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Modularity is a major design principle in interaction networks. Various studies have shown that protein interaction networks in prokaryotes and eukaryotes display a modular structure. A majority of the studies have been performed for the yeast interaction network, for which data have become abundant. The systematic examination of the human protein interaction network, however, is still in an early phase. To assess whether the human interaction network similarly displays a modular structure, we assembled a large protein network consisting of over 30,000 interactions. More than 670 modules were subsequently identified based on the detection of cliques. Inspection showed that these modules included numerous known protein complexes. The extracted modules were scrutinized for their coherency with respect to function, localization and expression, thereby allowing us to distinguish between stable and dynamic modules. Finally, the examination of the overlap between modules identified key proteins linking distinct molecular processes.

Protein-protein interactions constitute the backbone of many molecular processes. This has motivated the recent construction of several large-scale human protein-protein interaction maps [1-10]. Although these maps clearly offer a wealth of information, their use is challenging: complexity, rapid growth, and fragmentation of interaction data hamper their usability. To overcome these hurdles, we have developed a publicly accessible database termed UniHI (Unified Human Interactome) for integration of human protein-protein interaction data. This database is designed to provide biomedical researchers a common platform for exploring previously disconnected human interaction maps. UniHI offers researchers flexible integrated tools for accessing comprehensive information about the human interactome. Several features included in the UniHI allow users to perform various types of network-oriented and functional analysis. At present, UniHI contains over 160,000 distinct interactions between 17,000 unique proteins from ten major interaction maps derived by both computational and experimental approaches [1-10]. Here we describe the details of the implementation and maintenance of UniHI and discuss the challenges that have to be addressed for a successful integration of interaction data.

Abstract Background Collections of transcription factor binding profiles (Transfac, Jaspar) are essential to identify regulatory elements in DNA sequences. Subsets of highly similar profiles complicate large scale analysis of transcription factor binding sites. Results We propose to identify and group similar profiles using two independent similarity measures: χ2 distances between position frequency matrices (PFMs) and correlation coefficients between position weight matrices (PWMs) scores. Conclusion We show that these measures complement each other and allow to associate Jaspar and Transfac matrices. Clusters of highly similar matrices are identified and can be used to optimise the search for regulatory elements. Moreover, the application of the measures is illustrated by assigning E-box matrices of a SELEX experiment and of experimentally characterised binding sites of circadian clock genes to the Myc-Max cluster.

The circadian clock, a fundamental biological regulator, governs essential cellular processes in health and disease. Circadian-based therapeutic strategies are increasingly gaining recognition as promising avenues. Aligning drug administration with the circadian rhythm can enhance treatment efficacy and minimize side effects. Yet, uncovering the optimal treatment timings remains challenging, limiting their widespread adoption. In this work, we introduce a high-throughput approach integrating live-imaging and data analysis techniques to deep-phenotype cancer cell models, evaluating their circadian rhythms, growth, and drug responses. We devise a streamlined process for profiling drug sensitivities across different times of the day, identifying optimal treatment windows and responsive cell types and drug combinations. Finally, we implement multiple computational tools to uncover cellular and genetic factors shaping time-of-day drug sensitivity. Our versatile approach is adaptable to various biological models, facilitating its broad application and relevance. Ultimately, this research leverages circadian rhythms to optimize anti-cancer drug treatments, promising improved outcomes and transformative treatment strategies., (© 2024. The Author(s).)

Most mammalian cells have molecular circadian clocks that generate widespread rhythms in transcript and protein abundance. While circadian clocks are robust to fluctuations in the cellular environment, little is known about the mechanisms by which the circadian period compensates for fluctuating metabolic states. Here, we exploit the heterogeneity of single cells both in circadian period and a metabolic parameter-protein stability-to study their interdependence without the need for genetic manipulation. We generated cells expressing key circadian proteins (CRYPTOCHROME1/2 (CRY1/2) and PERIOD1/2 (PER1/2)) as endogenous fusions with fluorescent proteins and simultaneously monitored circadian rhythms and degradation in thousands of single cells. We found that the circadian period compensates for fluctuations in the turnover rates of circadian repressor proteins and uncovered possible mechanisms using a mathematical model. In addition, the stabilities of the repressor proteins are circadian phase dependent and correlate with the circadian period in a phase-dependent manner, in contrast to the prevailing model., Competing Interests: Competing interests statement:The authors declare no competing interest.

Healthy mammalian cells have a circadian clock, a gene regulatory network that allows them to schedule their physiological processes to optimal times of the day. When healthy cells turn into cancer cells, the circadian clock often becomes cancer specifically disturbed, so there is an interest in the extraction of circadian features from gene expression data of cancer. This is challenging, as clinical gene expression samples of cancer are snapshot-like and the circadian clock is best examined using gene expression time series. In this study, we obtained lists of intersecting circadian genes in public gene expression time series data of lung tissue of mouse and baboon. We base our circadian gene lists on correlations of gene expression levels of circadian genes, which are closely associated to the phase differences between them. Combining circadian gene expression patterns of diurnal and nocturnal species of different ages provides circadian genes that are also important in healthy and cancerous human lung tissue. We tested the quality of the representation of the circadian clock in our gene lists by PCA-based reconstructions of the circadian times of the mouse and baboon samples. Then we assigned potential circadian times to the human lung tissue samples and find an intact circadian clock in the healthy human lung tissue, but an altered, weak clock in the adjacent cancerous lung tissue., (© 2024. The Author(s).)

