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Circadian clock oscillator properties that are crucial for synchronization with the environment (entrainment) are studied in experiment and theory. The ratio between stimulus (zeitgeber) strength and oscillator amplitude, and the rigidity of the oscillatory system (relaxation rate upon perturbation) determine entrainment properties. Coupling among oscillators affects both qualities resulting in increased amplitude and rigidity. Uncoupled lung clocks entrain to extreme zeitgeber cycles, whereas the coupled oscillator system in the suprachiasmatic nucleus (SCN) does not; however, when coupling in the SCN is inhibited, larger ranges of entrainment can be achieved., Daily rhythms in physiology, metabolism and behavior are controlled by an endogenous circadian timing system, which has evolved to synchronize an organism to periodically recurring environmental conditions, such as light–dark or temperature cycles. In mammals, the circadian system relies on cell-autonomous oscillators residing in almost every cell of the body. Cells of the SCN in the anterior hypothalamus are able to generate precise, long-lasting self-sustained circadian oscillations, which drive most rhythmic behavioral and physiological outputs, and which are believed to originate from the fact that the SCN tissue consists of tightly coupled cells (Aton and Herzog, 2005). In contrast, peripheral oscillators, such as lung tissue, exhibit seemingly damped and usually less precise oscillations, which are thought to be brought about by the lack of intercellular coupling. Precise synchronization of these rhythms within the organism, but also with the environment (so-called entrainment), is an essential part of circadian organization. Entrainment is one of the cornerstones of circadian biology (Roenneberg et al, 2003). In evolution, the phase of a rhythmic variable is selective rather than its endogenous period. Thus, the synchronization of endogenous rhythms to zeitgeber cycles of the environment (resulting in a specific phase of entrainment) is fundamental for the adaptive value of circadian clocks. In this study, we systematically investigated the properties of circadian oscillators that are essential for entrainment behavior and describe coupling as a primary determinant. As an experimental starting point of this study, we found that the circadian oscillators of lung tissue have a larger range of entrainment than SCN tissue—they readily entrained to extreme experimental temperature cycle of 20 or 28 h, whereas SCN tissue did not (Figure 4). For this purpose, we cultured SCN and lung slices derived from mice that express luciferase as fusion protein together with the clock protein PERIOD2 (Yoo et al, 2004). The detection of luciferase-driven bioluminescence allowed us to follow molecular clock gene activity in real-time over the course of several days. In theoretical analyses, we show that both the ratio of amplitude and zeitgeber strength and, importantly, inter-oscillator coupling are major determinants for entrainment. The reason for coupling being critical is twofold: (i) Coupling makes an oscillatory system more rigid, i.e., it relaxes faster in response to a perturbation, and (ii) coupling increases the amplitude of the oscillatory system. Both of these consequences of coupling lead to a smaller entrainment range, because zeitgeber stimuli affect the oscillatory system less if the relaxation is fast and the amplitude is high (Figure 1). From these theoretical considerations, we conclude that the lung clock probably constitutes a weak oscillatory system, likely because a lack in coupling leads to a slow amplitude relaxation. (Circadian amplitude is not particularly low in lung (Figure 4).) In contrast, the SCN constitutes a rigid oscillator, whereby coupling and its described consequences probably are the primary causes for this rigidity. We then tested these theoretical predictions by experimentally perturbing coupling in the SCN (with MDL and TTX; O'Neill et al, 2008; Yamaguchi et al, 2003) and find that, indeed, reducing the coupling weakens the circadian oscillatory system in the SCN, which results in an enlargement of the entrainment range (Figure 6). Why is the SCN designed to be a stronger circadian oscillator than peripheral organs? We speculate that the position of the SCN—as the tissue that conveys environmental timing information (i.e., light) to the rest of the body—makes it necessary to create a circadian clock that is robust against noisy environmental stimuli. The SCN oscillator needs to be robust enough to be protected from environmental noise, but flexible enough to fulfill its function as an entrainable clock even in extreme photoperiods (i.e., seasons). By the same token, peripheral clocks are more protected from the environmental zeitgebers due to intrinsic homeostatic mechanisms. Thus, they do not necessarily need to develop a strong oscillatory system (e.g., by strengthening the coupling), rather they need to stay flexible enough to respond to direct or indirect signals from the SCN, such as hormonal, neural, temperature or metabolic signals. Such a design ensures that only robust and persistent environmental signals trigger an SCN resetting response, while SCN signals can relatively easily be conveyed to the rest of the body. Thus, the robustness in the SCN clock likely serves as a filter for environmental noise. In summary, using a combination of simulation studies, analytical calculations and experiments, we uncovered critical features for entrainment, such as zeitgeber-to-amplitude ratio and amplitude relaxation rate. Coupling is a primary factor that governs these features explaining important differences in the design of SCN and peripheral oscillators that ensure a robust, but also flexible circadian system., Circadian clocks are endogenous oscillators driving daily rhythms in physiology and behavior. Synchronization of these timers to environmental light–dark cycles (‘entrainment') is crucial for an organism's fitness. Little is known about which oscillator qualities determine entrainment, i.e., entrainment range, phase and amplitude. In a systematic theoretical and experimental study, we uncovered these qualities for circadian oscillators in the suprachiasmatic nucleus (SCN—the master clock in mammals) and the lung (a peripheral clock): (i) the ratio between stimulus (zeitgeber) strength and oscillator amplitude and (ii) the rigidity of the oscillatory system (relaxation rate upon perturbation) determine entrainment properties. Coupling among oscillators affects both qualities resulting in increased amplitude and rigidity. These principles explain our experimental findings that lung clocks entrain to extreme zeitgeber cycles, whereas SCN clocks do not. We confirmed our theoretical predictions by showing that pharmacological inhibition of coupling in the SCN leads to larger ranges of entrainment. These differences between master and the peripheral clocks suggest that coupling-induced rigidity in the SCN filters environmental noise to create a robust circadian system.