Drug pairs selection and validation of PBPK models for drug templates. 13 pairs out of 18 drugs, which have the calculated TS equal to or better than 0.5, were selected for the in silico PBPK modeling. Drug pairs with TS below 0.5 were not considered to be structurally similar and were excluded in this study. The calculated TS for selected 13 pairs (Groups A-M) were listed in Table 1. Since both drugs in a pair will in turn serve as the template and target drug for cross validation, we used X-1 and X-2 to label two drugs in the pair, respectively, where X can be A to M.
Table 1
The calculated Tanimoto Coefficient between each pair of drugs.
Group
|
Drug 1
|
Drug 2
|
Tanimoto score
|
A
|
Bupropion
|
Dextromethorphan
|
0.50
|
B
|
Bufuralol
|
Bupropion
|
0.52
|
C
|
Dextromethorphan
|
Quinidine
|
0.57
|
D
|
Lorazepam
|
Midazolam
|
0.63
|
E
|
Alprazolam
|
Lorazepam
|
0.65
|
F
|
Lorazepam
|
Triazolam
|
0.69
|
G
|
Mephenytoin
|
Phenobarbital
|
0.74
|
H
|
Atomoxetine
|
Fluoxetine
|
0.78
|
I
|
Simvastatin
|
Pravastatin
|
0.82
|
J
|
Triazolam
|
Midazolam
|
0.84
|
K
|
Midazolam
|
Alprazolam
|
0.88
|
L
|
Theophylline
|
Caffeine
|
0.93
|
M
|
Imipramine
|
Desipramine
|
0.95
|
The predicted mean plasma concentration-time profiles overlaid with observed data of all 18 template drugs are shown in Fig. 2. Accordingly, Table 2[18, 21–36] exhibits the predicted PK parameters (CMax, TMax, AUC) versus observed values. From Table 2, excluding the drugs with observed PK parameters all unavailable (Dextromethorphan, Mephenytoin and Fluoxetine), the predicted PK parameters of most drugs are within the standard deviation ranges of their observed values. The predicted values of CMax, TMax and AUC for Theophyline are all slightly beyond the margin of error but still within the range of two-fold standard deviation. Overall, as shown in Fig. 2, the observed C-T profiles are within the 95% Confidence Interval (CI) ranges (the upper and lower grey dashed curves) of the simulated C-T curves. Therefore, the PBPK models for the template drugs have been well validated.
Table 2
The comparison between predicted and observed PK profiles of all drugs.
Drug name
|
Dosage
|
Pred/Obs
|
TMax (h)
|
CMax (ng/mL)
|
AUC (ng/mL∙h)
|
Bupropion
|
150 mg
|
Pred
|
2.16
|
61.62
|
721.88
|
Pred_V2
|
1.93
|
50.04
|
467.20
|
Pred_V3
|
1.86
|
71.84
|
614.66
|
Obs
|
(1.30, 5.10)
|
(34.00, 118.00)
|
(486.00, 1518.00)
|
Dextromethorphan
|
60 mg
|
Pred
|
1.56
|
13.13
|
195.70
|
Pred_V2
|
1.57
|
16.31
|
253.83
|
Pred_V3
|
2.69
|
162.33
|
3594.67
|
Obs
|
NA
|
NA
|
NA
|
Bufuralol
|
15 mg
|
Pred
|
1.49
|
55.62
|
386.06
|
Pred_V2
|
1.24
|
41.98
|
221.18
|
Pred_V3
|
1.75
|
18.66
|
151.83
|
Obs
|
(1.84, 2.74)
|
(56.00, 72.00)
|
(270.00, 430.00)
|
Quinidine
|
400 mg
|
Pred
|
1.16
|
1904.52
|
11632.95
|
Pred_V2
|
1.15
|
1554.16
|
9525.60
|
Pred_V3
|
1.66
|
2183.40
|
18988.42
|
Obs
|
(0.36, 2.54)
|
(1330.00, 2070.00)
|
(3800.00, 14860.00)
|
Lorazepam
|
2 mg
|
Pred
|
1.92
|
18.24
|
240.28
|
Pred_V2
|
1.92
|
21.86
|
314.64
|
Pred_V3
|
2.08
|
32.98
|
531.29
|
