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.

@InProceedings{PetrovWSC2012,
title = "Reconstructing species-based dynamics from reduced stochastic rule-based models",
booktitle = "Winter Simulation Conference",
publisher = "WSC",
year = "2012",
editor = "C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose,& A. M.~Uhrmacher",
author = "Tatjana Petrov and  Jerome Feret and Heinz Koeppl",
}