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. 2025 Mar 27;68(7):7737–7750. doi: 10.1021/acs.jmedchem.5c00340

Application of Machine Learning and Mechanistic Modeling to Predict Intravenous Pharmacokinetic Profiles in Humans

Xuelian Jia †,‡, Donato Teutonico §, Saroj Dhakal ∥, Yorgos M Psarellis ∥, Alexandra Abos ⊥, Hao Zhu †,‡, Panteleimon D Mavroudis ∥,*, Nikhil Pillai ∥,*
PMCID: PMC11998014  PMID: 40146185

Abstract

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Accurate prediction of new compounds’ pharmacokinetic (PK) profile in humans is crucial for drug discovery. Traditional methods, including allometric scaling and mechanistic modeling, rely on parameters from in vitro or in vivo testing, which are labor-intensive and involve ethical concerns. This study leverages machine learning (ML) to overcome these limitations by developing data-driven models. We compiled a large data set of small molecules’ physicochemical and PK properties from public sources and digitized human plasma concentration–time profiles for approximately 800 compounds from the literature. We introduced a hybrid modeling framework that combines ML with physiologically based pharmacokinetic modeling and a hierarchical ML framework that employs two steps of learning to directly estimate PK profiles. Tested on 106 drugs, these frameworks demonstrated prediction accuracies within a 2-fold and 5-fold error for 40–60% and 80%–90% of compounds, respectively, in both AUC and Cmax. Proposed approaches could enhance early molecular screening and design, advancing drug discovery capabilities.

1. Introduction

Drug discovery is a complex and time-intensive process that encompasses several critical stages, including target identification, lead compound discovery and optimization, and the selection of drug candidates for advancement into clinical trials.1−3 Prediction of a new molecule’s exposure in humans’ plasma is a critical first step toward understanding its efficacy and toxicity profile which is crucial for evaluating its potential as a candidate for further development.2,4,5 Advancing a new molecule to later stages of drug development before robust estimation of human exposure can lead to late-stage failures with substantial financial losses.3 Current approaches for predicting in vivo human PK profiles primarily rely on mathematical models that build upon the classical foundations of pharmacology such as in vitro/in vivo extrapolation, noncompartmental analysis (NCA), compartmental PK modeling, and physiological based PK (PBPK) modeling that involves a granular representation of human physiology.4 PBPK model parameters are generally divided into (i) system-specific parameters that represent physiological properties of the body (e.g., blood flows) and are usually based on the organism of interest and (ii) drug-specific parameters that are related to characteristics of the drug such as fraction unbound (Fu), pKa acidic/basic, etc. Traditionally, these parameters are experimentally determined from in vitro assays or from in vivo animal PK studies and then scaled to humans. However, these approaches are time-consuming, labor intensive, and costly, especially when screening a large number of preclinical compounds.6 In recent years, significant efforts have been made to enhance R&D productivity in the pharmaceutical industry, and computational modeling is now employed throughout drug discovery to streamline processes, lower experimental costs, and reduce animal use.6−12

Public databases like ChEMBL and PubChem provide extensive data on drug properties and activities.13,14 With large data sets, machine learning (ML) algorithms, which can adapt and learn patterns, have become an increasingly powerful tool in drug discovery.1,15,16 In particular, it is very common to predict the property/activity of a molecule by learning the quantitative structure–activity relationship (QSAR).17 With the development of advanced algorithms and chemical descriptors, QSAR models have become an efficient approach for rapidly screening a large number of compounds and prioritizing those with desirable properties and activities. The application of QSAR is particularly appealing in the initial stages of drug development, where mechanistic knowledge of how a new molecule distributes and/or is metabolized in the body and mediates its pharmacological effects is limited. Several QSAR models have been developed to predict PK parameters such as the area under the concentration curve (AUC), maximum concentration (Cmax), Fu, clearance (CL), and steady-state volume of distribution (VDss).18−21 Additional studies have also incorporated ML and mechanistic models to predict PK profiles in rats4,22−26 and humans.27,28

Building upon the previous efforts of our group, in this study, we developed a hybrid and a hierarchical ML framework to predict human PK profiles from molecular structures. Both frameworks follow a two-step modeling process. The hybrid framework combines ML and PBPK modeling, where ML models are first trained to predict physicochemical (PC) and PK parameters from chemical structures. These parameters are then used as inputs for PBPK simulations to predict human PK profiles. Hierarchical ML organizes tasks in a hierarchical manner to capture complex relationships.29 Our hierarchical ML framework also starts with training QSAR models to predict PK parameters from chemical structures, as in the first step of the hybrid framework. In the second step, these predicted parameters are used as features in a second ML model to predict the PK profiles. To achieve this, we curated publicly available data on human PK curves and PC/PK parameters, digitizing PK curves for approximately 800 drugs administered intravenously (IV). This represents the largest known curated database of human IV PK profiles for modeling purposes to date. The goal of this study is to assess whether using ML-derived parameters with PBPK simulations or standalone ML modeling can generate reasonable human exposure predictions and demonstrate the feasibility of conducting these predictions for new drug molecules in the initial stages of drug discovery (Figure 1).

