Effects of (Poly)phenols on Circadian Clock Gene-Mediated Metabolic Homeostasis in Cultured Mammalian Cells: A Scoping Review.

Circadian clocks regulate metabolic homeostasis. Disruption to our circadian clocks, by lifestyle behaviors such as timing of eating and sleeping, has been linked to increased rates of metabolic disorders. There is now considerable evidence that selected dietary (poly)phenols, including flavonoids, phenolic acids and tannins, may modulate metabolic and circadian processes. This review evaluates the effects of (poly)phenols on circadian clock genes and linked metabolic homeostasis in vitro, and potential mechanisms of action, by critically evaluating the literature on mammalian cells. A systematic search was conducted to ensure full coverage of the literature and identified 43 relevant studies addressing the effects of (poly)phenols on cellular circadian processes. Nobiletin and tangeretin, found in citrus, (-)-epigallocatechin-3-gallate from green tea, urolithin A, a gut microbial metabolite from ellagitannins in fruit, curcumin, bavachalcone, cinnamic acid, and resveratrol at low micromolar concentrations all affect circadian molecular processes in multiple types of synchronized cells. Nobiletin emerges as a putative retinoic acid-related orphan receptor (RORα/γ) agonist, leading to induction of the circadian regulator brain and muscle ARNT-like 1 (BMAL1), and increased period circadian regulator 2 (PER2) amplitude and period. These effects are clear despite substantial variations in the protocols employed, and this review suggests a methodological framework to help future study design in this emerging area of research.

A single incidental dark pulse during daytime attenuated food anticipatory behavior.

Using an open-source operant feeding device (FED3), we measured food-seeking nose poking behavior in mice. When the mice were exposed to 4 h restricted feeding at night, all mice exhibited robust food anticipatory nose poking starting ~4 h before scheduled mealtime. When the light-dark cycle was advanced by 6 h, mice exhibited two distinct bouts of anticipatory poking, one corresponding to actual mealtime which continued at the same time of day, and one corresponding to predicted mealtime which shifted parallel with the light-dark cycle. Likewise, two similar bouts of food-seeking behavior appeared when the light-dark cycle was delayed for 9 h. These data suggest that food anticipatory behavior is encoded to a circadian oscillator that entrains to the light-dark cycle. Two weeks after advancing the light-dark cycle, mice incidentally received a 3.5 h dark pulse in the middle of the day. This single dark pulse had a negligible effect on running wheel behavior but caused a temporary attenuation of both food anticipatory poking and pellet intake. These results suggest that the circadian oscillator controlling food anticipatory poking is sensitive to light disruption and that proper food anticipation is critical for sufficient food intake during temporally restricted feeding.

A Luciferase Imaging-Based Assay for Studying Temperature Compensation of the Circadian Clock.

The pace of circadian rhythms remains relatively unchanged across a physiologically relevant range of temperatures, a phenomenon known as temperature compensation. Temperature compensation is a defining characteristic of circadian rhythms, ensuring that clock-regulated processes occur at approximately the same time of day across a wide range of conditions. Despite the identification of several genes involved in the regulation of temperature compensation, the molecular mechanisms underlying this process are still not well understood. High-throughput assays of circadian period are essential for the investigation of temperature compensation. In this chapter, we present a luciferase imaging-based method that enables robust and accurate examination of temperature compensation in the plant circadian clock.

Modeling the Effects of Napping and Non-napping Patterns of Light Exposure on the Human Circadian Oscillator.

In early childhood, consolidation of sleep from a biphasic to a monophasic sleep-wake pattern, that is, the transition from sleeping during an afternoon nap and at night to sleeping only during the night, represents a major developmental milestone. Reduced napping behavior is associated with an advance in the timing of the circadian system; however, it is unknown if this advance represents a standard response of the circadian clock to altered patterns of light exposure or if it additionally reflects features of the developing circadian system. Using a mathematical model of the human circadian pacemaker, we investigated the impact of napping and non-napping patterns of light exposure on entrained circadian phases. Simulated light schedules were based on published data from 20 children (34.2 ± 2.0 months) with habitual napping or non-napping sleep patterns (15 nappers). We found the model predicted different circadian phases for napping and non-napping light patterns: both the decrease in afternoon light during the nap and the increase in evening light associated with napping toddlers' later bedtimes contributed to the observed circadian phase difference produced between napping and non-napping light schedules. We systematically quantified the effects on phase shifting of nap duration, timing, and light intensity, finding larger phase delays occurred for longer and earlier naps. In addition, we simulated phase response curves to a 1-h light pulse and 1-h dark pulse to predict phase and intensity dependence of these changes in light exposure. We found the light pulse produced larger shifts compared with the dark pulse, and we analyzed the model dynamics to identify the features contributing to this asymmetry. These findings suggest that napping status affects circadian timing due to altered patterns of light exposure, with the dynamics of the circadian clock and light processing mediating the effects of the dark pulse associated with a daytime nap.

