Positive Autoregulation Delays the Expression Phase of Mammalian Clock Gene Per2

In mammals, cellular circadian rhythms are generated by a transcriptional-translational autoregulatory network that consists of clock genes that encode transcriptional regulators. Of these clock genes, Period1 (Per1) and Period2 (Per2) are essential for sustainable circadian rhythmicity and photic entrainment. Intriguingly, Per1 and Per2 mRNAs exhibit circadian oscillations with a 4-hour phase difference, but they are similarly transactivated by CLOCK-BMAL1. In this study, we investigated the mechanism underlying the phase difference between Per1 and Per2 through a combination of mathematical simulations and molecular experiments. Mathematical analyses of a model for the mammalian circadian oscillator demonstrated that the slow synthesis and fast degradation of mRNA tend to advance the oscillation phase of mRNA expression. However, the phase difference between Per1 and Per2 was not reproduced by the model, which implemented a 1.1-fold difference in degradation rates and a 3-fold difference in CLOCK-BMAL1 mediated inductions of Per1 and Per2 as estimated in cultured mammalian cells. Thus, we hypothesized the existence of a novel transcriptional activation of Per2 by PER1/2 such that the Per2 oscillation phase was delayed. Indeed, only the Per2 promoter, but not Per1, was strongly induced by both PER1 and PER2 in the presence of CLOCK-BMAL1 in a luciferase reporter assay. Moreover, a 3-hour advance was observed in the transcriptional oscillation of the delta-Per2 reporter gene lacking cis-elements required for the induction by PER1/2. These results indicate that the Per2 positive feedback regulation is a significant factor responsible for generating the phase difference between Per1 and Per2 gene expression

Two Ck1δ transcripts regulated by m6A methylation code for two antagonistic kinases in the control of the circadian clock.

Fustin, J.-M., Kojima, R., Itoh, K., Chang, H.-Y., Shiqi, Y., Zhuang, B., . . . Okamura, H. (2018). Two Ck1δ transcripts regulated by m6A methylation code for two antagonistic kinases in the control of the circadian clock. Proceedings of the National Academy of Sciences of the United States of America, 115(23), 5980-5985. doi:10.1073/pnas.172137111

Modeling Light Adaptation in Circadian Clock: Prediction of the Response That Stabilizes Entrainment

Periods of biological clocks are close to but often different from the rotation period of the earth. Thus, the clocks of organisms must be adjusted to synchronize with day-night cycles. The primary signal that adjusts the clocks is light. In Neurospora, light transiently up-regulates the expression of specific clock genes. This molecular response to light is called light adaptation. Does light adaptation occur in other organisms? Using published experimental data, we first estimated the time course of the up-regulation rate of gene expression by light. Intriguingly, the estimated up-regulation rate was transient during light period in mice as well as Neurospora. Next, we constructed a computational model to consider how light adaptation had an effect on the entrainment of circadian oscillation to 24-h light-dark cycles. We found that cellular oscillations are more likely to be destabilized without light adaption especially when light intensity is very high. From the present results, we predict that the instability of circadian oscillations under 24-h light-dark cycles can be experimentally observed if light adaptation is altered. We conclude that the functional consequence of light adaptation is to increase the adjustability to 24-h light-dark cycles and then adapt to fluctuating environments in nature

Amplitude of circadian oscillations entrained by 24-h light-dark cycles.

An intriguing property of circadian clocks is that their free-running period is not exactly 24h. Using models for circadian rhythms in Neurospora and Drosophila, we determine how the entrainment of these rhythms is affected by the free-running period and by the amplitude of the external light-dark cycle. We first consider the model for Neurospora, in which light acts by inducing the expression of a clock gene. We show that the amplitude of the oscillations of the clock protein entrained by light-dark cycles is maximized when the free-running period is smaller than 24h. Moreover, if the amplitude of the light-dark cycle is very strong, complex oscillations occur when the free-running period is close to 24h. In the model for circadian rhythms in Drosophila, light acts by enhancing the degradation of a clock protein. We show that while the amplitude of circadian oscillations entrained by light-dark cycles is also maximized if the free-running period is smaller than 24h, the range of entrainment is centered around 24h in this model. We discuss the physiological relevance of these results in regard to the setting of the free-running period of the circadian clock.Journal ArticleResearch Support, Non-U.S. Gov'tinfo:eu-repo/semantics/publishe

A Model for the Circadian Rhythm of Cyanobacteria that Maintains Oscillation without Gene Expression

An intriguing property of the cyanobacterial circadian clock is that endogenous rhythm persists when protein abundances are kept constant either in the presence of translation and transcription inhibitors or in the constant dark condition. Here we propose a regulatory mechanism of KaiC phosphorylation for the generation of circadian oscillations in cyanobacteria. In the model, clock proteins KaiA and KaiB are assumed to have multiple states, regulating the KaiC phosphorylation process. The model can explain 1), the sustained oscillation of gene expression and protein abundance when the expression of the kaiBC gene is regulated by KaiC protein, and 2), the sustained oscillation of phosphorylated KaiC when transcription and translation processes are inhibited and total protein abundance is fixed. Results of this work suggest that KaiA and KaiB strengthen the nonlinearity of KaiC phosphorylation, thereby promoting the circadian rhythm in cyanobacteria

