INTRODUCTION
Physiologically based pharmacokinetic (PBPK) models,1,2) also known as physiologically based kinetic (PBK) models in the European Union,3) can be used to facilitate the drug development process4) and to simulate plasma/serum drug concentrations in patients.5–7) PBPK modeling is based on both physiological/anatomical properties of the relevant organs and the chemical properties of the target substance.8,9) Simplified PBPK models that use some fixed physiological system parameters are easier to handle than full PBPK models and are of use in the fields of drug discovery, poisoning, or therapeutic drug monitoring7,10–12) as well as in risk assessment for a variety of general chemicals or food components/additives.13) Although the metabolic profiles of disparate chemicals (including aromatic amines14,15)) traditionally have been elucidated in rodent studies,16) so-called new alternative methods (NAMs) for evaluating chemical safety have been widely investigated using in silico or in vitro approaches.17,18) The approach that applies simple PBPK modeling, without any reference to experimental pharmacokinetic data, has the potential to play significant roles in replacing and reducing the use of animals for estimating toxicokinetics or internal exposures of drugs, food components, and general chemicals.19)
By applying a light gradient boosting machine learning system (LightGBM20)), prediction accuracy was enhanced when estimating the apparent membrane permeability coefficients (Papp) across intestinal cell monolayers for 219 disparate chemicals using in silico-derived chemical descriptors.21) The likelihood of efflux transporters playing a role in the estimated intestinal permeability values of 301 chemicals was also predictable by machine learning.22) For medicines, the Papp across human colorectal carcinoma cell line (Caco-2) monolayers generally correlates with the fraction absorbed (Fa) after oral intake.23,24) Similarly, we previously calculated the Fa values of chemicals using in silico-estimated intestinal monolayer Papp values.21) In our system, the intestinal availability (Fg) values were traditionally estimated from the gut extraction ratios as one-tenth of the hepatic extraction ratios.25)
PBPK models require a set of input parameters to generate output time-series kinetic data. To improve the accessibility and feasibility of PBPK modeling, we previously generated PBPK model input parameters [i.e., absorption rate constants (ka), volumes of the systemic circulation (V1), and the hepatic intrinsic clearances (CLh,int)] in silico for a broad range of substances by applying a machine learning algorithm,25) along with Fa·Fg values from estimated membrane permeabilities, as mentioned above. The increasing availability of pharmacokinetic datasets for substances is a determinant factor for validating updated in silico models for estimating input parameter values for human PBPK models. The aim of the current study was to update in silico estimation systems for Fa·Fg, ka, and V1 values of substances derived from in silico-generated chemical descriptors. Furthermore, the plasma concentration versus time data of 355 disparate substances in humans after virtual oral administrations of 1.0-mg/kg doses were generated using these in silico input parameters for human PBPK models.
MATERIALS AND METHODS
In our previous study, human blood concentration versus time datasets for 212 disparate chemicals were generated using PBPK models with in silico-estimated input parameters.25) To expand the scope of this machine learning-based system, we carried out a literature survey for reported in vivo pharmacokinetic datasets (used for verification of PBPK-generated data) and were able to add 143 chemicals (including 88 medicines from a new Japanese drug database, shown in Supplementary Table S1). Moreover, human blood concentrations versus time data of 10 medicines were used as a secondary dataset. The structural variability of the 212 original chemicals, the 143 additional chemicals, and the 10 secondary medicines were confirmed in a two-dimensional plane (with 25 partitions, Supplementary Fig. S1) that represents the chemical space. Blood-to-plasma concentration ratios and liver (kidney)-to-plasma concentration ratios of the compounds were estimated from the plasma unbound fraction and octanol–water partition coefficient values generated using in silico tools,25) as outlined in Supplementary Materials and Methods. Simplified human PBPK models consisting of gut, liver, central, and kidney compartments were described previously.25) The necessary input parameters for PBPK models, i.e., fraction absorbed × intestinal availability (Fa·Fg), ka, V1, and CLh,int, are conventionally computed to achieve the best fit to reported human plasma concentrations.25) The acceptability criterion for the predictive abilities of in silico systems was a threefold error (compared with in vivo values) in human PBPK-modeled plasma Cmax and areas under the concentration–time curve (AUC) values after oral doses of 1.0 mg/kg per day.
