Circadian clock effects on cellular proliferation: Insights from theory and experiments

Oscillations of the cellular circadian clock have emerged as an important regulator of many physiological processes, both in health and in disease. One such process, cellular proliferation, is being increasingly recognized to be affected by the circadian clock. Here, we review how a combination of experimental and theoretical work has furthered our understanding of the way circadian clocks couple to the cell cycle and play a role in tissue homeostasis and cancer. Finally, we discuss recently introduced methods for modeling coupling of clocks based on techniques from survival analysis and machine learning and highlight their potential importance for future studies. Addresses 1 Department of Data Science, Dana-Farber Cancer Institute, Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA, USA 2 Department of Stem Cell and Regenerative Biology Biology, Harvard University, Cambridge, MA, USA 3 Center for Cancer Evolution, Dana-Farber Cancer Institute, Ludwig Center at Harvard, Boston, MA, USA 4 The Broad Institute of Harvard and MIT, Cambridge, MA, USA Corresponding author: Chakrabarti, Shaon (shaon@jimmy.harvard. edu) a Present address: Simons Centre for the Study of Living Machines, National Centre for Biological Sciences (TIFR), Bengaluru, 560065, India. Current Opinion in Cell Biology 2020, 67:17–26 This review comes from a themed issue on Differentiation and disease Edited by Carien Niessen and Nicolas Plachta For a complete overview see the Issue and the Editorial https://doi.org/10.1016/j.ceb.2020.07.003 0955-0674/© 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons. org/licenses/by/4.0/).


Introduction
Biochemical oscillations are ubiquitous in living organisms, arising from complex spatioetemporal interactions between genes, proteins and metabolites [1]. The circadian ('circa' d about, 'diem' d day, in Latin) clock represents a special class of such biochemical oscillators; it has an intrinsic period of approximately 24 h and is thought to have evolved in organisms to allow anticipation of daily changes in the environment tied to the Earth's rotation [2,3]. These oscillations are selfsustained in single cells under constant environmental conditions and can be entrained by external cues such as light. It has become increasingly clear that the circadian clock plays an important role in regulating the cell cycle, thus affecting cellular proliferation in multiple contexts such as tissue homeostasis and cancer [4]. With a focus on the mammalian circadian clock, here we review recent progress in our understanding of the nature of coupling of the clock with the cell cycle. Recent reviews have summarized experimental evidence of this coupling and its potential consequences on human health [5,6], we provide a perspective on how a synergy between experimental and theoretical studies has led to significant insights in this rapidly growing field. We also discuss the potential usefulness of novel theoretical and computational approaches rooted in biostatistics and machine learning and, using a few recent studies as examples, discuss how such approaches in a data-rich age may prove invaluable for the future of circadian research.

Basic architecture of the mammalian circadian clock
Sustained oscillations in mammalian cells arise from a canonical set of interlocked transcriptionale translational feedback loops (TTFLs, Figure 1a), although the absolute necessity of transcription has been questioned, for example, from observations of circadian peroxiredoxin oscillations in human red blood cells which lack nuclei [7]. Heterodimers of the BMAL1 and CLOCK proteins bind Ebox motifs in the promoters of Per2 and Cry1, leading to transcription and translation of the latter. PER2 and CRY1 proteins eventually are transported back into the nucleus, where they repress BMAL1 and CLOCK to decrease their own expression. Finally, degradation of PER2 and CRY1 over time allows BMAL1eCLOCK driven expression to switch back on, thereby establishing the circadian oscillation. In a second interconnected loop the BMAL1eCLOCK heterodimer induces transcription of Ror and Rev-erb genes, which in turn stimulate/inhibit Bmal1 expression, respectively, by binding to ROR response elements (Figure 1a). We refer the interested reader to Transcriptional-translational feedback loops (TTFLs) that generate circadian oscillations and coupling to the cell cycle. (a) The core feedback loops involving BMAL1, Clock, Per, Cry, Rev-Erb, and Ror are shown along with a few example modes of coupling of the clock to the cell cycle. The colored ovals represent proteins. (b) A schematic of some common approaches to mathematical modeling of the circadian clock and how it can drive cellular proliferation. The reactions from panel (a) are modeled using ordinary differential equations (ODEs), generating temporal dynamics of various components of the TTFLs [10][11][12][13][14]. These time-dependent molecular concentrations can then be used to define transition rates between various phases of the cell cycle, which can in turn be used in age-structured models to connect single-cell dynamics to population-level growth [25]. recent reviews providing detailed descriptions of the biochemical pathways involved [8,9]. The importance of these interconnected feedback loops in generating robust oscillations, and how the period and amplitude of the emergent oscillations are affected by genetic perturbations, have been studied in detail using mathematical models of these TTFLs [10e13] (Figure 1b). Fitting such models to gene expression data sets has also suggested tissue-specific differences in network motifs that underlie the essential feedback loops generating circadian oscillations [14].

