Analyzing the Effects of Coarse-scale Modeling of Genetic Regulatory Networks

Fine-scale models such as stochastic master equations can provide a very accurate description of the real genetic regulatory system but inadequate time series data and limitations on cell specific measurements in biological experiments prevent the accurate inference of the parameters of such a fine-scale model. Furthermore, the use of fine-scale stochastic models is restricted by the inherent computational complexity involved in its simulation. In this paper, we theoretically analyze the effect on the transient and steady state behavior of coarse-scale Markov chain modeling as compared to fine scale stochastic master equation models. Utilizing a reduction mapping that maintains the collapsed steady state probability distribution of stochastic master equation models, we provide bounds on the expected deviation of the transient behavior.