Design and Synthesis of Pleuromutilin Derivatives as Antibacterial Agents Using Quantitative Structure–Activity Relationship Model

The quantitative structure–activity relationship (QSAR) is one of the most popular methods for the virtual screening of new drug leads and optimization. Herein, we collected a dataset of 955 MIC values of pleuromutilin derivatives to construct a 2D-QSAR model with an accuracy of 80% and a 3D-QSAR model with a non-cross-validated correlation coefficient (r2) of 0.9836 and a cross-validated correlation coefficient (q2) of 0.7986. Based on the obtained QSAR models, we designed and synthesized pleuromutilin compounds 1 and 2 with thiol-functionalized side chains. Compound 1 displayed the highest antimicrobial activity against both Staphylococcus aureus ATCC 29213 (S. aureus) and Methicillin-resistant Staphylococcus aureus (MRSA), with minimum inhibitory concentrations (MICs) < 0.0625 μg/mL. These experimental results confirmed that the 2D and 3D-QSAR models displayed a high accuracy of the prediction function for the discovery of lead compounds from pleuromutilin derivatives.


Introduction
The widespread use of antibiotics in humans has led to the rapid emergence of many drug-resistant strains.Almost all antibacterial agents have developed antibiotic resistance, which has posed a serious threat to global public health [1,2].Methicillinresistant Staphylococcus aureus (MRSA) is a top-priority pathogen listed by the Centers for Disease Control (CDC) [3].It is estimated that each year, approximately 72,000 cases of serious invasive disease and 10,000 deaths are caused by MRSA in the US [4,5].Therefore, the development of new antibacterial agents with novel structures and unique antimicrobial mechanisms is urgently needed to fight antimicrobial resistance [6,7].
Pleuromutilin (Figure 1) is a natural compound with a specific tricyclic diterpene structure produced by the Pleurotus mutilus [8].After the discovery of pleuromutilin in 1951, tremendous efforts have been made to modify its scaffold to explore the structure-activity relationship (SAR) [9].Modification of the pleuromutilin tricyclic ring does not improve their antibacterial activities significantly [10].However, the presence of a thioether group at the side chain of pleuromutilin and a basic group enhances antibacterial activity dramatically [11].Modifications of the side chain of pleuromutilin have led to tiamulin [12] and valnemulin [13] (Figure 1) for veterinary use.After that, retapamulin [14] and lefamulin [15] (Figure 1) were successfully developed for human use.Pleuromutilin compounds display good antibacterial activity against bacteria and mycoplasma by interacting with the 50S subunit of bacterial ribosomes to inhibit bacterial protein synthesis, but does not bind to mammalian ribosomes [16,17].
three-dimensional structure of compound molecules to establish a link between the characteristic structure and its activity for obtaining better QSAR models [22].
In this study, the biological activity of target compounds 1 and 2 (Figure 1) was first designed and predicted based on the established 2D-and 3D-QSAR model.Subsequently, we synthesized and tested their antibacterial activities in vitro.The structure of pleuromutilin and the structure of the now-available pleuromutilin derivatives are shown in Figure 1.The quantitative structure-activity relationship (QSAR) has proved to be effective for scientific research in many disciplines, especially in the development of new generations of selective drugs [18].To find new drug leads, efficient and stable procedures are required to screen chemical databases and virtual libraries for molecules with known activity.To this end, the QSAR model provides an effective way to explore and exploit the relationship between chemical structures and their biological effects for the development of new drug candidates [19][20][21].The approach to building QSAR models can often be described as applying data analysis methods and statistical data, and the established model can accurately predict the biological activities or properties of a compound based on its structure.The 2D-QSAR is a method for quantitatively describing the relationship between the physicochemical and other measurable properties of a structure and its activity through a linear or non-linear model.This method has widely been used in many fields, such as medicine, pharmacy, and chemistry [22].However, the 3D-QSAR introduces the three-dimensional structure of compound molecules to establish a link between the characteristic structure and its activity for obtaining better QSAR models [22].
In this study, the biological activity of target compounds 1 and 2 (Figure 1) was first designed and predicted based on the established 2D-and 3D-QSAR model.Subsequently, we synthesized and tested their antibacterial activities in vitro.The structure of pleuromutilin and the structure of the now-available pleuromutilin derivatives are shown in Figure 1.