Figure 1.

Figure 1

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Workflow of the study. Human PK profiles after IV administration were collected and digitized from the database curated by Lombardo et al. Various PC and PK parameters were compiled from multiple data sources, as well. Predictive QSAR models for these PC and PK parameters were developed after a comprehensive search for optimal combinations of different ML algorithms and chemical descriptors. For new compounds lacking experimental parameter values, we can input the SMILES string to obtain the predicted parameters. These predictions can be used as the input for PBPK simulation with IV dosing of a 1 mg/kg dose, representing the hybrid modeling framework. Alternatively, the PC and PK parameters can be used to train another ML model to directly predict concentrations at different time points with IV dosing of 1 mg/kg dose, representing the hierarchical ML modeling framework. PBPK sketch was adapted with permission from ref. (4) © 2023 Mavroudis, Teutonico, Abos and Pillai.

2. Results and Discussion

2.1. PK Profiles Overview

After digitization of PK curves from the literature, we obtained PK profiles for approximately 800 compounds administered IV. After curation, we obtained PK profiles for 773 compounds (Figure 2). Among these, 106 compounds that had all of the observed PC/PK parameter values were used as a test set in both the hybrid and hierarchical ML frameworks for PK profile prediction. To ensure an unbiased evaluation, these 106 compounds were excluded from the training sets used to develop the PC/PK QSAR models. The remaining 667 compounds served as the training set in the hierarchical ML framework. As shown in Table 1, the training set comprises 8715 concentration values for 667 compounds at various time points, while the test set includes 1351 concentration values for 106 compounds.

Figure 2.

Figure 2

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Overlayed IV PK profiles in training set (A) and test set (B). IV PK profiles were obtained from digitization of literature mined PK curves. PK profiles were normalized to 1 mg/kg dose.

Table 1. Modeling Set Information for PC/PK Parameters and Concentrations in PK Profiles.

Parameter Training set size Test set size Unit Transformation
Fu 4042 633   Log10
CL 1287 177 L/h/kg Log10
VDss 1287 177 L/kg Log10
pKa acidic 5306 776    
pKa basic 5687 815    
Concentration 8715 data points for 667 compounds 1351 data points for 106 compounds ng/mL Log10
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2.2. PC/PK Parameter Data Sets Overview

Modeling sets for PC and PK parameters were collected from multiple sources and varied in size. The number of compounds in the training and test sets for each PC and PK parameter is listed in Table 1. The distributions of original PK parameter values were skewed, especially for CL, and VDss (Figure S1A-C). Therefore, we transformed the original values into their base-10 logarithms to get closer to normal distribution for modeling purposes. The distributions of the parameter values in the training and test sets are shown in Figure 3A–E. For all PC and PK parameters, the distribution of values in the test set is within the range of the training sets.

Figure 3.

Figure 3

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Data distribution of training and test sets for PC/PK parameters and PK profiles. (A) Fu values in base-10 logarithm (lg), (B) CL values in base-10 logarithm, (C) VDss values in base-10 logarithm, (D) pKa acidic, (E) pKa basic, and (F) concentration values in base-10 logarithm at different time points in PK profiles for compounds in the training and test sets.

In this study, we used computational pKa and logP values to enable efficient data integration and evaluation of the modeling frameworks. While experimental pKa acidic/basic and logP data sets are available in public databases and literature, their coverage is limited. For example, the pKa data set from DataWarrior includes 3244 pKa acidic values and 3668 pKa basic values, and a logP data set curated by Mansouri et al. comprises 4123 compounds.30,31 However, among the 773 drug compounds with curated human PK profiles, only 29 have either acidic or basic pKa values, and 83 have experimental logP values. This limited overlap in drug compounds poses challenges for establishing an appropriate chemical space for QSAR modeling and may lead to inaccuracies in predicting these values for drug PK profile modeling. In contrast, the ChEMBL database contains computational pKa values for a broader range of drugs and drug-like compounds, with ∼570 compounds overlapping with the 773 drugs that have human PK profiles. For compounds in the ChEMBL database with available experimental pKa values, we examined their correlation with computational pKa values, which demonstrated reasonable accuracy (Figure S1D-E). Moreover, replacing the computational logP values with experimental logP values for the 83 overlapping compounds did not result in an improvement in PK profile prediction performance (Table S2). This outcome may be attributed to the variability in experimental logP values, which are often measured under different conditions and setups. Given that many studies on PK profile modeling25,32 and pKa prediction33,34 rely on computationally derived logP and pKa values, we also opted to use computationally derived values in this study. Moving forward, as more freely available experimental pKa and logP data for drugs are published, these data sets can be incorporated into our modeling framework to enhance predictive accuracy and further validate our models.

