Qualitative Transition Systems for the Abstraction and Comparison of Transient Behavior in Parametrized Dynamic Models

Abstract

Quantitative models in Systems Biology depend on a large number of free parameters, whose values completely determine behavior of models. These parameters are often estimated by fitting the system to observed experimental measurements and data. The response of a model to parameter variation defines qualitative changes of the system’s behavior. The influence of a given parameter can be estimated by varying it in a certain range. Some of these ranges produce similar system dynamics, making it possible to define general trends for trajectories of the system (e.g. oscillating behavior) in such parameter ranges. Such trends can be seen as a qualitative description of the system’s dynamics within a parameter range. In this work, we define an automata-based formalism to formally describe the qualitative behavior of systems’ dynamics. Qualitative behaviors are represented by finite transition systems whose states contain predicate valuation and whose transitions are labeled by probabilistic delays. Biochemical system’ dynamics are automatically abstracted in terms of these qualitative transition systems by a random sampling of trajectories. Furthermore, we use graph theoretic tools to compare the resulting qualitative behaviors and to estimate those parameter ranges that yield similar behaviors. We validate this approach on published biochemical models and show that it enables rapid exploration of models’ behavior, that is estimation of parameter ranges with a given behavior of interest and identification of some bifurcation points.