A Period2 Phosphoswitch Regulates and Temperature Compensates Circadian Period

Phosphorylation of DNA-binding domains of CLOCK-BMAL1 complex for PER-dependent inhibition in circadian clock of mammalian cells

In mammals, CLOCK and BMAL1 proteins form a heterodimer that binds to E-box sequences and activates transcription of target genes, including Period (Per). Translated PER proteins then bind to the CLOCK-BMAL1 complex to inhibit its transcriptional activity. However, the molecular mechanism and the impact of this PER-dependent inhibition on the circadian clock oscillation remain elusive. We previously identified Ser38 and Ser42 in a DNA-binding domain of CLOCK as phosphorylation sites at the PER-dependent inhibition phase. In this study, knockout rescue experiments showed that nonphosphorylatable (Ala) mutations at these sites shortened circadian period, whereas their constitutive-phospho-mimetic (Asp) mutations completely abolished the circadian rhythms. Similarly, we found that nonphosphorylatable (Ala) and constitutive-phospho-mimetic (Glu) mutations at Ser78 in a DNA-binding domain of BMAL1 also shortened the circadian period and abolished the rhythms, respectively. The mathematical modeling predicted that these constitutive-phospho-mimetic mutations weaken the DNA binding of the CLOCK-BMAL1 complex and that the nonphosphorylatable mutations inhibit the PER-dependent displacement (reduction of DNA-binding ability) of the CLOCK-BMAL1 complex from DNA. Biochemical experiments supported the importance of these phosphorylation sites for displacement of the complex in the PER2-dependent inhibition. Our results provide direct evidence that phosphorylation of CLOCK-Ser38/Ser42 and BMAL1-Ser78 plays a crucial role in the PER-dependent inhibition and the determination of the circadian period.

Hierarchical and scaffolded phosphorylation of two degrons controls PER2 stability

The duration of the transcription-repression cycles that give rise to mammalian circadian rhythms is largely determined by the stability of the PERIOD (PER) protein, the rate-limiting components of the molecular clock. The degradation of PERs is tightly regulated by multisite phosphorylation by casein kinase 1 (CK1δ/ε). In this phosphoswitch, phosphorylation of a PER2 degron [degron 2 (D2)] causes degradation, while phosphorylation of the PER2 familial advanced sleep phase (FASP) domain blocks CK1 activity on the degron, stabilizing PER2. However, this model and many other studies of PER2 degradation do not include the second degron of PER2 that is conserved in PER1, termed degron 1 (D1). We examined how these two degrons contribute to PER2 stability, affect the balance of the phosphoswitch, and how they are differentiated by CK1. Using PER2-luciferase fusions and real-time luminometry, we investigated the contribution of both D2 and of CK1-PER2 binding. We find that D1, like D2, is a substrate of CK1 but that D1 plays only a 'backup' role in PER2 degradation. Notably, CK1 bound to a PER1:PER2 dimer protein can phosphorylate PER1 D1 in trans. This scaffolded phosphorylation provides additional levels of control to PER stability and circadian rhythms.

Analysis of morphology, histology characteristics, and circadian clock gene expression of Onychostoma macrolepis at the overwintering period and the breeding period

Fish typically adapt to their environment through evolutionary traits, and this adaptive strategy plays a critical role in promoting species diversity. Onychostoma macrolepis is a rare and endangered wild species that exhibits a life history of overwintering in caves and breeding in mountain streams. We analyzed the morphological characteristics, histological structure, and expression of circadian clock genes in O. macrolepis to elucidate its adaptive strategies to environmental changes in this study. The results showed that the relative values of O. macrolepis eye diameter, body height, and caudal peduncle height enlarged significantly during the breeding period. The outer layer of the heart was dense; the ventricular myocardial wall was thickened; the fat was accumulated in the liver cells; the red and white pulp structures of the spleen, renal tubules, and glomeruli were increased; and the goblet cells of the intestine were decreased in the breeding period. In addition, the spermatogenic cyst contained mature sperm, and the ovaries were filled with eggs at various stages of development. Throughout the overwintering period, the melano-macrophage center is located between the spleen and kidney, and the melano-macrophage center in the cytoplasm has the ability to synthesize melanin, and is arranged in clusters to form cell clusters or white pulp scattered in it. Circadian clock genes were identified in all organs, exhibiting significant differences between the before/after overwintering period and the breeding period. These findings indicate that the environment plays an important role in shaping the behavior of O. macrolepis, helping the animals to build self-defense mechanisms during cyclical habitat changes. Studying the morphological, histological structure and circadian clock gene expression of O. macrolepis during the overwintering and breeding periods is beneficial for understanding its unique hibernation behavior in caves. Additionally, it provides an excellent biological sample for investigating the environmental adaptability of atypical cavefish species.

Temperature compensation through kinetic regulation in biochemical oscillators

Nearly all circadian clocks maintain a period that is insensitive to temperature changes, a phenomenon known as temperature compensation (TC). Yet, it is unclear whether there is any common feature among different systems that exhibit TC. From a general timescale invariance, we show that TC relies on the existence of certain period-lengthening reactions wherein the period of the system increases strongly with the rates in these reactions. By studying several generic oscillator models, we show that this counterintuitive dependence is nonetheless a common feature of oscillators in the nonlinear (far-from-onset) regime where the oscillation can be separated into fast and slow phases. The increase of the period with the period-lengthening reaction rates occurs when the amplitude of the slow phase in the oscillation increases with these rates while the progression speed in the slow phase is controlled by other rates of the system. The positive dependence of the period on the period-lengthening rates balances its inverse dependence on other kinetic rates in the system, which gives rise to robust TC in a wide range of parameters. We demonstrate the existence of such period-lengthening reactions and their relevance for TC in all four model systems we considered. Theoretical results for a model of the Kai system are supported by experimental data. A study of the energy dissipation also shows that better TC performance requires higher energy consumption. Our study unveils a general mechanism by which a biochemical oscillator achieves TC by operating in parameter regimes far from the onset where period-lengthening reactions exist.

Network switches and their role in circadian clocks

Circadian rhythms are generated by complex interactions among genes and proteins. Self-sustained ∼24 h oscillations require negative feedback loops and sufficiently strong nonlinearities that are the product of molecular and network switches. Here, we review common mechanisms to obtain switch-like behavior, including cooperativity, antagonistic enzymes, multisite phosphorylation, positive feedback, and sequestration. We discuss how network switches play a crucial role as essential components in cellular circadian clocks, serving as integral parts of transcription-translation feedback loops that form the basis of circadian rhythm generation. The design principles of network switches and circadian clocks are illustrated by representative mathematical models that include bistable systems and negative feedback loops combined with Hill functions. This work underscores the importance of negative feedback loops and network switches as essential design principles for biological oscillations, emphasizing how an understanding of theoretical concepts can provide insights into the mechanisms generating biological rhythms.

