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.

Coupling allows robust mammalian redox circadian rhythms despite heterogeneity and noise.

Circadian clocks are endogenous oscillators present in almost all cells that drive daily rhythms in physiology and behavior. There are two mechanisms that have been proposed to explain how circadian rhythms are generated in mammalian cells: through a transcription-translation feedback loop (TTFL) and based on oxidation/reduction reactions, both of which are intrinsically stochastic and heterogeneous at the single cell level. In order to explore the emerging properties of stochastic and heterogeneous redox oscillators, we simplify a recently developed kinetic model of redox oscillations to an amplitude-phase oscillator with 'twist' (period-amplitude correlation) and subject to Gaussian noise. We show that noise and heterogeneity alone lead to fast desynchronization, and that coupling between noisy oscillators can establish robust and synchronized rhythms with amplitude expansions and tuning of the period due to twist. Coupling a network of redox oscillators to a simple model of the TTFL also contributes to synchronization, large amplitudes and fine-tuning of the period for appropriate interaction strengths. These results provide insights into how the circadian clock compensates randomness from intracellular sources and highlight the importance of noise, heterogeneity and coupling in the context of circadian oscillators.

p53 and p21 dynamics encode single-cell DNA damage levels, fine-tuning proliferation and shaping population heterogeneity.

Cells must accurately and quickly detect DNA damage through a set of checkpoint mechanisms that enable repair and control proliferation. Heterogeneous levels of cellular stress and noisy signaling processes can lead to phenotypic variability but little is known about their role in underlying proliferation heterogeneity. Here we study two previously published single cell datasets and find that cells encode heterogeneous levels of endogenous and exogenous DNA damage to shape proliferation heterogeneity at the population level. Using a comprehensive time series analysis of short- and long-term signaling dynamics of p53 and p21, we show that DNA damage levels are quantitatively translated into p53 and p21 signal parameters in a gradual manner. Analyzing instantaneous proliferation and signaling differences among equally-radiated cells, we identify time-localized changes in the period of p53 pulses that drive cells out of a low proliferative state. Our findings suggest a novel role of the p53-p21 network in quantitatively encoding DNA damage strength and fine-tuning proliferation trajectories.

Are circadian amplitudes and periods correlated? A new twist in the story.

Three parameters are important to characterize a circadian and in general any biological clock: period, phase and amplitude. While circadian periods have been shown to correlate with entrainment phases, and clock amplitude influences the phase response of an oscillator to pulse-like zeitgeber signals, the co-modulations of amplitude and periods, which we term twist, have not been studied in detail. In this paper we define two concepts: parametric twist refers to amplitude-period correlations arising in ensembles of self-sustained clocks in the absence of external inputs, and phase space twist refers to the co-modulation of an individual clock's amplitude and period in response to external zeitgebers. Our findings show that twist influences the interaction of oscillators with the environment, facilitating entrainment, fastening recovery to pulse-like perturbations or modifying the response of an individual clock to coupling. This theoretical framework might be applied to understand the emerging properties of other oscillating systems.

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).

Analyses of circRNA Expression throughout the Light-Dark Cycle Reveal a Strong Regulation of Cdr1as, Associated with Light Entrainment in the SCN.

Circular RNAs (circRNAs) are a large class of relatively stable RNA molecules that are highly expressed in animal brains. Many circRNAs have been associated with CNS disorders accompanied by an aberrant wake-sleep cycle. However, the regulation of circRNAs in brain homeostasis over daily light-dark (LD) cycles has not been characterized. Here, we aim to quantify the daily expression changes of circRNAs in physiological conditions in healthy adult animals. Using newly generated and public RNA-Seq data, we monitored circRNA expression throughout the 12:12 h LD cycle in various mouse brain regions. We identified that Cdr1as, a conserved circRNA that regulates synaptic transmission, is highly expressed in the suprachiasmatic nucleus (SCN), the master circadian pacemaker. Despite its high stability, Cdr1as has a very dynamic expression in the SCN throughout the LD cycle, as well as a significant regulation in the hippocampus following the entry into the dark phase. Computational integration of different public datasets predicted that Cdr1as is important for regulating light entrainment in the SCN. We hypothesize that the expression changes of Cdr1as in the SCN, particularly during the dark phase, are associated with light-induced phase shifts. Importantly, our work revises the current beliefs about natural circRNA stability and suggests that the time component must be considered when studying circRNA regulation.