Temperature–amplitude coupling for stable biological rhythms at different temperatures

<div><p>Most biological processes accelerate with temperature, for example cell division. In contrast, the circadian rhythm period is robust to temperature fluctuation, termed temperature compensation. Temperature compensation is peculiar because a system-level property (i.e., the circadian period) is stable under varying temperature while individual components of the system (i.e., biochemical reactions) are usually temperature-sensitive. To understand the mechanism for period stability, we measured the time series of circadian clock transcripts in cultured C6 glioma cells. The amplitudes of <i>Cry1</i> and <i>Dbp</i> circadian expression increased significantly with temperature. In contrast, other clock transcripts demonstrated no significant change in amplitude. To understand these experimental results, we analyzed mathematical models with different network topologies. It was found that the geometric mean amplitude of gene expression must increase to maintain a stable period with increasing temperatures and reaction speeds for all models studied. To investigate the generality of this temperature–amplitude coupling mechanism for period stability, we revisited data on the yeast metabolic cycle (YMC) period, which is also stable under temperature variation. We confirmed that the YMC amplitude increased at higher temperatures, suggesting temperature-amplitude coupling as a common mechanism shared by circadian and 4 h-metabolic rhythms.</p></div

Sensitivities of period and amplitude to temperature in a detailed mammalian circadian model [30].

<p>(A-D) Temperature-dependent time series of oscillatory variables for the model proposed by Kim and Forger (2012). We used the original parameter set described [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005501#pcbi.1005501.ref030" target="_blank">30</a>] and randomly increased the reaction rate parameters. Here we show examples of calculated time series for <i>Bmal1</i>, <i>Per2</i>, <i>Cry1</i>, and <i>Reverb</i> mRNAs at high (red) and low temperature (blue). Parameter values are listed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005501#pcbi.1005501.s001" target="_blank">S1 Text</a>. (E) Distribution of geometric mean of all relative amplitudes (180 variables) as a function of relative period for 2,495 parameter sets as reaction rates are increased. We randomly increased parameter values from 1.1- to 1.9-fold and generated a total of 10,000 parameter sets. The average parameter increase was ~1.5-fold. Of these sets, oscillations are sustained for 2,495. For each set, we plot the distribution of period change. (F) Variation in the parameter sets yielding relatively stable period (ratio of the new period to the original period >0.8). We assume that the parameter for “volume ratio between cytosol and nucleus (<i>Nf</i>)” is not sensitive to temperature and so was fixed. Ordinary differential equations were solved numerically using the Euler method with Δ<i>t</i> = 0.001.</p

Amplitude adjustment for temperature compensation in a two-variable model.

<p>(A,B) Oscillatory orbits (A) and time series of protein (B) at higher temperature (with higher reaction speeds) and at lower temperature (with lower reaction speeds). Parameters are <i>k</i> = 0.0625, <i>a</i> = 0.0923, <i>v</i> = 0.529, <i>s</i> = 1.48, and <i>d</i> = 0.0507 for lower temperature and <i>k</i> = 0.0976, <i>a</i> = 0.302, <i>v</i> = 2.15, <i>s</i> = 2.80, and <i>d</i> = 0.0778 for higher temperature in Eqs (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005501#pcbi.1005501.e002" target="_blank">1</a>) and (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005501#pcbi.1005501.e003" target="_blank">2</a>), while the other parameters <i>h</i> = 0.5, <i>K</i>_<i>v</i> = 0.5, <i>K</i>_<i>S</i> = 0.5, <i>α</i> = 4, <i>γ</i> = 4, and <i>ε</i> = 0.02 are fixed. (C) Period and amplitude (<i>Y</i>) sensitivities as a function of the positive feedback regulation rate <i>v</i>. Other parameters were fixed to values for higher temperature as in (A). Small-amplitude oscillations occur through a supercritical Hopf bifurcation at <i>v</i> = 0.866. As <i>v</i> increases, amplitude of oscillation sharply increases. (D) Period and amplitude sensitivities with increasing temperature, for which we increased all the reaction rates <i>k</i>, <i>b</i>, <i>a</i>, <i>s</i>, and <i>d</i> by different ratios. Activation energies (<i>E</i>_<i>i</i>) of <i>k</i>, <i>v</i>, <i>a</i>, <i>s</i>, and <i>d</i> are 335, 1057, 893, 480, and 322, respectively. With this setting, two examples at lower temperature (T = 298K) and higher temperature (T = 308K) are depicted in (A). Eqs (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005501#pcbi.1005501.e002" target="_blank">1</a>) and (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005501#pcbi.1005501.e003" target="_blank">2</a>) were solved numerically by the Runge–Kutta method with Δ<i>t</i> = 0.01 using XPPAUT [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005501#pcbi.1005501.ref034" target="_blank">34</a>].</p