Circadian rhythm regulates the function of immune cells and participates in the development of tumors

Circadian rhythms are present in almost all cells and play a crucial role in regulating various biological processes. Maintaining a stable circadian rhythm is essential for overall health. Disruption of this rhythm can alter the expression of clock genes and cancer-related genes, and affect many metabolic pathways and factors, thereby affecting the function of the immune system and contributing to the occurrence and progression of tumors. This paper aims to elucidate the regulatory effects of BMAL1, clock and other clock genes on immune cells, and reveal the molecular mechanism of circadian rhythm's involvement in tumor and its microenvironment regulation. A deeper understanding of circadian rhythms has the potential to provide new strategies for the treatment of cancer and other immune-related diseases.

Protocols for in vitro reconstitution of the cyanobacterial circadian clock

Circadian clocks are intracellular systems that orchestrate metabolic processes in anticipation of sunrise and sunset by providing an internal representation of local time. Because the ~24-h metabolic rhythms they produce are important to health across diverse life forms there is growing interest in their mechanisms. However, mechanistic studies are challenging in vivo due to the complex, that is, poorly defined, milieu of live cells. Recently, we reconstituted the intact circadian clock of cyanobacteria in vitro. It oscillates autonomously and remains phase coherent for many days with a fluorescence-based readout that enables real-time observation of individual clock proteins and promoter DNA simultaneously under defined conditions without user intervention. We found that reproducibility of the reactions required strict adherence to the quality of each recombinant clock protein purified from Escherichia coli. Here, we provide protocols for preparing in vitro clock samples so that other labs can ask questions about how changing environments, like temperature, metabolites, and protein levels are reflected in the core oscillator and propagated to regulation of transcription, providing deeper mechanistic insights into clock biology.

The molecular basis for cellular function of intrinsically disordered protein regions

Intrinsically disordered protein regions exist in a collection of dynamic interconverting conformations that lack a stable 3D structure. These regions are structurally heterogeneous, ubiquitous and found across all kingdoms of life. Despite the absence of a defined 3D structure, disordered regions are essential for cellular processes ranging from transcriptional control and cell signalling to subcellular organization. Through their conformational malleability and adaptability, disordered regions extend the repertoire of macromolecular interactions and are readily tunable by their structural and chemical context, making them ideal responders to regulatory cues. Recent work has led to major advances in understanding the link between protein sequence and conformational behaviour in disordered regions, yet the link between sequence and molecular function is less well defined. Here we consider the biochemical and biophysical foundations that underlie how and why disordered regions can engage in productive cellular functions, provide examples of emerging concepts and discuss how protein disorder contributes to intracellular information processing and regulation of cellular function.

The Function, Regulation, and Mechanism of Protein Turnover in Circadian Systems in Neurospora and Other Species

Circadian clocks drive a large array of physiological and behavioral activities. At the molecular level, circadian clocks are composed of positive and negative elements that form core oscillators generating the basic circadian rhythms. Over the course of the circadian period, circadian negative proteins undergo progressive hyperphosphorylation and eventually degrade, and their stability is finely controlled by complex post-translational pathways, including protein modifications, genetic codon preference, protein-protein interactions, chaperon-dependent conformation maintenance, degradation, etc. The effects of phosphorylation on the stability of circadian clock proteins are crucial for precisely determining protein function and turnover, and it has been proposed that the phosphorylation of core circadian clock proteins is tightly correlated with the circadian period. Nonetheless, recent studies have challenged this view. In this review, we summarize the research progress regarding the function, regulation, and mechanism of protein stability in the circadian clock systems of multiple model organisms, with an emphasis on Neurospora crassa, in which circadian mechanisms have been extensively investigated. Elucidation of the highly complex and dynamic regulation of protein stability in circadian clock networks would greatly benefit the integrated understanding of the function, regulation, and mechanism of protein stability in a wide spectrum of other biological processes.

PAS Dimerization at the Nexus of the Mammalian Circadian Clock

Circadian rhythms are genetically encoded molecular clocks for internal biological timekeeping. Organisms from single-cell bacteria to humans use these clocks to adapt to the external environment and synchronize their physiology and behavior to solar light/dark cycles. Although the proteins that constitute the molecular 'cogs' and give rise to circadian rhythms are now known, we still lack a detailed understanding of how these proteins interact to generate and sustain the ∼24-hour circadian clock. Structural studies have helped to expand the architecture of clock proteins and have revealed the abundance of the only well-defined structured regions in the mammalian clock called Per-ARNT-Sim (PAS) domains. PAS domains are modular, evolutionarily conserved sensory and signaling domains that typically mediate protein-protein interactions. In the mammalian circadian clock, PAS domains modulate homo and heterodimerization of several core clock proteins that assemble into transcription factors or repressors. This review will focus on the functional importance of the PAS domains in the circadian clock from a biophysical and biochemical standpoint and describe their roles in clock protein interactions and circadian timekeeping.

Mammalian circadian clock proteins form dynamic interacting microbodies distinct from phase separation

Liquid-liquid phase separation (LLPS) underlies diverse biological processes. Because most LLPS studies were performed in vitro using recombinant proteins or in cells that overexpress protein, the physiological relevance of LLPS for endogenous protein is often unclear. PERIOD, the intrinsically disordered domain-rich proteins, are central mammalian circadian clock components and interact with other clock proteins in the core circadian negative feedback loop. Different core clock proteins were previously shown to form large complexes. Circadian clock studies often rely on experiments that overexpress clock proteins. Here, we show that when Per2 transgene was stably expressed in cells, PER2 protein formed nuclear phosphorylation-dependent slow-moving LLPS condensates that recruited other clock proteins. Super-resolution microscopy of endogenous PER2, however, revealed formation of circadian-controlled, rapidly diffusing nuclear microbodies that were resistant to protein concentration changes, hexanediol treatment, and loss of phosphorylation, indicating that they are distinct from the LLPS condensates caused by protein overexpression. Surprisingly, only a small fraction of endogenous PER2 microbodies transiently interact with endogenous BMAL1 and CRY1, a conclusion that was confirmed in cells and in mice tissues, suggesting an enzyme-like mechanism in the circadian negative feedback process. Together, these results demonstrate that the dynamic interactions of core clock proteins are a key feature of mammalian circadian clock mechanism and the importance of examining endogenous proteins in LLPS and circadian clock studies.

Generalized Michaelis-Menten rate law with time-varying molecular concentrations

The Michaelis-Menten (MM) rate law has been the dominant paradigm of modeling biochemical rate processes for over a century with applications in biochemistry, biophysics, cell biology, systems biology, and chemical engineering. The MM rate law and its remedied form stand on the assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium (quasi-steady state) much faster than the molecular concentrations change. Yet, this assumption is not always justified. Here, we relax this quasi-steady state requirement and propose the generalized MM rate law for the interactions of molecules with active concentration changes over time. Our approach for time-varying molecular concentrations, termed the effective time-delay scheme (ETS), is based on rigorously estimated time-delay effects in molecular complex formation. With particularly marked improvements in protein-protein and protein-DNA interaction modeling, the ETS provides an analytical framework to interpret and predict rich transient or rhythmic dynamics (such as autogenously-regulated cellular adaptation and circadian protein turnover), which goes beyond the quasi-steady state assumption.