Mathematical Modeling in Circadian Rhythmicity.

Circadian clocks are autonomous systems able to oscillate in a self-sustained manner in the absence of external cues, although such Zeitgebers are typically present. At the cellular level, the molecular clockwork consists of a complex network of interlocked feedback loops. This chapter discusses self-sustained circadian oscillators in the context of nonlinear dynamics theory. We suggest basic steps that can help in constructing a mathematical model and introduce how self-sustained generations can be modeled using ordinary differential equations. Moreover, we discuss how coupled oscillators synchronize among themselves or entrain to periodic signals. The development of mathematical models over the last years has helped to understand such complex network systems and to highlight the basic building blocks in which oscillating systems are built upon. We argue that, through theoretical predictions, the use of simple models can guide experimental research and is thus suitable to model biological systems qualitatively.

Mathematical modelling identifies conditions for maintaining and escaping feedback control in the intestinal epithelium.

The intestinal epithelium is one of the fastest renewing tissues in mammals. It shows a hierarchical organisation, where intestinal stem cells at the base of crypts give rise to rapidly dividing transit amplifying cells that in turn renew the pool of short-lived differentiated cells. Upon injury and stem-cell loss, cells can also de-differentiate. Tissue homeostasis requires a tightly regulated balance of differentiation and stem cell proliferation, and failure can lead to tissue extinction or to unbounded growth and cancerous lesions. Here, we present a two-compartment mathematical model of intestinal epithelium population dynamics that includes a known feedback inhibition of stem cell differentiation by differentiated cells. The model shows that feedback regulation stabilises the number of differentiated cells as these become invariant to changes in their apoptosis rate. Stability of the system is largely independent of feedback strength and shape, but specific thresholds exist which if bypassed cause unbounded growth. When dedifferentiation is added to the model, we find that the system can recover faster after certain external perturbations. However, dedifferentiation makes the system more prone to losing homeostasis. Taken together, our mathematical model shows how a feedback-controlled hierarchical tissue can maintain homeostasis and can be robust to many external perturbations.

Inter-layer and inter-subject variability of diurnal gene expression in human skin.

The skin is the largest human organ with a circadian clock that regulates its function. Although circadian rhythms in specific functions are known, rhythms in the proximal clock output, gene expression, in human skin have not been thoroughly explored. This work reports 24 h gene expression rhythms in two skin layers, epidermis and dermis, in a cohort of young, healthy adults, who maintained natural, regular sleep-wake schedules. 10% of the expressed genes showed such diurnal rhythms at the population level, of which only a third differed between the two layers. Amplitude and phases of diurnal gene expression varied more across subjects than layers, with amplitude being more variable than phases. Expression amplitudes in the epidermis were larger and more subject-variable, while they were smaller and more consistent in the dermis. Core clock gene expression was similar across layers at the population-level, but were heterogeneous in their variability across subjects. We also identified small sets of biomarkers for internal clock phase in each layer, which consisted of layer-specific non-core clock genes. This work provides a valuable resource to advance our understanding of human skin and presents a novel methodology to quantify sources of variability in human circadian rhythms.

Venn diagram analysis overestimates the extent of circadian rhythm reprogramming.

