Characterizing the Effect of Coarse-Scale PBN Modeling on Dynamics and Intervention Performance of Genetic Regulatory Networks Represented by Stochastic Master Equation Models

Fine-scale models based on stochastic master 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, there is limited time-series experimental data available for inference of such fine-scale models. Furthermore, the computational complexity involved in the design of optimal intervention strategies to favorably effect system dynamics for such detailed models is enormous. Thus, there is a need to design mappings from fine-scale models to coarse-scale models while maintaining sufficient structure for the problem at hand and to study the effect of intervention policies designed using coarse-scale models when applied to fine-scale models. In this paper, we propose a mapping from a fine-scale model represented by a stochastic master equation to a coarse-scale model represented by a probabilistic Boolean network that maintains the collapsed steady state probability distribution of the detailed model. We also derive bounds on the performance of the intervention strategy designed using the coarse-scale model when applied to the fine-scale model.