Section: New Results

Analysis of Biological Pathways

We have improved our framework to design and analyze biological networks. This framework focused on protein-protein interaction networks described as graph rewriting systems. Such networks can be used to model some signaling pathways that control the cell cycle. The task is made difficult due to the combinatorial blow up in the number of reachable species (i.e., non-isomorphic connected components of proteins).

Automatic Reduction of Differential Semantics

Participants : Ferdinanda Camporesi, Vincent Danos [University of Edinburgh] , Jérôme Feret, Walter Fontana [Harvard Medical School] , Russ Harmer [Harvard Medical School] , Jean Krivine [Paris VII] .

We have developed an abstract interpretation-based framework that enables the reduction of the differential semantics for protein-protein interaction networks. Results are sound since trajectories in the abstract system are projections of the trajectories in the concrete system.

The flow of information is a key element in our model reduction framework because it enables the identification of the correlations which are useless when computing observables of interest. Thus there is a need of providing good trade-off in the description of the flow of information throughout the biochemical structure of chemical species.

The notion of symmetries between sites is also important, since knowing that two sites have exactly the same capabilities of interaction enable exact quotienting (or lumping) of the set of reachable species.

In [13] , [14] , we have proposed a heterogeneous over-approximation of the flow of information where the flow that is attached to an agent can depend on its relative position in a chemical species. Moreover, we have showed how to use symmetries between sites so as to define another model reduction and we have proposed an algebraic product to combine model reductions, the product of two reduced models being the least abstract model which is at least as abstract as both model.

Automatic Reduction of Stochastic Semantics

Participants : Ferdinanda Camporesi, Jérôme Feret, Thomas Henzinger [Institute of Science and Technology, Austria] , Heinz Koeppl [ETH Zürich] , Tatjana Petrov [ETH Zürich] .

We have proposed an abstract interpretation-based framework for reducing the state-space of stochastic semantics for protein-protein interaction networks. Our framework ensures that the trace distribution of the reduced system is the exact projection of the trace distribution of the concrete system. Moreover, when the abstraction is complete, if any pair of concrete states that have the same abstraction are equipropable at initial state, any pair of concrete states that share the same abstraction are equiprobable at any time $t$.

In [12] , we have formalized the model reduction framework for the stochastic semantics and we have established the relationships with the notions of lumpability, and bisimulation is established.