Abstract: Molecular biological models usually suffer from a large combinatorial explosion. Indeed, proteins form complexes and modify each other, which leads to the formation of a huge number of distinct chemical species. Thus we cannot generate explicitly the quantitative semantics of these models, and it is even harder to compute their properties.
In this extended abstract, we summarize a framework for reducing the combinatorial complexity of models of biochemical networks. We use rules-based languages to describe the interactions between proteins. Then we compile these models into continuous-time Markov chains. Finally, we use backward bisimulations in order to reduce the dimension of the state space of these Markov chains. More specifically, these backward bisimulations are defined thanks to an abstraction of the control flow of information within chemical species and thanks to an algorithm which detects which protein sites have the same capabilities of interaction.

@inProceedings{ICNAAM2010,
   author =    {Ferdinanda Camporesi and J\'er\^ome Feret and  Heinz Koeppl and Tatjana Petrov},
   title =     {Automatic reduction of stochastic rules-based models in a nutshell},
   editor =    {T.E.\ Simos},
   booktitle = {Proceedings of the International Conference of Numerical Analysis and Applied Mathematics ICNAAM$\,$'10},
   address =   {Rhodes, Greece},
   series =    {American Institute of Physics Conference Proceedings},
   number = {1281},
   issue = {2},
   publisher = {American Institute of Physics},
   pages =     {1330-1334},
   month =     {19--25 September},
   year =      {2010},
}