Reconstructing species-based dynamics from reduced stochastic rule-based models

Authors:
Tatjana Petrov;Jerome Feret;Heinz Koeppl
Affiliations:
ETH Zurich, Switzerland;DI-ENS (INRIA, ENS, CNRS), Paris, France;ETH Zurich, Switzerland
Venue:
Proceedings of the Winter Simulation Conference
Year:
2012

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Abstract

Many bio-molecular reactions inside the cell are characterized by complex-formation and mutual modification of a few constituent molecules that give rise to a combinatorial number of reachable complexes or species. For such cases rule-based models (or site-graph-rewrite rules), offer a compact model description, by enumerating only the necessary context of interacting molecules. Such a model specification induces symmetries in the underlying Markov chain, which we have recently exploited for model reduction, based on a backward Markovian bisimulation. Interestingly, the method showed a theoretical possibility of reconstructing the high-dimensional species-based dynamics from the aggregate state. In this paper, we present a procedure for reconstructing the high-dimensional species-based dynamics from the aggregate state, and we provide an algorithm for computing such de-aggregation functions explicitly. The algorithm involves counting the automorphisms of a connected site-graph, and has a quadratic time complexity in the number of molecules which constitute the site-graphs of interest. We provide illustrating case studies.