2.3. Predictive QSAR Modeling for PC/PK Parameters

For each PC/PK parameter, we developed 15 individual QSAR models using three types of ML algorithms and five types of descriptors. Each model was trained using a 10-fold cross-validation process, and its performance was tested on a withheld test set accounting for around 12% of the entire data set. We further developed the consensus model by averaging predictions from individual QSAR models. The heatmap in Figure 4 displays the R2 values for all models on the test set. The best models, which showed the highest R2 and lowest GMFE in predictions, are detailed in Table 2. The scatter plots in Figure 5 illustrate the correlations between observed and predicted parameter values from the best models. For Fu, the best model is the SVM algorithm informed with merged descriptors, which achieved a GMFE of 2-fold and predicted 60% of the test set compounds within a 2-fold error. For CL and VDss, the consensus model was superior, which achieved GMFE of 2-fold and 1.88-fold, respectively, with 64 and 62% of compounds predicted within a 2-fold error. The best model for pKa acidic is the XGBoost approach trained with RDKit descriptors, which achieved GMFE of 1.1-fold and predicted 98% of the test set compounds within a 2-fold error. The consensus model also proved to be the best for pKa basic, with a GMFE of 1.26-fold and 91% of compounds predicted within a 2-fold error.

Figure 4.

Figure 4

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Performance of combinatory QSAR models for PC/PK parameters. The R2 values for the test set of each parameter are shown here.

Table 2. Performance of the Best Models for PC/PK Parameters and Concentrations in PK Profiles.

Parameter Algorithm Descriptor R2 MAE RMSE GMFEa <2-folda
Fu SVM Merged 0.69 0.30 0.41 2.01 60%
CL Consensus Consensus 0.48 0.31 0.42 2.00 64%
VDss Consensus Consensus 0.60 0.28 0.35 1.88 62%
pKa acidic XGBoost RDKit 0.94 0.61 1.05 1.10 98%
pKa basic Consensus Consensus 0.91 0.67 0.98 1.28 91%
Concentration in PK profiles RF Fu, CL, VDss, pKa acidic, pKa basic, time, infusion time 0.59 0.37 0.49 2.33 55%
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a

Calculated after converting predictions to the original scale, <2-fold: percentage of compounds in test set with less than 2-fold prediction error.

Figure 5.

Figure 5

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Scatter plots of observed and predicted values from the best model. (A) Fu values in base-10 logarithms (lg), (B) CL values in base-10 logarithms, (C) VDss values in base-10 logarithms, (D) pKa acidic, (E) pKa basic, and (F) concentration values in base-10 logarithms at different time points in PK profiles for compounds in the training and test sets.

As shown in Figure 4, QSAR models trained using molecular descriptors, including RDKit, Mordred, and merged descriptors, generally outperformed those trained with fingerprints like MACCS and FCFP6. Consensus predictions generated comparable or even better results than the individual models. The advantage of the consensus method is that it can mitigate the weaknesses or biases of single models and enhance predictions across a broader chemical diversity.17,35,36 pKa acidic and basic parameters, which measure the acidity and basicity of a compound in water solution, can be accurately predicted because of simple mechanisms. However, predicting Fu, CL, and VDss remains challenging due to the complex interactions with proteins, involvement in various biological processes, and significant interindividual variability in the data. Despite these challenges, our models achieved an average 2-fold error, comparable to or better than other published models for the same parameters.19−21,37,38 This performance meets common acceptance limits, such as the “2-fold” criterion.16,39

2.4. Hybrid Modeling Results

The physiological parametrization is already available in the PBPK software used in this modeling exercise (i.e., PK-Sim) while the drug-specific properties need to be provided typically by the user for each individual drug. In the hybrid modeling framework, QSAR predicted PC/PK parameters were used as inputs for PBPK simulations. The required input parameters are detailed in Table S3. For the 106 test set compounds that have all observed PC/PK parameter values and observed PK profiles, control PBPK simulations were also conducted using the observed parameters as input. The resulting simulations were compared to the observed human PK profiles, and AUC and Cmax fold errors were calculated. We initially utilized the PK-Sim standard distribution model. As shown in Figure 6A, control PBPK simulations achieved more compounds within a 2-fold error than did the hybrid approach. However, the hybrid approach demonstrated comparable or even better performance in the higher fold error range (less than 3-fold and less than 5-fold). Figure 7 presents several examples of predicted PK profiles by the hybrid approach and their comparison with control PBPK simulations using the observed parameters. The compounds showing well-predicted PK profiles in both the hybrid approach and control PBPK simulations (Figure 7A) have accurate predictions of PC/PK parameters (<2-fold). Compounds with poorly predicted PK profiles compared to the control typically have inaccurate predictions in Fu and CL. For example, compound ID 240 exhibited a 41-fold error in CL prediction (observed: 5.016, predicted: 0.121 L/h/kg), which likely caused a much higher concentration than the control simulation. Similarly, compound ID 484, despite good predictions for pKa and Fu, had a 2.46-fold error in CL prediction (observed: 0.84, predicted: 0.34 L/h/kg), leading to a higher AUC of predicted PK profile using the hybrid approach. Nonetheless, there are cases where the hybrid approach outperforms the control PBPK simulations. For instance, compounds with IDs 789 and 1325 showed slightly higher CL predictions than observed but resulted in more accurate PK profile predictions. This is likely because ML models can mitigate errors that may occur due to variability in either recording or performing the experiment. QSAR predicted and observed PC/PK parameter values for the 106 test set compounds are provided in Supporting Information, Data sets. Predicted PK curves for these compounds are listed in Figures S2-3.

