Two-State Stochastic Model of In Vivo Observations of Transcriptional Bursts

In vivo measurements of gene expression in single cells show behavior that has been interpreted as stochastic bursts of transcription. In one case, these data have been interpreted as random ON-OFF transitions of the gene, but there is no experimental measurements or theoretical treatment of the number of transcripts produced at each burst event. In another case, such data have been interpreted to indicate multiple underlying transcriptional states. Here, we place both of these experiments in a common theoretical framework. In it, we couple two stochastic processes, one for synthesis of transcripts and one for their removal. Analysis of the resulting model is greatly aided by the existence of exact solutions of the master equation. We find the bursting limit of the exact solutions for our two-state gene expression model and show the occurrence of bursts of multiple sizes and durations by exact stochastic simulations. We also demonstrate that data from <i>Drosophila melanogaster</i> interpreted in terms of multiple underlying transcription states is fully compatible with underlying two-state ON or OFF transcriptional behavior. We discuss what experimental data is required to unambiguously determine the number of underlying promoter states.