# Physiologically Based Pharmacokinetic Modeling of Metoprolol Enantiomers and α-Hydroxymetoprolol to Describe CYP2D6 Drug-Gene Interactions

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## Abstract

**:**

_{last}(1.27) and C

_{max}values (1.23) over all studies. For DGI predictions, 18 out of 18 DGI AUC

_{last}ratios and 18 out of 18 DGI C

_{max}ratios were within two-fold of the observed ratios. The newly developed and carefully validated model was applied to calculate dose recommendations for CYP2D6 polymorphic patients and will be freely available in the Open Systems Pharmacology repository.

## 1. Introduction

_{1}-blocking activity of metoprolol [15], and it is almost exclusively formed via CYP2D6 [16]. Therefore, α-hydroxymetoprolol/metoprolol urinary metabolic ratios are employed for CYP2D6 phenotyping [17]. Overall, CYP2D6 is estimated to be responsible for 80% of metoprolol metabolism in normal metabolizers [14]. Depending on the CYP2D6 phenotype, only 1.5–12% of orally administered metoprolol are excreted unchanged in urine [18].

_{1}-adrenoceptors in rats than the (R)-enantiomer [19]. Moreover, in ultrarapid metabolizers (UMs) and normal metabolizers, but not in poor metabolizers, the (S)-metoprolol area under the plasma concentration–time curve (AUC) is significantly higher than the AUC of (R)-metoprolol, showing the enantiopreference of CYP2D6 towards the (R)-enantiomer [18,20]. The distribution of CYP2D6 genotypes varies substantially between ethnicities. For instance, 5.7% of the US and 0.9% of Middle Eastern or Oceanian populations were found to be poor metabolizers (AS = 0), whereas the prevalence of ultrarapid metabolizers (AS > 2) was 2.2% in the US and 11.2% in Middle Eastern or Oceanian populations [21,22]. Interestingly, the reduced-function CYP2D6*10 allele occurs more often in East Asian populations than the CYP2D6*1 allele (42% vs. 34%), which results in an overall decreased CYP2D6 activity compared to other populations [23].

## 2. Materials and Methods

#### 2.1. Software

^{®}and MoBi

^{®}(Open Systems Pharmacology Suite 9.1). Published clinical study data were digitized with GetData Graph Digitizer 2.26.0.20 (© S. Fedorov) according to best practices [30]. Pharmacokinetic parameters (area under the plasma concentration-time curve from the time of the first concentration measurement to the time of the last concentration measurement (AUC

_{last}) and maximum plasma concentration (C

_{max})) and model performance metrics (mean relative deviation (MRD), geometric mean fold error (GMFE), DGI AUC

_{last}, and C

_{max}ratios) were calculated using Python (version 3.7.4, Python Software Foundation, Wilmington, DE, USA) in Visual Studio Code (version 1.49.1, Microsoft Corporation, Redmond, WA, USA). Plots were also generated using Python in Visual Studio Code.

#### 2.2. PBPK Model Building

_{cat}) values were optimized for studies of the training dataset where the volunteers were either normal metabolizers or not phenotyped. Racemic metoprolol plasma concentration–time profiles were modeled by the administration of racemic doses of metoprolol (50% (R)- and 50% (S)-metoprolol and the use of a customized “observer” within PK-Sim

^{®}, which adds up the simulated (R)- and (S)-metoprolol plasma concentrations to directly display the racemic metoprolol plasma concentration–time profiles. Figure 1 provides an overview of metoprolol metabolic pathways.

#### 2.3. DGI Modeling

_{max}= maximum reaction velocity, S = free substrate concentration, K

_{m}= Michaelis-Menten constant, k

_{cat}= catalytic rate constant, and E = enzyme concentration.

_{m}) values were kept constant over the whole range of modeled activity scores. CYP2D6 k

_{cat}values were optimized for each activity score separately. CYP2D6 poor metabolizers (AS = 0) were assumed to show no CYP2D6 activity (0%), whereas populations with two wildtype alleles (AS = 2) were used as reference (100%) to calculate relative k

_{cat}values according to Equation (2).