Watching the clock in glioblastoma

Glioblastoma (GBM) is the most prevalent malignant primary brain tumor, accounting for 14.2% of all diagnosed tumors and 50.1% of all malignant tumors, and the median survival time is approximately 8 months irrespective of whether a patient receives treatment without significant improvement despite expansive research (Ostrom QT, Price M, Neff C, et al. CBTRUS statistical report: primary brain and other central nervous system tumors diagnosed in the United States in 2015-2019. Neurooncology. 2022; 24(suppl 5):v1-v95.). Recently, important roles for the circadian clock in GBM tumorigenesis have been reported. Positive regulators of circadian-controlled transcription, brain and muscle ARNT-like 1 (BMAL1), and circadian locomotor output cycles kaput (CLOCK), are highly expressed also in GBM and correlated with poor patient prognosis. BMAL1 and CLOCK promote the maintenance of GBM stem cells (GSCs) and the establishment of a pro-tumorigenic tumor microenvironment (TME), suggesting that targeting the core clock proteins may augment GBM treatment. Here, we review findings that highlight the critical role the circadian clock plays in GBM biology and the strategies by which the circadian clock can be leveraged for GBM treatment in the clinic moving forward.

Mammalian circadian clock proteins form dynamic interacting microbodies distinct from phase separation

Liquid-liquid phase separation (LLPS) underlies diverse biological processes. Because most LLPS studies were performed in vitro or in cells that overexpress protein, the physiological relevance of LLPS is unclear. PERIOD proteins are central mammalian circadian clock components and interact with other clock proteins in the core circadian negative feedback loop. Different core clock proteins were previously shown to form large complexes. Here we show that when transgene was stably expressed, PER2 formed nuclear phosphorylation-dependent LLPS condensates that recruited other clock proteins. Super-resolution microscopy of endogenous PER2, however, revealed formation of circadian-controlled, rapidly diffusing microbodies that were resistant to protein concentration changes, hexanediol treatment, and loss of phosphorylation, indicating that they are distinct from the LLPS condensates caused by overexpression. Surprisingly, only a small fraction of endogenous PER2 microbodies transiently interact with endogenous BMAL1 and CRY1, a conclusion that was confirmed in cells and in mice tissues, suggesting an enzyme-like mechanism in the circadian negative feedback process. Together, these results demonstrate that the dynamic interactions of core clock proteins is a key feature of mammalian circadian clock mechanism and the importance of examining endogenous proteins in LLPS and circadian studies.

Regulation of Pol II Pausing during Daily Gene Transcription in Mouse Liver

Cell autonomous circadian oscillation is present in central and various peripheral tissues. The intrinsic tissue clock and various extrinsic cues drive gene expression rhythms. Transcription regulation is thought to be the main driving force for gene rhythms. However, how transcription rhythms arise remains to be fully characterized due to the fact that transcription is regulated at multiple steps. In particular, Pol II recruitment, pause release, and premature transcription termination are critical regulatory steps that determine the status of Pol II pausing and transcription output near the transcription start site (TSS) of the promoter. Recently, we showed that Pol II pausing exhibits genome-wide changes during daily transcription in mouse liver. In this article, we review historical as well as recent findings on the regulation of transcription rhythms by the circadian clock and other transcription factors, and the potential limitations of those results in explaining rhythmic transcription at the TSS. We then discuss our results on the genome-wide characteristics of daily changes in Pol II pausing, the possible regulatory mechanisms involved, and their relevance to future research on circadian transcription regulation.

Alternative polyadenylation factor CPSF6 regulates temperature compensation of the mammalian circadian clock

A defining property of circadian clocks is temperature compensation, characterized by the resilience of their near 24-hour free-running periods against changes in environmental temperature within the physiological range. While temperature compensation is evolutionary conserved across different taxa of life and has been studied within many model organisms, its molecular underpinnings remain elusive. Posttranscriptional regulations such as temperature-sensitive alternative splicing or phosphorylation have been described as underlying reactions. Here, we show that knockdown of cleavage and polyadenylation specificity factor subunit 6 (CPSF6), a key regulator of 3'-end cleavage and polyadenylation, significantly alters circadian temperature compensation in human U-2 OS cells. We apply a combination of 3'-end-RNA-seq and mass spectrometry-based proteomics to globally quantify changes in 3' UTR length as well as gene and protein expression between wild-type and CPSF6 knockdown cells and their dependency on temperature. Since changes in temperature compensation behavior should be reflected in alterations of temperature responses within one or all of the 3 regulatory layers, we statistically assess differential responses upon changes in ambient temperature between wild-type and CPSF6 knockdown cells. By this means, we reveal candidate genes underlying circadian temperature compensation, including eukaryotic translation initiation factor 2 subunit 1 (EIF2S1).

The role of environmental signals in the expression of rhythmic cardiac proteins and their influence on cardiac pathologies

We know that numerous proteins expressed in the heart are influenced by environmental signals (such as light and diet), which cause either an increase or decrease in their expression. Cardiovascular health is sensitive to diet composition (macronutrient content), as well as the percentage of energy, frequency and regularity of meal intake during the 24-hour cycle, and the fasting period. Furthermore, light is an important synchronizer of the circadian clock and, in turn, of several physiological processes, among them cardiovascular physiology. In this chapter, we address the effects of these environmental cues and the known mechanisms that lead to this variation in protein expression in the heart, as well as cardiac function.

PERIOD phosphorylation leads to feedback inhibition of CK1 activity to control circadian period

PERIOD (PER) and Casein Kinase 1δ regulate circadian rhythms through a phosphoswitch that controls PER stability and repressive activity in the molecular clock. CK1δ phosphorylation of the familial advanced sleep phase (FASP) serine cluster embedded within the Casein Kinase 1 binding domain (CK1BD) of mammalian PER1/2 inhibits its activity on phosphodegrons to stabilize PER and extend circadian period. Here, we show that the phosphorylated FASP region (pFASP) of PER2 directly interacts with and inhibits CK1δ. Co-crystal structures in conjunction with molecular dynamics simulations reveal how pFASP phosphoserines dock into conserved anion binding sites near the active site of CK1δ. Limiting phosphorylation of the FASP serine cluster reduces product inhibition, decreasing PER2 stability and shortening circadian period in human cells. We found that Drosophila PER also regulates CK1δ via feedback inhibition through the phosphorylated PER-Short domain, revealing a conserved mechanism by which PER phosphorylation near the CK1BD regulates CK1 kinase activity.

