text: The Hill equation can be applied in modelling the rate at which a gene product is produced when its parent gene is being regulated by transcription factors (e.g., activators and/or repressors). Doing so is appropriate when a gene is regulated by multiple binding sites for transcription factors, in which case the transcription factors may bind the DNA in a cooperative fashion.
  If the production of protein from gene  is up-regulated (activated) by a transcription factor , then the rate of production of protein  can be modeled as a differential equation in terms of the concentration of activated  protein:
  where  is the maximal transcription rate of gene .
  Likewise, if the production of protein from gene  is down-regulated (repressed) by a transcription factor , then the rate of production of protein  can be modeled as a differential equation in terms of the concentration of activated  protein:
  where  is the maximal transcription rate of gene .