Mathematical Modeling of Rhythmic Gene Expression: Impact of Negative Autoregulation on Amplitude Preservation

The mammalian circadian clock is an endogenous biochemical oscillator that generates rhythmicity with a period of about 24 hours in the expression of numerous clock-controlled genes (CCGs) mainly by controlling their transcription or mRNA stability. There are hurdles for propagating high amplitude oscillations from the circadian clock to CCG expression. Long molecular half-lives decrease relative oscillation amplitudes, and half-lives of proteins are, indeed, often long enough to significantly reduce amplitude. A question, then, arises; how does the gene expression process overcome the amplitude-dampening effect to retain strong rhythmicity?Here we theoretically investigate negative autoregulation as a possible scenario for propagation of strong circadian rhythmicity. We considered a CCG coding for, e.g., a transcription factor that undergoes post-translational modifications and represses its own expression. We studied mathematical models with or without the negative autoregulation, which were formulated in terms of parameters directly observable in omics scale data. Our analyses show that amplitudes can be strongly propagated with negative autoregulation, overcoming limits due to long half-lives. Moreover, when modification steps were increased, reliable and precise rhythm propagation, defying random cell-to-cell variation in rates and lifetimes, was readily achievable. Our results are general enough to be applicable to a variety of oscillation phenomena.