2022 Volume 47 Issue 11 Pages 453-456
Physiologically based pharmacokinetic (PBPK) modeling has the potential to estimate internal chemical exposures. Algorithms for predicting the input parameters for PBPK modeling, such as absorption rate constants (ka), were previously reported for 323 chemicals in rats. In this study, a currently updated system for estimating the fraction absorbed × intestinal availability of compounds, along with a modified estimation system that generates ka values, is reported, based on the previously analyzed 323 primary compounds, 10 secondary compounds, and 39 additional substances. The in silico estimation of input parameters for PBPK models (i.e., fraction absorbed × intestinal availability and ka) was adapted for an updated panel of 372 chemicals using machine learning algorithms based on between 16 and 18 in silico-calculated chemical properties. Simplified human PBPK models were then used to calculate virtual areas under the plasma concentration–time curve (AUC) based on two sets of input parameters, i.e., traditionally derived values from in vivo data and those calculated in silico using the current updated machine learning systems. The AUC data sets were well correlated; the current correlation coefficient increased from 0.61 to 0.82 (p < 0.01, n = 372). Therefore, the above-described computational methods constitute a new alternative approach that could contribute to chemical safety evaluations.
Although experimental time-series concentration data for non-pharmaceutical chemicals, unknowingly exposed to humans, are rarely available, the United States Environmental Protection Agency (EPA) has a public database of time-course concentration data in animals for approximately 200 environmentally-relevant chemicals (Sayre et al., 2020). We have shared the collected blood concentrations versus time data sets after oral administration in rats (Kamiya et al., 2021a, 2021b) with Wambaugh and his associates in Center for Computational Toxicology and Exposure, U.S. EPA (Cook et al., 2022). Our research group estimated pharmacokinetic parameters in rats derived from these corresponding plasma concentration–time curves for simplified physiologically based pharmacokinetic (PBPK) models. A wide range of in vitro and/or in silico non-animal-based new approach methodologies (NAMs) for chemical safety and risk assessments is currently being developed. By applying a light gradient boosting machine learning system (LightGBM), in silico prediction accuracy was enhanced when estimating the apparent membrane permeability coefficients (Papp) across intestinal cell monolayers for 219 disparate chemicals via an approach that incorporated in silico-derived chemical descriptors (Kamiya et al., 2021c). The possible roles of efflux transporters in the estimated intestinal permeability values of 301 chemicals were also predictable by machine learning (Shimizu et al., 2022). PBPK modeling, also known as PBK modeling in the European Union (Paini et al., 2019), that uses both the chemical properties of substances and the physiological properties of various organ systems has the potential to reduce animal testing by estimating internal chemical exposures. Simplified PBPK models with four organ systems have been established for a range of substances, as described previously (Kamiya et al., 2021a, 2021b).
Algorithms for predicting the input parameters for PBPK models, such as absorption rate constants (ka), were previously established to facilitate modeling of the plasma (and tissue) concentrations of 323 chemicals after virtual oral administrations in rats (Kamiya et al., 2021a). In the previous study, the PBPK model input parameters for rats of diverse compounds could be precisely estimated with a modeling approach designed to integrate nested cross-validation using a ridge regression system with an enlarged set of up to 100 chemical descriptors (Kamiya et al., 2021a). In this study, we report a modified estimation system and its application to the previously analyzed 323 primary substances, previous 10 secondary substances, and 39 additional substances to generate the fractions absorbed × intestinal availability (Fa·Fg) of compounds, along with a currently updated system for estimating input ka values.
Blood concentrations versus time data sets after oral administration in rats (Kamiya et al., 2021a, 2021b) of the previously analyzed 323 primary and 10 secondary chemicals (Kamiya et al., 2021b) obtained by a literature survey underwent machine learning, along with 39 new additional chemicals, including medicines from a Japanese drug database (Supplemental Table S1). The variety of compounds in the chemical space (Kamiya et al., 2021b, 2021c, 2021a, 2019) was previously evaluated for the examined chemicals in studies on intestinal permeability (Kamiya et al., 2021c, Shimizu et al., 2022) and rat pharmacokinetics (Kamiya et al., 2019, 2021b, 2021a). Traditionally, the necessary input parameters for PBPK models, i.e., Fa·Fg, ka, volume of the systemic circulation (V1), and hepatic intrinsic clearance (CLh,int), have been computed to give the best fit to reported/measured plasma concentrations using nonlinear regression analyses (Kamiya et al., 2021a, 2021b), as briefly outlined in the Supplemental materials and methods. We generated input pharmacokinetic parameters for a broad range of 372 chemicals in silico with a machine learning algorithm that utilized LightGBM without in vivo reference studies (Kamiya et al., 2021a, 2021b); this approach is also briefly outlined in the Supplemental materials and methods. The Fa values were previously calculated from estimated intestinal monolayer Papp values (Kamiya et al., 2021c) from the apical side to the basal side (referred to as A to B): 100 × (logPapp A to B)2.4 / (1.0 + (logPapp A to B)2.4). The Fg values were previously estimated from the gut extraction ratios as one-tenth of the hepatic extraction ratios in the hepatic well-stirred model (Kamiya et al., 2021a, 2021b). The values estimated using the modified ka and Fa·Fg models were extensively validated with a modeling approach designed to integrate nested cross-validation (Kamiya et al., 2021a, 2021b) in a similar way to that used for our previous system for V1 and CLh,int.