_{cat, rel, AS=i}= k

_{cat}for the investigated activity score relative to AS = 2, k

_{cat, AS=i}= k

_{cat}for the investigated activity score, and k

_{cat, AS = 2}= k

_{cat}for AS = 2.

#### 2.4. PBPK Model Evaluation

_{max}values. All AUC values (predicted as well as observed) were calculated from the time of the first concentration measurement to the time of the last concentration measurement (AUC

_{last}).

_{last}and C

_{max}values (Equation (4)) were calculated.

_{last}or C

_{max}value of study i, ${\mathsf{\rho}}_{\mathrm{i}}$ = corresponding observed AUC

_{last}or C

_{max}value of study i, and m = number of studies.

#### 2.5. DGI Modeling Evaluation

_{last}ratios (Equation (5)) and DGI C

_{max}ratios (Equation (6)) were evaluated to assess, if the impact of the observed DGIs was well described by the model.

_{last, DGI}= AUC

_{last}of variant activity score or phenotype, while AUC

_{last, reference}= AUC

_{last}of AS = 2 or normal metabolizer phenotype.

_{max, DGI}= C

_{max}of variant activity score or phenotype, C

_{max, reference}= C

_{max}of AS = 2 or normal metabolizer phenotype. As a quantitative measure of the prediction accuracy, GMFE values of the predicted DGI AUC

_{last}ratios and DGI C

_{max}ratios were calculated according to Equation (4).

## 3. Results

#### 3.1. Metoprolol PBPK Model Development and Evaluation

_{last}and C

_{max}values, respectively, are presented in Figure 3. Predicted plasma concentrations were predominantly (88.3%) within two-fold of the corresponding observed concentrations. Furthermore, a total of 72 out of 75 of the predicted AUC

_{last}values (several studies included measurements of multiple analytes) and 64 out of 66 of the predicted C

_{max}values were within the two-fold acceptance criterion. The metoprolol model GMFE values were 1.27 (range 1.01–2.94) for the predicted AUC

_{last}values, and 1.23 (range 1.00–2.97) for the predicted C

_{max}values. The MRD values and predicted to observed AUC

_{last}and C

_{max}ratios for all 48 clinical studies and all measured analytes are provided in Supplementary Tables S2.6.4–S2.6.7.

_{u}), which were gathered from literature and used unmodified as model input parameters. Setting a sensitivity threshold of 0.5 (100% parameter value change = 50% change of predicted AUC), the only other parameter value that the model predictions were sensitive to is the CYP2D6 (R)-metoprolol → O-demethylmetoprolol catalytic rate constant (optimized). A comprehensive visual and quantitative presentation of the sensitivity analysis results can be found in Supplementary Section S2.6.7.

#### 3.2. Metoprolol CYP2D6 DGI Model Development and Evaluation

_{cat, rel}values for the different CYP2D6 activity scores. The identified values for both CYP2D6 pathways and both metoprolol enantiomers are given in Table 3.

_{last}and C

_{max}ratios were in very good agreement with the observed DGI ratios, demonstrating that the impact of the different CYP2D6 activity scores on the pharmacokinetics of racemic metoprolol, (R)-, and (S)-metoprolol and the metabolite α-hydroxymetoprolol was well described by the model. Specifically, 18 out of 18 AUC

_{last}and 17 out of 18 C

_{max}ratios were within the prediction success limits suggested by Guest et al. adopted for DGI evaluations [52], as visualized in Figure 5. Predicted DGI AUC

_{last}ratios show an overall GMFE of 1.21 (range 1.00–1.69), while predicted DGI C

_{max}ratios showed an overall GMFE of 1.21 (range 1.00–1.56). The predicted and observed ratios and corresponding predicted to observed DGI AUC

_{last}and C

_{max}ratios for all studies are provided in Supplementary Table S3.3.2.

