Conceived and designed the experiments: BK. Performed the experiments: BK. Analyzed the data: BK. Contributed reagents/materials/analysis tools: XC LL. Wrote the paper: BK Y-YL Y-XL.
The authors have declared that no competing interests exist.
Circadian clocks are endogenous time-keeping systems that temporally organize biological processes. Gating of cell cycle events by a circadian clock is a universal observation that is currently considered a mechanism serving to protect DNA from diurnal exposure to ultraviolet radiation or other mutagens. In this study, we put forward another possibility: that such gating helps to insulate the circadian clock from perturbations induced by transcriptional inhibition during the M phase of the cell cycle. We introduced a periodic pulse of transcriptional inhibition into a previously published mammalian circadian model and simulated the behavior of the modified model under both constant darkness and light–dark cycle conditions. The simulation results under constant darkness indicated that periodic transcriptional inhibition could entrain/lock the circadian clock just as a light–dark cycle does. At equilibrium states, a transcriptional inhibition pulse of certain periods was always locked close to certain circadian phases where inhibition on Per and Bmal1 mRNA synthesis was most balanced. In a light–dark cycle condition, inhibitions imposed at different parts of a circadian period induced different degrees of perturbation to the circadian clock. When imposed at the middle- or late-night phase, the transcriptional inhibition cycle induced the least perturbations to the circadian clock. The late-night time window of least perturbation overlapped with the experimentally observed time window, where mitosis is most frequent. This supports our hypothesis that the circadian clock gates the cell cycle M phase to certain circadian phases to minimize perturbations induced by the latter. This study reveals the hidden effects of the cell division cycle on the circadian clock and, together with the current picture of genome stability maintenance by circadian gating of cell cycle, provides a more comprehensive understanding of the phenomenon of circading gating of cell cycle.
Circadian clock and cell cycle are two important biological processes that are essential for nearly all eukaryotes. The circadian clock governs day and night 24 h periodic molecular processes and physiological behaviors, while cell cycle controls cell division process. It has been widely observed that cell division does not occur randomly across day and night, but instead is normally confined to specific times during day and night. These observations suggest that cell cycle events are gated by the circadian clock. Regarding the biological benefit and rationale for this intriguing gating phenomena, it has been postulated that circadian gating helps to maintain genome stability by confining radiation-sensitive cell cycle phases to night. Bearing in mind the facts that global transcriptional inhibition occurs at cell division and transcriptional inhibition shifts circadian phases and periods, we postulate that confining cell division to specific circadian times benefits the circadian clock by removing or minimizing the side effects of cell division on the circadian clock. Our results based on computational simulation in this study show that periodic transcriptional inhibition can perturb the circadian clock by altering circadian phases and periods, and the magnitude of the perturbation is clearly circadian phase dependent. Specifically, transcriptional inhibition initiated at certain circadian phases induced minimal perturbation to the circadian clock. These results provide support for our postulation. Our postulation and results point to the importance of the effect of cell division on the circadian clock in the interaction between circadian and cell cycle and suggest that it should be considered together with other factors in the exploitation of circadian cell cycle interaction, especially the phenomena of circadian gating of cell cycle.
For organisms living on the surface of the earth or in shallower aquatic biotopes, the ability to adjust their metabolic processes and behaviors according to a 24-hour periodicity, and the synchronization of their internal molecular processes may provide important evolutionary advantages. Circadian clocks are endogenous time-keeping devices that are responsible for the ≈24-hour biochemical rhythm of almost all organisms ranging from simple single cellular prokaryotes to complex multi-cellular eukaryotes. Circadian clocks coordinate synchronization between internal biological processes and between environmental cues and internal biological processes.
An endogenous circadian clock consists of single or multiple autoregulatory oscillator(s) composed of interconnected transcriptional feedback loops
The cell cycle is another fundamental clock-like periodic biological process for which interesting molecular details have been elucidated. At the molecular level, a similar regulatory scenario to the circadian clock is observed, with transcriptional and translational feedback loops underlying the cell cycle engine mechanism. The phenomena of coupling between cell cycle and circadian cycle were observed and investigated over 40 years ago
This prompts two questions. Why is there widespread gating of the cell cycle by a circadian clock mechanism in most organisms? And is there any reciprocal “gating” effect of the cell cycle on the circadian clock? As yet, there is no clear answer to this second question. However, recent findings by Nagoshi demonstrate that cell division can indeed influence circadian period length
It is not easy to experimentally study the cell cycle mediated effects of transcription inhibition on the circadian clock. It is, however, feasible to investigate this problem with mathematical modeling. A number of modeling approaches have already been successfully employed to individually study circadian clocks and the cell cycle
In this study, we investigate the hypothetical effects of global transcription inhibition in cell cycle M phase on the properties of the mammalian circadian clock and explore the implications of this effect on circadian gating of the cell cycle. Our simulation results show that transcriptional inhibition could entrain the circadian clock and at equilibrium entrainment, transcriptional inhibition pulses are always located at certain circadian phases, where they minimize inhibition induced circadian perturbation.