Circadian stabilization loop: the regulatory hub and therapeutic target promoting circadian resilience and physiological health.

The circadian clock is a fundamental biological mechanism that orchestrates essential cellular and physiological processes to optimize fitness and health. The basic functional unit is the cell-autonomous oscillator, consisting of intersecting negative feedback loops. Whereas the core loop is primarily responsible for rhythm generation, auxiliary loops, most notably the secondary or stabilization loop, play pivotal roles to confer temporal precision and molecular robustness. The stabilization loop contains opposing nuclear receptor subfamilies REV-ERBs and retinoic acid receptor-related orphan receptors (RORs), competing to modulate rhythmic expression of the basic helix-loop-helix ARNT like 1 ( Bmal1) genes in the core loop as well as other clock-controlled genes. Therefore, REV-ERBs and RORs are strategically located to interface the oscillator and the global transcriptomic network, promoting cellular homeostasis and physiological fitness throughout lifespan. Disruption of REV-ERB and ROR functions has been linked with diseases and aging, and pharmacological manipulation of these factors has shown promise in various mouse disease models. Nobiletin is a natural compound that directly binds to and activates RORα/γ, modulating circadian rhythms, and shows robust in vivo efficacies to combat clock-associated pathophysiologies and age-related decline. Results from several studies demonstrate an inverse relation between nobiletin efficacy and clock functional state, where nobiletin elicits little effect in young and healthy mice with growing efficacy as the clock is perturbed by environmental and genetic challenges. This mode of action is consistent with the function of the stabilization loop to promote circadian and physiological resilience. Future studies should further investigate the function and mechanism of REV-ERBs and RORs, and test strategies targeting these factors against disease and aging.

The central circadian regulator CCA1 functions in Glycine max during defense to a root pathogen, regulating the expression of genes acting in effector triggered immunity (ETI) and cell wall metabolism.

Expression of the central circadian oscillator components CIRCADIAN CLOCK ASSOCIATED 1 (CCA1), TIMING OF CAB1 (TOC1), GIGANTEA (GI), and CONSTANS (CO) occurs in Glycine max root cells (syncytia) parasitized by the nematode Heterodera glycines while undergoing resistance, indicating a defense role. GmCCA1-1 relative transcript abundance (RTA) in roots experiencing overexpression (OE) or RNA interference (RNAi) is characterized by rhythmic oscillations, compared to a ribosomal protein gene (GmRPS21) control. A GmCCA1-1 RTA change, advancing by 12 h, exists in H. glycines-infected as compared to uninfected controls in wild-type, H. glycines-resistant, G. max[Peking/PI 548402]. The G. max[Peking/PI 548402] transgenic controls exhibit the RTA change by 4 h post infection (hpi), not consistently occurring in the H. glycines-susceptible G. max[Williams 82/PI 518671] until 56 hpi. GmCCA1-1 expression is observed to be reduced in H. glycines-infected GmCCA1-1-OE roots as compared to non-infected transgenic roots with no significant change observed among RNAi roots. The GmCCA1-1 expression in transgenic GmCCA1-1-OE roots remains higher than control and RNAi roots. Decreased GmCCA1-1 mRNA among infected roots shows the altered expression is targeted by H. glycines. Gene expression of proven defense genes including 9 different mitogen activated protein kinases (GmMAPKs), NON-RACE SPECIFIC DISEASE RESISTANCE 1 (GmNDR1-1), RPM1-INTERACTING PROTEIN 4 (GmRIN4-4), and the secreted xyloglucan endotransglycosylase/hydrolase 43 (GmXTH43) in GmCCA1-1-OE and GmCCA1-1-RNAi roots, compared to controls, reveal a significant role of GmCCA1-1 expression in roots undergoing defense to H. glycines parasitism. The observation that GmCCA1-1 regulates GmXTH43 expression links the central circadian oscillator to the functionality of the secretion system.

