Optimizing Oscillators for Specific Tasks Predicts Preferred Biochemical Implementations

Oscillatory processes are used throughout cell biology to control time-varying physiology including the cell cycle, circadian rhythms, and developmental patterning. It has long been understood that free-running oscillations require feedback loops where the activity of one component depends on the concentration of another. Oscillator motifs have been classified by the positive or negative net logic of these loops. However, each feedback loop can be implemented by regulation of either the production step or the removal step. These possibilities are not equivalent because of the underlying structure of biochemical kinetics. By computationally searching over these possibilities, we find that certain molecular implementations are much more likely to produce stable oscillations. These preferred molecular implementations are found in many natural systems, but not typically in artificial oscillators, suggesting a design principle for future synthetic biology. Finally, we develop an approach to oscillator function across different reaction networks by evaluating the biosynthetic cost needed to achieve a given phase coherence. This analysis predicts that phase drift is most efficiently suppressed by delayed negative feedback loop architectures that operate without positive feedback. PACS numbers 47.15.-x