Figure 6.

Figure 6

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Hybrid modeling performance in predicting PK profiles of 106 test set compounds. Bar plots show the percentage of compounds in the test set that have <2-fold, 2- to 3-fold, 3- to 5-fold, and >5-fold errors in AUC and Cmax using simulations from (A) PK-Sim standard (CtrlPBPK_s and hybrid_s) distribution model or (B) the mean of simulations (CtrlPBPK_m and hybrid_m) from five different distribution models. Box plots show the distribution of fold errors in AUC and Cmax (observed/predicted) using (C) mean of control PBPK simulations (CtrlPBPK_m) or (D) mean of hybrid simulations (hybrid_m) from five different distribution models.

Figure 7.

Figure 7

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Example of predicted PK profiles from the hybrid modeling. hybrid_s means PK profiles from PBPK simulation using the QSAR predicted parameters (with PK-Sim distribution model). CtrlPBPK_s means PK profiles from control PBPK simulation using the observed parameters (with PK-Sim distribution model). (A) Four compounds represent well predicted PK profiles from both hybrid_s and CtrlPBPK_s. (B) Four compounds represent well predicted PK profiles by CtrlPBPK_s but not hybrid_s. (C) Four compounds represent well predicted PK profiles by hybrid_s but not CtrlPBPK_s. The identifier shown here is same as that in the Lombardo data set.

We also explored the influence of different distribution models, including the PK-Sim standard,40 Berezhkovskiy,41 Poulin and Theil,42 Rodgers et al.,43 and Schmidt,44 on prediction performance. For the 106 test set compounds, the range of simulations spanned by different distribution models is provided in Figures S4-5. In some cases, such as those with compound IDs 31 and 72, all models resulted in similar exposure predictions. However, for compounds such as IDs 315 and 461, the PK profiles showed significant variability across different distribution models. This is due to the intrinsic way of how the distribution models were parametrized. For instance, the Rodgers et al.,43 and the Schmidt44 distribution models take into account electrostatic interactions driven by the drug pKa and the physiological pH which is not the case for other distribution models.45 For this reason, the same PC parameters of a specific drug may result in different predictions depending on the distribution model considered. For new compounds without a clear ADME mechanism, it is challenging to determine which distribution model is most suitable for each compound. Therefore, we conducted PBPK simulations using different distribution models and averaged the results. As shown in Figure 6, the mean simulations generally performed better than, for instance, those using only the PK-Sim standard distribution model. The hybrid approach with mean simulations predicted 43% of the AUC and 39% of the Cmax within a 2-fold error, and 80% of the AUC and 82% of the Cmax within a 5-fold error.

2.5. Hierarchical ML Modeling Results

The PC/PK parameters and administration route information for 667 compounds were used to train ML models to predict the concentrations of a compound at different time points (Table 1). The training was performed using various combinations of PC/PK parameters as features and two ML algorithms (performance details are provided in Table S4). The best-performing model was an RF algorithm, trained with pKa acidic, pKa basic, Fu, CL, VDss, and infusion time (Table 2). This model achieved an R2 of 0.59 and RMSE of 0.49 (ng/mL) on the 106 compounds test set. The GMFE for predicted concentration values was 2.33, with 55% of the concentrations falling within a 2-fold error. The concentrations at different time points for the same compounds were combined to calculate the AUC and Cmax values of the curve. Figure 8 shows the distribution and percentage of fold errors in AUC and Cmax values compared to the observed PK profiles for the test set compounds. 60% of the AUC and 59% of the Cmax were within a 2-fold error, and 92% of the AUC and 88% of the Cmax were within a 5-fold error. The mean fold errors for AUC and Cmax were 2.3 and 2.75, respectively. The predicted PK profiles, from both the hybrid simulation and the hierarchical ML framework, were overlaid with the observed PK profiles (Figures S4,5). Both methods provided reasonable predictions of the PK profiles, with the hierarchical ML approach showing fewer outliers and slightly better performance than the hybrid approach (Figures 6, 8, and Table S5). Specifically, the hierarchical ML framework achieved lower GMFE for PK profile derived AUC and Cmax, as well as a higher proportion of compounds with less than 2-, 3-,5-fold errors in AUC and Cmax compared to the hybrid approach, indicating improved predictive reliability. Further analysis of feature importance revealed that time and CL had the highest importance in predicting concentrations. VDss also demonstrated relatively high importance, while pKa acidic/basic, infusion time, and Fu exhibited lower importance scores (Table S6).

