Reachability analysis based model validation in systems biology

Systems biology is an emerging multi-disciplinary area, which aims to understand the underneath regulatory mechanisms of the biomolecular interaction networks inside the cell through dynamical system approaches. The first challenge in systems biology is how to obtain an accurate and predictable computational model for the biomolecular networks under study. However, due to limited experimental data, it is unavoidable to have incomplete or even wrong models. Therefore, it is a critical task in systems biology to check the model's correctness, which is called model validation problem. This paper will focus on this issue, and propose a (un-)reachability analysis based model validation method. In particular, Petri net models are investigated, and the validation process is evaluated by the reachability of state equations. It is shown that the reachability can be checked by the existence of integer solutions of Diophantine equations. Two methods are proposed to solve the equations. The first one is by Smith normal form test, and the other is by integer programming. Two case studies are provided to demonstrate these two approaches. These tests can screen out the unreachable states and offer the hints to modify the model structure, which provides us more insights of the regulatory mechanism and helps biologists to generate hypotheses and design experiments.