A Time-Embedding Network Models the Ontogeny of 23 Hepatic Drug Metabolizing Enzymes

Abstract

Pediatric patients are at elevated risk of adverse drug reactions, and there is insufficient information on drug safety in children. Complicating risk assessment in children, there are numerous age-dependent changes in the absorption, distribution, metabolism, and elimination of drugs. A key contributor to age-dependent drug toxicity risk is the ontogeny of drug metabolism enzymes, the changes in both abundance and type throughout development from the fetal period through adulthood. Critically, these changes affect not only the overall clearance of drugs but also exposure to individual metabolites. In this study, we introduce time-embedding neural networks in order to model population-level variation in metabolism enzyme expression as a function of age. We use a time-embedding network to model the ontogeny of 23 drug metabolism enzymes. The time-embedding network recapitulates known demographic factors impacting 3A5 expression. The time-embedding network also effectively models the nonlinear dynamics of 2D6 expression, enabling a better fit to clinical data than prior work. In contrast, a standard neural network fails to model these features of 3A5 and 2D6 expression. Finally, we combine the time-embedding model of ontogeny with additional information to estimate age-dependent changes in reactive metabolite exposure. This simple approach identifies age-dependent changes in exposure to valproic acid and dextromethorphan metabolites and suggests potential mechanisms of valproic acid toxicity. This approach may help researchers evaluate the risk of drug toxicity in pediatric populations.

Figure 1:. The time-embedding network identifies age-dependent patterns among many variables, reducing them to an interpretable, low-dimensional, sparsely-sampled embedding.

The time-embedding forms the backbone of the model. The time-embedding is a matrix of column-vectors comprising discrete, sparsely sampled points interpolated over time. Samples from the interpolated time-embedding are combined with time-independent control variables and passed to a decoder network, which is a neural network two adjacent hidden layers and three adjacent output layers. This neural network is trained to output log-normal mixture distributions that maximize the likelihood of the observed expression data. The time-embedding features are learned simultaneously while training the decoder network by backpropagation.

Figure 2:. Enzyme expression data on 23 enzymes collected by Hines et al reflect known age-dependent patterns of metabolizing enzyme expression.

(A) Liver specimens in the dataset included samples from patients with a diverse background of ages, ethnicities and genders. In particular, samples are densely distributed in the critical period of development from birth to one month of age. (B) A correlation plot of enzyme expression among the 23 enzymes shows two main clusters, one corresponding to fetal pattern enzyme expression and one corresponding to adult pattern expression.

Figure 3:. The time-embedding network accurately estimates enzyme abundance and predicts enzyme detection.

(A) Scatter plot of model predicted expression versus measured sample expression for all enzymes exhibits a strong correlation (R² = 0.72). (B) Receiver operator curve of model predicted detection versus detected protein in liver samples for all enzymes exhibits strong predictive capacity (AUC = 0.92).

Figure 4:. time-embedding networks accurately estimate age-dependent population-level expression patterns for 23 drug metabolism enzymes.

(A) Mean model estimates of enzyme log expression over 8 distinct age groups. Model estimates from leave-one-out cross-validated experiments were used. (B) Mean log expression for each enzyme and age group calculated from the training data. Crosses indicate bins without sufficient data to estimate population means. (C) Model estimates of log expression for each enzyme and age group are strongly correlated with the training data (R² = 0.98). (D) Model estimates of detection rates for each enzyme and age group are strongly correlated with the training data (R² = 0.86)

Figure 5:. A subset of four of the 23 modeled enzymes qualitatively demonstrates that the time-embedding network captures age-dependent, population-level distributions in metabolism enzyme expression.

Blue lines and error bars show the model predicted mean expression and standard deviation, while grey triangles show measured expression in liver samples. Model predictions between conception and age 18 were binned into the same age groups used during modeling, and the mean and standard deviation of the joint distribution was plotted (Data and Methods). Inset plots show model predicted detection rates (blue circles) and detection rates calculated from the data (grey bars). Age axis is plotted on a semilog scale (Data and Methods).

Figure 6:. The time-embedding network capture interpretable, biologically relevant patterns of drug metabolism enzyme expression.

(A) The learned time-embedding feature vectors for our model are a type of time-dependent dimensionality reduction which may capture information about regulation of enzyme expression. The data is well described with as few as three time-embedding features. (B) Signed sensitivity analysis reveals specific dependencies between enzymes and time-embedding features.

Figure 7:. The time-embedding network captures known demographic variation in CYP 3A5 expression.

African Americans express CYP 3A5 more frequently and at much higher levels than Caucasian patients. The time-embedding network is able to identify this trend in the data, predicting substantial and statistically significant increases in CYP 3A5 expression in African Americans compared to Caucasians in simulated input data. In contrast, the neural network ontogeny model was unable to detect any demographic difference in CYP 3A expression.

Figure 8:. An existing literature model agrees with data from Hines et al, but does not capture population variation and age-related dynamics observed in pediatric liver samples.

The time-embedding network achieved slightly lower average RMSE over all enzymes (0.59 vs 0.57, p = 0.047, one-tailed, paired t-test). In addition, the time-embedding network captured patterns in age-dependent expression which cannot be captured by simple curve fitting models. For example, CYP2D6 displays a slight decrease in expression after one year of age compared to infant and adult expression. The age axis is shown on a log-scale.

Figure 9:. The time-embedding network of CYP2D6 maturation predicts tramadol clearance in clinical data better than standard pharmacokinetic models or an alternative neural network ontogeny model.

(A) A one-parameter pharmacokinetic model based on time-embedding estimates of CYP2D6 expression is well-correlated with tramadol clearance data (R² = 0.41), and is substantially better than a pharmacokinetic model from the same study (R² = 0.18). (B) In contrast, the neural network ontogeny model failed to capture age-dependent dynamics during childhood when compared to the time-embedding network (R² = 0.33), and it explained less of the variance than the time-embedding network, as measured by likelihood (likelihood ratio 18.3, p = 0.016, likelihood-ratio test). Dashed lines show one standard deviation of model-predicted distributions.

Figure 10:. Combining metabolism ontogeny models with a simple pharmacokinetics model and the XenoSite reactivity model reveals age-dependent changes in reactive metabolite exposure.

(A,B) Modeling the relative abundance of dextromethorphan metabolites as a function of age reflects trends observed in clinical data, which suggest that children have increased levels of dextrorphan metabolites and decreased levels of methoxymorphinan, relative to adults. (C) Valproic acid (VPA) is a known hepatoxic drug with several covalently reactive metabolites including 4-ene VPA (2), and 2,4-diene VPA (3). The XenoSite reactivity model identifies 2,4-diene-VPA as a strongly reactive, and potentially toxic metabolite of valproic acid (VPA). (D) Modeling the relative abundance of VPA metabolites as a function of age suggests that children may have increased exposure to 2,4-diene VPA.