Figure 8.

Figure 8

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Hierarchical ML modeling performance in predicting PK profiles of 106 test set compounds. (A) Box plot shows the distribution of fold errors in AUC and Cmax. (Observed/predicted) (B) bar plot shows the percentage of compounds in the test set that have <2-fold, 2- to 3-fold, 3- to 5-fold, and >5-fold errors in AUC and Cmax.

In Figure 9, we present examples of predicted PK profiles from hierarchical ML modeling. Some compounds, such as IDs 219 and 315, which displayed poor predictions in both the hybrid approach and control PBPK simulations, were accurately captured in the hierarchical ML approach (Figures 9B, S2). This may be due to missing mechanisms for these compounds (such as transporters, etc.) in the general PBPK model utilized for this study and/or not accounting for variability in the populations studied across different literature sources (e.g., elderly, young, women, men) in the PBPK model. Effective ML models can generalize better across various drugs and populations if trained on sufficiently diverse and comprehensive data sets.16 This ability to generalize makes them more robust in predicting drug behavior in populations not previously studied explicitly. While PBPK models may need specific adjustments for new populations/mechanisms to capture the biological variability, the hierarchical ML method, based solely on chemical structures, is particularly useful for the rapid screening of a large number of compounds, even before their chemical synthesis.46 The hybrid approach incorporates PBPK simulation that focuses on the chemical’s interaction with biological systems, which can provide interpretable insights into mechanisms determining the observed PK profiles. Both methods have distinct advantages and can be effectively combined in practical applications.

Figure 9.

Figure 9

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Example of the predicted PK profiles from hierarchical ML modeling. (A) Four compounds represent well predicted PK profiles by both the hybrid and hierarchical ML approach. (B) Four compounds represent well predicted PK profiles by hierarchical ML but not hybrid approaches. (C) Four compounds represent well predicted PK profiles by hybrid approaches but not hierarchical ML approaches. (D) Four compounds represent badly predicted PK profiles by both the hybrid and hierarchical ML approaches. The red line represents the hierarchical ML predicted PK profile, purple dots are observed PK profiles data, the blue line represents the mean simulation from hybrid approach, and shaded area represents the span of simulations from five distribution models. The identifier shown here is same as that in the Lombardo data set.

Since the hierarchical ML model was developed based on chemical structures, predictions for chemicals with structures significantly different from those in the training set compounds may not be reliable. We further explored whether implementing an applicability domain (AD) could improve the performance of the hierarchical ML model. A common method to define a QSAR model’s AD involves predicting only compounds that meet a certain similarity threshold to their nearest neighbor (NN) in the training set.47,48 For each of the 106 test set compounds, we calculated the Jaccard and Euclidean distances to the training sets for predicting different PC/PK parameters. The NN was defined as the compound with the shortest distance from the query compound. The distribution of test set compound distances to the NN across different training sets is detailed in Figure S6. We further attempted to predict compounds within AD thresholds using Jaccard similarity values of 0.4 and 0.5, based on FCFP6 descriptors. Compounds were considered in-AD if their similarity values to those of NN exceeded the AD threshold across all training sets. However, we observed no improvement in PK profile prediction performance for the in-AD compounds (Figure S7). Implementing AD for the developed model is challenging because the model involves two steps of learning and the relationship between structures and PK profiles is not straightforward.

The limitation of the current hierarchical ML framework lies in treating each time point independently without incorporating temporal relationships between measurements. This approach may result in disjointed predictions, as observed for compounds such as IDs 789, 1167, and 1210 (Figure S5), where the predicted concentration at certain time points is underestimated and appears lower than at subsequent time points. Such discrepancies may also arise from digitization errors, where the ordering of concentrations for closely spaced time points is inadvertently reversed, or from natural fluctuations in the actual PK profiles.

2.6. External Validation Using Recently Approved Drugs

To further validate the predictive performance of both the hybrid and hierarchical ML modeling approaches, we selected seven drugs recently approved by the FDA (from 2019 to 2023) and predicted their IV PK profiles using the developed modeling frameworks. The observed concentration versus time profiles were digitized from published literature.49−55 The digitized PK profiles were normalized to a 1 mg/kg dose for comparison with the predictions. As shown in Figure 10, the hierarchical ML model reasonably predicted most of the compounds, with all the compounds predicted within a 4-fold error and four compounds within a 2-fold error in AUC and Cmax. The performance of the hybrid approach was less accurate, especially for Abrocitinib and Gadopiclenol. The CL for Abrocitinib was underestimated by our QSAR model (observed: 0.722, predicted: 0.240 L/h/kg), resulting in a higher overall concentration in both modeling frameworks. The CL for gadopiclenol was overestimated by the QSAR model (observed: 0.079, predicted: 0.243 L/h/kg). This prediction error resulted in a lower concentration curve in the hierarchical ML model predictions but not in the hybrid model predictions. One probable reason is that we were using a base full PBPK model to generate simulations without accounting for active transporters and other metabolic information. The accuracy of PK predictions could be further improved with more high-quality data to enhance the QSAR model for in vivo PK parameters, especially CL.