The circadian clock modulates key physiological processes in many organisms. This widespread role of circadian rhythms is typically characterized at the molecular level by profiling the transcriptome at multiple time points. Subsequent analysis identifies transcripts with altered rhythms between control and perturbed conditions, that is, are differentially rhythmic (DiffR). Commonly, Venn diagram analysis (VDA) compares lists of rhythmic transcripts to catalog transcripts with rhythms in both conditions, or that have gained or lost rhythms. However, unavoidable errors in rhythmicity detection propagate to the final DiffR classification resulting in overestimated DiffR. We show using artificial experiments on biological data that VDA indeed produces excessive false DiffR hits both in the presence and absence of true DiffR transcripts. We review and benchmark hypothesis testing and model selection approaches that instead compare circadian amplitude and phase of transcripts between the two conditions. These methods identify transcripts that 'gain', 'lose', 'change', or have the 'same' rhythms; the third category is missed by VDA. We reanalyzed three studies on the interplay between metabolism and the clock in the mouse liver that used VDA. We found not only fewer DiffR transcripts than originally reported, but VDA overlooked many relevant DiffR transcripts. Our analyses confirmed some and contradicted other conclusions in the original studies and also generated novel insights. Our conclusions equally apply to circadian studies using other omics technologies. We believe that avoiding Venn diagrams and using our convenient r-package comparerhythms will improve the reliability of analyses in chronobiology.

Principles underlying the complex dynamics of temperature entrainment by a circadian clock.

Autonomously oscillating circadian clocks resonate with daily environmental (zeitgeber) rhythms to organize physiology around the solar day. Although entrainment properties and mechanisms have been studied widely and in great detail for light-dark cycles, entrainment to daily temperature rhythms remains poorly understood despite that they are potent zeitgebers. Here we investigate the entrainment of the chronobiological model organism Neurospora crassa, subject to thermocycles of different periods and fractions of warm versus cold phases, mimicking seasonal variations. Depending on the properties of these thermocycles, regularly entrained rhythms, period-doubling (frequency demultiplication) but also irregular aperiodic behavior occurs. We demonstrate that the complex nonlinear phenomena of experimentally observed entrainment dynamics can be understood by molecular mathematical modeling.

Intercellular coupling between peripheral circadian oscillators by TGF-ß signaling.

Coupling between cell-autonomous circadian oscillators is crucial to prevent desynchronization of cellular networks and disruption of circadian tissue functions. While neuronal oscillators within the mammalian central clock, the suprachiasmatic nucleus, couple intercellularly, coupling among peripheral oscillators is controversial and the molecular mechanisms are unknown. Using two- and three-dimensional mammalian culture models in vitro (mainly human U-2 OS cells) and ex vivo, we show that peripheral oscillators couple via paracrine pathways. We identify transforming growth factor-ß (TGF-ß) as peripheral coupling factor that mediates paracrine phase adjustment of molecular clocks through transcriptional regulation of core-clock genes. Disruption of TGF-ß signaling causes desynchronization of oscillator networks resulting in reduced amplitude and increased sensitivity toward external zeitgebers. Our findings reveal an unknown mechanism for peripheral clock synchrony with implications for rhythmic organ functions and circadian health.

Live-cell imaging of circadian clock protein dynamics in CRISPR-generated knock-in cells.

The cell biology of circadian clocks is still in its infancy. Here, we describe an efficient strategy for generating knock-in reporter cell lines using CRISPR technology that is particularly useful for genes expressed transiently or at low levels, such as those coding for circadian clock proteins. We generated single and double knock-in cells with endogenously expressed PER2 and CRY1 fused to fluorescent proteins allowing us to simultaneously monitor the dynamics of CRY1 and PER2 proteins in live single cells. Both proteins are highly rhythmic in the nucleus of human cells with PER2 showing a much higher amplitude than CRY1. Surprisingly, CRY1 protein is nuclear at all circadian times indicating the absence of circadian gating of nuclear import. Furthermore, in the nucleus of individual cells CRY1 abundance rhythms are phase-delayed (~5 hours), and CRY1 levels are much higher (>5 times) compared to PER2 questioning the current model of the circadian oscillator.

Circadian rhythms in septic shock patients.

