Molecular mechanisms that regulate the coupled period of the mammalian circadian clock.

Biophysical Journal Volume 106 May 2014 2071–2081 2071 Molecular Mechanisms that Regulate the Coupled Period of the Mammalian Circadian Clock Jae Kyoung Kim,†* Zachary P. Kilpatrick,‡ Matthew R. Bennett,§{ and Kre
simir Josic‡jj* † Mathematical Biosciences Institute, The Ohio State University, Columbus, Ohio; ‡Department of Mathematics, University of Houston, Houston, Texas; §Department of Biochemistry & Cell Biology and {Institute of Biosciences and Bioengineering, Rice University, Houston, Texas; and jjDepartment of Biology and Biochemistry, University of Houston, Houston, Texas ABSTRACT In mammals, most cells in the brain and peripheral tissues generate circadian (~24 h) rhythms autonomously. These self-sustained rhythms are coordinated and entrained by a master circadian clock in the suprachiasmatic nucleus (SCN). Within the SCN, the individual rhythms of each neuron are synchronized through intercellular signaling. One important feature of SCN is that the synchronized period is close to the population mean of cells’ intrinsic periods. In this way, the synchronized period of the SCN stays close to the periods of cells in peripheral tissues. This is important because the SCN must entrain cells throughout the body. However, the mechanism that drives the period of the coupled SCN cells to the population mean is not known. We use mathematical modeling and analysis to show that the mechanism of transcription repression in the intracellular feedback loop plays a pivotal role in regulating the coupled period. Specifically, we use phase response curve analysis to show that the coupled period within the SCN stays near the population mean if transcriptional repression occurs via protein sequestration. In contrast, the coupled period is far from the mean if repression occurs through highly nonlinear Hill-type regulation (e.g., oligomer- or phosphorylation-based repression), as widely assumed in previous mathematical models. Furthermore, we find that the timescale of intercellular coupling needs to be fast compared to that of intracellular feedback to maintain the mean period. These findings reveal the important relationship between the intracellular transcriptional feedback loop and intercellular coupling. This relationship explains why transcriptional repression appears to occur via protein sequestration in multicellular organisms, mammals, and Drosophila, in contrast with the phosphorylation-based repression in unicellular organisms and syncytia. That is, transition to protein sequestration is essential for synchronizing multiple cells with a period close to the population mean (~24 h). INTRODUCTION Physiological and metabolic processes such as sleep, blood pressure, and hormone secretion exhibit circadian (~24 h) rhythms in mammals (1). These rhythms are mainly regulated by the master circadian clock in the suprachiasmatic nucleus (SCN) of the hypothalamus (2). The SCN consists of ~20,000 neurons, each of which exhibits rhythmic gene expression. These rhythms are mediated by an intracellular transcriptional feedback loop, in which PER/CRY dimers inhibit their own transcriptional activators, BMAL1/ CLOCK dimers (3,4). The neuronal population’s rhythm is synchronized through intercellular coupling via various neurotransmitters, such as VIP, AVP, GRP, and GABA (5). In particular, experimental evidence points to VIP as a major coupling signal (6), without which SCN fails to synchronize individual rhythms (7). Intercellular coupling within the SCN plays a pivotal role in generating robust and coherent rhythms. Individual cells within the SCN oscillate at their own periods and phases. Intercellular coupling synchronizes these rhythms, resulting in a global rhythm (7–9,50). Furthermore, a broad distribution of periods of individual cells becomes narrow with the coupling, which allows precise timekeeping by Submitted December 11, 2013, and accepted for publication February 25, 2014. *Correspondence: or SCN (Fig. 1) (7,8,10,50). Coupling can also restore the rhythms among cells that lose rhythms due to mutations (11,12). These properties of coupling within SCN have been widely explored with mathematical models. Mathematical models of SCN have shown how VIP signaling can synchronize heterogeneous rhythms (13–16) and confirmed that coupling increases the resistance of rhythms to genetic mutation (11,12), intrinsic noise (17), and external entrainment signal (18). One feature of intercellular coupling within the SCN that is not shared by other coupled biological oscillators (e.g., segmentation clock) (19–21) is that the coupled period, i.e., the global period at which all cells synchronize, is close to the population mean period of the individual cells (Fig. 1) (7,8,10,50). This feature is important because the SCN functions as a master clock that entrains peripheral clocks (1). That is, individual cells in peripheral tissues (e.g., liver and heart) generate rhythms autonomously with periods of ~24 h but are entrained by the rhythms of SCN. The closer the period of the SCN to the periods of peripheral clocks, the more likely that entrainment occurs; this generates coherent systemic rhythms in the organism (1,22). However, it is not understood what drives the period of the coupled SCN close to the population mean. Furthermore, mathematical models based on genetic feedback loops have shown significant differences (~3–6 h) between the coupled period Editor: Richard Bertram. Ó 2014 by the Biophysical Society 0006-3495/14/05/2071/11 $2.00 http://dx.doi.org/10.1016/j.bpj.2014.02.039 2072 Kim et al. FIGURE 1 Coupling maintains population mean of periods in circadian clocks. When intercellular coupling within the SCN is disrupted either by (A) enzymatic dispersion or (B) VIP/, the distribution of periods of individual neurons broadens. However, the mean periods (indicated by arrows at the top of each panel) do not significantly change when coupling is disrupted. Panel A: WT, 23.3 5 1 and dispersed SCN, 22.7 5 2.9; panel B: WT, 23.6 5 1.7 and VIP/, 25 5 4. Panels A and B are reproduced from Ono et al. (8) and Aton et al. (7), respectively, with permission from Nature Publishing Group Ltd. To see this figure in color, go online. and population mean, inconsistent with experimental findings (Fig. 1) (13–15). Previous mathematical models have typically relied on Hill functions to describe transcriptional repression in the negative feedback loop (13–15). However, in a recent theoretical study it was shown that circadian clocks behave very differently when transcriptional repression occurs via protein sequestration, in which repressor inhibits a transcriptional activator via 1:1 stoichiometric binding (Fig. 2 A), rather than highly nonlinear Hill-type regulation (Fig. 2 B and see Fig. S1 in the Supporting Material) (23). That is, a model based on protein sequestration successfully reproduced various experimental observations that have not been addressed by previous models based (...truncated)