Sustainability of RNA-interference in Rule Based Modelling

RNA interference (RNAi) is a mechanism whereby small pieces of RNA directly control gene expression in target messenger RNA by identifying complementary sequences. We model RNAi in terms of rule-based modelling. Interpreting a small interfering RNA (siRNA) as a primitive agent, the model provides a finegrained interpretation to directly capture the fundamental interactions (e.g., hybridization, denaturation, cleavage, copying, degradation) among double and single strands of RNA and siRNA. We investigate the sustainability of RNAi, which is characterized by the population level of double-stranded RNA (dsRNA) during the interference. Our model aims to capture the individual level of each agent in RNAi in terms of the Galton–Watson multitype branching processes determined by the modelling. Each siRNA has a type that represents its original position inside the dsRNA from which it was cleaved. The probability of extinction of populations of siRNA is investigated and analyzed for both primer-dependent and -independent synthesis of RNAi, which are important topics in experimental biology from the perspective of the difference between animal and plant RNAi. The sustainability is shown to be invariant under some appropriate model refinements for the primer-dependent synthesis. This invariance guarantees the sufficiency of the compact description of our rule based modelling in capturing the sustainability of RNAi.