Obs
|
(0.50, 6.00)
|
(15.80, 25.60)
|
(197.20, 268.80)
|
Midazolam
|
7.5 mg
|
Pred
|
0.60
|
39.97
|
99.77
|
Pred_V2
|
0.52
|
25.45
|
56.18
|
Pred_V3
|
0.87
|
39.58
|
383.67
|
Obs
|
(0.22, 1.21)
|
(25.90, 80.20)
|
(64.00, 163.70)
|
Alprazolam
|
0.8 mg
|
Pred
|
1.23
|
12.22
|
193.14
|
Pred_V2
|
1.44
|
12.92
|
323.18
|
Pred_V3
|
2.16
|
7.74
|
327.10
|
Obs
|
(0.70, 2.30)
|
(8.20, 14.40)
|
(173.20, 291.60)
|
Triazolam
|
0.25 mg
|
Pred
|
0.72
|
2.34
|
13.94
|
Pred_V2
|
0.49
|
1.26
|
11.88
|
Pred_V3
|
1.47
|
1.80
|
24.95
|
Obs
|
(0.35, 2.15)
|
(1.70, 4.30)
|
NA
|
Mephenytoin
|
100 mg
|
Pred
|
0.61
|
265.55
|
2576.76
|
Pred_V2
|
0.61
|
324.97
|
3089.24
|
Pred_V3
|
0.36
|
299.34
|
584.59
|
Obs
|
NA
|
NA
|
NA
|
Phenobarbital
|
216 mg
|
Pred
|
2.07
|
5235.78
|
660577.85
|
Pred_V2
|
4.02
|
5658.75
|
691539.10
|
Pred_V3
|
4.03
|
4977.22
|
930922.01
|
Obs
|
2.00
|
5100.00
|
NA
|
Fluoxetine*
|
20 mg
|
Pred
|
4.36
|
6.50
|
186.21
|
Pred_V2
|
5.32
|
6.04
|
192.74
|
Pred_V3
|
2.68
|
13.89
|
291.07
|
Obs
|
NA
|
NA
|
NA
|
Atomoxetine
|
20 mg
|
Pred
|
1.25
|
169.56
|
1390.42
|
Pred_V2
|
0.74
|
61.41
|
192.74
|
Pred_V3
|
1.84
|
35.78
|
486.50
|
Obs
|
(0.50, 1.55)
|
(106.16, 178.16)
|
NA
|
Simvastatin
|
10 mg
|
Pred
|
1.20
|
2.11
|
7.03
|
Pred_V2
|
1.20
|
0.52
|
1.69
|
Pred_V3
|
1.20
|
24.03
|
78.42
|
Obs
|
(1.00, 1.40)
|
(2.60, 4.60)
|
(7.40, 14.78)
|
Pravastatin
|
20 mg
|
Pred
|
0.96
|
40.60
|
130.36
|
Pred_V2
|
1.08
|
206.61
|
578.24
|
Pred_V3
|
1.56
|
130.85
|
489.70
|
Obs
|
(1.00, 1.20)
|
(30.80, 42.20)
|
(92.00, 126.80)
|
Theophylline
|
100 mg
|
Pred
|
0.75
|
2589.22
|
29614.81
|
Pred_V2
|
0.62
|
2372.22
|
19458.59
|
Pred_V3
|
0.62
|
1897.37
|
10003.06
|
Obs
|
(1.38, 1.82)
|
(1727.91, 2036.31)
|
(21499.55, 24439.65)
|
caffeine
|
100 mg
|
Pred
|
1.18
|
2540.84
|
13709.29
|
Pred_V2
|
1.25
|
1952.50
|
10269.04
|
Pred_V3
|
1.50
|
2114.02
|
12859.90
|
Obs
|
(0.33, 2.00)
|
(1598.00, 2280.00)
|
(10700.00, 24438.00)
|
Imipramine
|
50 mg
|
Pred
|
3.03
|
25.37
|
250.72
|
Pred_V2
|
3.13
|
28.18
|
300.21
|
Pred_V3
|
3.64
|
83.87
|
1082.01
|
Obs
|
(2.80, 3.80)
|
(20.90, 36.90)
|
NA
|
Desipramine
|
50 mg
|
Pred
|
5.42
|
13.56
|
264.97
|
Pred_V2
|
6.26
|
17.10
|
353.36
|
Pred_V3
|
6.25
|
50.66
|
1042.14
|
Obs
|
(2.00, 10.00)
|
(12.1, 20.1)
|
(211.60, 413.20)
|
Pred: Predicted drug PK parameters from the unchanged SimCYP drug template (except Fluoxetine). Pred_V2: Predicted drug PK parameters using SimCYP with input parameters (log Po:w, pKa ,B/P and Fu) from ADMET Predictor. Pred_V3: Predicted drug PK parameters using SimCYP with input parameters (log Po:w, pKa ,B/P, Fu, Peff, Vd, and CYP parameters) from ADMET Predictor. Obs: drug PK parameter reported by clinical research. For Fluoxetine especially, the SimCYP drug template is modified to enable the predicted profile fit the clinically reported curve. |