In a previous study, we calculated Fa values based on the in silico-generated Papp values21) from the apical side to the basal side (referred to as A to B) as Fa = (logPapp A to B)2.4/(1.0 + (logPapp A to B)2.4). Fg values were previously estimated from the gut extraction ratios as one-tenth of the hepatic extraction ratios (in the well-stirred model). In the current study, the chemical descriptor sets (containing 1710 parameters) of in silico physicochemical properties were obtained as described previously.25) Based on these chemical descriptor sets, we applied the machine learning algorithm LightGBM20) to Fa·Fg, ka, and V1 values under nested cross-validation systems and establish new prediction systems based on 29, 11, and 12 in silico-derived descriptors, respectively.26,27) Briefly, in our nested cross-validation approach, 90% of chemicals out of 355 chemicals were applied to inner cross-validation according to the reported methods.13) The optimized parameters in 10 inner models were then applied to obtain the mean predictors in 10 outer sets. The traditionally determined human PBPK model input values (hereafter referred to as in vivo derived) were compared with the in silico estimated values generated using our previous approach25) and the current updated computational approach; these three sets of input parameters were statistically evaluated using Prism software (GraphPad Software, San Diego, CA, U.S.A.). Average absolute fold errors for Fa·Fg, ka, V1, and CLh,int values were also evaluated as described previously.25)
RESULTS AND DISCUSSION
In the past, human metabolic profiles for substances such as food-derived pyrrolizidine alkaloids (e.g., neopetasitenine, its metabolite petasitenine, and senkirkine) were allometrically extrapolated from rat in vivo and in vitro datasets.28,29) If human internal exposures of a diverse range of compounds could be generated without any reference to experimental pharmacokinetic data by using PBPK models with in silico-generated input parameters (based on in silico chemical descriptors), it would greatly facilitate and simplify forward dosimetry after virtual oral administrations for application in fields such as risk assessment and drug development. In the current study, simplified PBPK models using three sets of input parameters (in vivo-derived values13,30) and in silico-derived values based on our previous25) and herein updated systems) were used to estimate three sets of human plasma (and tissue) concentrations after virtual oral administrations for an enlarged panel of 355 chemicals and 10 secondary medicines.
First, the in silico-derived input parameters for human PBPK models for the 212 previously modeled chemicals and the 143 additional chemicals were evaluated using the previously reported machine learning system that was developed using data from the 212 substances.25) These parameter values were compared with the traditional in vivo-derived input parameters (Fig. 1). When our previous machine-learning system25) (in which Fa was derived from apparent permeabilities estimated from 17 chemical descriptors21) using LightGBM, ka was derived from 65 chemical descriptors25) using ridge regression, V1 was derived from 64 chemical descriptors25) using ridge regression, and CLh,int was derived from 17 chemical descriptors25) using LightGBM) was applied to the expanded panel of 355 chemicals, the correlation coefficients of the resulting Fa·Fg, ka, V1, and CLh,int values, respectively, were 0.28 (p < 0.01, Fig. 1A), 0.36 (p < 0.01, Fig. 1B), 0.56 (p < 0.01, Fig. 1C), and 0.85 (p < 0.01, Fig. 1D). Moreover, the average absolute fold errors for Fa·Fg, ka, V1, and CLh,int were 2.02, 2.32, 2.18, and 2.56, respectively, for the previous estimation systems.25)
Next, the output values of the human PBPK models were generated for the 355 chemicals based on both the traditionally determined input values and those estimated using our previous in silico system. The results are shown in Fig. 2. The PBPK-modeled human plasma Cmax values generated using the in vivo-derived and the previous in silico-derived sets of input parameters were correlated (r = 0.43, p < 0.01, Fig. 2A). Moreover, there was a low but significant correlation (r = 0.43, p < 0.01) between the human plasma AUC values of the 355 chemicals obtained using the in vivo-derived and the previous in silico-derived sets of input parameters (Fig. 2B). The average absolute fold errors for the output plasma Cmax and AUC values of the 355 chemicals in humans were 3.49 and 3.63, respectively, under the previous estimation systems.25)
To develop more accurate in silico PBPK model input parameter estimation systems, the machine-learning system (LightGBM) was updated using the new primary panel of 355 chemicals as described in Supplementary Materials and Methods. The updated LightGBM in silico prediction systems for estimating Fa·Fg, ka, and V1 in humans used 29, 11, and 12 chemical descriptors (Supplementary Table S2). However, the CLh,int values for the new panel of 355 diverse chemicals could be reliably estimated using previous system.25) The correlation coefficients of 0.84 (Fig. 3A), 0.90 (Fig. 3B), and 0.96 (Fig. 3C), respectively, for the Fa·Fg, ka, and V1 values compared with the in-vivo derived parameters, were statistically significant for the 355 chemicals (p < 0.01). The average absolute fold errors for the Fa·Fg,ka, and V1 values were improved to 1.40, 1.47, and 1.35, respectively, under the updated estimation systems (hereafter termed the current systems).