BACKGROUND: Despite the intensive efforts to improve the diagnosis and therapy of sepsis over the last decade, the mortality of septic shock remains high and causes substantial socioeconomical burden of disease. The function of immune cells is time-of-day-dependent and is regulated by several circadian clock genes. This study aims to investigate whether the rhythmicity of clock gene expression is altered in patients with septic shock. METHODS: This prospective pilot study was performed at the university hospital Charité-Universitätsmedizin Berlin, Department of Anesthesiology and Operative Intensive Care Medicine (CCM, CVK). We included 20 patients with septic shock between May 2014 and January 2018, from whom blood was drawn every 4 h over a 24-h period to isolate CD14-positive monocytes and to measure the expression of 17 clock and clock-associated genes. Of these patients, 3 whose samples expressed fewer than 8 clock genes were excluded from the final analysis. A rhythmicity score SP was calculated, which comprises values between -1 (arrhythmic) and 1 (rhythmic), and expression data were compared to data of a healthy study population additionally. RESULTS: 77% of the measured clock genes showed inconclusive rhythms, i.e., neither rhythmic nor arrhythmic. The clock genes NR1D1, NR1D2 and CRY2 were the most rhythmic, while CLOCK and ARNTL were the least rhythmic. Overall, the rhythmicity scores for septic shock patients were significantly (p < 0.0001) lower (0.23 ± 0.26) compared to the control group (12 healthy young men, 0.70 ± 0.18). In addition, the expression of clock genes CRY1, NR1D1, NR1D2, DBP, and PER2 was suppressed in septic shock patients and CRY2 was significantly upregulated compared to controls. CONCLUSION: Molecular rhythms in immune cells of septic shock patients were substantially altered and decreased compared to healthy young men. The decrease in rhythmicity was clock gene-dependent. The loss of rhythmicity and down-regulation of clock gene expression might be caused by sepsis and might further deteriorate immune responses and organ injury, but further studies are necessary to understand underlying pathophysiological mechanisms. Trail registration Clinical trial registered with www.ClinicalTrials.gov (NCT02044575) on 24 January 2014.

Synergies of Multiple Zeitgebers Tune Entrainment.

Circadian rhythms are biological rhythms with a period close to 24 h. They become entrained to the Earth's solar day via different periodic cues, so-called zeitgebers. The entrainment of circadian rhythms to a single zeitgeber was investigated in many mathematical clock models of different levels of complexity, ranging from the Poincaré oscillator and the Goodwin model to biologically more detailed models of multiple transcriptional translational feedback loops. However, circadian rhythms are exposed to multiple coexisting zeitgebers in nature. Therefore, we study synergistic effects of two coexisting zeitgebers on different components of the circadian clock. We investigate the induction of period genes by light together with modulations of nuclear receptor activities by drugs and metabolism. Our results show that the entrainment of a circadian rhythm to two coexisting zeitgebers depends strongly on the phase difference between the two zeitgebers. Synergistic interactions of zeitgebers can strengthen diurnal rhythms to reduce detrimental effects of shift-work and jet lag. Medical treatment strategies which aim for stable circadian rhythms should consider interactions of multiple zeitgebers.

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.

Searching Novel Clock Genes Using RNAi-Based Screening.

RNA interference (RNAi) allows for the selective downregulation of gene expression by neutralizing targeted mRNA molecules and has frequently been used in high-throughput screening endeavors. Here, we describe a protocol for the highly parallel RNAi-mediated downregulation of gene expression in order to search for components involved in circadian rhythm generation. We use lentiviral gene transfer to deliver shRNA expressing plasmids into circadian reporter cells ensuring for efficient and stable knockdown. Circadian rhythms are monitored using live-cell bioluminescence recording of synchronized reporter cells over several days. In addition, we present a new software tool (ChronoStar) for efficient, parallel time-series analysis to extract rhythm parameters such as period, phase, amplitude, and damping.