QSAR Model Evaluation
The most simplistic predictive models of chemical properties rely on the similarity principle; especially, the compounds with similar structures have similar properties [21].Therefore, we selected pleuromutilin derivatives whose side chains were modified but whose tricyclic diterpene structures were untouched, as the molecular target for QSAR predictions.
Ninety-six randomly selected untrained molecules were used for activity prediction with the 2D-QSAR model, and the prediction results were represented by the classification model labels (class-0, class-1, and class-2).The test set output showed the actual negative logarithmic value of minimum inhibitory concentrations (pMICs), as well as the test and prediction model labels, which were subsequently evaluated for comparison.
The model predicts four possible results: true positive (TP), false positive (FP), false negative (FN), and true negative (TN).Based on the prediction results, we used precision (precision or positive predictive value, PPV), recall (recall or sensitivity, true positive rate, TPR), F1-score (F1-value), and the confusion matrix to evaluate the model quality [23,24].The four results of the model evaluation (Table 1) were calculated using the following formula: The confusion matrix, also known as the error matrix, is a standard format for representing accuracy evaluations, which is expressed in the form of a matrix with n rows and n columns.Based on the test result (class-exp.) and the prediction result (class-pred.), the confusion matrix was established as shown in Figure 2. The results showed that the higher the number of two-by-two data in the diagonal grid, the higher the number of experimental results that agree with the predicted results.Finally, we built a 2D-QSAR model with 80% accuracy.The 3D-QSAR model mainly responds to the accuracy of the model by detecting the correlation coefficient r 2 (the fitting ability of the response model) and the cross-validation coefficient q 2 (the predictive ability of the response model).Generally, r 2 > 0.8 and q 2 > 0.6 indicate a better accuracy of the model [25].The established model obtained better values of r 2 (0.9836) and q 2 (0.7986).The linear regression plots for the training and test sets are shown in Figure 3A,B, and the regression equation was built as Y = 0.9836X + 0.1023 and Y = 0.8436X + 1.3031.The differences between the experimental and the calculated values for MIC and both molecules in the training set and the test set are presented in Figure 3C.Force field models were visualized used PyMol software 3.8 version (DeLano Scientific LLC, San Carlos, CA, USA), and the template was set using the molecules with the highest antimicrobial activity in the training set (Figure 3D).The pleuromutilin ring and the thiazole ring were surrounded by a yellow profile, indicating that the bulky groups did not increase the antibacterial activity against MRSA.The blue profile was surrounded at 1- The 3D-QSAR model mainly responds to the accuracy of the model by detecting the correlation coefficient r 2 (the fitting ability of the response model) and the cross-validation coefficient q 2 (the predictive ability of the response model).Generally, r 2 > 0.8 and q 2 > 0.6 indicate a better accuracy of the model [25].The established model obtained better values of r 2 (0.9836) and q 2 (0.7986).The linear regression plots for the training and test sets are shown in Figure 3A,B, and the regression equation was built as Y = 0.9836X + 0.1023 and Y = 0.8436X + 1.3031.The differences between the experimental and the calculated values for MIC and both molecules in the training set and the test set are presented in Figure 3C.Force field models were visualized used PyMol software 3.8 version (DeLano Scientific LLC, San Carlos, CA, USA), and the template was set using the molecules with the highest antimicrobial activity in the training set (Figure 3D).The pleuromutilin ring and the thiazole ring were surrounded by a yellow profile, indicating that the bulky groups did not increase the antibacterial activity against MRSA.The blue profile was surrounded at 1-methyl-1H-1,2,3-triazole, indicating that it contained electronegative groups which were more beneficial to exhibiting anti-MRSA activity.The 3D view of the aligned molecules is also shown in Figure 3E.This information allows users to confirm the molecular alignment and validate the QSAR model.

Activity Prediction and Screening of New Compounds
Here, we designed and synthesized compounds 1 and 2 as examples to demonstrate the accuracy of our QSAR models.Compounds 1 and 2 contained a novel 7,8-dihydroquinolin-5(6H)-one and biphenyl side chain, respectively, which had not been reported by any study.The predicted results for compounds 1 and 2 are shown in Table 2.The MICs of both compounds predicted by the 2D-QSAR model were in the range of 0-0.5 µg/mL.In the 3D-QSAR model, compound 2 was predicted with higher activity than that of compound 2.

