  We study the effects of multiple binding sites in the promoter of a genetic
oscillator. We evaluate the regulatory function of a promoter with multiple
binding sites in the absence of cooperative binding, and consider different
hypotheses for how the number of bound repressors affects transcription rate.
Effective Hill exponents of the resulting regulatory functions reveal an
increase in the nonlinearity of the feedback with the number of binding sites.
We identify optimal configurations that maximize the nonlinearity of the
feedback. We use a generic model of a biochemical oscillator to show that this
increased nonlinearity is reflected in enhanced oscillations, with larger
amplitudes over wider oscillatory ranges. Although the study is motivated by
genetic oscillations in the zebrafish segmentation clock, our findings may
reveal a general principle for gene regulation.