Evaluation of Inherent differences among software platforms. The predicted PK parameters of the 18 modified drug templates by replacing the ADME parameters with those predicted by ADMET predictor are listed in Table 2. The C-T profiles of those 18 drugs are shown in Fig. 3 (V2) and Fig. 4 (V3). In V2, most drugs exhibit satisfying prediction results. As is shown in Fig. 4, 14 out of 18 drugs have most part of their experimental data point lay within the predicted confidence interval. Only Triazolam, Atomoxetine, Simvastatin and Pravastatin have nearly or more than half of the data points exceed the confidence interval, showing poor prediction performance. In V3, it is demonstrated that Bupropion, Caffeine, and Phenobarbital show a very good overlay between the clinical report and predicted result from modified drug template, with the observed data laying within the confidence interval of predicted curve. As to Fluoxetine, Alprazolam, Quinidine, and Triazolam, although the predicted results do not show an excellent overlay with the experimental data, most of the clinical data points lays within the confidence interval of the prediction profiles. For Lorazepam, although the observed data all at or around the upper confidence interval of the predicted profile, the shape of the predict curve shares a high similarity with that of the observed PK profile. Unfortunately, the other drugs do not show very satisfying prediction results, using clinical data points as reference.
To quantitatively measure the deviation of predicted concentration profiles from the experimental data, the difference between observed and predicted values of evaluated by NRMSE (Table 3). The lower the NRMSE value is, the smaller the difference between the predicted and experimental concentration profile is, i.e., the better performance the created model for the drug is. The average NRMSE of V2 is 0.26, compared with the average value of 0.43 for V3, showing that V2 can introduce less prediction error when combining the two software platforms for prediction. For V2 especially, although Dextromethorphan possesses the NRMSE value as large as 0.45, this should be caused by the deviation of the curve from the first data point. All the rest data points are all very close to the predicted curve. 14 of 18 drugs have NRMSE values smaller than 0.4, and 7 of them are smaller than 0.2, showing satisfying prediction and collaboration quality of the two software. For V3, the top three drugs, Caffeine, Phenobarbital, and Bupropion, all have very small NRMSE values, which is consistent with the fact that the simulated C-T curves well overlaid with the experimental data points as shown in Fig. 3. Interestingly, the NRMSE values of Fluoxetine (0.41), Alprazolam (0.28), Quinidine (0.53), and Triazolam (0.29) are quite different, even though the simulated C-T curves of the four drugs are relatively satisfactory. Taken together, both the overlay of simulated C-T curves with the measured C-T data points and NRMSE should be used to evaluate the quality of the predicted ADME parameters by ADMET predictor. Overall, the predicted ADME parameters by ADMET Predictor can produce satisfactory C-T curves using SimCYP simulator for about half of the tested drugs.