Syntheses
To explore the accuracy of the established 2D-and 3D-QSAR models, we performed concise syntheses of compounds 1 and 2. To synthesize compound 1, pleuromutilin was used as the starting material and converted into 22-O-tosylpleuromutilin 3. Compound 6 was synthesized from the nucleophilic addition reaction of cyclohexanedione 4 with 1,1-dimethoxytrimethylamine, followed by cyclization with 2-cyanoethanethioamide.The electrophilic nature of 3 facilitated its nucleophilic substitution reaction with pyridine 6 to yield target compound 1 under the base condition (Scheme 1).Compound 2 was directly obtained by the reaction of pleuromutilin and 4-biphenylsulfonyl chloride with one step (Scheme 2).

Activity Prediction and Screening of New Compounds
Here, we designed and synthesized compounds 1 and 2 as examples to demonstrate the accuracy of our QSAR models.Compounds 1 and 2 contained a novel 7,8-dihydroquinolin-5(6H)-one and biphenyl side chain, respectively, which had not been reported by any study.The predicted results for compounds 1 and 2 are shown in Table 2.The MICs of both compounds predicted by the 2D-QSAR model were in the range of 0-0.5 μg/mL.In the 3D-QSAR model, compound 2 was predicted with higher activity than that of compound 2.

Syntheses
To explore the accuracy of the established 2D-and 3D-QSAR models, we performed concise syntheses of compounds 1 and 2. To synthesize compound 1, pleuromutilin was used as the starting material and converted into 22-O-tosylpleuromutilin 3. Compound 6 was synthesized from the nucleophilic addition reaction of cyclohexanedione 4 with 1,1dimethoxytrimethylamine, followed by cyclization with 2-cyanoethanethioamide.The electrophilic nature of 3 facilitated its nucleophilic substitution reaction with pyridine 6 to yield target compound 1 under the base condition (Scheme 1).Compound 2 was directly obtained by the reaction of pleuromutilin and 4-biphenylsulfonyl chloride with one step (Scheme 2).

Activity Prediction and Screening of New Compounds
Here, we designed and synthesized compounds 1 and 2 as examples to demonstrate the accuracy of our QSAR models.Compounds 1 and 2 contained a novel 7,8-dihydroquinolin-5(6H)-one and biphenyl side chain, respectively, which had not been reported by any study.The predicted results for compounds 1 and 2 are shown in Table 2.The MICs of both compounds predicted by the 2D-QSAR model were in the range of 0-0.5 μg/mL.In the 3D-QSAR model, compound 2 was predicted with higher activity than that of compound 2.

Syntheses
To explore the accuracy of the established 2D-and 3D-QSAR models, we performed concise syntheses of compounds 1 and 2. To synthesize compound 1, pleuromutilin was used as the starting material and converted into 22-O-tosylpleuromutilin 3. Compound 6 was synthesized from the nucleophilic addition reaction of cyclohexanedione 4 with 1,1dimethoxytrimethylamine, followed by cyclization with 2-cyanoethanethioamide.The electrophilic nature of 3 facilitated its nucleophilic substitution reaction with pyridine 6 to yield target compound 1 under the base condition (Scheme 1).Compound 2 was directly obtained by the reaction of pleuromutilin and 4-biphenylsulfonyl chloride with one step (Scheme 2).The structures of the synthesized compounds 1 and 2 were characterized via nuclear magnetic resonance spectroscopy ( 1 H NMR and 13 C NMR, the spectra are shown in Figures S1 and S2).In the 1 H NMR spectrum of compound 1, a pyridine proton and six methylene protons in 7,8-dihydroquinolin-5(6H)-one were observed in 8.49 and in the range of 2.39-3.42ppm, respectively.Additionally, the 13 C NMR spectra of compound 1 exhibited the characteristic signals of 168.71 and the range of 164.31-140.17ppm for C=O and C=C(H) in 7,8-dihydroquinolin-5(6H)-one, respectively, which further confirmed the formation of the compounds.For compound 2, nine typical benzene protons and five characteristic signals for C in biphenyl were observed in 7.48-7.26ppm in the 1 H NMR spectrum and in 130.70-126.93 ppm in the 13 C NMR spectra, respectively.To further confirm the structure of compound 1, a colorless and block-like crystal (CCDC: 2219819, the crystal data and structural refinement results are shown in Table S1) was obtained using the slow evaporation method at room temperature as highlighted in Figure 4.
magnetic resonance spectroscopy ( 1 H NMR and 13 C NMR, the spectra ar ures S1 and S2).In the 1 H NMR spectrum of compound 1, a pyridine proto ylene protons in 7,8-dihydroquinolin-5(6H)-one were observed in 8.49 and 2.39-3.42ppm, respectively.Additionally, the 13 C NMR spectra of compo the characteristic signals of 168.71 and the range of ppm C=C(H) in 7,8-dihydroquinolin-5(6H)-one, respectively, which further con mation of the compounds.For compound 2, nine typical benzene proton acteristic signals for C in biphenyl were observed in 7.48-7.26ppm in the trum and in 130.70-126.93 ppm in the 13 C NMR spectra, respectively.To the structure of compound 1, a colorless and block-like crystal (CCDC: 221 data and structural refinement results are shown in Table S1) was obtained evaporation method at room temperature as highlighted in Figure 4.

