  We study the response of an autoregulated gene to a range of concentrations
of signal molecules. We show that transcriptional leakage and noise due to
translational bursting have the opposite effects. In a positively autoregulated
gene, increasing the noise converts the response from graded to binary, while
increasing the leakage converts the response from binary to graded. Our
findings support the hypothesis that, being a common phenomenon, leaky
expression may be a relatively easy way for evolutionary tuning of the type of
gene response without changing the type of regulation from positive to
negative.
