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Bilateral Contracts and Grants with Industry
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Bilateral Contracts and Grants with Industry
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Section: New Results

Abstraction of Rule-Based Biological Models

Stochastic fragments: A framework for the exact reduction of the stochastic semantics of rule-based models

Participants : Jérôme Feret, Heinz Koeppl [École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland] , Tatjana Petrov [École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland] .

Protein-protein interaction networks, Stochastic systems, Backward bisimulations, Model reduction. In [9] , we propose an abstract interpretation-based framework for reducing the state space of stochastic semantics for protein-protein interaction networks. Our approach consists in quotienting the state space of networks. Yet interestingly, we do not apply the widely-used strong lumpability criterion which imposes that two equivalent states behave similarly with respect to the quotient, but a weak version of it. More precisely, our framework detects and proves some invariants about the dynamics of the system: indeed the quotient of the state space is such that the probability of being in a given state knowing that this state is in a given equivalence class, is an invariant of the semantics. Then we introduce an individual-based stochastic semantics (where each agent is identified by a unique identifier) for the programs of a rule-based language (namely Kappa) and we use our abstraction framework for deriving a sound population-based semantics and a sound fragments-based semantics, which give the distribution of the traces respectively for the number of instances of molecular species and for the number of instances of partially defined molecular species. These partially defined species are chosen automatically thanks to a dependency analysis which is also described in [9] .

An algebraic approach for inferring and using symmetries in rule-based models

Participant : Jérôme Feret.

Graph rewriting, Single-pushout semantics, Symmetries, Bisimulations, Model reduction. Symmetries arise naturally in rule-based models, and under various forms. Besides automorphisms between site graphs, which are usually built within the semantics, symmetries can take the form of pairs of sites having the same capabilities of interactions, of some protein variants behaving exactly the same way, or of some linear, planar, or 3D molecular complexes which could be seen modulo permutations of their axis and/or mirror-image symmetries. In [16] , we propose a unifying handling of symmetries in Kappa. We follow an algebraic approach, that is based on the single pushout semantics of Kappa. We model classes of symmetries as finite groups of transformations between site graphs, which are compatible with the notion of embedding (that is to say that it is always possible to restrict a symmetry that is applied with the image of an embedding to the domain of this embedding) and we provide some assumptions that ensure that symmetries are compatible with pushouts. Then, we characterise when a set of rules is symmetric with respect to a group of symmetries and, in such a case, we give sufficient conditions so that this group of symmetries induces a forward bisimulation and/or a backward bisimulation over the population semantics.