The Stochastic Signature of Mixed Promoter States

Gene promoters typically contain multiple binding sites for transcription factors. This allows for distinct transcription-factor binding configurations, each characterized by a different transcriptional activity of the regulated gene. However, at a given transcription-factor concentration, the promoter is not expected to exhibit a single configuration, but, instead, a ``mixed state'' with fractional probabilities for the different configurations. What is the nature of these mixed promoter states at the single-cell level? We investigate this question by measuring simultaneously, in individual cells, the concentration of the CI transcription factor and the transcriptional output of the regulated promoter, P$_{RM}$, in \textit{E. coli}. We use the mRNA copy-number statistics to reconstruct the stochastic kinetics of the different promoter configurations and calculate their probabilities at each CI concentration. We find that the mRNA distribution for cells in a mixed state can be described as a convolution of the pure-state distributions, indicating rapid switching between the pure promoter states. Thus, mixed promoter states do not result in different cell populations but instead appear as a new, well-defined promoter activity.