Statistical mechanical model of coupled transcription from multiple promoters due to transcription factor titration

Transcription factors (TFs) with regulatory action at multiple promoter targets is the rule rather than the exception, with examples ranging from the cAMP receptor protein (CRP) in E. coli that regulates hundreds of different genes simultaneously to situations involving multiple copies of the same gene, such as plasmids, retrotransposons, or highly replicated viral DNA. When the number of TFs heavily exceeds the number of binding sites, TF binding to each promoter can be regarded as independent. However, when the number of TF molecules is comparable to the number of binding sites, TF titration will result in correlation ("promoter entanglement") between transcription of different genes. We develop a statistical mechanical model which takes the TF titration effect into account and use it to predict both the level of gene expression for a general set of promoters and the resulting correlation in transcription rates of different genes. Our results show that the TF titration effect could be important for understanding gene expression in many regulatory settings.