Molecular mechanisms and mathematical models of circadian clock-cell cycle coupling
Early seminal studies demonstrated the existence of coupling between the canonical TTFL components of the circadian network and the cell cycle, revealing regulation of c-Myc transcription by PER2 [15] and regulation of the G2/M inhibitor Wee1 by BMAL1e CLOCK [16] (Figure 1a). Since then, a variety of molecular interactions between the two cellular oscillators have been uncovered [6]. Circadian modulation of the cell cycle is thought to occur primarily via coupling to the G1-S and G2-M transitions [6] (Figure 1a), although an earlier fate decision to enter G1 or G0 phases has also been suggested to be under circadian control in adult brain neurogenesis [17]. A number of modeling studies have predicted clock-controlled cell cycle entry: a model of BMAL1-driven enhancement of a CyclinD/Cdk4-6 inhibitor (posited to be p21) was able to explain enhanced cell proliferation after BMAL1 ablation in the subgranular zone of the adult hippocampus [17]. In another study, we investigated the possible origin of surprising intermitotic time correlations in colon cancer cell lineages, both in the absence and presence of the chemotherapeutic agent cisplatin. Our mathematical model predicted circadian control of cell cycle entry as an important regulator of cell cycle speed [18]. These models suggest early control of cell cycle progression by the circadian clock and point to an interesting avenue for further experimental and theoretical studies.  (Figure 1a). The G2/M transition is affected by transcriptional regulation of Wee1 by BMAL1eCLOCK [16]. The resulting circadian oscillations in WEE1 in turn regulates Cyclin B1 expression, thereby allowing circadian control over the G2/M transition [23] (Figure 1a). Mathematical models investigating the consequences of these various modes of coupling have led to interesting and nonintuitive insights d for instance, it was shown that the domain of entrainment does not increase with increasing modes of clock and cell cycle coupling [24]. This result was based on the modeling prediction that the domain of entrainment via a combination of Wee1, p21, and cyclin E was not larger than the domain of entrainment through Wee1, p21, or cyclin E on their own. This interesting prediction suggests that perhaps the presence of multiple modes of coupling may provide redundancy rather than facilitating entrainment [24].
Although there are increasing reports of circadian driving of the cell cycle, relatively few studies have investigated the reverse coupling d modulation of the circadian clock by the cell cycle. An interesting combination of time-lapse microscopy and stochastic modeling of coupled oscillators provided strong evidence for a dominant reverse coupling in single mouse fibroblasts [26]. Using a maximum likelihood approach to infer the coupling function between the two oscillators, the authors found the strongest interaction to be an acceleration of the circadian phase right around the cell division event [26]. Although this work did not provide a mechanistic basis for the reverse coupling, more recent experiments have uncovered two modes of this regulation: (1) ubiquitination and subsequent degradation of Rev-erb-a is dependent on CDK-1 mediated phosphorylation of Rev-erb-a and controls the circadian oscillation amplitude [27] and (2) the transcription factor MYC disrupts the circadian clock in cancer cells by downregulating the core clock genes BMAL1 and CLOCK, either via upregulating Rev-erb-a [28] or by forming a complex with MIZ1 [29]. In turn, disruption of the clock affects cellular proliferation: upregulation of MYC attenuates the clock and promotes cell proliferation whereas its downregulation results in strengthening of the clock and reduction of cell proliferation [29]. Finally, the larger scale consequences of this reverse coupling (in addition to the previously discovered circadian clock to cell cycle coupling) were recently investigated using modeling; the authors predicted that bidirectional coupling results in more robust synchronization than unidirectional coupling [30].

