Electronic Notes in Theoretical Computer Science (ENTCS)
Fragments-based Model Reduction: Some Case Studies
Electronic Notes in Theoretical Computer Science (ENTCS)
Fragments and Chemical Organisations
Electronic Notes in Theoretical Computer Science (ENTCS)
Biochemical reaction rules with constraints
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
Formal Reduction for Rule-based Models
Electronic Notes in Theoretical Computer Science (ENTCS)
Probabilistic model checking of biological systems with uncertain kinetic rates
Theoretical Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
Containment in Rule-Based Models
Electronic Notes in Theoretical Computer Science (ENTCS)
DPO transformation with open maps
ICGT'12 Proceedings of the 6th international conference on Graph Transformations
Abstraction of graph-based models of bio-molecular reaction systems for efficient simulation
CMSB'12 Proceedings of the 10th international conference on Computational Methods in Systems Biology
Reconstructing species-based dynamics from reduced stochastic rule-based models
Proceedings of the Winter Simulation Conference
Complex functional rates in rule-based languages for biochemistry
Transactions on Computational Systems Biology XIV
Abstraction and training of stochastic graph transformation systems
FASE'13 Proceedings of the 16th international conference on Fundamental Approaches to Software Engineering
Complex Functional Rates in the Modeling of Nano Devices (Extended Abstract)
Electronic Notes in Theoretical Computer Science (ENTCS)
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Rule-based approaches (as in our own Kappa, or the BNG language, or many other propositions allowing the consideration of "reaction classes'') offer new and more powerful ways to capture the combinatorial interactions that are typical of molecular biological systems. They afford relatively compact and faithful descriptions of cellular interaction networks despite the combination of two broad types of interaction: the formation of complexes (a biological term for the ubiquitous non-covalent binding of bio-molecules), and the chemical modifications of macromolecules (aka post-translational modifications). However, all is not perfect. This same combinatorial explosion that pervades biological systems also seems to prevent the simulation of molecular networks using systems of differential equations. In all but the simplest cases the generation (and even more the integration) of the explicit system of differential equations which is canonically associated to a rule set is unfeasible. So there seems to be a price to pay for this increase in clarity and precision of the description, namely that one can only execute such rule-based systems using their stochastic semantics as continuous time Markov chains, which means a slower if more accurate simulation. In this paper, we take a fresh look at this question, and, using techniques from the abstract interpretation framework, we construct a reduction method which generates (typically) far smaller systems of differential equations than the concrete/canonical one. We show that the abstract/reduced differential system has solutions which are linear combinations of the canonical ones. Importantly, our method: 1) does not require the concrete system to be explicitly computed, so it is intensional, 2) nor does it rely on the choice of a specific set of rate constants for the system to be reduced, so it is symbolic, and 3) achieves good compression when tested on rule-based models of significant size, so it is also realistic.