Entrainment of a circadian cycle to light is a well established biological observation. Light induced transcriptional alteration or protein degradation contributes to such entrainment. To assess whether M-phase transcriptional inhibition can also serve as an entrainment cue for the circadian clock, we numerically simulated a mammalian circadian model modified from the model published by Goldbeter et.al.
The square wave (green) oscillates between a maximum value, which represents the maximum transcription rate of the mRNAs, and zero, which represents the inhibition of transcription during M phase. The period of the square wave represents cell cycle period. The transcription of the three mRNA species (black, blue, and cyan) are simultaneously inhibited during the M phase.
Cell cycle M-phase is introduced into the mammalian circadian model as transcriptional inhibition cycles of different periods. For each period, transcriptional inhibitions are imposed at various circadian phases with an interval of 30 minutes. The resulting models are simulated. Simulation data are sampled at equilibrium state and circadian periods are calculated for each simulation. The calculated periods are combined and plotted against transcriptional inhibition periods.
Next, we assessed the distribution of cell cycle M-phase (transcriptional inhibition pulse) on the circadian phase of the coupled system at equilibrium entrainment. To this end, the phases of the circadian cycles where inhibition pulses occurred were determined at equilibrium of every simulation and plotted against the cell cycle periods. As shown in
The cell cycle M-phase is introduced into the mammalian circadian model as transcriptional inhibition cycles of different periods. For each period, transcriptional inhibitions are imposed at various circadian phases with an interval of 30 minutes. The resulting models are simulated. Simulation data are sampled at equilibrium state and the circadian phases where cell cycle M-phase is located are calculated for each simulation. The calculated phases are combined and plotted against transcriptional inhibition periods.
Simulations are performed as described in
If inhibition occurs at circadian phases where synthesis of clock gene mRNAs are actively expressed, circadian rhythms will possibly be perturbed. However, if inhibition occurs at circadian phases either without clock gene mRNA expression or with balanced synthesis of two antagonistic genes, there will be no or minimal effect on the circadian clock.
Our simulation so far studied the effect of M-phase transcriptional inhibition in DD condition. In reality, light cycle and cell cycle always influence the circadian cycle simultaneously. Furthermore, experiments studying circadian entrainment of cell cycle phases are all conducted under the condition of a light-dark cycle. To directly compare experimental results with our simulation, we have to introduce a LD cycle into our model. Our working hypothesis is that entrainment of cell cycle phases, especially of the M-phase, to certain circadian phases is meant to minimize circadian perturbation induced by cell cycle progression, in particular by M-phase global transcriptional inhibition. Our objective is to determine whether, in the presence of a LD cycle, one or more circadian phase(s) can be identified, where the imposition of transient transcriptional inhibition does not significantly alter the circadian cycle. To this end, we conducted simulations with a model incorporating both a light-dark cycle and transcriptional inhibition cycle effects. There are three ways to conduct such a simulation study. Two different effects can be introduced either simultaneously or sequentially. Since mammals normally live under light-dark cycle conditions, we assume a light cycle factor intrinsic to the mammalian circadian clock and that a LD cycle is the background condition of other molecular processes. Thus, we first introduced a light cycle into the model, and the transcriptional inhibition cycle was introduced after the system reached a new equilibrium state. Since human and mouse cells
The LD cycle is first introduced into the circadian model, and the resulting model is simulated. When the model reaches equilibrium, transcriptional inhibitions are introduced into the model at different circadian phases. The system changes after inhibition imposition is depicted by the difference in Per mRNA level at light onset between pre- and post-inhibition imposition. “+” denotes Per mRNA level at light onset before inhibition imposition; “.” denotes Per mRNA level at light onset after inhibition perturbation.
We further did similar simulation study in the mammalian circadian model with 19 equations published by Goldbeter et al.
It has been demonstrated that circadian systems are robust to molecular noise and entrainment of circadian clock by light cycles can occur in the presence of molecular noise
The effects of the cell cycle period on the entrainment in the presence of noise were studied by changing the periods of the square waves imposed onto the circadian model with noise. The periods of the coupled model and the circadian phases (with the peak of Per mRNA as the reference phase) where the troughs of the square wave occurred are determined. The distributions of the resulting circadian periods and the phases of transcriptional inhibition occurrence resulting from one simulation are displayed here.