The ability of PBPK models with in silico input parameters (estimated using the current machine-learning systems) to generate accurate output plasma Cmax and AUC values for the 355 chemicals was evaluated by comparing the Cmax and AUC values with those modeled using traditional in vivo-derived parameters. The output plasma Cmax (r = 0.87, p < 0.01, Fig. 4A) and AUC (r = 0.73, p < 0.01, Fig. 4B) values for all 355 chemicals were well correlated. Using the current parameter estimation systems, the average absolute fold errors for the output plasma Cmax and AUC values of the 355 chemicals in humans were improved to 2.06 and 2.73, respectively.
Plasma Cmax and AUC output values after virtual oral administrations of the 10 secondary medicines (carvedilol, dapsone, ethionamide, hydrochlorothiazide, meloxicam, quazepam, sulfamethoxazole, trifluoperazine, trimethoprim, and venlafaxine) were also compared using in silico-derived (with current estimation systems) and in vivo-derived input parameters (Fa·Fg, ka, V1, and CLh,int) for human PBPK models. The output plasma Cmax (r = 0.87, p < 0.01, n = 365; Fig. 4A) and AUC (r = 0.73, p < 0.01, n = 365; Fig. 4B) values of the 365 substances (355 primary chemicals plus 10 secondary medicines) modeled using in silico- and in vivo-derived input parameters were well correlated. The current estimation system for human PBPK models yielded output values with average absolute fold errors of 2.08 and 2.76, respectively, for the plasma Cmax and AUC values of the whole panel of 365 chemicals, in a roughly similar manner to the results of the primary 355 chemicals used for the cross-validations.
Virtual chemical exposure levels in liver and kidney were also estimated using these simplified PBPK models along with human plasma levels. The time-dependent concentrations of chemicals in human tissues can also be virtually generated in a similar manner to that used for concentrations in rat livers, kidneys, and plasma.25) In the current study, good correlations were obtained for virtual Cmax and AUC values generated by in silico- and in vivo-based PBPK models (Supplementary Table S3) in human liver and kidney for the expanded set of 355 primary chemicals and 10 secondary medicines using the current in silico-derived input parameters; significant correlation coefficients (p < 0.01) for hepatic Cmax (r = 0.84) and AUC (r = 0.86) values and renal Cmax (r = 0.75) and AUC (r = 0.76) values were obtained (data not shown).
Traditionally, the human metabolic profiles for substances such as food-derived toxic compounds were allometrically extrapolated from rat concentration profiles determined in vivo.28,29) We previously used the current approach to PBPK modeling with in silico estimation of input parameters to generate virtual concentrations in plasma (and in tissues) after oral doses of 323 chemicals in rats. We could successfully generate PBPK model input parameters for rat models calculated from a small number of chemical properties by machine-learning prediction tools.26) Rat PBPK modeling31) will also make increasingly important contributions to computational toxicology and facilitate assessment of the potential risks of industrial or food chemicals. In terms of human PBPK modeling, the previously used ridge regression approach32) is a method for estimating the coefficients of multiple-regression models. The currently applied LightGBM20) systems use a gradient boosting framework that uses tree-based learning algorithms. The mechanism leading to the current improvements in estimations of PBPK input parameters is not clear at present, but the applicability to human pharmacokinetics of updated input parameter estimation systems using LightGBM for PBPK modeling has been demonstrated in the present study.
In the current study, we selected human plasma Cmax and AUC values as the PBPK-modeled output results generated from the current predictive input parameter systems. However, this PBPK-modeling approach also can be used to generate virtual time-dependent blood concentrations over various time scales in humans. In clinical practice, such simple visualization of human blood concentration trends would be of use for evaluating the need for prompt emergency treatments in various cases of poisoning caused by accidental or intentional drug ingestion. Using machine learning to predict the pharmacokinetics of general substances without any reference to experimental data would have great potential both in basic research and clinical practice. In conclusion, using PBPK model input parameters calculated from updated sets of between 11 and 29 chemical properties (that themselves are generated using in silico prediction tools), the output concentrations of 355 primary chemicals in plasma (and liver and kidney) could be reliably estimated by simplified PBPK models after virtual oral doses in humans in comparison with those in vivo-based PBPK models. The above-described computational methods constitute a new alternative approach (a so-called NAM) that could contribute to chemical safety evaluations. This approach to human PBPK modeling could enhance the effectiveness of computational toxicology for assessing the potential risk of drugs, food materials, and general chemicals. The simplified PBPK models described here, which are easy to manage, have the potential to predict a variety of drug internal exposures in humans, which would be of use to a wide range of industrial researchers. Moreover, paramedical staff could use the virtual pharmacokinetic profiles as a useful guide when assessing poisoning or therapeutic drug monitoring in human subjects or patients.