#### 3.3. Metoprolol Dose Adaptation for CYP2D6 DGIs

_{ss}) matched the AUC

_{ss}(±10%) of a 100 mg twice daily metoprolol regimen in AS = 2 (wildtype) subjects. Predictions of plasma concentration-time profiles for individuals with different activity scores, all administered with 100 mg of metoprolol tartrate twice daily, are shown in Figure 6a. Simulations for different activity scores after dose adaptation are shown in Figure 6b. The resulting model-based dose adaptations compared to the Dutch Pharmacogenetics Working Group (DPWG) guideline recommendations for metoprolol [28] are shown in Figure 6c. The corresponding AUC

_{ss}values before (Figure 6d) and after (Figure 6e) dose adaptation are visualized in the lower panel.

## 4. Discussion

_{m}values from in vitro literature [39], these K

_{m}values were assumed to be the same across all CYP2D6 activity scores. Using metoprolol as the substrate, only three genotype-specific in vitro K

_{m}values (*1, *2 and *17 isoforms), could be obtained from literature (metoprolol α-hydroxylation and O-demethylation), showing a slightly higher K

_{m}for the *17 allele (AS = 0.5) [8]. Other studies reported no clear trend of K

_{m}values using a wide range of CYP2D6 substrates to investigate the enzyme kinetics of the reduced-function alleles *10 and *17 in comparison to the wildtype *1 allele [55]. Hence, due to an insufficient amount of data, the same K

_{m}values were used in the model across all activity scores. The final optimized k

_{cat, rel}values increased with increasing activity scores, reflecting an apparent correlation of metoprolol oral clearance with the CYP2D6 activity score [9]. Plasma concentration–time profiles and DGI AUC

_{last}and C

_{max}ratios of all analyzed clinical studies were well described by the final model.

_{m}and k

_{cat}, that would be necessary for a mechanistic implementation of the respective metabolic pathways, are not available in the literature. Consequently, the authors decided to incorporate an unspecific hepatic clearance process in addition to the CYP2D6-dependent pathways.

## 5. Conclusions

## Supplementary Materials

_{last}values goodness-of-fit plots for the final metoprolol model, Figure S2.6.12: AUC

_{last}goodness-of-fit plots for the final metoprolol model, Figure S2.6.13: C

_{max}values goodness-of-fit plots for the final metoprolol model, Figure S2.6.14: AUC

_{last}goodness-of-fit plots for the final metoprolol model, Table S2.6.6: Predicted and observed AUC

_{last}and C

_{max}values (metoprolol, α-hydroxymetoprolol), Table S2.6.7: Predictedandobserved AUC

_{last}and C

_{max}values ((R)-metoprolol,(S)-metoprolol), Figure S2.6.15: Sensitivity analysis of the (R)-metoprolol (upper panel) and (S)-metoprolol (lower panel) model, Table S3.1.1: k

_{cat},

_{rel}values for the different CYP2D6 activity scores, Figure S3.2.1: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.2.2: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.2.3: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.2.4: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.2.5: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.2.6: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction., Figure S3.2.7: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.2.8: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.2.9: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.2.10: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.2.11: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.2.12: Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction, Figure S3.3.13: Predicted versus observed metoprolol DGI ratios. Comparison of predicted versus observed AUC

_{last}ratios (a) and C

_{max}ratios (b) for metoprolol CYP2D6 DGI-studies, Table S3.3.2: Geometric mean fold error of predicted metoprolol DGI AUC

_{last}andC

_{max}ratios, Table S4.0.1: System-dependent parameters.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Implemented metoprolol metabolic pathways. (R)- and (S)-metoprolol are both metabolized via two different CYP2D6-dependent metabolic pathways: α-hydroxylation and O-demethylation, as well as by an unspecific hepatic clearance process. The four α-hydroxymetoprolol diastereomers (stereocenters are marked with asterisks) were modeled as one single compound due to lacking published clinical data. CL

_{hep}: hepatic clearance, CYP2D6: cytochrome P450 2D6.