Does the circadian clock 'gate' the cell cycle?
Although studies of the molecular mechanisms of clockecell cycle coupling are relatively recent, reports of the preponderance of cell divisions at specific times of the day have existed since the early 1900s. A study of the dinoflagellate Ceratium fusus in the waters of the English Channel suggested that these unicellular organisms divide mostly between 1ame3.30 am [35]. Later studies of both unicellular eukaryotes [36] and prokaryotes [31] in culture showed that after entrainment to 12 h light and dark cycles, a large fraction of cell divisions occurred during a relatively short period of time around the late subjective night. These studies led to the use of the term 'circadian gating' (Figure 2a have suggested gating to be the predominant mode of coupling. In the zebrafish study, different lightedark (LD) cycles were imposed on a zebrafish-FUCCI cell line in culture. From the observation that the differing LD cycles made no difference to the average cell cycle length, while the number of mitosis events oscillated with time in all LD conditions, the authors suggested a gating mechanism over phase locking [40]. More studies will be necessary to elucidate the precise nature of the coupling in various organisms and cell types. Recent developments in generating endogenous reporters of the circadian clock using CRISPR knock ins will undoubtedly prove invaluable in this endeavor [42].

Use of survival analysis to model the circadian clock-cell cycle coupling
Nonlinear dynamical systems have been the most popular modeling approach for understanding how the circadian clock couples to the cell cycle [26,33,34]. Recently, we and others independently introduced methods from survival analysis to model the clockecell cycle coupling [18,39]. Survival analysis is a set of statistical tools to analyze data where the variable of interest is time until an event occurs [43], for instance, in medical fields where time to death of patients is under study. The distinguishing factor of survival analysis is that it naturally deals with various scenarios of censoring, where the end of the observation period or other competing events precludes observation of the time to event for many individuals [44]. A basic introduction to survival and competing risks analysis in the context of single-cell time-lapse data is discussed in our recent work [18].
As shown in Figure 3a, the formalism of survival analysis lends itself naturally to the analysis of time-lapse microscopy data of proliferating cells. The central quantity is the hazard function h, which in this context is interpreted as the instantaneous rate of division of cells of a particular age a, given that the cells have survived until time a since birth (Figure 3b). The circadian clock can then be modeled as modulating the hazard function [18,39] and an analytic expression for the likelihood of observing a set of single-cell division times can be used for making inferences of underlying model parameters (Figure 3b top). In a recent work, this approach was combined with cubic B-splines to

Consequences of the circadian clock-cell cycle coupling in adult (cancer) stem cells
Although most cells across mammalian tissues are fully differentiated and hence postmitotic, adult stem cells make up a small but essential portion of tissues. These stem cells retain the capability of proliferating and generating new cells of the tissue, thus playing a critical role in tissue homeostasis, regeneration, and tumorigenesis. Understanding cell cycle control mechanisms in these stem cells is therefore essential, and regulation by the circadian clock has been demonstrated in adult skin, intestine, blood, hair, bone, and nerve stem cells [45]. Intriguingly, pluripotent stem cells do not exhibit circadian oscillations of the canonical TTFL genes [46],   Step 1 Select 168 genes Step 2 Estimate 168 peak times c Gene 2

Gene 1
Step 1 Select G=10-16 rhythmic genes Step 2 Construct G-dim expression space Step 3 Low dim projection + fit MVNs + interpolate Step 2). This data is then projected down to a lower dimensional space using a projection operator calculated from the N data points corresponding to one time point (Step 3). Separate multivariate although noncanonical 24-h oscillations have been reported in metabolic programs of these cells [47].
Over the last few years, important connections between the circadian clock and cancer stem cells have emerged [4]. Traditionally, the circadian clock has been thought of as a tumor suppressor [48]. In support of this idea, B16 melanoma cells in vitro and tumors in vivo were found to suppress clock genes, and their proliferation was strongly reduced upon restoring clock function [49]. In addition, in support of the idea of circadian genes acting as tumor suppressors, an earlier study showed a direct proteineprotein interaction between PER2 and the tumor suppressor P53; by forming a stable trimeric complex with P53 and P53's negative regulator MDM2, PER2 prevented ubiquitination of MDM2, and the resulting degradation of P53 [50]. Intriguingly however, recent studies have suggested the possibility of circadian genes aiding tumor maintenance in some contexts. For example, it was observed that while glioblastoma stem cells, differentiated glioblastoma cells, and noncancerous brain cultures exhibited circadian rhythms, only the glioblastoma stem cells showed a strong dependence on BMAL1 and Clock for optimal cell growth [51]. Similar effects were observed in hematopoietic cells, where Clock and Bmal1 are required for leukemia cell growth in a murine model of acute myeloid leukemia, and circadian disruption impaired cell cycle progression [52]. Although these results are apparently contradictory and suggest a complex relationship between the circadian clock and cancer, theoretical modeling is well poised to shed light onto these complexities. For example, a study coupling ODEs to model chemical reactions and age-structured population models to describe population growth (Figure 1b) investigated the effects of Per/Cry mutations and BMAL1 knockouts on cellular proliferation. This study concluded that depending on the autonomous period of the cell cycle (cell cycle length in the absence of coupling to the circadian clock) a disrupted circadian clock can lead to both enhancement and decrease of the cellular growth rate [25].