The role of cell-autonomous circadian oscillation of Cry transcription in circadian rhythm generation.

The current model of the mammalian circadian clock describes cell-autonomous and negative feedback-driven circadian oscillation of Cry and Per transcription as the core circadian rhythm generator. However, the actual contribution of this oscillation to circadian rhythm generation remains undefined. Here we perform targeted disruption of cis elements indispensable for cell-autonomous Cry oscillation. Mice lacking overt cell-autonomous Cry oscillation show robust circadian rhythms in locomotor activity. In addition, tissue-autonomous circadian rhythms are robust in the absence of overt Cry oscillation. Unexpectedly, although the absence of overt Cry oscillation leads to severe attenuation of Per oscillation at the cell-autonomous level, circadian rhythms in Per2 accumulation remain robust. As a mechanism to explain this counterintuitive result, Per2 half-life shows cell-autonomous circadian rhythms independent of Cry and Per oscillation. The cell-autonomous circadian clock may therefore remain partially functional even in the absence of overt Cry and Per oscillation because of circadian oscillation in Per2 degradation.

The circadian oscillator analysed at the single-transcript level.

The circadian clock is an endogenous and self-sustained oscillator that anticipates daily environmental cycles. While rhythmic gene expression of circadian genes is well-described in populations of cells, the single-cell mRNA dynamics of multiple core clock genes remain largely unknown. Here we use single-molecule fluorescence in situ hybridisation (smFISH) at multiple time points to measure pairs of core clock transcripts, Rev-erbα (Nr1d1), Cry1 and Bmal1, in mouse fibroblasts. The mean mRNA level oscillates over 24 h for all three genes, but mRNA numbers show considerable spread between cells. We develop a probabilistic model for multivariate mRNA counts using mixtures of negative binomials, which accounts for transcriptional bursting, circadian time and cell-to-cell heterogeneity, notably in cell size. Decomposing the mRNA variability into distinct noise sources shows that clock time contributes a small fraction of the total variability in mRNA number between cells. Thus, our results highlight the intrinsic biological challenges in estimating circadian phase from single-cell mRNA counts and suggest that circadian phase in single cells is encoded post-transcriptionally.

The Compound Eye Possesses a Self-Sustaining Circadian Oscillator in the Cricket Gryllus bimaculatus.

Many insects show daily and circadian changes in morphology and physiology in their compound eye. In this study, we investigated whether the compound eye had an intrinsic circadian rhythm in the cricket Gryllus bimaculatus. We found that clock genes period (per), timeless (tim), cryptochrome 2 (cry2), and cycle (cyc) were rhythmically expressed in the compound eye under 12-h light/12-h dark cycles (LD 12:12) and constant darkness (DD) at a constant temperature. After the optic nerves were severed (ONX), a weak but significant rhythmic expression persisted for per and tim under LD 12:12, while under DD, tim and cyc showed rhythmic expression. We also found that more than half of the ONX compound eyes exhibited weak but significant circadian electroretinographic rhythms. These results clearly demonstrate that the cricket compound eye possesses an intrinsic circadian oscillator which can drive the circadian light sensitivity rhythm in the eye, and that the circadian clock in the optic lobe exerts its influence on the oscillator in the eye.

A Logic NAND Gate for Controlling Gene Expression in a Circadian Rhythm in Cyanobacteria.

To enable circadian control of gene expression in cyanobacteria, we constructed a genetic logic gate (NAND) using orthogonal promoters via modular CRISPR interference. The NAND gates were tested in Synechococcus elongatus PCC 7942 using a fluorescent reporter. The NAND gate dynamics were characterized based on the affinity of the dCas9 complex to the output element. Upon connecting tight gene repressions with the circadian promoter (the purF gene; peak expression at dawn), inversed peak expressions were obtained as an output of the NAND gate although the retroactivities were shown in the ON and OFF states. A dark-responsive genetic element of the NAND gate was also expanded to an AND gate in S. elongatus PCC 7942. These cyanobacterial NAND and AND gates could facilitate the control of gene expressions in dynamic metabolic engineering technologies, thereby enabling the cyanobacteria to serve as biosolar cell factories.

Quantitative Study of Dual Circadian Oscillator Models under Different Skeleton Photoperiods.