**Figure 2.**Metoprolol plasma concentrations. Model predictions of metoprolol and its metabolite α-hydroxymetoprolol plasma concentration-time profiles of selected (

**a**–

**c**) intravenous and (

**d**–

**l**) oral studies of the training and test datasets, compared to observed data [43,44,45,47,48,49,50]. Population predictions (n = 100) are shown as lines with ribbons (arithmetic mean ± standard deviation (SD)), symbols represent the corresponding observed data ± SD. Detailed information on all clinical studies is listed in Supplementary Table S2.2.1. iv: intravenous, po: oral.

**Figure 3.**Goodness-of-fit plots of the final metoprolol model. Predicted versus observed (

**a**,

**b**) plasma concentrations, (

**c**,

**d**) AUC

_{last}values and (

**e**,

**f**) C

_{max}values for the training (left column) and test (right column) datasets. The solid black line indicates the line of identity, solid grey lines show two-fold deviation, dashed grey lines indicate 1.25-fold deviation. Detailed information on all clinical studies is listed in Supplementary Table S2.2.1. AUC

_{last}: area under the plasma concentration-time curve from the time of the first concentration measurement to the time of the last concentration measurement, C

_{max}: maximum plasma concentration, vs: versus.

**Figure 4.**Metoprolol plasma concentrations of the modeled CYP2D6 drug-gene interaction. Model predictions of (

**a**–

**c**) (R)-metoprolol and (S)-metoprolol as well as (

**d**–

**f**) metoprolol and α hydroxymetoprolol plasma concentration-time profiles of selected metoprolol CYP2D6 DGI studies, compared to observed data [18,51]. Population predictions (n = 100) are shown as lines with ribbons (arithmetic mean ± standard deviation (SD)), symbols represent the corresponding observed data ± SD. Detailed information on all clinical studies is listed in Supplementary Table S2.2.1. AS: activity score, po: oral.

**Figure 5.**Predicted versus observed metoprolol DGI ratios. Comparison of predicted versus observed (

**a**) DGI AUC

_{last}ratios and (

**b**) DGI C

_{max}ratios for all analyzed metoprolol CYP2D6 DGI studies. The straight black line indicates the line of identity, curved black lines show prediction success limits proposed by Guest et al. including 1.25-fold variability [52]. Solid grey lines indicate two-fold deviation, dashed grey lines show 1.25-fold deviation. Detailed information on all clinical studies as well as the plotted values are listed in Tables S2.2.1 and S3.3.2 of the Supplementary Materials. AUC

_{last}: area under the plasma concentration-time curve from the time of the first concentration measurement to the time of the last concentration measurement, C

_{max}: maximum plasma concentration, DGI: drug-gene interaction, vs: versus.

**Figure 6.**Model-based CYP2D6 DGI dose recommendations. (

**a**) Simulations of metoprolol exposure in individuals with different CYP2D6 activity scores, all administered with 100 mg metoprolol twice daily. (

**b**) Simulations of metoprolol exposure in individuals with different CYP2D6 activity scores, administered with the model-based dose recommendations. Doses were adjusted to match the AUC

_{168–180 h}of 100 mg metoprolol twice daily in AS = 2 (wt) individuals. (

**c**) Model-based dose adjustments, compared to the DPWG guideline recommendations for metoprolol [28]. (

**d**) Metoprolol AUC

_{168–180 h}values for administration of 100 mg twice daily to individuals with different CYP2D6 activity scores. (

**e**) Metoprolol AUC

_{ss}values for administration of the model-based dose recommendations to individuals with different CYP2D6 activity scores. The dotted horizontal line marks the wt AUC

_{ss}. *: value interpolated due to a lack of clinical studies with AS = 1, ‡: dose titration or change of medication recommended, AS: activity score, AUC

_{ss}: area under the plasma concentration-time curve during steady state (168–180 h), bid: twice daily, DPWG: Dutch Pharmacogenetics Working Group, IM: intermediate metabolizer, NM: normal metabolizer, PM: poor metabolizer, po: oral, UM: ultrarapid metabolizer, wt: wild type.

