A critical signal for phenotype transition driven by negative feedback loops.

The biological rhythms governed by negative feedback loops have undergone extensive investigation. However, developing reliable and versatile warning signals to predict periodic fluctuations in physiological processes and behaviors associated with these rhythms remains a challenge. Here, we monitored the heart rate and tracked ovulation dates of 91 fertile women. The finding strongly links the velocity (derivative) of heart rate with ovulation in menstrual cycles, providing a predictive warning signal. Similarly, an analysis of calcium signaling in the suprachiasmatic nucleus (SCN) of mice reveals that the maximum velocity of rising calcium signal aligns with locomotor activity offsets. To demonstrate the generality of derivative-transitions link, numerical simulations using a negative feedback loop model were conducted. Statistical analysis indicated that over 90% of the oscillations exhibited a correlation between maximum velocity and transition points. Consequently, the maximum velocity derived from oscillatory curves holds significant potential as an early warning signal for critical transitions.