The daily proportion of light and dark hours (photoperiod) changes annually and plays an important role in the synchronization of seasonal biological phenomena, such as reproduction, hibernation, and migration. In mammals, the first step of photoperiod transduction occurs in the suprachiasmatic nuclei (SCN), the circadian pacemaker that also coordinates 24-h activity rhythms. Thus, in parallel with its role in annual synchronization, photoperiod variation acutely shapes day/night activity patterns, which vary throughout the year. Systematic studies of this behavioral modulation help understand the mechanisms behind its transduction at the SCN level. To explain how entrainment mechanisms could account for daily activity patterns under different photoperiods, Colin Pittendrigh and Serge Daan proposed a conceptual model in which the pacemaker would be composed of 2 coupled, evening (E) and morning (M), oscillators. Although the E-M model has existed for more than 40 years now, its physiological bases are still not fully resolved, and it has not been tested quantitatively under different photoperiods. To better explore the implications of the E-M model, we performed computer simulations of 2 coupled limit-cycle oscillators. Four model configurations were exposed to systematic variation of skeleton photoperiods, and the resulting daily activity patterns were assessed. The criterion for evaluating different model configurations was the successful reproduction of 2 key behavioral phenomena observed experimentally: activity psi-jumps and photoperiod-induced changes in activity phase duration. We compared configurations with either separate light inputs to E and M or the same light inputs to both oscillators. The former replicated experimental results closely, indicating that the configuration with separate E and M light inputs is the mechanism that best reproduces the effects of different skeleton photoperiods on day/night activity patterns. We hope this model can contribute to the search for E and M and their light input organization in the SCN.

Quantitative Studies for Cell-Division Cycle Control.

The cell-division cycle (CDC) is driven by cyclin-dependent kinases (CDKs). Mathematical models based on molecular networks, as revealed by molecular and genetic studies, have reproduced the oscillatory behavior of CDK activity. Thus, one basic system for representing the CDC is a biochemical oscillator (CDK oscillator). However, genetically clonal cells divide with marked variability in their total duration of a single CDC round, exhibiting non-Gaussian statistical distributions. Therefore, the CDK oscillator model does not account for the statistical nature of cell-cycle control. Herein, we review quantitative studies of the statistical properties of the CDC. Over the past 70 years, studies have shown that the CDC is driven by a cluster of molecular oscillators. The CDK oscillator is coupled to transcriptional and mitochondrial metabolic oscillators, which cause deterministic chaotic dynamics for the CDC. Recent studies in animal embryos have raised the possibility that the dynamics of molecular oscillators underlying CDC control are affected by allometric volume scaling among the cellular compartments. Considering these studies, we discuss the idea that a cluster of molecular oscillators embedded in different cellular compartments coordinates cellular physiology and geometry for successful cell divisions.

Modulation of transcriptional burst frequency by histone acetylation.

Many mammalian genes are transcribed during short bursts of variable frequencies and sizes that substantially contribute to cell-to-cell variability. However, which molecular mechanisms determine bursting properties remains unclear. To probe putative mechanisms, we combined temporal analysis of transcription along the circadian cycle with multiple genomic reporter integrations, using both short-lived luciferase live microscopy and single-molecule RNA-FISH. Using the Bmal1 circadian promoter as our model, we observed that rhythmic transcription resulted predominantly from variations in burst frequency, while the genomic position changed the burst size. Thus, burst frequency and size independently modulated Bmal1 transcription. We then found that promoter histone-acetylation level covaried with burst frequency, being greatest at peak expression and lowest at trough expression, while remaining unaffected by the genomic location. In addition, specific deletions of ROR-responsive elements led to constitutively elevated histone acetylation and burst frequency. We then investigated the suggested link between histone acetylation and burst frequency by dCas9p300-targeted modulation of histone acetylation, revealing that acetylation levels influence burst frequency more than burst size. The correlation between acetylation levels at the promoter and burst frequency was also observed in endogenous circadian genes and in embryonic stem cell fate genes. Thus, our data suggest that histone acetylation-mediated control of transcription burst frequency is a common mechanism to control mammalian gene expression.

Involvement of cortisol and sirtuin1 during the response to stress of hypothalamic circadian system and food intake-related peptides in rainbow trout, Oncorhynchus mykiss.

