Velocity response curves support the role of continuous entrainment in circadian clocks.

Circadian clocks drive endogenous oscillations in organisms across the tree of life. The Earth's daily light/dark cycle entrains these clocks to the environment. Two major theories of light entrainment have been presented in the literature. The discrete theory emphasizes the instantaneous phase-shifting behavior of short pulses of light, and the continuous theory emphasizes changes to the period of oscillations in constant-light conditions. Historically, the primary tool for predicting and understanding discrete entrainment has been the PRC, which measures discrete adjustments to the clock's phase. The authors present a unified theory, which relies on a velocity response curve (VRC), similar in shape to a PRC, but that describes continuous adjustments to the clock's speed. The VRC explains data from both discrete and continuous light experiments and is therefore an invaluable tool to understand entrainment. The authors relate VRC features to specific entrainment behaviors, such as seasonal adjustments to the phase of entrainment. Furthermore, they estimate a VRC from PRC data and successfully reproduce additional PRC data. Finally, they entrain a VRC-based model to natural light/dark cycles, demonstrating the unified theory's ability to predict clock behavior in the face of a fluctuating signal. The results indicate that a VRC-based model not only provides a comprehensive understanding of entrainment but also has excellent predictive capabilities.