Velocity response curves demonstrate the complexity of modeling entrainable clocks.

Circadian clocks are biological oscillators that regulate daily behaviors in organisms across the kingdoms of life. Their rhythms are generated by complex systems, generally involving interlocked regulatory feedback loops. These rhythms are entrained by the daily light/dark cycle, ensuring that the internal clock time is coordinated with the environment. Mathematical models play an important role in understanding how the components work together to function as a clock which can be entrained by light. For a clock to entrain, it must be possible for it to be sped up or slowed down at appropriate times. To understand how biophysical processes affect the speed of the clock, one can compute velocity response curves (VRCs). Here, in a case study involving the fruit fly clock, we demonstrate that VRC analysis provides insight into a clock׳s response to light. We also show that biochemical mechanisms and parameters together determine a model׳s ability to respond realistically to light. The implication is that, if one is developing a model and its current form has an unrealistic response to light, then one must reexamine one׳s model structure, because searching for better parameter values is unlikely to lead to a realistic response to light.