Topological sensitivity analysis for systems biology

Significance Mathematical models are widely used to study natural systems. They allow us to test and generate hypotheses, and help us to understand the processes underlying the observed behavior. However, such models are, by necessity, simplified representations of the true systems, so it is critical to understand the impact of assumptions made when using a particular model. Here we provide a method to assess how uncertainty about the structure of a natural system affects the conclusions we can draw from mathematical models of its dynamics. We use biological examples to illustrate the importance of considering uncertainty in both model structure and parameters. We show how solely considering the latter source of uncertainty can result in misleading conclusions and incorrect model inferences. Mathematical models of natural systems are abstractions of much more complicated processes. Developing informative and realistic models of such systems typically involves suitable statistical inference methods, domain expertise, and a modicum of luck. Except for cases where physical principles provide sufficient guidance, it will also be generally possible to come up with a large number of potential models that are compatible with a given natural system and any finite amount of data generated from experiments on that system. Here we develop a computational framework to systematically evaluate potentially vast sets of candidate differential equation models in light of experimental and prior knowledge about biological systems. This topological sensitivity analysis enables us to evaluate quantitatively the dependence of model inferences and predictions on the assumed model structures. Failure to consider the impact of structural uncertainty introduces biases into the analysis and potentially gives rise to misleading conclusions.