Working group: "Computational Biology"

2012, the 7th of February

Tatjana Petrov

Title: Abstraction, decomposition and reconstruction of stochastic semantics of rule-based models.

Internal dependencies of multi-site post-translational modifications and conformational changes of signaling proteins reflect the rich internal logic of proteins. Since chemical kinetics operates on states which are based on descriptions of full molecular species, often times a model becomes too complex to analyze. We discuss a method for decomposition, abstraction and reconstruction of the stochastic semantics of rule-based systems with conserved number of agents. Abstraction is induced by counting entities that are more abstract than species, fragments. The rule-set can be decomposed to smaller rule-sets, so that the fragment-based dynamics of the whole rule-set is exactly a composition of species-based dynamics of smaller rule-sets. The reconstruction of the transient species-based dynamics is possible for certain initial distributions. If all the rules in a rule set are reversible, the full reconstruction of the species-based dynamics is always possible at the stationary distribution. We use a case study of colloidal aggregation to demonstrate that the method can reduce the state space of the underlying Markov process exponentially (with respect to the standard species-based description).