Malpighian tubules of Rhodnius prolixus: More than post-prandial diuresis

Rhodnius prolixus, a major vector of Chagas disease, may be considered the model upon which the foundations of insect physiology and biochemistry were built. It is an obligate blood feeder in which the blood meal triggers growth, development and reproduction. The blood meal also triggers a post-prandial diuresis to maintain osmotic homeostasis. In R. prolixus, as with other insects, the Malpighian tubules play a critical role in this diuresis, and much has been learned about diuresis in R. prolixus, and in other model insects. But the post-genomic era has brought new insights, identifying functions quite apart from diuresis for Malpighian tubules. Indeed, microarrays, transcriptomes, and proteomics have revealed the major roles that Malpighian tubules play in immunity, detoxification, pesticide resistance, and in tolerance to overall stress. This is particularly relevant to R. prolixus since gorging on blood creates several challenges in addition to osmotic balance. Xenobiotics may be present in the blood or toxins may be produced by metabolism of blood; and these must be neutralized and excreted. These processes have not been well described at the molecular level for Malpighian tubules of R. prolixus. This paper will review the involvement of Malpighian tubules in immunity and detoxification, identifying new aspects for Malpighian tubule physiology of R. prolixus by virtue of a transcriptome analysis. The transcriptome analysis indicates the potential of Malpighian tubules of R. prolixus to mount a robust innate immune response, and to contribute to antioxidant production and heme detoxification.

Mathematical insights into the role of dopamine signaling in circadian entrainment

The circadian clock in the mammalian brain comprises interlocked molecular feedback loops that have downstream effects on important physiological functions such as the sleep-wake cycle and hormone regulation. Experiments have shown that the circadian clock also modulates the synthesis and breakdown of the neurotransmitter dopamine. Imbalances in dopamine are linked to a host of neurological conditions including Parkinson's disease, attention-deficit/hyperactivity disorder, and mood disorders, and these conditions are often accompanied by circadian disruptions. We have previously created a mathematical model using nonlinear ordinary differential equations to describe the influences of the circadian clock on dopamine at the molecular level. Recent experiments suggest that dopamine reciprocally influences the circadian clock. Dopamine receptor D1 (DRD1) signaling has been shown to aid in the entrainment of the clock to the 24-hour light-dark cycle, but the underlying mechanisms are not well understood. In this paper, we use our mathematical model to support the experimental hypothesis that DRD1 signaling promotes circadian entrainment by modulating the clock's response to light. We model the effects of a phase advance or delay, as well as the therapeutic potential of a REV-ERB agonist. In addition to phase shifts, we study the influences of photoperiod, or day length, in the mathematical model, connect our findings with the experimental and clinical literature, and determine the parameter that affects the critical photoperiod that signals seasonal changes to physiology.

Evolution of casein kinase 1 and functional analysis of new doubletime mutants in Drosophila

Circadian clocks are timing devices that rhythmically adjust organism's behavior, physiology, and metabolism to the 24-h day-night cycle. Eukaryotic circadian clocks rely on several interlocked transcription-translation feedback loops, where protein stability is the key part of the delay between transcription and the appearance of the mature proteins within the feedback loops. In bilaterian animals, including mammals and insects, the circadian clock depends on a homologous set of proteins. Despite mostly conserved clock components among the fruit fly Drosophila and mammals, several lineage-specific differences exist. Here we have systematically explored the evolution and sequence variability of insect DBT proteins and their vertebrate homologs casein kinase 1 delta (CKIδ) and epsilon (CKIε), dated the origin and separation of CKIδ from CKIε, and identified at least three additional independent duplications of the CKIδ/ε gene in Petromyzon, Danio, and Xenopus. We determined conserved regions in DBT specific to Diptera, and functionally tested a subset of those in D. melanogaster. Replacement of Lysine K224 with acidic residues strongly impacts the free-running period even in heterozygous flies, whereas homozygous mutants are not viable. K224D mutants have a temperature compensation defect with longer free-running periods at higher temperatures, which is exactly the opposite trend of what was reported for corresponding mammalian mutants. All DBTs of dipteran insects contain the NKRQK motif at positions 220-224. The occurrence of this motif perfectly correlates with the presence of BRIDE OF DOUBLETIME, BDBT, in Diptera. BDBT is a non-canonical FK506-binding protein that physically interacts with Drosophila DBT. The phylogeny of FK506-binding proteins suggests that BDBT is either absent or highly modified in non-dipteran insects. In addition to in silico analysis of DBT/CKIδ/ε evolution and diversity, we have identified four novel casein kinase 1 genes specific to the Drosophila genus.

How phosphorylation impacts intrinsically disordered proteins and their function

Phosphorylation is the most common post-translational modification (PTM) in eukaryotes, occurring particularly frequently in intrinsically disordered proteins (IDPs). These proteins are highly flexible and dynamic by nature. Thus, it is intriguing that the addition of a single phosphoryl group to a disordered chain can impact its function so dramatically. Furthermore, as many IDPs carry multiple phosphorylation sites, the number of possible states increases, enabling larger complexities and novel mechanisms. Although a chemically simple and well-understood process, the impact of phosphorylation on the conformational ensemble and molecular function of IDPs, not to mention biological output, is highly complex and diverse. Since the discovery of the first phosphorylation site in proteins 75 years ago, we have come to a much better understanding of how this PTM works, but with the diversity of IDPs and their capacity for carrying multiple phosphoryl groups, the complexity grows. In this Essay, we highlight some of the basic effects of IDP phosphorylation, allowing it to serve as starting point when embarking on studies into this topic. We further describe how recent complex cases of multisite phosphorylation of IDPs have been instrumental in widening our view on the effect of protein phosphorylation. Finally, we put forward perspectives on the phosphorylation of IDPs, both in relation to disease and in context of other PTMs; areas where deep insight remains to be uncovered.

Decoupling PER phosphorylation, stability and rhythmic expression from circadian clock function by abolishing PER-CK1 interaction

Robust rhythms of abundances and phosphorylation profiles of PERIOD proteins were thought be the master rhythms that drive mammalian circadian clock functions. PER stability was proposed to be a major determinant of period length. In mammals, CK1 forms stable complexes with PER. Here we identify the PER residues essential for PER-CK1 interaction. In cells and in mice, their mutation abolishes PER phosphorylation and CLOCK hyperphosphorylation, resulting in PER stabilization, arrhythmic PER abundance and impaired negative feedback process, indicating that PER acts as the CK1 scaffold in circadian feedback mechanism. Surprisingly, the mutant mice exhibit robust short period locomotor activity and other physiological rhythms but low amplitude molecular rhythms. PER-CK1 interaction has two opposing roles in regulating CLOCK-BMAL1 activity. These results indicate that the circadian clock can function independently of PER phosphorylation and abundance rhythms due to another PER-CRY-dependent feedback mechanism and that period length can be uncoupled from PER stability.

Casein Kinase 1 and Human Disease: Insights From the Circadian Phosphoswitch

Biological systems operate in constant communication through shared components and feedback from changes in the environment. Casein kinase 1 (CK1) is a family of protein kinases that functions in diverse biological pathways and its regulation is beginning to be understood. The several isoforms of CK1 take part in key steps of processes including protein translation, cell-cell interactions, synaptic dopaminergic signaling and circadian rhythms. While CK1 mutations are rarely the primary drivers of disease, the kinases are often found to play an accessory role in metabolic disorders and cancers. In these settings, the dysregulation of CK1 coincides with increased disease severity. Among kinases, CK1 is unique in that its substrate specificity changes dramatically with its own phosphorylation state. Understanding the process that governs CK1 substrate selection is thus useful in identifying its role in various ailments. An illustrative example is the PERIOD2 (PER2) phosphoswitch, where CK1δ/ε kinase activity can be varied between three different substrate motifs to regulate the circadian clock.

