Molecular level dynamics of genetic oscillator--the effect of protein-protein interaction.

Uncovering how interactions of a set of molecular components influence the system's dynamic behavior is important for understanding intracellular processes and elucidating design principles, but unfortunately, there are limited efforts for studying this issue. Here, we study the effect of distinct post-translational dynamics controlled by protein dimerization on oscillations in the repressilator. For this, we propose three biologically motivated model scenarios of the repressilator with monomer or dimer being the active form of repressor, and with protein-protein interactions. It is found that the dimer dissociation constant can tune oscillatory regions, frequency and amplitude. Introducing a modified linear noise approximation to evaluate fluctuations of amplitude and period in the oscillatory systems, we show that different dimerization leads to a different effect on period and amplitude in reducing noise. The manipulation of the circuit's biochemical properties provides a practical strategy for designing a robust and tunable oscillator.