Previously calculated Fa values of chemicals were estimated using in silico-estimated apparent permeability values for the pH-dependent intestinal monolayer (Kamiya et al., 2021c). However, this system might give sometimes overestimated values for chemicals. A modified estimation method using LightGBM for calculating Fa·Fg and ka for 372 chemicals after oral administrations in rats was established; the method encompasses 16 and 18 chemical descriptors for predicting Fa·Fg and ka, respectively. These descriptors and their relative importance in this study are summarized in Supplemental Table S2. The traditionally determined PBPK model input values (hereafter referred to as in vivo-derived) were correlated with the computationally estimated values (in silico-derived) generated using the previous systems for influx Papp, and CLh-based Fa·Fg and ka in rats for the 372 chemicals (Fig. 1A and 1B); the correlation coefficients of 0.22 and 0.70 were significant (p < 0.01). The average absolute fold errors for the Fa·Fg and ka values generated using our previous systems were 3.47 and 2.12, respectively. In a preliminary study, the ka estimating system (Kamiya et al., 2021b) that uses 18 chemical properties based on 246 chemicals gave a correlation coefficient of 0.77 for in vivo- and in silico-derived ka values for the current set of 372 chemicals (data not shown). The in vivo-derived values of Fa·Fg and ka were also correlated with in silico-derived values estimated using the current systems in rats for the 372 chemicals (Fig. 1D and 1E); the correlation coefficients of 0.86 and 0.79 were significant (p < 0.01). The average absolute fold errors for the Fa·Fg and ka values generated by the current system were 2.06 and 1.65 and respectively. These results indicated that the rat Fa·Fg and ka values of a diverse range of chemicals could be estimated from a set of chemical descriptors generated using standard in silico tools.
Correlations between in vivo-derived and in silico-derived input Fa·Fg (A, D) and ka values (B, E) and PBPK modeled output AUC values in rat plasma (C, F) for 372 chemicals based on traditional in vivo-derived and previously (A–C) and currently (D–F) estimated input parameters. Solid lines indicate direct correspondence, and dashed/dotted lines indicate twofold/tenfold ranges, respectively.
The values of Fa·Fg and ka, along with V1 and CLh,int, were generated in silico using the above-mentioned current systems and the previous estimation methods based on physicochemical properties (Kamiya et al., 2021a, 2021b). The concentrations of 372 chemicals in rat plasma generated by PBPK models after virtual oral administrations of 1.0-mg/kg doses were evaluated using a total of three sets of input parameters: either traditionally in vivo-derived (Kamiya et al., 2021a, 2021b) or in silico-estimated using the previous and current systems. When the traditionally determined input values Fa·Fg, ka, V1, and CLh,int for the 372 chemicals were replaced with the corresponding in silico-estimated input values, the output AUC values in rat plasma generated by PBPK models using the previous and current sets of input parameters were both correlated with the AUC values obtained using the traditional method: the correlation coefficients in rat plasma were 0.61 and 0.82, respectively, for the previous and current sets of input parameters (p < 0.01, as shown in Fig. 1C and 1F). The average absolute fold errors for the AUC values in rats were 4.32 and 2.56, respectively, with the previous and current sets. In PBPK modeling, predictions are, on average, within a factor of two of the experimental data have frequently been considered adequate (WHO 2010). Data sources for non-pharmaceutical chemicals are generally limited (Sayre et al., 2020), but more numbers of pharmacokinetic data sets in animals or humans would help improving the estimations of Fa·Fg, ka, V1 and/or CLh,int values of substances generated in silico. In computational toxicology, improved in silico systems for estimating PBPK model input parameter should help to facilitate rat PBPK modeling applications.
In conclusion, virtual concentrations in plasma (and in tissues) after oral doses of 372 chemicals in rats could be estimated using simplified PBPK models with in silico-generated input parameters calculated from a small number of chemical properties (16–18) by currently updated machine-learning prediction tools. The above-described computational methods constitute a new alternative approach (a so-called NAM) that could contribute to chemical safety evaluations. Rat PBPK modeling will make increasingly important contributions to computational toxicology and facilitate assessment of the potential risk of non-pharmaceutical, industrial or food chemicals.
This work was supported in part by the Japan Chemical Industry Association Long-range Research Initiative Program. We thank Drs. Yusuke Kamiya, Masato Kitajima, Junya Ohori, Kentaro Handa, Hiroshi Yano, Masaya Fujii, Jun Tomizawa, Wataru Kobari, Airi Kato, Tasuku Sato, Masayoshi Utsumi, Tomonori Miura, Shohei Otsuka, Norie Murayama, Fumiaki Shono, and Kimito Funatsu for their assistance. We are also grateful to David Smallbones for copyediting a draft of this article.
The authors declare that there is no conflict of interest.