Figure 10.

Figure 10

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PK profiles predictions of recently approved drugs.

2.7. Comparison with Other PK Prediction Models

In this study, we curated a large data set of human in vivo concentration–time profiles (∼800 compounds) along with PC/PK parameters from public resources to enable PK profile modeling across diverse drug compounds. The prediction of PK profiles by combining ML and mechanistic modeling has been explored in a few recent studies,4,25−28 and our hybrid modeling framework has demonstrated a high-throughput approach with comparable performance. For instance, Geci et al. developed a hybrid modeling approach that integrated in silico predictions of PK parameters from existing tools with PBPK simulations, achieving 71 and 78% of AUC and Cmax predictions, respectively, within a 5-fold error.27 Gruber et al. developed a model that combined deep learning with a surrogate PBPK model to predict human PK parameters from chemical structures, while providing concentration–time profiles for nine examples.28 In another modeling approach called DeepCt, rat PK profiles were predicted using a deep learning framework that incorporates compartmental PK models.26 For the hierarchical ML modeling framework, conceptually similar approaches have been reported in the literature for predicting rat PK profiles.22,24,25 To the best of our knowledge, there are currently no published pure ML frameworks specifically designed for predicting human PK profiles across a wide range of drugs.

Regarding the hierarchical ML modeling framework, although we utilized conventional algorithms, our approach introduced a novel and practical framework for predicting concentration–time PK profiles in humans from chemical structures. In the second step of the hierarchical ML framework, we trained a random forest model that predicts concentrations at each time point independently. Although this approach does not explicitly account for temporal dependencies, it offers simplicity and robustness for irregularly sampled data. Time-series deep learning models, such as recurrent neural networks (RNNs) and neural ordinary differential equations (Neural-ODEs), can take time–concentration sequences as input and generate smooth, continuous predictions.56 However, RNNs often assume evenly sampled data, which is uncommon in PK studies, as drug dosing schedules and PK measurements vary significantly across clinical studies for different drugs.57 Neural-ODEs, which are neural networks that model the evolution of hidden states continuously using ODEs, can handle unevenly sampled data points.58,59 However, like other deep learning approaches, both Neural-ODEs and RNNs tend to be computationally intensive, complex to implement, and susceptible to overfitting, particularly when sample sizes are small. Our study lays the groundwork for ML modeling and performance evaluation. In the future, with the collection and curation of more comprehensive and suitable PK profiles, it will become feasible to more effectively leverage advanced deep learning techniques such as RNNs and Neural-ODEs, to further enhance predictive accuracy and model performance.

3. Conclusions

In this study, we developed a hybrid modeling framework that integrates ML with mechanistic modeling, alongside a hierarchical ML modeling framework that involves two step learning to predict human PK profiles by utilizing chemical structures. Both frameworks achieve reasonable exposure predictions for most of the drug compounds in the test data set, with the hierarchical ML modeling framework performing better than the hybrid approach. The hierarchical ML model, trained on diverse and comprehensive data, generalizes well across different drugs. Our work also highlights the benefits of considering multiple distribution models in the hybrid approach, which provides variability in addition to a single PK profile estimate. This study utilizes publicly available human PK studies for a large number of diverse drugs to develop novel frameworks for predicting human PK profiles. With the ML models presented here as a starting point, we expect that more advanced ML algorithms can push the predictive performance even higher. For example, scientific ML approaches enable the fusion of different information sources for better predictive performance or system identification from real-world data (which could in this case lift the dose-linearity assumption).60,61 This effort aims to enable earlier PK profile prediction in the drug development process and ultimately assist in prioritizing compounds for future evaluation.

4. Experimental Section

4.1. Human PK Profiles Data

The database curated by Lombardo et al. contains PK parameters for 1352 drug compounds administered IV, which include plasma protein binding (PPB), in vivo CL, and VDss.62 Most of the corresponding literature provides concentration–time plots for the PK studies. After retrieving the available literature, concentration–time profiles were digitized from the PK curves using a digitizer tool developed by Delineate Inc. (https://delineate.pro/). This digitizer, powered by large language modeling (LLM),63 can automatically identify axes, extract time and concentration data for each point, and collect dose and unit information, ensuring efficient data extraction.

