Gene regulation and Hill functions
Transcription factors can activate or repress expression.
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Transcription factors can activate or repress expression. A Hill response describes a saturating nonlinear relationship between regulator concentration and production. The Hill coefficient controls the steepness of the response; it is a model parameter, not automatically a measured count of binding sites. Fitting a curve does not establish a unique molecular mechanism.
Worked example
For activation H(x)=x^2/(K^2+x^2), H(K)=0.5. Increasing x far above K moves H toward one rather than increasing without bound.