Velocity response curves demonstrate the complexity of modeling entrainable clocks

Abstract

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.

Entrainment Maps

“…This approach has led to methods based on the PRC and does not explicitly take into account the periodic nature of the forcing signal. The second paradigm assumes that entrainment occurs through continuous adjustments to the speed of the oscillator and involves a velocity response curve (VRC) (Beersma et al, 1999;Rand et al, 2004;Taylor et al, 2010Taylor et al, , 2014. The VRC characterizes regions in the circadian phase space where the speed of the oscillator increases or decreases as a function of a change of parameter-for example, light intensity.…”

A systems theoretic approach to analysis and control of mammalian circadian dynamics

“…These approaches include mechanistic and empirical process modeling [11–19], robustness and sensitivity analysis [13, 20–25], and optimal control [10, 26–29]. This review highlights the role of systems engineering in developing an understanding of, and artificially exerting control over, the mammalian circadian system.…”