PERIOD Phosphoclusters Control Temperature Compensation of the Drosophila Circadian Clock

Ambient temperature varies constantly. However, the period of circadian pacemakers is remarkably stable over a wide-range of ecologically- and physiologically-relevant temperatures, even though the kinetics of most biochemical reactions accelerates as temperature rises. This thermal buffering phenomenon, called temperature compensation, is a critical feature of circadian rhythms, but how it is achieved remains elusive. Here, we uncovered the important role played by the Drosophila PERIOD (PER) phosphodegron in temperature compensation. This phosphorylation hotspot is crucial for PER proteasomal degradation and is the functional homolog of mammalian PER2 S478 phosphodegron, which also impacts temperature compensation. Using CRISPR-Cas9, we introduced a series of mutations that altered three Serines of the PER phosphodegron. While all three Serine to Alanine substitutions lengthened period at all temperatures tested, temperature compensation was differentially affected. S44A and S45A substitutions caused undercompensation, while S47A resulted in overcompensation. These results thus reveal unexpected functional heterogeneity of phosphodegron residues in thermal compensation. Furthermore, mutations impairing phosphorylation of the per s phosphocluster showed undercompensation, consistent with its inhibitory role on S47 phosphorylation. We observed that S47A substitution caused increased accumulation of hyper-phosphorylated PER at warmer temperatures. This finding was corroborated by cell culture assays in which S47A slowed down phosphorylation-dependent PER degradation at high temperatures, causing PER degradation to be excessively temperature-compensated. Thus, our results point to a novel role of the PER phosphodegron in temperature compensation through temperature-dependent modulation of the abundance of hyper-phosphorylated PER. Our work reveals interesting mechanistic convergences and differences between mammalian and Drosophila temperature compensation of the circadian clock.

Circadian clock synchrony and chronotherapy opportunities in cancer treatment

Cell-autonomous, tissue-specific circadian rhythms in gene expression and cellular processes have been observed throughout the human body. Disruption of daily rhythms by mistimed exposure to light, food intake, or genetic mutation has been linked to cancer development. Some medications are also more effective at certain times of day. However, a limited number of clinical studies have examined daily rhythms in the patient or drug timing as treatment strategies. This review highlights advances and challenges in cancer biology as a function of time of day. Recent evidence for daily rhythms and their entrainment in tumors indicate that personalized medicine should include understanding and accounting for daily rhythms in cancer patients.

Time-keeping and decision-making in living cells: Part I

To survive and reproduce, a cell must process information from its environment and its own internal state and respond accordingly, in terms of metabolic activity, gene expression, movement, growth, division and differentiation. These signal–response decisions are made by complex networks of interacting genes and proteins, which function as biochemical switches and clocks, and other recognizable information-processing circuitry. This theme issue of Interface Focus (in two parts) brings together articles on time-keeping and decision-making in living cells—work that uses precise mathematical modelling of underlying molecular regulatory networks to understand important features of cell physiology. Part I focuses on time-keeping: mechanisms and dynamics of biological oscillators and modes of synchronization and entrainment of oscillators, with special attention to circadian clocks.

Mathematical analysis of robustness of oscillations in models of the mammalian circadian clock

Circadian rhythms in a wide range of organisms are mediated by molecular mechanisms based on transcription-translation feedback. In this paper, we use bifurcation theory to explore mathematical models of genetic oscillators, based on Kim & Forger’s interpretation of the circadian clock in mammals. At the core of their models is a negative feedback loop whereby PER proteins (PER1 and PER2) bind to and inhibit their transcriptional activator, BMAL1. For oscillations to occur, the dissociation constant of the PER:BMAL1 complex, K^d, must be ≤ 0.04 nM, which is orders of magnitude smaller than a reasonable expectation of 1–10 nM for this protein complex. We relax this constraint by two modifications to Kim & Forger’s ‘single negative feedback’ (SNF) model: first, by introducing a multistep reaction chain for posttranscriptional modifications of Per mRNA and posttranslational phosphorylations of PER, and second, by replacing the first-order rate law for degradation of PER in the nucleus by a Michaelis-Menten rate law. These modifications increase the maximum allowable K^d to ~2 nM. In a third modification, we consider an alternative rate law for gene transcription to resolve an unrealistically large rate of Per2 transcription at very low concentrations of BMAL1. Additionally, we studied extensions of the SNF model to include a second negative feedback loop (involving REV-ERB) and a supplementary positive feedback loop (involving ROR). Contrary to Kim & Forger’s observations of these extended models, we find that, with our modifications, the supplementary positive feedback loop makes the oscillations more robust than observed in the models with one or two negative feedback loops. However, all three models are similarly robust when accounting for circadian rhythms (~24 h period) with K^d ≥ 1 nM. Our results provide testable predictions for future experimental studies.

The circadian rhythm aligns bodily functions to the day/night cycle and is important for our health. The rhythm originates from an intracellular molecular clock mechanism that mediates rhythmic gene expression. It is long understood that transcriptional negative feedback with sufficient time delay is key to generating circadian oscillations. However, some of the most widely cited mathematical models for the circadian clock suffer from problems of parameter ‘fragilities’. That is, sustained oscillations are possible only for physically unrealistic parameter values. A recent model by Kim & Forger nicely incorporates the inhibitory binding of PER proteins to their transcription activator BMAL1, but oscillations in the Kim-Forger model require a binding affinity between PER and BMAL1 that is orders of magnitude larger than observed binding affinities of protein complexes. To rectify this problem, we make several physiologically credible modifications to the Kim-Forger model, which allow oscillations to occur with more realistic binding affinities. The modified model is further extended to explore the potential roles of supplementary feedback loops in the mammalian clock mechanism. Ultimately, accurate models of the circadian clock will provide better predictive tools for chronotherapy and chrono-pharmacology studies.

Casein kinase 1 and disordered clock proteins form functionally equivalent, phospho-based circadian modules in fungi and mammals

Circadian clocks rely on negative feedback loops. The core circadian inhibitors, FRQ in Neurospora and PERs in animals, are progressively hyperphosphorylated, inactivated, and degraded. CK1 is essential for these clocks. Despite our knowledge of the role of CK1, it is not known how many other kinases are required and how multisite phosphorylation might contribute to circadian timekeeping. We show here that CK1 alone is sufficient to slowly phosphorylate low-affinity sites in FRQ or PER2. The reaction is nearly temperature compensated, and the phosphorylation state of FRQ or PER2 corresponds to the time elapsed since the start of the reaction. Thus, CK1 and FRQ or PER2 form equivalent modules that are in principle capable of measuring time on a circadian scale.

