Koeppl, H. ; Petrov, T. (2012)
Reductions of stochastic rule-based models: HOG pathway in yeast.
ICSB : The 13th International Conference on Systems Biology.
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Kurzbeschreibung (Abstract)

During induction of signal transduction pathways, transient complex formation and post-translational modification of proteins give rise to a combinatorial number of distinct molecular species. Standard chemical kinetics is impractical to describe such combinatorial assembly processes, since it requires the enumeration of all reachable species. However, it is not the species, but the proteins' domains, sites, that have interaction capabilities - binding or modifying other proteins. Groups of sites interact between each-other and transmit the information within the system. Rule-based languages, such as Kappa or BioNetGen, put proteins instead of the species in a center stage; their modification and binding is explicitly traced instead of abstracting every new bound protein into a new species. Rule-based languages compactly describe models, by mentioning only those aspects of molecules that are important for triggering an event. We show how to reduce rule-based models, by exploiting the limited context on which events are conditioned. The main idea is to detect coarse-grained variables - fragments, such that the stochastic evolution of the system can be described self-consistently as a function of fragments abundances. The method is performed entirely by static analysis of the rules, and was shown to perform even exponential reduction of the size of the underlying state space. The technique also defines a particular decomposition of the stochastic system into smaller, independent stochastic systems operating over the fragments variables. We built a detailed model of High osmolarity glycerol (HOG) pathway in S. cerevisiae, based on evidence documented in literature. The model comprises 41 proteins and 443 rules. Without polymerization effects, the number of species involving Hog1 already counts up to 1476. The stochastic model can be decomposed into 20 independent smaller modules. For example, the scaffold Pbs2 is shown to have 3 independently interacting groups of sites, making the number of species at least 4 times larger than the number of fragments involving Pbs2. Together with Hog1, Ste50 and Ste11, Pbs2 theoretically exhibits unbounded polymerization, such that the number of species grows exponentially with proteins' abundances, while the number of fragments remains constant.

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