Title: Markov chain aggregation and its application to rule-based modelling,
Abstract: Rule-based modelling allows to represent molecular interactions in a compact
and natural way. The underlying molecular dynamics, by the laws of stochastic
chemical kinetics, behaves as a continuous-time Markov chain. However, this
Markov chain enumerates all possible reaction mixtures, rendering the analysis
of the chain computationally demanding and often prohibitive in practice. We
here describe how it is possible to efficiently find a smaller, aggregate
chain, which preserves certain properties of the original one. Formal methods
and lumpability notions are used to define algorithms for automated and
efficient construction of such smaller chains (without ever constructing the
original ones). We here illustrate the method on an example and we discuss the
applicability of the method in the context of modelling large signalling
pathways.