Circadian clocks are timing systems that rhythmically adjust physiology and metabolism to the 24-h day–night cycle. Eukaryotic circadian clocks are based on transcriptional–translational feedback loops (TTFLs). Yet TTFL-core components such as Frequency (FRQ) in Neurospora and Periods (PERs) in animals are not conserved, leaving unclear how a 24-h period is measured on the molecular level. Here, we show that CK1 is sufficient to promote FRQ and mouse PER2 (mPER2) hyperphosphorylation on a circadian timescale by targeting a large number of low-affinity phosphorylation sites. Slow phosphorylation kinetics rely on site-specific recruitment of Casein Kinase 1 (CK1) and access of intrinsically disordered segments of FRQ or mPER2 to bound CK1 and on CK1 autoinhibition. Compromising CK1 activity and substrate binding affects the circadian clock in Neurospora and mammalian cells, respectively. We propose that CK1 and the clock proteins FRQ and PERs form functionally equivalent, phospho-based timing modules in the core of the circadian clocks of fungi and animals.

Uncovering the dynamics of a circadian-dopamine model influenced by the light-dark cycle

The neurotransmitter dopamine (DA) is known to be influenced by the circadian timekeeping system in the mammalian brain. We have previously created a single-cell differential equations model to understand the mechanisms behind circadian rhythms of extracellular DA. In this paper, we investigate the dynamics in our model and study different behaviors such as entrainment to the 24-hour light-dark cycle and robust periodicity versus decoupling, quasiperiodicity, and chaos. Imbalances in DA are often accompanied by disrupted circadian rhythms, such as in Parkinson's disease, hyperactivity, and mood disorders. Our model provides new insights into the links between the circadian clock and DA. We show that the daily rhythmicity of DA can be disrupted by decoupling between interlocked loops of the clock circuitry or by quasiperiodic clock behaviors caused by misalignment with the light-dark cycle. The model can be used to further study how the circadian clock affects the dopaminergic system, and to help develop therapeutic strategies for disrupted DA rhythms. .

Backward simulation for inferring hidden biomolecular kinetic profiles

Our backward simulation (BS) is an approach to infer the dynamics of individual components in ordinary differential equation (ODE) models, given the information on relatively downstream components or their sums. Here, we demonstrate the use of BS to infer protein synthesis rates with a given profile of protein concentrations over time in a circadian system. This protocol can also be applied to a wide range of problems with undetermined dynamics at the upstream levels.

For complete details on the use and execution of this protocol, please refer to Lim et al. (2021).

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Inference of upstream dynamics with information on the downstream profile

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Applies to infer protein synthesis rates with a given circadian protein profile

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Widely applicable to systems biology models with known downstream profiles

Timeless in animal circadian clocks and beyond

TIMELESS (TIM) was first identified as a molecular cog in the Drosophila circadian clock. Almost three decades of investigations have resulted in an insightful model describing the critical role of Drosophila TIM (dTIM) in circadian timekeeping in insects, including its function in mediating light entrainment and temperature compensation of the molecular clock. Furthermore, exciting discoveries on its sequence polymorphism and thermosensitive alternative RNA splicing have also established its role in regulating seasonal biology. Although mammalian TIM (mTIM), its mammalian paralog, was first identified as a potential circadian clock component in 1990s due to sequence similarity to dTIM, its role in clock regulation has been more controversial. Mammalian TIM has now been characterized as a DNA replication fork component and has been shown to promote fork progression and participate in cell cycle checkpoint signaling in response to DNA damage. Despite defective circadian rhythms displayed by mtim mutants, it remains controversial whether the regulation of circadian clocks by mTIM is direct, especially given the interconnection between the cell cycle and circadian clocks. In this review, we provide a historical perspective on the identification of animal tim genes, summarize the roles of TIM proteins in biological timing and genomic stability, and draw parallels between dTIM and mTIM despite apparent functional divergence.

Oncogenic and Circadian Effects of Small Molecules Directly and Indirectly Targeting the Core Circadian Clock

Circadian rhythms are essential for controlling the cell cycle, cellular proliferation, and apoptosis, and hence are tightly linked to cell fate. Several recent studies have used small molecules to affect circadian oscillations; however, their concomitant cellular effects were not assessed, and they have not been compared under similar experimental conditions. In this work, we use five molecules, grouped into direct versus indirect effectors of the circadian clock, to modulate periods in a human osteosarcoma cell line (U2OS) and determine their influences on cellular behaviors, including motility and colony formation. Luciferase reporters, whose expression was driven via Bmal1- or Per2-promoters, were used to facilitate the visualization and quantitative analysis of circadian oscillations. We show that all molecules increase or decrease the circadian periods of Bmal1 and Per2 in a dose-dependent manner, but period length does not correlate with the extent of cell migration or proliferation. Nonetheless, molecules that affected circadian oscillations to a greater degree resulted in substantial influence on cellular behaviors (ie, motility and colony formation), which may also be attributable to noncircadian targets. Furthermore, we find that the ability and extent to which the molecules are able to affect oscillations is independent of whether they are direct or indirect modulators. Because of the numerous connections and feedback between the circadian clock and other pathways, it is important to consider the effects of both in assessing these and other compounds.

Circadian NAD(P)(H) cycles in cell metabolism

Intrinsic circadian clocks are present in all forms of photosensitive life, enabling daily anticipation of the light/dark cycle and separation of energy storage and utilization cycles on a 24-h timescale. The core mechanism underlying circadian rhythmicity involves a cell-autonomous transcription/translation feedback loop that in turn drives rhythmic organismal physiology. In mammals, genetic studies have established that the core clock plays an essential role in maintaining metabolic health through actions within both brain pacemaker neurons and peripheral tissues and that disruption of the clock contributes to disease. Peripheral clocks, in turn, can be entrained by metabolic cues. In this review, we focus on the role of the nucleotide NAD(P)(H) and NAD⁺-dependent sirtuin deacetylases as integrators of circadian and metabolic cycles, as well as the implications for this interrelationship in healthful aging.

Differential effects of SUMO1 and SUMO2 on circadian protein PER2 stability and function

Posttranslational modification (PTM) of core circadian clock proteins, including Period2 (PER2), is required for proper circadian regulation. PER2 function is regulated by casein kinase 1 (CK1)-mediated phosphorylation and ubiquitination but little is known about other PER2 PTMs or their interaction with PER2 phosphorylation. We found that PER2 can be SUMOylated by both SUMO1 and SUMO2; however, SUMO1 versus SUMO2 conjugation had different effects on PER2 turnover and transcriptional suppressor function. SUMO2 conjugation facilitated PER2 interaction with β-TrCP leading to PER2 proteasomal degradation. In contrast, SUMO1 conjugation, mediated by E3 SUMO-protein ligase RanBP2, enhanced CK1-mediated PER2S662 phosphorylation, inhibited PER2 degradation and increased PER2 transcriptional suppressor function. PER2 K736 was critical for both SUMO1- and SUMO2-conjugation. A PER2K736R mutation was sufficient to alter PER2 protein oscillation and reduce PER2-mediated transcriptional suppression. Together, our data revealed that SUMO1 versus SUMO2 conjugation acts as a determinant of PER2 stability and function and thereby affects the circadian regulatory system and the expression of clock-controlled genes.

