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Formal abstraction of quantitative semantics for protein-protein interaction cellular network models.


The project AbstractCell aims at designing efficient approximations and algorithms to compute the properties of protein-protein interaction networks. The behaviour of a cell is driven by interactions between proteins: proteins assemble with each other and activate one another in order to receive, propagate, and integrate signals. Such protein-protein interaction networks control apoptosis (cell death), mitosis (cell duplication), specialisation and migration of the cell. When these networks fail, the cell life cycle is damaged, which may ultimately cause cancer. Understanding such interaction networks is a very difficult task. Firstly, modellers of molecular signalling networks must cope with the combinatorial explosion of protein states generated by post-translational modifications and complex formation. Secondly, the state of the art is always evolving. New assumptions about interactions are always made and former assumptions are validated or refuted by new experiments. Thus, it is not obvious to understand which assumptions are compatible with each others. Yet, the design of accurate models is needed: not only can it lead to a breakthrough in biology, but also provide new tools for the pharmaceutics industry that would avoid very costly in vivo experiments (namely by detecting in silico that a potential treatment cannot work) and search for more complex drug combinations.

Rule-based models provide a powerful way of describing cellular networks. These models consist of formal rules stipulating the (partial) contexts wherein specific protein-protein interactions occur. These contexts specify molecular patterns that are usually less detailed than molecular species. This way, rule-based approaches enable a concise description of molecular signalling networks; moreover models can be easily tuned or updated to modify the set of hypotheses about protein interactions. Yet in order to test the consistency of a set of hypotheses, one has to compute the behaviour of a model, which is actually the goal of the present project proposal. The behaviour of a model can be formally described by either a stochastic or a differential semantics. However, both do not scale very well because either the number of instances of proteins (typically 106 proteins), or the number of different proteins (typically more than 1030) is too large.

We propose to use the abstract interpretation framework in order to reduce the dimension of both differential and stochastic semantics. Abstract interpretation is a theory of approximations between semantics. We will use this framework to design formal (and automated) methods for constructing coarse-grained and self-consistent dynamical systems aimed at molecular patterns that are distinguishable by the dynamics of the original systems. This way, by construction, the trajectories of the reduced systems will be projections of trajectories of the initial systems. We are going to design tools for integrating the reduced differential semantics and to simulate the (reduced or not) stochastic semantics.

The novelty of our approach relies on its formal foundation. Expressing possible abstractions in the formal abstract interpretation framework will give certain guarantees about the result (which is exact by design) and, additionally, a better understanding of the abstraction mechanisms. Our project will lead to more reliable and more efficient modelling methods which enable biologists to tackle novel challenges in Systems Biology.