Quantification of an Adverse Outcome Pathway Network by Bayesian Regression and Bayesian Network Modeling

Abstract

The adverse outcome pathway (AOP) framework has gained international recognition as a systematic approach linking mechanistic processes to toxicity endpoints. Nevertheless, successful implementation into risk assessments is still limited by the lack of quantitative AOP models (qAOPs) and assessment of uncertainties. The few published qAOP models so far are typically based on data-demanding systems biology models. Here, we propose a less data-demanding approach for quantification of AOPs and AOP networks, based on regression modeling and Bayesian networks (BNs). We demonstrate this approach with the proposed AOP #245, "Uncoupling of photophosphorylation leading to reduced ATP production associated growth inhibition," using a small experimental data set from exposure of Lemna minor to the pesticide 3,5-dichlorophenol. The AOP-BN reflects the network structure of AOP #245 containing 2 molecular initiating events (MIEs), 3 key events (KEs), and 1 adverse outcome (AO). First, for each dose-response and response-response (KE) relationship, we quantify the causal relationship by Bayesian regression modeling. The regression models correspond to dose-response functions commonly applied in ecotoxicology. Secondly, we apply the fitted regression models with associated uncertainty to simulate 10 000 response values along the predictor gradient. Thirdly, we use the simulated values to parameterize the conditional probability tables of the BN model. The quantified AOP-BN model can be run in several directions: 1) prognostic inference, run forward from the stressor node to predict the AO level; 2) diagnostic inference, run backward from the AO node; and 3) omnidirectionally, run from the intermediate MIEs and/or KEs. Internal validation shows that the AOP-BN can obtain a high accuracy rate, when run is from intermediate nodes and when a low resolution is acceptable for the AO. Although the performance of this AOP-BN is limited by the small data set, our study demonstrates a proof-of-concept: the combined use of Bayesian regression modeling and Bayesian network modeling for quantifying AOPs. Integr Environ Assess Manag 2021;17:147-164. © 2020 The Authors. Integrated Environmental Assessment and Management published by Wiley Periodicals LLC on behalf of Society of Environmental Toxicology & Chemistry (SETAC).

Keywords: Conditional probability tables; Dose-response curve; Key event relationships; Quantitative AOP; Uncertainty.

Figure 1

Components of an adverse outcome pathway (AOP) (A). Conceptual model of an AOP‐BN (Bayesian network) for quantification of the tentative AOP #245 (see Supplemental Data Figure S1 for more details) (B). The nodes are defined in Table 1. The numbered arrows identify the causal relationships defined in Table 2. AOP = adverse outcome pathway; DCP = 3,5‐dichlorophenol; ETR = electron transfer rate; Fv/Fm = maximum quantum yield of photosystem II; LPO = lipid peroxidation; OXPHOS = oxidative phosphorylation; ROS = reactive oxygen species.

Figure 2

Observed and simulated causal relationships: dose–response (A, D) and response–response (B, C, E–H) relationships. Colored dots show the measured values; the color code indicates the experimental treatment dose (see legend) in mg/L. The grey dots are simulated response values; a subset of 1000 out of 10 000 simulated values is displayed. For plots (A) and (D), the x‐axis is in log‐scale. The values DCP = 0 mg/L are displayed at 0.05 mg/L. The vertical and horizontal grid lines correspond to the intervals of the BN nodes (Table 1). The regression models are described in Table 2. AOP = adverse outcome pathway; BN = Bayesian network; DCP = 3,5‐dichlorophenol; ETR = electron transfer rate; Fv/Fm = maximum quantum yield of photosystem II; LPO = lipid peroxidation; OXPHOS = oxidative phosphorylation; ROS = reactive oxygen species.

Figure 3

Examples of CPTs generated from simulated data, illustrating causal relationships with different levels of variability. Low variability: dose–response relationship DCP → OXPHOS (Figure 2A) (A). Intermediate variability: key event relationship OXPHOS → ETR (Figure 2B) (B). High variability: key event relationship ROS → Fv/Fm (Figure 2E) (C). The remaining CPTs are shown in Table S2. The CPTs shown here are transposed for alignment with the plots in Figure 2. CPT = conditional probability tables; DCP = 3,5‐dichlorophenol; ETR = electron transfer rate; Fv/Fm = maximum quantum yield of photosystem II; OXPHOS = oxidative phosphorylation; ROS = reactive oxygen species.

Figure 4

Prognostic inference. The AOP‐BN model is run forwards from the stressor node with evidence set at different stressor concentration intervals: low (A), intermediate (B), high (C). In each node, the states (intervals) are shown to the left, while the probabilities are shown to the right both as values and as bars. The mean and standard deviation are given below each node. Evidence entered to a node is indicated by thin lines around the bar with 100% probability. AOP = adverse outcome pathway; BN = Bayesian network; DCP = 3,5‐dichlorophenol; ETR = electron transfer rate; Fv/Fm = maximum quantum yield of photosystem II; LPO = lipid peroxidation; OXPHOS = oxidative phosphorylation; ROS = reactive oxygen species.

Figure 5

Diagnostic inference. The AOP‐BN model is run backwards from the adverse outcome node (fronds number): high fronds number (weakly adverse outcome) (A); low fronds number (strongly adverse outcome) (B). For more explanation, see Figure 4. AOP = adverse outcome pathway; BN = Bayesian network; DCP = 3,5‐dichlorophenol; ETR = electron transfer rate; Fv/Fm = maximum quantum yield of photosystem II; LPO = lipid peroxidation; OXPHOS = oxidative phosphorylation; ROS = reactive oxygen species.

Figure 6

Combination of prognostic and diagnostic inference. The AOP‐BN model is run omnidirectionally from intermediate nodes: from molecular initiating events (A); from key events (B). For more explanation, see Figure 4. AOP = adverse outcome pathway; BN = Bayesian network; DCP = 3,5‐dichlorophenol; ETR = electron transfer rate; Fv/Fm = maximum quantum yield of photosystem II; LPO = lipid peroxidation; OXPHOS = oxidative phosphorylation; ROS = reactive oxygen species.