The perceptron consisted of 1444 artificial neurons in the input layer, 10 artificial neurons in the hidden layer and 1 neuron in the output layer. The Bayesian Regularization Backpropagation method was used to train the network, and the learning was completed in 58 epochs. Data from the learning dataset was randomly divided into a training set (75%) and a validation set (25%). ANN analysis was performed on the training and validation sets by an iterative minimization program to optimize parameters. This model was used to predict the RT of 343 molecules in the MCMRT database and 2434 isomeric candidates for 136 unknown identities observed on four output CMs (see Retention Time projection and calibration). From the 343 molecules, 293 with observed experimental RT on CM 03^local were used as the external set to validate the generalization ability of the learned ANN via predicted–experimental projection. The predicted RTs of these molecules were projected onto CM 03^local and compared with their experimental RTs.

Retention Time projection and calibration. The projection of RT values from one CM onto another is performed in pairs by MATLAB R2021b. For each pair of input (or reference–input) and output CMs, experimental RTs of calibrants are used to build a gaussian process (GP) based nonlinear regression model between RTs in the two CMs. The basis and kernel functions in GP were set as constant and rational quadratic, respectively. The hyperparameters were optimized with the quasi–newton method. This model allowed adjusting all the experimental and predicted RTs via experimental/predicted–experimental projections to make them comparable to the output CM.

Experimental–experimental projection and calibration. CMs 03, 22 and 28 with different mobile phases (i.e., A1B1, A2B2 and A3B3) were used as input CMs, respectively. For each input CM, the remaining 29 CMs were used as output CMs. To study the effect of specific LC setups on experimental–experimental projections, these output CMs were divided into four groups based on their mobile phase composition and running time: CMsA, CMsB, CMsC and CMsD, respectively. Specifically, the output CMs in CMsA and CMsB had the same mobile phase composition as the input CM, while those in CMsC and CMsD had different mobile phase compositions from the input CM. The running time of the output CM in CMsA and CMsC was < 45 min, while that in CMsB and CMsD was ≥ 45 min. Three CMs, including CMs 07, 24 and 27, were used as reference–input CMs for input CMs 03, 22 and 28, respectively. The experimental RTs of 33 calibrants in set A were used to train projection and reference–projection models. To study the effect of reference–input CMs on projection and calibration results, CMs 01, 05, 15 and 18 with different LC setups were also used as reference–input CMs for input CM 03, respectively.

Predicted–experimental projection and calibration. CM 03^online and CM 07^local were used as input and reference–input CMs, respectively. The remaining 29 local CMs were used as output CMs, respectively. 33 calibrants in Set A were used to train projection models, of which 28 calibrants used experimental RT, while the remaining 5 calibrants used predicted RT due to the lack of experimental RT on CM 03^online. For reference–projection models, the experimental RTs of the 33 calibrants were used. The predicted RT for all the molecules in MCMRT was projected from CM 03^online onto given output CMs using projection models, and the rpRT was derived from their experimental RT on CM 07^local using reference–projection models.

Filtering and ranking isomeric candidates. 136 unknown identities were selected from all the molecules in MCMRT, with monoisotopic masses from 98 to 1449 Da and log Kow values from − 8.1 to 9.8. By searching for their chemical formulas on the websites of ChemSpider and PubChem, a total of 2343 isomeric candidates (2 − 40 in each) were obtained (Supplementary Table S10). The RT of these candidates was predicted using the proposed ANN model and transferred from CM 03^online onto CMs 08^local, 15^local, 24^local and 26^local, respectively, using predicted − experimental projections. The rpRT of the 136 identities were derived from their experimental RT on CM 07^local using reference–projection models. Before filtering these isomeric candidates, the optimal filtering RT error threshold was determined for each output CM using a ROC curve. Thus, the number of true negatives (TN), true positives (TP), false negatives (FN) and false positives (FP) were calculated. TN was the number of false identities with an RT error above the error threshold, TP was the number of true identities with an RT error below the error threshold, FN was the number of true identities with an RT error above the error threshold, and FP was the number of false identities with an RT error below the error threshold. The true positive rate (TPR) was calculated as TP/(TP + FN) and the false positive rate (FPR) was calculated as FP/(FP + TN). These candidates were ranked by comparing the predicted RT with their experimental RT (before calibration) and rpRT (after calibration).

Data availability.

The MCMRT database, including chemical information, LC conditions, and experimental RT data are available in the Supplementary Data, as well as the raw and statistical results for experimental–experimental and predicted–experimental projections before and after calibration.

Code availability.

The source code of RT projection, QSRR modeling and SOM clustering algorithm was provided in GitHub (https://github.com/Yanzi-Zhang-oss/Post-projection-calibration-of-retention-time-across-liquid-chromatography-setups).

Competing interests

The authors declare no competing interests.

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Generic and accurate prediction of retention times in liquid chromatography by post-projection calibration

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