Light dark cycles and transcriptional inhibition cycles initiated at different circadian phases (with light onset as the reference) were imposed onto circadian models, and the Per mRNA concentration differences at light onset before and after transcriptional inhibition were calculated. Results from 100 simulations were averaged.
Interactions between the circadian clock and the cell cycle engine have been suggested by many experimental observations in various organisms
Experimental observations suggesting an interaction between the circadian clock and the cell cycle are, in most cases, simply the non-random distribution of certain cell cycle events across circadian phases or fluctuations of cell cycle regulatory gene expression with circadian periodicity. Mechanistic details of this interaction are so far not known, yet in some instances, specific molecular links have been proposed
To simulate the effects of the cell cycle on the circadian clock, appropriate molecular links have to be identified and corresponding parameters have to be determined. Compared to the evidence for a dependence of the cell cycle on the circadian clock, evidence for the reverse effect is rare. The most pertinent evidence came from fluorescent imaging of gene expression in individual NIH3T3 mouse fibroblasts with circadian rhythm
We thus focused here on the potential effects of M-phase global transcriptional inhibition on the circadian clock. One has to bear in mind, however, that cell cycle progression involves complicated transcriptional, translational and post-translational regulations. Consistent with Eskin's experimental observation, our simulation study confirmed that transcriptional inhibition changed both phase and period of the circadian clock.
Two interesting points emerge from our computational simulation. The first one is the entrainment of the circadian period by the cell cycle. This entrainment occurs only at cell cycle periods close to one half, twice or equal to the intrinsic circadian model period of 23.85 h, namely 11, 22, 23, 24, 46, 47 and 48 h. At other cell cycle periods, entrainment rarely occurred. The second point is that when the circadian clock system reaches a new equilibrium state after perturbation by periodic transcriptional inhibition, the circadian phase(s) where transcriptional inhibition pulses are locked, is (are) focused rather than randomly distributed across the whole circadian clock period. For the 22 hour period, transcriptional inhibition remains at the circadian phase following the Per mRNA peak, for the 23 hour period, two steady state phases exist, one equivalent to that of the 22 hour period, the other one close to the middle between two Per mRNA peaks. For the 24-hour period, one unique steady state appears again, in this case close to the middle between two Per mRNA peaks.
Further inspection showed that these positions are close to phases where the synthesis rate curves of the Per and Bmal1 mRNAs intersect. It is evident that at the intersection points, the difference between the synthesis rates of these two molecules is zero and transcriptional inhibition pulses influence their synthesis to the same extent. According to the accepted mechanism of circadian clock regulation, Per exerts a negative feedback on itself, but positively affects Bmal1 expression. Similarly, Bmal1 regulates itself negatively, but regulates Per positively. This regulation regime causes an anti-phasic oscillation of these two molecules with respect to each other. When transcriptional inhibition is imposed on the circadian system, several different responses occur, depending on the circadian phase where transcriptional inhibition happens. At circadian phases where Bmal1 synthesis rate reaches maximum and Per synthesis rate is zero, transcriptional inhibition induces maximum delay of accumulation of Bmal1 mRNA, but does not affect Per mRNA synthesis. At these circadian phases, transcriptional inhibition causes maximal perturbation of the circadian system. At other phases, transcriptional inhibition delays the accumulation of one of these two mRNAs, while accumulation of the other is accelerated. The effects are also quantitatively different, depending on the exact circadian phase of transcriptional inhibition. In some phases, transcriptional inhibition delays Per mRNA accumulation but accelerates Bmal1 mRNA accumulation, while in other phases the reverse is observed. The influence on one mRNA is always associated by a simultaneous influence on the other mRNA. The magnitude of counterbalance is determined by the difference between the synthesis rates of the two molecules at that phase. The more the disturbances are balanced, the less is the circadian system affected by the transcriptional inhibition at that circadian phase. It is obvious that near the intersection points of
Still, at cell cycle periods other than those mentioned above, transcriptional inhibition pulses were also found locked to other phases, e.g. circadian phase distribution for 10 and 43 hours in
In the physiological context, a circadian clock is always under the influence of a light-dark cycle. To place our simulation in a more physiological context, we also simulated the cell cycle and circadian clock interaction in the presence of a light-dark cycle. To this end, we incorporated both a light-dark cycle and the transcriptional inhibition cycle into the mammalian model. Our simulation results revealed two windows in the circadian cycle, where transient transcriptional inhibition induced only transient and small alterations to the circadian clock regulatory system. With the beginning of the light cycle taken as the 0 reference phase (CT0), one window is close to 15 h, and the other window is close to 19 h, corresponding to the middle and late night respectively. Although there is to our knowledge no experimental evidence for mammals supporting the entrainment of cell cycle M-phase to circadian phases close to the first window in our simulation, evidence from a mouse liver regeneration study revealed indeed the entrainment of hepatocyte cell cycle mitosis to phases close to this second window
The current view of circadian entrainment of the cell cycle is that the circadian clock helps to maintain genome stability by timing mutation sensitive cell cycle phases to circadian phases with least exposure to mutagens. Our simulation suggests that circadian entrainment of the cell cycle could also help to maintain circadian clock stability by minimizing cell division induced perturbation of the circadian clock. These two notions are not mutual exclusive. They complement each other and in combination provide for a fuller picture of an elusive phenomenon.