Determination of MIC
The MICs of compounds 1 and 2 were determined as shown in Tabl 1 which bears a carbonitrile-substituted 7,8-dihydroquinolin-5(6H)-o showed the highest inhibitory effect on MRSA and S. aureus ATCC 292 0.0625 μg/mL for both strains, exhibiting a significantly higher activity tha lin.However, compound 2 with a biphenyl side chain failed to achieve bet MIC = 1 μg/mL for both strains.To our knowledge, no pleuromutilin de 7,8-dihydroquinolin-5(6H)-one side chain had been reported, which mad evaluate the anti-bacterial activities of compound 1 with structurally simi The MIC results of compound 1 were consistent with the predicted trends o model, but the 3D-QSAR model was more accurate in the prediction of compound 2.

Molecular Docking Study
To investigate the possible binding pattern of compounds 1 and 2

Determination of MIC
The MICs of compounds 1 and 2 were determined as shown in Table 3. Compound 1 which bears a carbonitrile-substituted 7,8-dihydroquinolin-5(6H)-one side chain showed the highest inhibitory effect on MRSA and S. aureus ATCC 29213 with MIC < 0.0625 µg/mL for both strains, exhibiting a significantly higher activity than that of tiamulin.However, compound 2 with a biphenyl side chain failed to achieve better results, with MIC = 1 µg/mL for both strains.To our knowledge, no pleuromutilin derivative with a 7,8-dihydroquinolin-5(6H)-one side chain had been reported, which made it difficult to evaluate the antibacterial activities of compound 1 with structurally similar compounds.The MIC results of compound 1 were consistent with the predicted trends of the 2D-QSAR model, but the 3D-QSAR model was more accurate in the prediction of the activity of compound 2.

Molecular Docking Study
To investigate the possible binding pattern of compounds 1 and 2 to the peptidyl transferase center (PTC) domain of ribosome, molecular docking experiments were carried out using Autodock Vina [26].Redocking the X-ray structure of lefamulin into 5HL7 [27] gave the best conformation of compounds 1 and 2, which exhibited a similar binding pattern to that of lefamulin (Figure 5A).
The results showed that the affinity free energy of compound 1 and 2 was −9.69 and −8.13 kcal/mol, respectively.The hydrogen bonds formed between the hydroxyl groups (eight-membered ring) and C=O (ester) of the docked compounds and the residues of G-2532 and G-2088 were the key interactions (Figure 5B,C), which is similar to our previous report [28].However, the carbonyl in the side chain of compound 1 formed an additional hydrogen bond with A-2466 (Figure 5B) when compared to compound 2. Furthermore, no π-π or cation-π between the residues and the pyridine or benzene rings of the docked compounds was observed.
Int. J. Mol.Sci.2024, 25, x FOR PEER REVIEW 8 of 16 [27] gave the best conformation of compounds 1 and 2, which exhibited a similar binding pattern to that of lefamulin (Figure 5A).The results showed that the affinity free energy of compound 1 and 2 was −9.69 and −8.13 kcal/mol, respectively.The hydrogen bonds formed between the hydroxyl groups (eight-membered ring) and C=O (ester) of the docked compounds and the residues of G-2532 and G-2088 were the key interactions (Figure 5B,C), which is similar to our previous report [28].However, the carbonyl in the side chain of compound 1 formed an additional hydrogen bond with A-2466 (Figure 5B) when compared to compound 2. Furthermore, no π-π or cation-π interaction between the residues and the pyridine or benzene rings of the docked compounds was observed.

