  Genetic oscillators are present in the cells of many organisms and control
several biological processes. The common feature of such oscillators is the
presence of a protein which represses the transcription of its own gene.
Recently, it has been shown that for many genes transcription is not a
continuous process, but that it proceeds in bursts. We study here the
relationship between bursty transcription and the robustness of protein
oscillations. We concentrate on the temporal profile of mRNA production by
studying regimes where this profile changes but the amount of mRNA produced is
kept fixed. For systems with different degrees of cooperativity we show that in
general bursts are associated with more robust oscillations, but when they are
too short and intense they can have the opposite effect. In other words, we
show that, in terms of the regularity of the oscillations generated, there is
an optimal value for the intensity of the bursts.