Among the multiple clinical studies, data measured in healthy adult humans after a single-dose IV administration were selected. Studies involving coadministration and premedication with other drugs were removed. The autodigitized PK dynamics data were manually checked to correct digitization errors (e.g., missing the first few data points, axis alignment errors, etc.) as well as errors in dose, time, and concentration. Further preprocessing of the data involved standardizing the reported human PK data by converting doses and concentration values into consistent units, using a standard body weight of 70 kg and a corresponding body surface area of 1.73 m2.62 For compounds tested at multiple doses, data from doses close to 1 mg/kg were selected. To facilitate comparison across compounds and align with modeling assumptions, dose-linearity was assumed for all compounds in the data set, and all PK profiles were normalized to a 1 mg/kg dose. Additionally, to ensure data consistency, PK curves for all compounds were overlaid, and two outliers with exceptionally high concentrations (ID 41: alfentanil64 and ID 1217: thiopentone)65 were removed.

4.2. PC/PK Parameter Data Sets and Curation

The minimal input properties for small molecule drugs needed for PBPK modeling include CL, Fu, molecular weight (MW), lipophilicity (e.g., logP), pKa acidic, pKa basic, and the number of halogens. To increase the modeling set size of Lombardo et al., we further collected CL and VDss values from the eDrug3D database.66 Compounds in eDrug3D which were already in the Lombardo et al. paper were removed, and the values from the Lombardo publication were kept. Fu values were collected from two publicly available data sets: one curated by Watanabe et al.38 and another from the OPERA modeling suite.31 The pKa acidic and pKa basic data sets were downloaded from the ChEMBL database.14 The pKa acidic and pKa basic values in ChEMBL were calculated by using the ChemAxon software (http://www.chemaxon.com).

Chemical structures were represented using SMILES67 that were retrieved from PubChem web site.13 Before QSAR modeling, chemical structures were curated and standardized to enable rigorous model development. In the curation process, salts were stripped from the molecules, duplicates were removed, and SMILES strings were converted into their canonical forms and further standardized by using the MolVS package. The corrected SMILES strings were then used to calculate the MW, logP, and number of halogens using the RDkit cheminformatics package version 2024.03.3 (https://www.rdkit.org). In this study, we focused on the small molecule drugs, so the compounds with an MW > 900 Da were excluded.

4.3. Chemical Descriptors and ML Algorithms for QSAR Modeling

Five types of descriptors, including chemical fingerprints and molecular descriptors, were used in this study. Functional connectivity fingerprints with a diameter of 6 (FCFP6), consisting of 1024 circular fingerprints, have been used successfully in similarity search and QSAR modeling.68 The Molecular ACCess System (MACCS) keys, consisting of 166 substructure fingerprints, were also employed.69 Both types of fingerprints were calculated using the RDKit package. Additionally, 208 RDKit molecular descriptors, including topological, compositional, and electrotopological state descriptors, were also calculated using the RDKit package. Furthermore, a total of 1613 two-dimensional descriptors were calculated using the Python package Mordred.70 Feature selection was conducted on the training set to remove descriptors with missing values, those exhibiting low variance (variance <0.2), and one from any pair of descriptors that were highly correlated with each other (Pearson correlation >0.85). The number of selected Mordred descriptors was around 190 for different training sets. We also explored merging the MACCS, RDKit, and all the Mordred descriptors to take advantage of the different chemical representations. To prevent overfitting, the number of descriptors was reduced by removing low variance and correlated descriptors. The number of selected merged descriptors was around 270 for different data sets. All the molecular descriptor values were standardized for compounds in each training set before model development.

Three types of ML algorithms were used in this study: random forest (RF), support vector machine (SVM), and extreme gradient boosting (XGBoost). RF is an ensemble algorithm that constructs many randomized decision trees and outputs the mean prediction of the forest trees to improve the prediction accuracy and avoid overfitting.71 XGBoost is also an ensemble approach that iteratively trains an ensemble of shallow decision trees, with each iteration using the error residuals of the previous model to fit the next model.72 The SVM regression model aims to find a function of descriptors-activity space that has a limited deviation (epsilon) from the actual activity value for all the training data, and at the same time is as flat as possible to avoid overfitting.73,74 Regression QSAR models for each parameter endpoint were developed using the combination of one type of descriptor (FCFP6, MACCS, RDKit, Modred, Merged) and ML algorithm (RF, SVM, XGBoost) and thus resulting in 15 models for each individual parameter. The consensus QSAR model, which was generated by averaging predictions from individual models, was also used in this study.17,35,36

The curated data sets for each parameter (modeling set) were split into a training set with approximately 88% of the data and a test set with the remaining 12% of the data. To prevent potential biases in model evaluation, we removed compounds from the training set that share identical descriptors in any of the descriptor sets with those in the test set. The training set was used to train QSAR models using the standard 10-fold cross validation (10fcv), while the test set was reserved for the final evaluation. In the 10fcv procedure, the training set was split into 10-fold, with 9-fold used to train the model and the remaining fold used to evaluate the model. This process was repeated 10 times, such that each fold served as the test set once. Hyperparameters for building the model (e.g., tree depth in RF or XGBoost, kernel function for SVM) were tuned using GridSearchCV using metrics including R(2) and fold error. Detailed information about the hyperparameters is presented in Table S1 and can be found in a previous study.75

