A Hidden Markov Model for Transcriptional Regulation in Single Cells

We discuss several issues pertaining to the use of stochastic biochemical systems for modeling transcriptional regulation in single cells. By appropriately choosing the system state, we can model transcriptional regulation by a hidden Markov model (HMM). This opens the possibility of using well-known techniques for the statistical analysis and stochastic control of HMMs to mathematically and computationally study transcriptional regulation in single cells. Unfortunately, in all but a few simple cases, analytical characterization of the statistical behavior of the proposed HMM is not possible. Moreover, analysis by Monte Carlo simulation is computationally cumbersome. We discuss several techniques for approximating the HMM by one that is more tractable. We employ simulations, based on a biologically relevant transcriptional regulatory system, to show the relative merits and limitations of various approximation techniques and provide general guidelines for their use.