Adverse outcome pathways: opportunities, limitations and open questions.

Adverse outcome pathways (AOPs) are a recent toxicological construct that connects, in a formalized, transparent and quality-controlled way, mechanistic information to apical endpoints for regulatory purposes. AOP links a molecular initiating event (MIE) to the adverse outcome (AO) via key events (KE), in a way specified by key event relationships (KER). Although this approach to formalize mechanistic toxicological information only started in 2010, over 200 AOPs have already been established. At this stage, new requirements arise, such as the need for harmonization and re-assessment, for continuous updating, as well as for alerting about pitfalls, misuses and limits of applicability. In this review, the history of the AOP concept and its most prominent strengths are discussed, including the advantages of a formalized approach, the systematic collection of weight of evidence, the linkage of mechanisms to apical end points, the examination of the plausibility of epidemiological data, the identification of critical knowledge gaps and the design of mechanistic test methods. To prepare the ground for a broadened and appropriate use of AOPs, some widespread misconceptions are explained. Moreover, potential weaknesses and shortcomings of the current AOP rule set are addressed (1) to facilitate the discussion on its further evolution and (2) to better define appropriate vs. less suitable application areas. Exemplary toxicological studies are presented to discuss the linearity assumptions of AOP, the management of event modifiers and compensatory mechanisms, and whether a separation of toxicodynamics from toxicokinetics including metabolism is possible in the framework of pathway plasticity. Suggestions on how to compromise between different needs of AOP stakeholders have been added. A clear definition of open questions and limitations is provided to encourage further progress in the field.

Mathematical modelling of liver regeneration after intoxication with CCl(4).

Liver regeneration is a complex process, having evolved to protect animals from the consequences of liver loss caused by food toxins. In this study, we established a mathematical spatial-temporal model of the liver lobule regenerating after CCl(4) intoxication. The aim of modelling the regeneration process by matching experimental observations with those from a mathematical model is to gain a better understanding of the process and to recognize which parameters are relevant for specific phenomena. In order to set up a realistic minimal model, we first reconstructed a schematised liver lobule after determination of: (i) the mean number of hepatocytes between the central vein and the periphery of the lobule, (ii) the mean size of the hepatocytes and (iii) the mean number of hepatocyte columns in the inner, midzonal and peripheral ring of the lobule. In a next step, we determined the time course of cell death and BrdU incorporation after intoxication of male Sprague Dawley rats with CCl(4), thereby differentiating between inner, midzonal and peripheral hepatocytes. These parameters were used to construct a model. The basic unit of this model is the individual cell. The detailed behaviour of the cells is studied, controlled by the model parameters: (1) probability of cell division at defined positions of the lobule at a given time, (2) "coordinated cell orientation", i.e., the ability of the cells to align during the regeneration process into columns towards the central vein of a liver lobule, (3) cell cycle duration, (4) the migration activity and (5) the polarity of the hepatocytes resulting in polar cell-cell adhesion between them. In a schematised lobule, the model shows that CCl(4) initially induced cell death of a pericentral ring of hepatocytes, followed by a wave of proliferation that starts in the surviving hepatocytes next to the inner ring of dead cells and continues to the peripheral hepatocytes, finally restoring the characteristic micro-architecture of the lobule in a 7-day process. This model was used to systematically analyze the influence of parameters 1-5. Interestingly, coordinated cell orientation and cell polarity were identified to be the most critical parameters. Elimination led to destruction of the characteristic micro-architecture of the lobule and to a high degree of disorder characterized by hexagonal cell structures. Our model suggests that the ability of hepatocytes to realign after cell division by a process of coordinated cell orientation (model parameter 2) in combination with cell polarity (model parameter 5) may be at least as critical as hepatocyte proliferation (model parameter 1) itself.

A single-cell-based model of tumor growth in vitro: monolayers and spheroids.

To what extent the growth dynamics of tumors is controlled by nutrients, biomechanical forces and other factors at different stages and in different environments is still largely unknown. Here we present a biophysical model to study the spatio-temporal growth dynamics of two-dimensional tumor monolayers and three-dimensional tumor spheroids as a complementary tool to in vitro experiments. Within our model each cell is represented as an individual object and parametrized by cell-biophysical and cell-kinetic parameters that can all be experimentally determined. Hence our modeling strategy allows us to study which mechanisms on the microscopic level of individual cells may affect the macroscopic properties of a growing tumor. We find the qualitative growth kinetics and patterns at early growth stages to be remarkably robust. Quantitative comparisons between computer simulations using our model and published experimental observations on monolayer cultures suggest a biomechanically-mediated form of growth inhibition during the experimentally observed transition from exponential to sub-exponential growth at sufficiently large tumor sizes. Our simulations show that the same transition during the growth of avascular tumor spheroids can be explained largely by the same mechanism. Glucose (or oxygen) depletion seems to determine mainly the size of the necrotic core but not the size of the tumor. We explore the consequences of the suggested biomechanical form of contact inhibition, in order to permit an experimental test of our model. Based on our findings we propose a phenomenological growth law in early expansion phases in which specific biological small-scale processes are subsumed in a small number of effective parameters.