ADMET Result
For further evaluation of PK properties, compounds 1 and 2 were evaluated for their absorption, distribution, metabolism, excretion, and toxicity (ADMET) in silico (Table 4).Distribution coefficient P resulted in a poor aqueous solubility but Caco-2 permeability was optimal.Compounds 1 and 2 were considered to be not only non-penetrating of the blood-brain barrier, but also non-inhibitors against CYP450 1A2 and 3A4.The low halflife (T1/2) indicated the fast metabolism of 1 and 2. Furthermore, compounds 1 and 2 were considered low-toxicity by predicting the Ames result and LD50.

Build the 2D/3D-QSAR Model
The 2D-QSAR model was built based on a dataset consisting of 955 small molecules with MIC activity values against MRSA (SMILES names and their MIC values were found in Table S2) collected from available reports [22,23,, with MIC ranging from 0 to 256 µg/mL, which were converted to pMIC to build the model.In this study, python 3.8, sklearn, and RDkit packages were used to complete the modeling work [67].All the structures of selected compounds were converted to SMILES format by ChemDraw software, 17.0 version.
The random forest algorithm in integration science was applied to model the pMIC values of the target dataset for classification, and random forest classifier for decision tree modeling was used to solve the classification problem [68].Before modeling, according to MIC values, we classified the dataset into three categories, including ≥5.95, 5.33-5.95,and <5.33, which denoted class-0, class-1, and class-2, respectively.The whole dataset was divided into the training set and test set which were randomly assigned by 8:1, the training set was used for model development, and the test set was used for model evaluation.
The building of the 3D-QSAR model requires selecting suitable small-molecule compounds and iteratively debugging the training and test sets.We used Cloud 3D-QSAR by integrating the functions of molecular structure generation, alignment, molecular interaction field (MIF) computing, and results analysis to provide a one-stop solution [69].The most widely common CoMFA method was applied to our Cloud 3DQSAR server.A grid box step size of 1.0 Å was applied and the energy cutoff was set to 30 kcal/mol.For the MIFs, the steric field used a carbon atom probe, while the electrostatic field used a + 1 charged probe with negligible volume [69].The partial least-squares (PLS) technique was applied to reduce the dimensionality in a regression context using orthogonal components.The server is free and provided at http://chemyang.ccnu.edu.cn/ccb/server/cloud3dQSAR/(accessed on 6 December 2023).The relevant date about building the 3D-QSAR model can be found in Tables S3 and S4.
The SMILES and MIC values were uploaded to the website and divided into a training set (36 compounds) and a test set (15 compounds).After setting the iteration number to 300, the dataset was submitted, and the system debugged and built the model.The cloud system utilized hundreds of datasets to develop different CoMFA models.PLS and LOO CV were used to calculate r 2 and q 2 values.Based on the evaluation results, the cloud system displayed the top 50 models as the modeling results.

Synthesis of Compound 3
Pleuromutilin (379 mg, 1 mmol) in 8 mL DCM was added to Et 3 N (304 mg, 3 mmol).The mixture was stirred and tosyl chloride (210 mg, 1.1 mmol) was slowly added at room temperature.After reaction overnight, the solvent was extracted by 3× NaCl and 3× H 2 O.The combined organic layers were dried with magnesium sulfate and evaporated.Purification by flash chromatography provided compound 3 (274 mg, 72%) as a white solid.

In Vitro Efficacy
The MICs of compounds 1 and 2, as well as tiamulin used as a control drug, were determined to assess their antibacterial activity against MRSA and S. aureus ATCC 29213.The MIC values were recorded as the lowest drug concentration fully visible in the 96-well plate at 37 • C to inhibit bacterial growth.Compounds were diluted to working concentrations using ultrapure water containing no more than 5% dimethyl sulfoxide (DMSO).The experiments were performed according to the broth micro-dilution methods, using Mueller-Hinton broth medium (MHB) at half dilution and two replicate tests for each drug.

