Since the advent of techniques to investigate gene expression on a large scale, numerous circadian rhythms in mRNA abundance have been reported. These rhythms generally differ in amplitude and phase. First studies on circadian rhythms of transcription on a large scale are also emerging. We investigated to what extent the same circadian regulatory mechanism of transcription can give rise to rhythms in RNA amount that differ in phase solely based on a parameter that is not regulated by the circadian clock. Using a discrete-time approach, we modeled a sinusoidal rhythm in transcription with various constant exponential RNA decay rates. We found that the slower the RNA is degraded the later the phase of the RNA amount rhythm compared to the phase of the transcriptional rhythm. However, we also found that the phase of the rhythm in RNA amount is limited to a time frame spanning the first quarter of the period following the phase of the transcriptional rhythm. This finding is independent of the amplitude and vertical shift of the transcriptional rhythm or even of the way RNA degradation is modeled. We confirmed our results with a continuous-time model, which also allowed us to derive a simple formula that relates the phase of a rhythm in mRNA amount solely to the phase and period of its sinusoidal transcriptional rhythm and its constant mRNA half-life. This simple formula even holds true for the best sinusoidal approximations of a non-sinusoidal rhythm of transcription and mRNA amount. When using our discrete-time approach to model constant rates of transcription with a sinusoidal RNA half-life, on the other hand, we found that varying the constant component of the system, i.e. the rate of transcription, does not change the phase of the rhythm in RNA amount. In summary, our data show that at least four distinct circadian regulatory mechanisms are required to allow for all phases in rhythms of RNA amount, one for each quarter of the period.
Available at: http://works.bepress.com/bruce_kessler/26/