Developing quantitative Adverse Outcome Pathways: An ordinary differential equation-based computational framework

The Adverse Outcome Pathway (AOP) biological framework was introduced in 2012, yet defining a mathematical/computational framework for quantitative AOP (qAOP) development remains an open problem. In order to properly unravel the intricate biological mechanisms described by AOPs and provide quantitative predictions to support risk assessment, a computational model should provide a clear time-course prediction of key events (KEs), as well as describe the key event relationships (KERs) linking a molecular initiating event (MIE) to an adverse outcome (AO). Ultimately, the mathematical description of those links entails the possibility of quantitatively predicting adverse effects based on early events.

Here, we propose an ordinary differential equation (ODE) - based qAOP framework, as ODEs provide a time-course description of KEs and KERs. We illustrate how the application of computational techniques, such as Bayesian inference and Leave-one-out cross-validation (LOO-CV), can assist AOP development, introducing concepts of qAOP model selection and qAOP updating. Furthermore, we compare ODE and response–response based qAOP models, showing that ODE-based qAOPs can avoid erroneous predictions potentially resulting from response–response qAOPs. Finally, we show how ODE parameter variability can be linked to AO variability across a population. Overall, this framework serves as a valuable mathematical and computational tool for the development of qAOP models, enhancing our comprehension of intricate biological pathways associated with adverse outcomes.