Molecular Modeling
We used smina [70] to perform the docking.In the protocol, ligands were constructed using chem3D with energy minimization.The X-ray crystal structure (PDB ID: 5HL7) [26] was used as ribosome reporter.After removing water, metal ions, and ligands, the combination pocket was positioned at x, y, and z of 17, −77.9, and −2.6 and the size was set to 20 × 20 × 20 Å. Lefamulin (ligand) was redocked and compared with original structure.The parameter of exhaustiveness arg and num_modes arg were set to 120 and 9, respectively.Interacting intermolecular hydrogen bonds were assessed using LigPlot 2.2 version and PyMol software 3.8 version.

ADMET Evaluation
The Lipinski rule describes the druggability of molecules, which bases pharmacokinetic drug properties such as absorption, distribution, metabolism, and excretion on specific molecular properties.In this study, physicochemical properties such as absorption, distribution, metabolism, excretion, and toxicity of compounds 1 and 2 were predicted using the ADMET online prediction tool.The tool is free and provided at https://admet.scbdd.com/home/index/(accessed on 6 December 2023).

Conclusions
To screen the quality of pleuromutilin-like drugs more efficiently, the QSAR model was constructed in this study based on a large amount of experimental data.Random forest was used for establishing the 2D-QSAR model, which fit multiple categorical decision trees on various subsamples of the dataset and used averaging to improve prediction accuracy and control overfitting.The theoretical accuracy of the 2D-QSAR model established in this experiment was predicted as high as 80%.The 3D-QSAR model established in this study displayed good fitting and prediction abilities.We then designed and synthesized compounds 1 and 2 based on the 2D-and 3D-QSAR models.After determining their MIC, compound 1 displayed a higher antibacterial activity (MICs for both MRSA and S. aureus were <0.0625 µg/mL) than those of compound 2 and tiamulin, which was consistent with the predicted results of the 2D-QSAR model (0, i.e., the MIC of MRSA was in the range of ≥5.95).The prediction results of the 2D-QSAR model and 3D-QASR model for compound 1 were consistent with the experimental results; for compound 2, the 3D-QSAR model accurately predicted its activity compared to the 2D-QSAR model.This reflects the advantages of the 3D-QSAR: the 3D-QSAR introduces a three-dimensional stereo conformation, built by molecular superposition and iterative replacement of the training and test sets.Molecular docking revealed the improved activity of compound 1 attributed to the additional hydrogen bond with lower binding free energies (∆Gb) than those of compound 2, further demonstrating the predicted accuracy of QSAR models.Based on our experimental data, the developed 2D-and 3D-QSAR models in this study helped to improve the efficiency of finding highly active pleuromutilin derivatives.
Author Contributions: Conceptualization, writing-original draft preparation, R.S. and Y.Y.; resources, J.Z. and Q.L.; resources and validation, H.Z. and G.L.; formal analysis, investigation, and data curation, J.Z. and Y.Y.; conceptualization, project administration, writing-review and editing, J.Z. and Y.Y.All authors have read and agreed to the published version of the manuscript.

16 Figure 3 .
Figure 3.The evaluation results of 3D-QSAR model.(A) Training set linear regression; (B) test set linear regression; (C) residual value (experimental value-predictive value); (D) the field contour maps of the CoMFA models; (E) aligned molecules displayed by server.

Figure 3 .
Figure 3.The evaluation results of 3D-QSAR model.(A) Training set linear regression; (B) test set linear regression; (C) residual value (experimental value-predictive value); (D) the field contour maps of the CoMFA models; (E) aligned molecules displayed by server.

Figure 4 .
Figure 4. Crystal structure of compound 1 with ellipsoids set at 75% probability.

Figure 4 .
Figure 4. Crystal structure of compound 1 with ellipsoids set at 75% probability.

Figure 5 .
Figure 5. Superimposition of lefamulin (red) and compounds 1 (yellow) and 2 (cyan) docked to the binding pocket of ribosome (A).Binding modes of compounds 1 (B) and 2 (C) to 5H17.Important residues are drawn as sticks.Hydrogen bonds are shown as dashed red lines.

Figure 5 .
Figure 5. Superimposition of lefamulin (red) and compounds 1 (yellow) and 2 (cyan) docked to the binding pocket of ribosome (A).Binding modes of compounds 1 (B) and 2 (C) to 5H17.Important residues are drawn as sticks.Hydrogen bonds are shown as dashed red lines.