Table 3
Calculated NRMSE between predicted results by modified drug template and experimental concentration profiles of drugs
Name
|
NRMSE V2
|
NRMSE V3
|
Alprazolam
|
0.26
|
0.28
|
Atomoxetine
|
0.35
|
0.40
|
Bufuralol
|
0.17
|
0.36
|
Bupropion
|
0.18
|
0.26
|
Caffeine
|
0.13
|
0.13
|
Desipramine
|
0.35
|
0.70
|
Dextromethorphan
|
0.45
|
0.93
|
Fluoxetine
|
0.10
|
0.41
|
Imipramine
|
0.21
|
0.51
|
Lorazepam
|
0.25
|
0.53
|
Mephenytoin
|
0.24
|
0.48
|
Midazolam
|
0.27
|
0.29
|
Phenobarbital
|
0.14
|
0.22
|
Pravastatin
|
0.42
|
0.53
|
Quinidine
|
0.08
|
0.53
|
Simvastatin
|
0.56
|
0.52
|
Theophylline
|
0.12
|
0.29
|
Triazolam
|
0.41
|
0.29
|
Predicted concentration profiles for the in silico PBPK models. The C-T profiles predicted by all three versions (Versions 1, 2, and 3) of PBPK models are shown in Fig. 5. The NRMSE value is also calculated to measure the difference between observed and predicted values of three versions respectively and summarized in Table 4. The table cell is marked with “*” if the NRMSE values of V1, V2, or V3 is lower than 0.2. In the following, we grouped all the 13 drug pairs / 26 drug pair sets into three groups according to their Tanimoto scores for the sake of discussion.
Table 4
Calculated NRMSE between predicted (three versions) and experimental concentration profiles of drugs in each drug pair set. The NRMSEs of the target and template drugs, which are adopted from Table 3, measure the quality of the ADME prediction using ADMET Predictor and/or the inherent difference between the two software. The Tanimoto scores in the last column come from Table 1.
Drug Group
|
Drug Pair Set
|
NRMSE (Different versions vs Obs)
|
Tanimoto score
|
V1
|
V2
|
V3
|
Group I
|
A-1
|
*0.14
|
*0.13
|
0.49
|
0.50
|
A-2
|
0.26
|
*0.19
|
0.50
|
0.50
|
B-1
|
0.44
|
0.49
|
0.49
|
0.52
|
B-2
|
0.67
|
0.49
|
*0.07
|
0.52
|
C-1
|
0.64
|
0.34
|
0.31
|
0.57
|
C-2
|
0.68
|
0.67
|
*0.13
|
0.57
|
D-1
|
*0.14
|
*0.16
|
0.48
|
0.63
|
D-2
|
0.61
|
*0.16
|
*0.19
|
0.63
|
E-1
|
0.22
|
0.32
|
0.35
|
0.65
|
E-2
|
0.43
|
0.56
|
0.35
|
0.65
|
F-1
|
0.24
|
*0.19
|
0.33
|
0.69
|
F-2
|
0.88
|
0.28
|
0.27
|
0.69
|
Group II
|
G-1
|
0.94
|
0.94
|
*0.04
|
0.74
|
G-2
|
0.58
|
0.56
|
*0.14
|
0.74
|
H-1
|
0.56
|
0.56
|
0.52
|
0.78
|
H-2
|
0.44
|
0.08
|
*0.02
|
0.78
|
I-1
|
0.49
|
0.36
|
*0.04
|
0.82
|
I-2
|
0.34
|
0.38
|
0.21
|
0.82
|
J-1
|
0.43
|
0.57
|
*0.14
|
0.84
|
J-2
|
0.45
|
*0.13
|
*0.12
|
0.84
|
K-1
|
0.69
|
0.67
|
*0.06
|
0.88
|
K-2
|
0.20
|
*0.15
|
0.38
|
0.88
|
Group III
|
L-1
|
0.34
|
*0.06
|
*0.12
|
0.93
|
L-2
|
0.22
|
*0.19
|
*0.17
|
0.93
|
M-1
|
*0.08
|
*0.10
|
0.66
|
0.95
|
M-2
|
*0.13
|
*0.15
|
0.40
|
0.95
|
