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Section: New Results
Analysis of Biological Pathways
We have improved our framework to design and analyze biological networks in Kappa . This framework focuses 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).
Semantics
Participants : Jonathan Hayman, Tobias Heindel [CEA-List] .
Keywords: Graph rewriting, Single Push-Out semantics.
Domain-specific rule-based languages can be understood intuitively as transforming graph-like structures, but due to their expressivity these are difficult to model in `traditional' graph rewriting frameworks.
In [16] , we introduce pattern graphs and closed morphisms as a more abstract graph-like model and show how Kappa can be encoded in them by connecting its single-pushout semantics to that for Kappa. This level of abstraction elucidates the earlier single-pushout result for Kappa, teasing apart the proof and guiding the way to richer languages, for example the introduction of compartments within cells.
Causality Analysis
We use causal analysis so as to extract minimal concurrent scenarios that lead to the activation of given events.
Implementation
Participant : Jérôme Feret.
Keywords: Causality, Counter-examples, Compression.
This year, we have re-implemented in OpenKappa the strong compression method that is described in [48] . The new implementation is very efficient, it has been used to extract minimal scenarios from traces of several hundred of thousands causally related events, that were generated during the simulation of a model of the WnT signaling pathway.
Framework
Participant : Jonathan Hayman.
Keywords: Abstraction, Causality, Compression.
Standard notions of independence of rule applications fail to provide adequately concise causal histories, leading to the earlier formulation of strong and weak forms of trajectory compression for Kappa. In [15] , we give a simple categorical account of how forms of compression can be uniformly obtained. This generalisation also describes a way for the user to specify their own levels of compression between weak and strong, which we call filtered compression. This is based on the idea of the user specifying the part of the type graph that represents the the structure which the compression technique should track through the trace.
Model Reduction
Participants : Ferdinanda Camporesi, Jérôme Feret, Jonathan Hayman.
Keywords: Context-sensitivity, Differential semantics, Model reduction.
Rule-based modeling allows very compact descriptions of protein-protein interaction networks. However, combinatorial complexity increases again when one attempts to describe formally the behaviour of the networks, which motivates the use of abstractions to make these models more coarse-grained. Context-insensitive abstractions of the intrinsic flow of information among the sites of chemical complexes through the rules have been proposed to infer sound coarse-graining, providing an efficient way to find macro-variables and the corresponding reduced models.
In [12] , we propose a framework to allow the tuning of the context-sensitivity of the information flow analyses and show how these finer analyses can be used to find fewer macro-variables and smaller reduced differential models.