A Deep Neural Network -- Mechanistic Hybrid Model to Predict Pharmacokinetics in Rat

TL;DR

The paper tackles predicting pharmacokinetic exposure from chemical structure in rats, a challenging task due to the nonlinear interplay of molecular properties and physiology and limited data. It introduces a hybrid framework that couples a graph-based neural network for molecular property prediction with a mechanistic PBPK model, using a surrogate to enable end-to-end training. The approach yields improved accuracy over prior models, demonstrates extrapolation to untrained endpoints such as AUC over 24 hours, and accommodates covariates like sex and formulation. This hybrid method can reduce development time and animal experiments by prioritizing compounds with favorable PK profiles and enables direct PK-oriented optimization. The framework lays groundwork for broader applications, including human PK and concentration-time profile training, with potential for uncertainty quantification forthcoming.

Abstract

An important aspect in the development of small molecules as drugs or agro-chemicals is their systemic availability after intravenous and oral administration. The prediction of the systemic availability from the chemical structure of a potential candidate is highly desirable, as it allows to focus the drug or agrochemical development on compounds with a favorable kinetic profile. However, such pre-dictions are challenging as the availability is the result of the complex interplay between molecular properties, biology and physiology and training data is rare. In this work we improve the hybrid model developed earlier [1]. We reduce the median fold change error for the total oral exposure from 2.85 to 2.35 and for intravenous administration from 1.95 to 1.62. This is achieved by training on a larger data set, improving the neural network architecture as well as the parametrization of mechanistic model. Further, we extend our approach to predict additional endpoints and to handle different covariates, like sex and dosage form. In contrast to a pure machine learning model, our model is able to predict new end points on which it has not been trained. We demonstrate this feature by predicting the exposure over the first 24h, while the model has only been trained on the total exposure.

Figures (12)

• Figure 1: Overview over our hybrid model structure consisting of a graph convolutional neural network for predicting a set of molecule properties. These molecule properties are the free parameters of a physiological model of rats predicting the pharmacokinetics. In practice, we approximate the PBPK model by a surrogate neural network.
• Figure 2: Overall accuracy of surrogate neural evaluated on a hold out test set of simulations. A median fold change error of 2-4% is small to the expected biological variability of the data of 50%.
• Figure 3: Some examples showing the full PBPK model and the surrogate model as a function of a single model parameter, while keeping the others fixed. In these examples the dependence on the hepatic clearance (top left) and dose (bottom right) is very accurately described by the surrogate. In the GFR example (top right) the surrogate is able to reproduce the shape of the PBPK, but shows a constant offset of about 20%, which is acceptable given the variability of the PK-data. The solubility example (bottom left) shows an offset of similar size, but is able to qualitatively reproduce the step-like behavior seen in the PBPK model. The small oscillations of about few % do not introduce major problems during training of the hybrid model.
• Figure 4: Number of data points for different sub-sets of the data set. Since the standard test for pharmaceuticals is on male rats using, for PO, a solution, most of our compounds are tested on male rats.
• Figure 5: Distribution of used dose in PO (left) and IV (right) measurements. High doses are typically tested only in PO experiments, hence they span much large dose range then the iv experiments.