Group I (TS ≤ 0.7). Six drug pairs, A-F, belong to this group. According to Table 4, the performance of the three protocols does not show an obvious pattern for Group I. The V1, V2 and V3 have two (A-1 and D-1), five (A-1, A-2, D-1, D-2 and F-1) and three (B-2, C-2 and D-2) pair sets in “*” table cells, respectively. Most of those pair sets also exhibit a good overlay between experimental data points and prediction curves as shown in Fig. 5, indicating the collaboration between SimCYP and ADMET Predictor is good. For the other groups from A-1 to F-2, all the three protocols have NRMSE values larger than 0.2 and the simulated C-T curves do not overlay with the experimental data points well. Interestingly, for D-2 drug pair set, though the NRMSE of the V2 model is the lowest, the predicted C-T curve by the V3 model has a better shape fitting the observed data as shown in Fig. 5. This phenomenon is caused by the deviation of the first data point from the predicted curve of V3, which caused its NRMSE is larger than that of V2. When this outlier is eliminated and the NRMSE value is recalculated, V3 become the best for this pair set (NRMSE are now 0.57, 0.16 and 0.06 for the V1, V2 and V3 protocols, respectively).
Group II (0.7 < TS ≤ 0.9). This group contains 5 drug pairs, G-K. As shown in Table 4, most drug pair sets have at least one version with NRMSE value lower than 0.2, except H-1 and I-2. It is worthy to mention that the NRMSE value of I-2 is only 0.21 and the predicted C-T curve exhibits a good consistency with experimental data (Fig. 5). The failure of H-1 model is likely caused by using problematic ADME parameters predicted by ADMET Predictor for the target drug. The “collaboration” between the two software should not be a problem for this drug pair since the NRMSE values of H-2 are very low for both the V2 and V3 models, which are 0.08 and 0.02 for the two models correspondingly. As shown in Table 4, the V3 version models apparently outperform the V1 and V2 models for most drug pair sets, as 7 out of 10 V3 models have NRMSE values lower than 0.2, while none of V1 models and 2 V2 models have their NRMSE values lower than 0.2. Interestingly, for drug pair set J-2, the V2 and V3 models have highly similar performance with good prediction result as shown in Fig. 5; however, for K-2, all of the three model versions do not exhibit satisfying prediction (Fig. 5), even though the NRMSE values of the V1 and V2 models are equal to or lower than the cutoff.
Group III (TS > 0.9). This group contains 2 drug pairs, L and M. As shown in Table 4, most models have satisfactory NRMSE values. For L-1 and L-2 drug pair sets, the predicted profiles of the V2 and V3 models are very close to the clinical data points. Interestingly, for M-1 and M-2 drug pair sets, the performance of the V3 models is very poor. Drug pair M has the structural similarity with the Taminoto score of 0.95, interestingly, the V3 models perform poorly while the V1 and V2 models have not only satisfactory NRMSE values, but also very well-overlayed C-T curves with measured data points. This phenomenon may be explained by the prediction error by ADMET Predictor and error caused by the inherent difference between the two software can be compensated by the small difference of the ADME parameters between the template and target drugs. Indeed, the NRMSE values of the two drugs in drug pair M, 0.51 and 0.70, are very large (Table 4).