Multiple random phosphorylations in clock proteins provide long delays and switches.

Theory predicts that self-sustained oscillations require robust delays and nonlinearities (ultrasensitivity). Delayed negative feedback loops with switch-like inhibition of transcription constitute the core of eukaryotic circadian clocks. The kinetics of core clock proteins such as PER2 in mammals and FRQ in Neurospora crassa is governed by multiple phosphorylations. We investigate how multiple, slow and random phosphorylations control delay and molecular switches. We model phosphorylations of intrinsically disordered clock proteins (IDPs) using conceptual models of sequential and distributive phosphorylations. Our models help to understand the underlying mechanisms leading to delays and ultrasensitivity. The model shows temporal and steady state switches for the free kinase and the phosphoprotein. We show that random phosphorylations and sequestration mechanisms allow high Hill coefficients required for self-sustained oscillations.

Nonlinear phenomena in models of the circadian clock.

The mammalian circadian clock is well-known to be important for our sleep-wake cycles, as well as other daily rhythms such as temperature regulation, hormone release or feeding-fasting cycles. Under normal conditions, these daily cyclic events follow 24 h limit cycle oscillations, but under some circumstances, more complex nonlinear phenomena, such as the emergence of chaos, or the splitting of physiological dynamics into oscillations with two different periods, can be observed. These nonlinear events have been described at the organismic and tissue level, but whether they occur at the cellular level is still unknown. Our results show that period-doubling, chaos and splitting appear in different models of the mammalian circadian clock with interlocked feedback loops and in the absence of external forcing. We find that changes in the degradation of clock genes and proteins greatly alter the dynamics of the system and can induce complex nonlinear events. Our findings highlight the role of degradation rates in determining the oscillatory behaviour of clock components, and can contribute to the understanding of molecular mechanisms of circadian dysregulation.

Neither per, nor tim1, nor cry2 alone are essential components of the molecular circadian clockwork in the Madeira cockroach.

Circadian clocks control rhythms in physiology and behavior entrained to 24 h light-dark cycles. Despite of conserved general schemes, molecular circadian clockworks differ between insect species. With RNA interference (RNAi) we examined an ancient circadian clockwork in a basic insect, the hemimetabolous Madeira cockroach Rhyparobia maderae. With injections of double-stranded RNA (dsRNA) of cockroach period (Rm´per), timeless 1 (Rm´tim1), or cryptochrome 2 (Rm´cry2) we searched for essential components of the clock´s core negative feedback loop. Single injections of dsRNA of each clock gene into adult cockroaches successfully and permanently knocked down respective mRNA levels within ~two weeks deleting daytime-dependent mRNA rhythms for Rm´per and Rm´cry2. Rm´perRNAi or Rm´cry2RNAi affected total mRNA levels of both genes, while Rm´tim1 transcription was independent of both, also keeping rhythmic expression. Unexpectedly, circadian locomotor activity of most cockroaches remained rhythmic for each clock gene knockdown employed. It expressed weakened rhythms and unchanged periods for Rm´perRNAi and shorter periods for Rm´tim1RNAi and Rm´cry2RNAi.As a hypothesis of the cockroach´s molecular clockwork, a basic network of switched differential equations was developed to model the oscillatory behavior of clock cells expressing respective clock genes. Data were consistent with two synchronized main groups of coupled oscillator cells, a leading (morning) oscillator, or a lagging (evening) oscillator that couple via mutual inhibition. The morning oscillators express shorter, the evening oscillators longer endogenous periods based on core feedback loops with either PER, TIM1, or CRY2/PER complexes as dominant negative feedback of the clockwork. We hypothesize that dominant morning oscillator cells with shorter periods express PER, but not CRY2, or TIM1 as suppressor of clock gene expression, while two groups of evening oscillator cells with longer periods either comprise TIM1 or CRY2/PER suppressing complexes. Modelling suggests that there is an additional negative feedback next to Rm´PER in cockroach morning oscillator cells.