Steady-state preserving reduction for genetic regulatory network models

Fine-scale models based on stochastic differential equations can provide the most detailed description of the dynamics of gene expression and imbed, in principle, all the information about the biochemical reactions involved in gene interactions. However, the computational complexity involved in the design of optimal intervention strategies to favorably effect system dynamics for such detailed models is enormous. Hence, there is a need to design mappings from fine-scale models to coarse-scale models while maintaining sufficient structure for the problem at hand. In this paper, we propose a mapping from a fine-scale model represented by a Chemical Master Equation to a coarse-scale model represented by a Probabilistic Boolean Network that maintains the collapsed steady state distribution of the detailed model. We also evaluate the performance of the intervention strategy designed using the coarse scale model when applied to the fine-scale model.