**Table 1.**CYP2D6 activity score assignment according to [33].

Activity Score | Projected Phenotype | Examples of Relevant CYP2D6 Genotypes |
---|---|---|

0 | PM | *3/*3, *3/*4, *4/*4, *5/*6 |

0.25 | IM | *4/*10, *5/*10 |

0.5 | *4/*41, *5/*17, *10/*10 | |

0.75 | *17/*10, *41/*10 | |

1 | *1/*4, *2/*5, *17/*17, *17/*41 | |

1.25 | NM | *1/*10, *2/*10, *35/*10 |

1.5 | *1/*41, *2/*17, *35/*41 | |

2 | *1/*1, *1/*2, *2/*35 | |

2.25 | *1x2/*17, *35x2/*41 | |

>2.25 | UM | *1/*1x3, *1/*35x2, *2x2/*9 |

Parameter | Unit | (R)-Metoprolol | (S)-Metoprolol | Description | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Value | Source | Literature | Reference | Value | Source | Literature | Reference | |||

MW | g/mol | 267.36 | Lit. | 267.36 | [34] | 267.36 | Lit. | 267.36 | [34] | Molecular weight |

pK_{a} (base) | - | 9.7 | Lit. | 9.70 | [34] | 9.7 | Lit. | 9.70 | [34] | Acid dissociation constant |

Solubility tart. (pH 7.4) | g/mL | 1.00 | Lit. | 1.00 | [35] | 1.00 | Lit. | 1.00 | [35] | Solubility |

Solubility succ. (pH 5.5) | g/mL | 0.16 | Lit. | 0.16 | [36] | 0.16 | Lit. | 0.16 | [36] | Solubility |

logP | - | 1.77 | Lit. | 1.77 | [37] | 1.77 | Lit. | 1.77 | [37] | Lipophilicity |

f_{u} | % | 88 | Lit. | 88 | [38] | 88 | Lit. | 88 | [38] | Fraction unbound |

CYP2D6 K_{m} ⭢ αHM | µmol/L | 10.08 | Lit. | 10.08 ^{‡} | [39] | 10.75 | Lit. | 10.75 ^{‡} | [39] | Michaelis-Menten constant |

CYP2D6 k_{cat} ⭢ αHM | 1/min | 6.02 | Optim. ^{†} | 7.50 | [39] | 6.55 | Optim. ^{†} | 8.27 | [39] | Catalytic rate constant |

CYP2D6 K_{m} ⭢ ODM | µmol/L | 8.82 | Lit. | 8.82 ^{‡} | [39] | 12.43 | Lit. | 12.43 ^{‡} | [39] | Michaelis-Menten constant |

CYP2D6 k_{cat} ⭢ ODM | 1/min | 9.87 | Optim. ^{†} | 12.30 | [39] | 8.21 | Optim. ^{†} | 10.37 | [39] | Catalytic rate constant |

CL_{hep., unsp.} | 1/min | 0.08 | Optim. | - | - | 0.09 | Optim. | - | - | Unspecific hepatic clearance |

GFR fraction | - | 1.00 | Asm. | - | - | 1.00 | Asm. | - | - | Filtered drug in the urine |

EHC continuous fraction | - | 1.00 | Asm. | - | - | 1.00 | Asm. | - | - | Bile fraction cont. released |

Intestinal permeability | cm/min | 4.14 × 10^{−5} | Optim. | 1.12 × 10^{−5} | Calc. [40] | 4.14 × 10^{−5} | Optim. | 1.12 × 10^{−5} | Calc. [40] | Transcellular intestinal perm. |

Cellular permeability | cm/min | 4.64 × 10^{−3} | Calc. | PK-Sim | [32] | 4.64 × 10^{−3} | Calc. | PK-Sim | [32] | Perm. into the cellular space |

Partition coefficients | - | Diverse | Calc. | R&R | [41,42] | Diverse | Calc. | R&R | [41,42] | Cell to plasma partitioning |

NR Weibull time parameter | min | 12.31 | Optim. | - | [43,44] | 12.31 | Optim. | - | [43,44] | Dissolution time (50%) |

