Models of transcription are often built around a picture of RNA polymerase and transcription factors (TFs) acting on a single copy of a promoter. However, most TFs are shared between multiple genes with varying binding affinities. Beyond that, genes often exist at high copy number-in multiple identical copies on the chromosome or on plasmids or viral vectors with copy numbers in the hundreds. Using a thermodynamic model, we characterize the interplay between TF copy number and the demand for that TF. We demonstrate the parameter-free predictive power of this model as a function of the copy number of the TF and the number and affinities of the available specific binding sites; such predictive control is important for the understanding of transcription and the desire to quantitatively design the output of genetic circuits. Finally, we use these experiments to dynamically measure plasmid copy number through the cell cycle.
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