FRQ-CK1 Interaction Underlies Temperature Compensation of the Neurospora Circadian Clock

Temperature compensation is a fundamental property of all circadian clocks; temperature compensation results in a relatively constant period length at different physiological temperatures, but its mechanism is unclear. Formation of a stable complex between clock proteins and casein kinase 1 (CK1) is a conserved feature in eukaryotic circadian mechanisms. Here, we show that the FRQ-CK1 interaction and CK1-mediated FRQ phosphorylation, not FRQ stability, are main mechanisms responsible for the circadian temperature compensation phenotypes in Neurospora. Inhibition of CK1 kinase activity impaired the temperature compensation profile. Importantly, both the loss of temperature compensation and temperature overcompensation phenotypes of the wild-type and different clock mutant strains can be explained by temperature-dependent alterations of the FRQ-CK1 interaction. Furthermore, mutations that were designed to specifically affect the FRQ-CK1 interaction resulted in impaired temperature compensation of the clock. Together, these results reveal the temperature-compensated FRQ-CK1 interaction, which results in temperature-compensated CK1-mediated FRQ and WC phosphorylation, as a main biochemical process that underlies the mechanism of circadian temperature compensation in Neurospora. IMPORTANCE Temperature compensation allows clocks to adapt to all seasons by having a relatively constant period length at different physiological temperatures, but the mechanism of temperature compensation is unclear. Stability of clock proteins was previously proposed to be a major factor that regulated temperature compensation. In this study, we showed that the interaction between CK1 and FRQ, but not FRQ stability, explains the circadian temperature compensation phenotypes in Neurospora. This study uncovered the key biochemical mechanism responsible for temperature compensation of the circadian clock and further established the mechanism for period length determination in Neurospora. Because the regulation of circadian clock proteins by CK1 and the formation of a stable clock complex with CK1 are highly conserved in eukaryotic clocks, a similar mechanism may also exist in animal clocks.

Cost-effective circadian mechanism: rhythmic degradation of circadian proteins spontaneously emerges without rhythmic post-translational regulation

Circadian protein oscillations are maintained by the lifelong repetition of protein production and degradation in daily balance. It comes at the cost of ever-replayed, futile protein synthesis each day. This biosynthetic cost with a given oscillatory protein profile is relievable by a rhythmic, not constant, degradation rate that selectively peaks at the right time of day but remains low elsewhere, saving much of the gross protein loss and of the replenishing protein synthesis. Here, our mathematical modeling reveals that the rhythmic degradation rate of proteins with circadian production spontaneously emerges under steady and limited activity of proteolytic mediators and does not necessarily require rhythmic post-translational regulation of previous focus. Additional (yet steady) post-translational modifications in a proteolytic pathway can further facilitate the degradation's rhythmicity in favor of the biosynthetic cost saving. Our work is supported by animal and plant circadian data, offering a generic mechanism for potentially widespread, time-dependent protein turnover.

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Rhythmic degradation of circadian proteins lowers the cost of protein synthesis

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This rhythmic degradation emerges without rhythmic post-translational regulation

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Extra, yet steady post-translational modifications enhance degradation rhythmicity

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This mechanism hints at how organisms afford the price of daily biological rhythms

Heavy Water Lengthens the Molecular Circadian Clock Period in the Suprachiasmatic Nucleus of Mice In Vitro

Heavy water lengthens the periods of circadian rhythms in various plant and animal species. Many studies have reported that drinking heavy water lengthens the periods of circadian activity rhythms of rodents by slowing the clock mechanism in the suprachiasmatic nucleus (SCN), the mammalian circadian center. The SCN clock is stable and robust against disturbance, due to its intercellular network. It is unclear whether this robustness provides resistance to the effects of heavy water. Here, we report that heavy water lengthened the rhythm period of clock gene expression of the SCN and peripheral tissues in vitro using a PERIOD2::LUCIFERASE bioluminescence reporter. Our results show that the period-elongation rate of the SCN is similar to those of other tissues. Therefore, the intercellular network of the SCN is not resistant to the period-elongation effect of heavy water.

Biochemical mechanisms of period control within the mammalian circadian clock

Genetically encoded biological clocks are found broadly throughout life on Earth, where they generate circadian (about a day) rhythms that synchronize physiology and behavior with the daily light/dark cycle. Although the genetic networks that give rise to circadian timing are now fairly well established, our understanding of how the proteins that constitute the molecular 'cogs' of this biological clock regulate the intrinsic timing, or period, of circadian rhythms has lagged behind. New studies probing the biochemical and structural basis of clock protein function are beginning to reveal how assemblies of dedicated clock proteins form and evolve through post-translational regulation to generate circadian rhythms. This review will highlight some recent advances providing important insight into the molecular mechanisms of period control in mammalian clocks with an emphasis on structural analyses related to CK1-dependent control of PER stability.

Phosphorylation of GAPVD1 Is Regulated by the PER Complex and Linked to GAPVD1 Degradation

Repressor protein period (PER) complexes play a central role in the molecular oscillator mechanism of the mammalian circadian clock. While the main role of nuclear PER complexes is transcriptional repression, much less is known about the functions of cytoplasmic PER complexes. We found with a biochemical screen for PER2-interacting proteins that the small GTPase regulator GTPase-activating protein and VPS9 domain-containing protein 1 (GAPVD1), which has been identified previously as a component of cytoplasmic PER complexes in mice, is also a bona fide component of human PER complexes. We show that in situ GAPVD1 is closely associated with casein kinase 1 delta (CSNK1D), a kinase that regulates PER2 levels through a phosphoswitch mechanism, and that CSNK1D regulates the phosphorylation of GAPVD1. Moreover, phosphorylation determines the kinetics of GAPVD1 degradation and is controlled by PER2 and a C-terminal autoinhibitory domain in CSNK1D, indicating that the regulation of GAPVD1 phosphorylation is a novel function of cytoplasmic PER complexes and might be part of the oscillator mechanism or an output function of the circadian clock.

The molecular clockwork of mammalian cells

Most organisms contain self-sustained circadian clocks. These clocks can be synchronized by environmental stimuli, but can also oscillate indefinitely in isolation. In mammals this is true at the molecular level for the majority of cell types that have been examined. A core set of "clock genes" form a transcriptional/translational feedback loop (TTFL) which repeats with a period of approximately 24 h. The exact mechanism of the TTFL differs slightly in various cell types, but all involve similar family members of the core cohort of clock genes. The clock has many outputs which are unique for different tissues. Cells in diverse tissues will convert the timing signals provided by the TTFL into uniquely orchestrated transcriptional oscillations of many clock-controlled genes and cellular processes.