Stress is conditioning animal welfare by negatively affecting a wide range of physiological and behavioral functions. This may be applied to circadian physiology and food intake. Cortisol, the stress-related hormone, may mediate such effect of stress, but other indirect mediators might be considered, such as sirtuin1. Then, either the independent modulatory effect or the existence of any interaction between mediators may be responsible. The circadian system is the main modulator of several integrative mechanisms at both central and peripheral levels that are rhythmically presented, thus influencing different processes such as food intake. In this way, food intake is controlled by the circadian system, as demonstrated by the persistence of such rhythms of food intake in the absence of environmental external cues. Our study aimed to evaluate the daily profile of hypothalamic mRNA abundance of circadian clock genes (clock1a, bmal1, per1 and rev-erbß-like), and food intake regulators (crf, pomc-a1, cart, and npy) in rainbow trout (Oncorhynchus mykiss), the impact of stress on such rhythms, and the involvement of cortisol and sirtuin1 as mediators. Four cohorts of trout were subjected to 1) normal stocking density (control group), 2) high stocking density for 72 hours (stress group), 3) normal stocking density and implanted with mifepristone, a glucocorticoid receptors antagonist, and 4) mifepristone administered and stressed for 72 hours. Fish from each group were sampled every 4-h along the 24-h LD cycle, and cortisol, glucose and lactate plasma levels were evaluated. Hypothalamic mRNA abundance of clock genes, food intake regulators, glucocorticoid receptors and sirtuin1 were qPCR assayed. Our results reveal the impact of stress on most of the genes assayed, but different mechanisms appear to be involved. The rhythm of clock genes displayed decreased amplitude and averaged levels in stressed trout, with no changes of the acrophase being observed. This effect was not prevented by mifepristone. On the contrary, the effect of stress on the daily profile of crf, pomc-a1, and npy was totally prevented by mifepristone administration. Accordingly, cortisol appears to mainly mediate the effect of stress on food intake regulators through binding to specific glucocorticoid receptors within trout hypothalamus, whereas sirtuin1 is apparently mediating such effects on the circadian system in the same brain region. Further research must be performed to clarify those mechanisms through which stress influences food intake and the circadian oscillator within the same brain region, hypothalamus, in rainbow trout, and the interaction among them all.

Reentrainment of the circadian pacemaker during jet lag: East-west asymmetry and the effects of north-south travel.

The normal alignment of circadian rhythms with the 24-h light-dark cycle is disrupted after rapid travel between home and destination time zones, leading to sleep problems, indigestion, and other symptoms collectively known as jet lag. Using mathematical and computational analysis, we study the process of reentrainment to the light-dark cycle of the destination time zone in a model of the human circadian pacemaker. We calculate the reentrainment time for travel between any two points on the globe at any time of the day and year. We construct one-dimensional entrainment maps to explain several properties of jet lag, such as why most people experience worse jet lag after traveling east than west. We show that this east-west asymmetry depends on the endogenous period of the traveler's circadian clock as well as daylength. Thus the critical factor is not simply whether the endogenous period is greater than or less than 24 h as is commonly assumed. We show that the unstable fixed point of an entrainment map determines whether a traveler reentrains through phase advances or phase delays, providing an understanding of the threshold that separates orthodromic and antidromic modes of reentrainment. Contrary to the conventional wisdom that jet lag only occurs after east-west travel across multiple time zones, we predict that the change in daylength encountered during north-south travel can cause jet lag even when no time zones are crossed. Our techniques could be used to provide advice to travelers on how to minimize jet lag on trips involving multiple destinations and a combination of transmeridian and translatitudinal travel.

Comparing Behavior and Clock Gene Expression between Caterpillars, Butterflies, and Moths.

Circadian behavior is widely observed in insects; however, the mechanisms that drive its evolution remain a black box. While circadian activity rhythms are well characterized in adults within the order Lepidoptera (i.e., most butterfly species are day active, while most moths are night active), much less is known about daily activity and clock gene expression in the larval stage. Additionally, direct comparison of clock gene expression between day-active and night-active species reared together has not been quantified. Our study characterized the daily rhythms of caterpillar feeding and activity in addition to the gene expression of 2 central circadian clock genes, period ( per) and timeless ( tim), in larvae and adults of the day-active butterfly Danaus plexippus and the night-active moth Heliothis virescens. We found that neither Danaus nor Heliothis caterpillars are strictly diurnal or nocturnal like their adult counterparts; however, we found that slight rhythms in feeding and activity can arise in response to external forces, such as temperature and host plant. Expression levels differed between genes, between butterfly larvae and adults, and between butterfly and moth species, even though expression levels of both per and tim oscillated with a similar phase over 24 hours across all treatments. Our study, the first of its kind to investigate circadian timekeeper gene expression in 2 life stages and 2 species, highlights interesting differences in core clock gene expression patterns that could have potential downstream effects on circadian rhythms.