In summary, highly regulated transcriptional processes are critical for normal functioning of the circadian clock. Global transcriptional inhibition during M-phase of the cell cycle might perturb normal progression of the circadian clock, and there might be circadian windows where transcriptional inhibition has little influence on normal circadian progression. One could therefore expect to find (a) molecular mechanism(s) which places the M-phase of the cell cycle in such windows to minimize or eliminate cell cycle induced perturbation. Our study is the first attempt to tackle this problem by computational simulation, and our results support this hypothesis.
The circadian model used in this study is from the mammalian model published by Leloup and Goldbeter in 1993
We did most of our simulations with the 16 equation model. In Goldbeter's circadian model, the dynamics of three clock gene mRNA levels are governed by the following three equations:
To incorporate the effects of cell cycle M-phase global transcriptional inhibition on the circadian clock, we modified Leloup's mammalian circadian model by letting parameters vsP, vsC, vsB oscillate between the optimized values of the original model and zero (or other values below optimum). The oscillation of these parameters reflects the periodic cell cycle M-phase. The periods of oscillation of these parameters mimic the cell cycle period, and the differences between the two oscillating values reflect the degree of M-phase transcriptional inhibition.
Although it is well known that chromosomes are highly condensed and transcription is globally inhibited during M-phase, there is no quantitative experimental result concerning the duration and extent of transcription inhibition in M-phase. Because the M-phase of the mammalian cell cycle lasts roughly 1–2 hours and is relatively constant compared to other cell cycle phases, we assume that the variation of these three parameters follows a square wave with a trough phase of relatively constant length of 30 minutes corresponding to the M-phase transcriptional inhibition pulse. We assume that transcription inhibition of circadian clock genes occurs at least at the middle part of M-phase. Based on this assumption, a duration of 30–60 minutes (roughly half the mammalian cell cycle M-phase length) of transcription inhibition is introduced into the model.
To implement this modification, we introduced a new parameter v into the original model, whose value is governed by the following formula:
To simulate oscillation of Per, Cry and Bmal1 mRNAs, vsP, vsC and vsB are all multiplied with the parameter v. The three equations governing the dynamics of the three mRNAs are thus modified as follows:
In this way, the decline of vsP, vsC and vsB mimics transcriptional inhibition, and the period of variation reflects the cell cycle period. We treat the two terms of transcriptional inhibition and cell cycle M-phase global inhibition as interchangeable in this study.
To study the effect of noise on the entrainment properties of periodic transcriptional inhibition, we introduced a white noise term into the differential equations of the original model as follows:
Although the mammalian circadian models we used in this study reflect general properties of mammalian circadian clock, the parameters are basically estimated from data collected from mouse experiments. So we just list mouse Refseq accession numbers for the genes and proteins. The three Per genes and proteins are collectively represented as one Per gene and protein respectively in the model and the two Cry genes and proteins are treated as is.
Genes:
Transcriptional inhibition induced changes under LD cycle conditions in the Goldbeter mammalian circadian model with 19 equations. The LD cycle is first introduced into the circadian model, and the resulting model is simulated. When the model reaches equilibrium, transcriptional inhibition is then introduced into the model. The system changes after inhibition imposition is depicted by the difference in Per mRNA level at light onset between pre- and post-inhibition imposition. “+” denotes Per mRNA level at light onset before inhibition imposition; “.” denotes that Per mRNA level at light onset after inhibition perturbation.
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Transcriptional inhibition induced changes under LD cycle conditions in the Udea Drosophila circadian model. Methods and interpretations are the same as
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Circadian oscillations are robust to noise. Noises are introduced into the mammalian circadian model as described in the
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Molecular processes included in the mammalian circadian models we used in this study (adapted from
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ODE file for the mammalian circadian model incorporating transcriptional inhibition.
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We thank Chao Wang for assistance in editing the MATLAB model file and other support at the beginning of this study. We also thank Lingyi Lu for help and Fudong Yu for valuable and suggestions. We thank Ruoyu Luo for help with numerical simulation in the presence of noise.