NR Weibull shape parameter | - | 0.72 | Optim. | - | [43,44] | 0.72 | Optim. | - | [43,44] | Dissolution profile shape |

CR Weibull time parameter | min | 331.92 | Optim. | - | [45] | 331.92 | Optim. | - | [45] | Dissolution time (50%) |

CR Weibull shape parameter | - | 1.53 | Optim. | - | [45] | 1.53 | Optim. | - | [45] | Dissolution profile shape |

^{†}: CYP2D6 k

_{cat}values were optimized in a fixed ratio (k

_{cat}

**⭢**αHM:k

_{cat}

**⭢**ODM) equivalent to the ratio of reported k

_{cat}values [39],

^{‡}: in vitro values corrected for binding in the assay, using estimated fraction unbound to microsomal protein (f

_{u, mic, estimated}= 84%) [46], αHM: α-hydroxymetoprolol, asm.: assumed, calc.: calculated, cont.: continuously, CR: controlled release, CYP2D6: cytochrome P450 2D6, EHC: enterohepatic circulation, GFR: glomerular filtration rate, hep.: hepatic, lit.: literature, NR: normal release, ODM: O-demethylmetoprolol, optim.: optimized, perm. permeability, PK-Sim: PK-Sim standard calculation method, R&R: Rodgers and Rowland calculation method, succ.: metoprolol succinate, tart.: metoprolol tartrate, unsp.: unspecific.

Activity Score | (R)-Metoprolol | (S)-Metoprolol | k_{cat, rel} | ||
---|---|---|---|---|---|

k_{cat} ⭢ αHM | k_{cat} ⭢ ODM | k_{cat} ⭢ αHM | k_{cat} ⭢ ODM | ||

0 | 0.00 1/min | 0.00 1/min | 0.00 1/min | 0.00 1/min | 0% |

0.5 | 1.65 1/min | 2.70 1/min | 1.82 1/min | 2.27 1/min | 19% |

1.25 | 5.73 1/min | 9.40 1/min | 6.30 1/min | 7.89 1/min | 64% |

1.5 | 6.38 1/min | 10.48 1/min | 7.03 1/min | 8.81 1/min | 72% |

2 | 10.17 1/min | 16.69 1/min | 11.19 1/min | 14.02 1/min | 100% |

3 | 19.03 1/min | 31.22 1/min | 20.93 1/min | 26.23 1/min | 213% |

_{cat}: catalytic rate constant, k

_{cat, rel}: catalytic rate constant relative to activity score = 2, ODM: O-demethylmetoprolol.

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**MDPI and ACS Style**

Rüdesheim, S.; Wojtyniak, J.-G.; Selzer, D.; Hanke, N.; Mahfoud, F.; Schwab, M.; Lehr, T.
Physiologically Based Pharmacokinetic Modeling of Metoprolol Enantiomers and α-Hydroxymetoprolol to Describe CYP2D6 Drug-Gene Interactions. *Pharmaceutics* **2020**, *12*, 1200.
https://doi.org/10.3390/pharmaceutics12121200

**AMA Style**

Rüdesheim S, Wojtyniak J-G, Selzer D, Hanke N, Mahfoud F, Schwab M, Lehr T.
Physiologically Based Pharmacokinetic Modeling of Metoprolol Enantiomers and α-Hydroxymetoprolol to Describe CYP2D6 Drug-Gene Interactions. *Pharmaceutics*. 2020; 12(12):1200.
https://doi.org/10.3390/pharmaceutics12121200

**Chicago/Turabian Style**

Rüdesheim, Simeon, Jan-Georg Wojtyniak, Dominik Selzer, Nina Hanke, Felix Mahfoud, Matthias Schwab, and Thorsten Lehr.
2020. "Physiologically Based Pharmacokinetic Modeling of Metoprolol Enantiomers and α-Hydroxymetoprolol to Describe CYP2D6 Drug-Gene Interactions" *Pharmaceutics* 12, no. 12: 1200.
https://doi.org/10.3390/pharmaceutics12121200