4.4. PBPK Simulation

In the hybrid modeling framework, PC/PK parameter values predicted by the QSAR models were used as inputs to the PBPK model to simulate concentration–time profiles (Figure 1). PBPK simulations using observed PC/PK parameter values as inputs served as controls for comparison. PBPK simulations were performed using a whole-body PBPK model implemented in the PK-Sim software version 11.045 (https://www.open-systems-pharmacology.org/). The model structure and its assumptions are detailed elsewhere.76 Briefly, this model incorporates multiple compartments representing organs, which are mathematically connected according to their physiology. Inputs to the model include drug-specific properties (e.g., lipophilicity, MW, and Fu) and anatomical and physiological information (e.g., tissue volumes and blood flow rates), which are combined to predict the time course of the drug distribution, metabolism, and excretion in the most relevant organ. Drug-specific properties are used to predict tissue permeability and partition coefficients thanks to permeability and distribution models implemented in the software, which, in turn, are used to predict the drug distribution across different compartments. Various distribution models have been developed and are available in PK-Sim to predict drug partition coefficients, which can sometimes result in different simulations. Since it is not possible to identify a priori the more appropriate distribution model to describe a specific drug, we explored all five distribution models available: PK-Sim standard,40 Berezhkovskiy,41 Poulin and Theil,42 Rodgers et al.,43 and Schmidt.44 Detailed descriptions of these models can be found in the original publications. For each compound, the PBPK simulations were performed by providing the drug-specific parameter values and the corresponding route of administration information (i.e., IV bolus or IV infusion duration in minutes). Simulations were performed using R version 4.3.2.77

4.5. Machine Learning Model to Predict PK Profiles

In the hierarchical ML framework, the concentration at each time point was directly predicted from a compound’s PC/PK parameters (Figure 1). These parameters’ values, derived either from observations or QSAR predictions, were used to train ML models. A feature selection process was conducted to evaluate different combinations of features, including CL, VDss, Fu, pKa acidic, pKa basic, logP, MW, and route of administration information (i.e., IV bolus or IV infusion duration in minutes) along with time. The RF and XGBoost algorithms were employed to model the relationship between these features and the concentration values using the 10fcv procedure. Further details of the framework as well as its performance in preclinical species can be seen in prior publication of the group.22

4.6. Statistical Analysis

In this study, the performance of regression models was evaluated by three commonly used metrics: coefficient of determination (R2), mean absolute error (MAE), and root mean square error (RMSE), as represented by eqs 1–3, respectively.

4.6. 1
4.6. 2
4.6. 3

Where yi, ŷi, and y̅ are the observed, predicted, and mean observed values of chemicals, respectively. A hold test set was used to evaluate the generalization ability of the trained models for each parameter. The model with the highest R2 and lowest MAE, RMSE were selected as the best model for future prediction of new compounds.

Models for some PK parameters were developed by using log-transformed values. To further evaluate the accuracy of the best model for parameter predictions, we transformed the log predictions back to the original scale and compared them with the observed values on the original scale to calculate the geometric mean fold error (GMFE). Additionally, we also calculated the percentage of compounds predicted within 2-fold, 3-fold, and 5-fold errors compared to the observed true values in the original scale.

4.6. 4

For evaluation of the PK profile prediction, we calculated the AUC and Cmax based on the predicted PK profile and calculated the AUC and Cmax fold errors after comparing them with those from the observed PK profile.

Acknowledgments

The authors would like to thank our colleagues, Dr. Majid Vakilynejad, Dr. Qingping Wang, Dr. Josh Dekeyser, Dr. Aiqun Li, Dr. Graham Lockwood from Sanofi, for their fruitful discussions and insightful suggestions. We would also like to thank Emily Nieves and Jawad Iqbal from Delineate Inc. for establishing LLM-based data digitization models and enabling clinical PK data retrieval from the respective publications (https://delineate.pro).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jmedchem.5c00340.

  • Curated modeling datasets for PC/PK properties; predicted and actual properties for 106 test set drugs, hyperparameters for models, unprocessed source PC/PK properties datasets (XLSX)

  • Supporting figures and tables (PDF)

Author Contributions

X.J.: methodology, software, formal analysis, data curation, writing – original draft, visualization. D.T.: methodology, software, writing – review and editing. S.D.: data curation, writing – review and editing. Y.M.P.: data curation, writing – review and editing. A.A.: methodology, writing – review and editing. H.Z.: methodology, writing– review and editing. P.D.M.: conceptualization, resources allocation, methodology, writing– review and editing. N.P.: conceptualization, methodology, writing – review and editing, supervision.

The authors declare the following competing financial interest(s): This project was supported by Sanofi. DT, SD, YMP, AA, PM, NP were employed by Sanofi during this project and may hold shares and/or Stock options. XJ was a CO-OP at Sanofi during this project.

Supplementary Material

jm5c00340_si_001.xlsx (5.7MB, xlsx)
jm5c00340_si_002.pdf (1.4MB, pdf)

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