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., Competing Interests: Conflict of interest The authors declare that they have no conflicts of interest with the contents of this article., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)

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, limit cycle 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, speeding upfastening 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., Competing Interests: No competing interests were disclosed., (Copyright: © 2024 del Olmo M et al.)

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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)

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., (© 2023. The Author(s).)

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)., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Schmal et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

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., (© The Author(s) 2022. Published by Oxford University Press on behalf of NAR Genomics and Bioinformatics.)

Sugarcane bagasse is commonly combusted to generate energy. Unfortunately, recycling strategies rarely consider the resulting ash as a potential fertilizer. To evaluate this recycling strategy for a sustainable circular economy, we characterized bagasse ash as a fertilizer and measured the effects of co-gasification and co-combustion of bagasse with either chicken manure or sewage sludge: on the phosphorus (P) mass fraction, P-extractability, and mineral P phases. Furthermore, we investigated the ashes as fertilizer for soybeans under greenhouse conditions. All methods in combination are reliable indicators helping to assess and predict P availability from ashes to soybeans. The fertilizer efficiency of pure bagasse ash increased with the ash amount supplied to the substrate. Nevertheless, it was not as effective as fertilization with triple-superphosphate and K 2 SO 4 , which we attributed to lower P availability. Co-gasification and co-combustion increased the P mass fraction in all bagasse-based ashes, but its extractability and availability to soybeans increased only when co-processed with chicken manure, because it enabled the formation of readily available Ca-alkali phosphates. Therefore, we recommend co-combusting biomass with alkali-rich residues to increase the availability of P from the ash to plants., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Dombinov, Herzel, Meiller, Müller, Willbold, Zang, da Fonseca-Zang, Adam, Klose, Poorter, Jablonowski and Schrey.)

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., (© 2021 The Authors. The FEBS Journal published by John Wiley & Sons Ltd on behalf of Federation of European Biochemical Societies.)

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.

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., (© 2022. The Author(s).)

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The handling editor declared a past collaboration with one of the authors HH., (Copyright © 2022 Grabe, Mahammadov, Olmo and Herzel.)

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., Competing Interests: The authors declare no competing interests., (© 2021 The Authors.)

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-β (TGF-β) as peripheral coupling factor that mediates paracrine phase adjustment of molecular clocks through transcriptional regulation of core-clock genes. Disruption of TGF-β 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., (Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).)

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.

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 S P 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.

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.

In-vivo single cell clonal analysis in the adult mouse kidney has previously shown lineage-restricted clonal proliferation within varying nephron segments as a mechanism responsible for cell replacement and local regeneration. To analyze ex-vivo clonal growth, we now preformed limiting dilution to generate genuine clonal cultures from one single human renal epithelial cell, which can give rise to up to 3.4 * 10 6 cells, and analyzed their characteristics using transcriptomics. A comparison between clonal cultures revealed restriction to either proximal or distal kidney sub-lineages with distinct cellular and molecular characteristics; rapidly amplifying de-differentiated clones and a stably proliferating cuboidal epithelial-appearing clones, respectively. Furthermore, each showed distinct molecular features including cell-cycle, epithelial-mesenchymal transition, oxidative phosphorylation, BMP signaling pathway and cell surface markers. In addition, analysis of clonal versus bulk cultures show early clones to be more quiescent, with elevated expression of renal developmental genes and overall reduction in renal identity markers, but with an overlapping expression of nephron segment identifiers and multiple identity. Thus, ex-vivo clonal growth mimics the in-vivo situation displaying lineage-restricted precursor characteristics of mature renal cells. These data suggest that for reconstruction of varying renal lineages with human adult kidney based organoid technology and kidney regeneration ex-vivo, use of multiple heterogeneous precursors is warranted.

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.

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., Competing Interests: The authors have declared that no competing interests exist.

Understanding entrainment of circadian rhythms is a central goal of chronobiology. Many factors, such as period, amplitude, Zeitgeber strength, and daylength, govern entrainment ranges and phases of entrainment. We have tested whether simple amplitude-phase models can provide insight into the control of entrainment phases. Using global optimization, we derived conceptual models with just three free parameters (period, amplitude, and relaxation rate) that reproduce known phenotypic features of vertebrate clocks: phase response curves (PRCs) with relatively small phase shifts, fast re-entrainment after jet lag, and seasonal variability to track light onset or offset. Since optimization found multiple sets of model parameters, we could study this model ensemble to gain insight into the underlying design principles. We found complex associations between model parameters and entrainment features. Arnold onions of representative models visualize strong dependencies of entrainment on periods, relative Zeitgeber strength, and photoperiods. Our results support the use of oscillator theory as a framework for understanding the entrainment of circadian clocks., (Copyright © 2020 Tokuda, Schmal, Ananthasubramaniam and Herzel.)

Entrainment denotes a process of coordinating the internal circadian clock to external rhythmic time-cues (Zeitgeber), mainly light. It is facilitated by stronger Zeitgeber signals and smaller period differences between the internal clock and the external Zeitgeber. The phase of entrainment ψ is a result of this process on the side of the circadian clock. On Earth, the period of the day-night cycle is fixed to 24 h, while the periods of circadian clocks distribute widely due to natural variation within and between species. The strength and duration of light depend locally on season and geographic latitude. Therefore, entrainment characteristics of a circadian clock vary under a local light environment and distribute along geoecological settings. Using conceptual models of circadian clocks, we investigate how local conditions of natural light shape global patterning of entrainment through seasons. This clock-side entrainment paradigm enables us to predict systematic changes in the global distribution of chronotypes., (Copyright © 2020 Schmal, Herzel and Myung.)