Cell-specific resetting of mouse islet cellular clocks by glucagon, glucagon-like peptide 1 and somatostatin.

AIM: Molecular clocks, operative in pancreatic islet cells, represent an intrinsic mechanism regulating intracellular metabolism and hormone secretion. Glucagon, somatostatin and glucagon-like peptide 1 (GLP-1) are essential coordinators of islet physiology. Here, we assess the synchronizing capacity of glucagon, somatostatin and GLP-1 on pancreatic α- and ß-cell circadian clocks. METHODS: Triple transgenic mice, expressing a circadian PER2::luciferase (luc) reporter combined with α- and ß-cell-specific fluorescent reporters, were employed. Isolated pancreatic islets and fluorescence-activated cell sorting-separated α- and ß-cells were synchronized with glucagon, somatostatin analogue or GLP-1 mimetics, with subsequent real-time PER2::luc bioluminescence recording. Gene expression of Gcgr, Sstr2, Sstr3 and Glp1r in islet cells was assessed by RNA sequencing and RT-qPCR. RESULTS: Glucagon and GLP-1 mimetics (liraglutide and exenatide) induced high-amplitude rhythmic expression of the PER2::luc reporter in ß-cells, but not in α-cells, while the somatostatin analogue octreotide generated a significant phase shift between α- and ß-cells. Enrichment of Gcgr and Glp1r transcripts was detected in ß-cells compared to their α-cell counterparts. The synchronizing effect of glucagon was dose-dependent and mediated by the adenylate cyclase signalling cascade, as it was diminished by adenylate cyclase inhibitor. CONCLUSION: We conclude that proglucagon-derived peptides and somatostatin exhibit receptor-mediated cell-specific synchronizing effects for mouse α- and ß-cell oscillators. Differential islet cell clock modulation by glucagon and somatostatin may represent a physiological mechanism underlying paracrine regulation of rhythmic glucagon and insulin secretion. The reported here strong synchronizing properties of GLP-1 mimetics, widely used for treatment of type 2 diabetes, are of high clinical relevance.

Influence of light and food on the circadian clock in liver of rainbow trout, Oncorhynchus mykiss.

Several reports support the existence of multiple peripheral oscillators in fish, which may be able to modulate the rhythmic functions developed by those tissues hosting them. Thus, a circadian oscillator has been proposed to be located within fish liver. In this vertebrate group, the role played by the circadian system in regulating metabolic processes in liver is mostly unknown. We, therefore investigated the liver of rainbow trout (Oncorhynchus mykiss) as a potential element participating in the regulation of circadian rhythms in fish by hosting a functional circadian oscillator. The presence and expression pattern of main components of the circadian molecular machinery (clock1a, bmal1, per1 and rev-erbß-like) were assessed. Furthermore, the role of environmental cues such as light and food, and their interaction in order to modulate the circadian oscillator was also assessed by exposing animals to constant conditions (absence of light for 48 h, and/or a 4 days fasting period). Our results demonstrate the existence of a functional circadian oscillator within trout liver, as demonstrated by significant rhythms of all clock genes assessed, independently of the environmental conditions studied. In addition, the daily profile of mRNA abundance of clock genes is influenced by both light (mainly clock1a and per1) and food (rev-erbß-like), which is indicative of an interaction between both synchronizers. Our results point to rev-erbß-like as possible mediator between the influence of light and food on the circadian oscillator within trout liver, since its daily profile is influenced by both light and food, thus affecting that of bmal1.

Computational modeling of the cell-autonomous mammalian circadian oscillator.

This review summarizes various mathematical models of cell-autonomous mammalian circadian clock. We present the basics necessary for understanding of the cell-autonomous mammalian circadian oscillator, modern experimental data essential for its reconstruction and some special problems related to the validation of mathematical circadian oscillator models. This work compares existing mathematical models of circadian oscillator and the results of the computational studies of the oscillating systems. Finally, we discuss applications of the mathematical models of mammalian circadian oscillator for solving specific problems in circadian rhythm biology.