Complementary phase responses via functional differentiation of dual negative feedback loops

Multiple feedback loops are often found in gene regulations for various cellular functions. In mammalian circadian clocks, oscillations of Period1 (Per1) and Period2 (Per2) expression are caused by interacting negative feedback loops (NFLs) whose protein products with similar molecular functions repress each other. However, Per1 expression peaks earlier than Per2 in the pacemaker tissue, raising the question of whether the peak time difference reflects their different dynamical functions. Here, we address this question by analyzing phase responses of the circadian clock caused by light-induced transcription of both Per1 and Per2 mRNAs. Through mathematical analyses of dual NFLs, we show that phase advance is mainly driven by light inputs to the repressor with an earlier expression peak as Per1, whereas phase delay is driven by the other repressor with a later peak as Per2. Due to the complementary contributions to phase responses, the ratio of light-induced transcription rates between Per1 and Per2 determines the magnitude and direction of phase shifts at each time of day. Specifically, stronger Per1 light induction than Per2 results in a phase response curve (PRC) with a larger phase advance zone than delay zone as observed in rats and hamsters, whereas stronger Per2 induction causes a larger delay zone as observed in mice. Furthermore, the ratio of light-induced transcription rates required for entrainment is determined by the relation between the circadian and light-dark periods. Namely, if the autonomous period of a circadian clock is longer than the light-dark period, a larger light-induced transcription rate of Per1 than Per2 is required for entrainment, and vice versa. In short, the time difference between Per1 and Per2 expression peaks can differentiate their dynamical functions. The resultant complementary contributions to phase responses can determine entrainability of the circadian clock to the light-dark cycle.

A mathematical model of circadian rhythms and dopamine

Background

The superchiasmatic nucleus (SCN) serves as the primary circadian (24hr) clock in mammals and is known to control important physiological functions such as the sleep-wake cycle, hormonal rhythms, and neurotransmitter regulation. Experimental results suggest that some of these functions reciprocally influence circadian rhythms, creating a highly complex network. Among the clock’s downstream products, orphan nuclear receptors REV-ERB and ROR are particularly interesting because they coordinately modulate the core clock circuitry. Recent experimental evidence shows that REV-ERB and ROR are not only crucial for lipid metabolism but are also involved in dopamine (DA) synthesis and degradation, which could have meaningful clinical implications for conditions such as Parkinson’s disease and mood disorders.

Methods

We create a mathematical model consisting of differential equations that express how the circadian variables are influenced by light, how REV-ERB and ROR feedback to the clock, and how REV-ERB, ROR, and BMAL1-CLOCK affect the dopaminergic system. The structure of the model is based on the findings of experimentalists.

Results

We compare our model predictions to experimental data on clock components in different light-dark conditions and in the presence of genetic perturbations. Our model results are consistent with experimental results on REV-ERB and ROR and allow us to predict the circadian variations in tyrosine hydroxylase and monoamine oxidase seen in experiments. By connecting our model to an extant model of dopamine synthesis, release, and reuptake, we are able to predict circadian oscillations in extracellular DA and homovanillic acid that correspond well with experimental observations.

Conclusions

The predictions of the mathematical model are consistent with a wide variety of experimental observations. Our calculations show that the mechanisms proposed by experimentalists by which REV-ERB, ROR, and BMAL1-CLOCK influence the DA system are sufficient to explain the circadian oscillations observed in dopaminergic variables. Our mathematical model can be used for further investigations of the effects of the mammalian circadian clock on the dopaminergic system. The model can also be used to predict how perturbations in the circadian clock disrupt the dopaminergic system and could potentially be used to find drug targets that ameliorate these disruptions.

Time to fight: targeting the circadian clock molecular machinery in cancer therapy

The circadian clock regulates a wide range of molecular pathways and biological processes. The expression of clock genes is often altered in cancer, fostering tumor initiation and progression. Inhibition and activation of core circadian clock genes, as well as treatments that restore circadian rhythmicity, have been successful in counteracting tumor growth in different experimental models. Here, we provide an up-to-date overview of studies that show the therapeutic effects of targeting the clock molecular machinery in cancer, both genetically and pharmacologically. We also highlight future areas for progress that offer a promising path towards innovative anticancer strategies. Substantial limitations in the current understanding of the complex interplay between the circadian clock and cancer in vivo need to be addressed in order to allow clock-targeting therapies in cancer.

The phosphorylation switch that regulates ticking of the circadian clock

In our 24/7 well-lit world, it's easy to skip or delay sleep to work, study, and play. However, our circadian rhythms are not easily fooled; the consequences of jet lag and shift work are many and severe, including metabolic, mood, and malignant disorders. The internal clock that keeps track of time has at its heart the reversible phosphorylation of the PERIOD proteins, regulated by isoforms of casein kinase 1 (CK1). In-depth biochemical, genetic, and structural studies of these kinases, their mutants, and their splice variants have combined over the past several years to provide a robust understanding of how the core clock is regulated by a phosphoswitch whereby phosphorylation of a stabilizing site on PER blocks phosphorylation of a distant phosphodegron. The recent structure of a circadian mutant form of CK1 implicates an internal activation loop switch that regulates this phosphoswitch and points to new approaches to regulation of the clock.

A design principle for posttranslational chaotic oscillators

Chaos behavior has been observed in various cellular and molecular processes. Here, we modeled reversible phosphorylation dynamics to elucidate a design principle for autonomous chaos generation that may arise from generic enzymatic reactions. A comprehensive parameter search demonstrated that the reaction system composed of a set of kinases and phosphatases and two substrates with two modification sites exhibits chaos behavior. All reactions are described according to the Michaelis-Menten reaction scheme without exotic functions being applied to enzymes and substrates. Clustering analysis of parameter sets that can generate chaos behavior revealed the existence of motif structures. These chaos motifs allow the two-substrate species to interact via enzyme availability and constrain the two substrates' dynamic changes in phosphorylation status so that they occur at different timescales. This chaos motif structure is found in several enzymatic reactions, suggesting that chaos behavior may underlie cellular autonomy in a variety of biochemical systems.

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Two substrates with reversible two-site phosphorylation can exhibit chaos behavior

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The chaos does not require autocatalysis or allosteric regulation of enzymes

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The chaos is a result of the coupling of two substrates via enzyme availability

Simple Kinetic Models in Molecular Chronobiology

Circadian rhythms are constituted by a complex dynamical system with intertwined feedback loops, molecular switches, and self-sustained oscillations. Mathematical modeling supports understanding available heterogeneous kinetic data, highlights basic mechanisms, and can guide experimental research. Here, we introduce the basic steps from a biological question to simple models providing insight into gene-regulatory mechanisms. We illustrate the general approach by three examples: modeling decay processes, clock-controlled genes, and self-sustained oscillations.

Introduction to the Clock System

Circadian (24-h) rhythms dictate almost everything we do, setting our clocks for specific times of sleeping and eating, as well as optimal times for many other basic functions. The physiological systems that coordinate circadian rhythms are intricate, but at their core, they all can be distilled down to cell-autonomous rhythms that are then synchronized within and among tissues. At first glance, these cell-autonomous rhythms may seem rather straight-forward, but years of research in the field has shown that they are strikingly complex, responding to many different external signals, often with remarkable tissue-specificity. To understand the cellular clock system, it is important to be familiar with the major players, which consist of pairs of proteins in a triad of transcriptional/translational feedback loops. In this chapter, we will go through each of the core protein pairs one-by-one, summarizing the literature as to their regulation and their broader impacts on circadian gene expression. We will conclude by briefly examining the human genetics literature, as well as providing perspectives on the future of the study of the molecular clock.