Circadian clock (de)synchronization: quantification and implications for cellular proliferation
A combination of experimental and theoretical approaches has provided fundamental insights into how individual cellular oscillators in mammalian tissues decode environmental information to stay synchronized [53e56] or become desynchronized by light perturbations, such as jet lag and similar protocols [57,58]. Many lines of evidence have suggested that synchrony among circadian clocks is crucial for maintaining healthy tissues, and desynchronization can lead to susceptibility to diseases such as cancer [4,59]. Using various tissues from mice exposed to chronic jet lag [60] and blood samples from humans undergoing a night shift protocol [61], it was observed that oscillations of circadian clock genes are dampened (presumably due to reduced synchrony among individual cells) and phase shifted. An in vitro jet lagelike protocol, developed to mimic these observations in cultured cancer cells [19], led to upregulation of cell cycle genes and a concomitant increase in cellular proliferation in human U2 osteosarcoma cells [19]. In mice, a jet-lag protocol was found to change expression levels of both tumor suppressor genes such as NF1 and oncogenes such as KRAS, which in turn were associated with clock genes such as Bmal1, Cry1, and Cry2 [62]. Cellular proliferation may therefore be linked to the degree of synchronicity among individual cellular circadian oscillators in a population of cells.
These results demonstrate the need to develop quantitative measures of clock (de)synchronicity in tissues of individual patients and investigate its association with disease, an endeavor to which computational modeling has made significant contributions over the years (Figure 4a). In early work, genome-wide expression patterns were used to infer body time [63] ( Figure 4b). In more recent work, a variety of machine learning methods have been used to infer either body time or the degree of clock (a)synchronicity from single patient samples, often using a much reduced set of core clock genes [64e69]. For example, TimeTeller is a recently developed method which defines a metric for clock dysfunction from single samples based on the phase relationships between various circadian genes in diseased tissues compared with normal ones [68] ( Figure 4c describes the TimeTeller workflow). Interestingly, this study demonstrated that the dysfunction metric was a prognostic factor for both disease-free survival and overall survival in primary breast cancer patients, independent of previously established prognostic factors such as the meta-PCNA gene signature [68]. Another study developed a 12 biomarker gene set from human epidermis [69], and used a previously developed method ZeitZeiger [65] to report circadian phase from single samples. This method performed well across body sites, age, sex, and detection platforms, which are essential elements for ease of clinical implementation [69]. Finally, a method to quantify relative coupling strength among individual cells has also been suggested based upon the idea that period and phase distributions in an ensemble of cells become narrower upon increasing coupling strength [70].

Conclusions and future directions
Much progress has been made in elucidating the basic principles of coupling of cellular circadian clocks, with each other as well as with other oscillators such as the cell cycle. Here, we have highlighted how a synergy between experiments and theoretical modeling has provided novel insights in this fast-growing field. Rapid developments in microscopy and image analysis techniques are allowing careful quantitative analyses of circadian clock coupling, and we believe that the next few years will see exciting developments in this area. The nature of circadian coupling with the cell cycle in diseases such as cancer and in response to drugs remains poorly understood, and in our opinion, represents an important avenue of future research. Novel theoretical approaches based on survival analysis [18,39] and machine learning [64e69] could provide important tools to analyze large quantities of data, from in vitro and in vivo as well as clinical studies. Such approaches could be coupled with evolutionary models of cancer progression that allow for time-dependent changes in cellular growth and death rates [71] to optimize treatment regimens accounting for the circadian behavior [72e74]. Optimizing treatment regimens based on the circadian clock remains a challenging frontier [75], and the combination of experimental and theoretical techniques will, no doubt, break important barriers in this endeavor.

Conflict of interest statement
Nothing declared.   Circadian clock synchronization of the cell cycle in zebrafish occurs through a gating mechanism rather than a periodphase locking process. J Biol Rhythm 2018, 33:137-150. Uses time lapse microscopy of zebrafish-FUCCI cells exposed to different light-dark (LD) cycles. No difference in average cell cycle length is observed for the different LD cycles, while the number of mitosis events