Transcription factor target site search and gene regulation in a background of unspecific binding sites

Response time and transcription level are vital parameters of gene regulation. They depend on how fast transcription factors (TFs) find and how efficient they occupy their specific target sites. It is well known that target site search is accelerated by TF binding to and sliding along unspecific DNA and that unspecific associations alter the occupation frequency of a gene. However, whether target site search time and occupation frequency can be optimized simultaneously is mostly unclear. We developed a transparent and intuitively accessible state-based formalism to calculate search times to target sites on and occupation frequencies of promoters of arbitrary state structure. Our formalism is based on dissociation rate constants experimentally accessible in live cell experiments. To demonstrate our approach, we consider promoters activated by a single TF, by two coactivators or in the presence of a competitive inhibitor. We find that target site search time and promoter occupancy differentially vary with the unspecific dissociation rate constant. Both parameters can be harmonized by adjusting the specific dissociation rate constant of the TF. However, while measured DNA residence times of various eukaryotic TFs correspond to a fast search time, the occupation frequencies of target sites are generally low. Cells might tolerate low target site occupancies as they enable timely gene regulation in response to a changing environment.