An intensity ratio of interlocking loops determines circadian period length

Bifidobacterium adolescentis-derived hypaphorine alleviates acetaminophen hepatotoxicity by promoting hepatic Cry1 expression

Acetaminophen (APAP)-induced liver injury (AILI) is a pressing public health concern. Although evidence suggests that Bifidobacterium adolescentis (B. adolescentis) can be used to treat liver disease, it is unclear if it can prevent AILI. In this report, we prove that B. adolescentis significantly attenuated AILI in mice, as demonstrated through biochemical analysis, histopathology, and enzyme-linked immunosorbent assays. Based on untargeted metabolomics and in vitro cultures, we found that B. adolescentis generates microbial metabolite hypaphorine. Functionally, hypaphorine inhibits the inflammatory response and hepatic oxidative stress to alleviate AILI in mice. Transcriptomic analysis indicates that Cry1 expression is increased in APAP-treated mice after hypaphorine treatment. Overexpression of Cry1 by its stabilizer KL001 effectively mitigates liver damage arising from oxidative stress in APAP-treated mice. Using the gene expression omnibus (GEO) database, we verified that Cry1 gene expression was also decreased in patients with APAP-induced acute liver failure. In conclusion, this study demonstrates that B. adolescentis inhibits APAP-induced liver injury by generating hypaphorine, which subsequently upregulates Cry1 to decrease inflammation and oxidative stress.

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).

Cell cycle period control through modulation of clock inputs

In this work, we study period control of the mammalian cell cycle via coupling with the cellular clock. For this, we make use of the oscillators’ synchronization dynamics and investigate methods of slowing down the cell cycle with the use of clock inputs. Clock control of the cell cycle is well established via identified molecular mechanisms, such as the CLOCK:BMAL1-mediated induction of the wee1 gene, resulting in the WEE1 kinase that represses the active form of mitosis promoting factor (MPF), the essential cell cycle component. To investigate the coupling dynamics of these systems, we use previously developed models of the clock and cell cycle oscillators and center our studies on unidirectional clock [Formula: see text] cell cycle coupling. Moreover, we propose an hypothesis of a Growth Factor (GF)-responsive clock, involving a pathway of the non-essential cell cycle complex cyclin D/CDK4. We observe a variety of rational ratios of clock to cell cycle period, such as: 1:1, 3:2, 4:3, and 5:4. Finally, our protocols of period control are successful in effectively slowing down the cell cycle by the use of clock modulating inputs, some of which correspond to existing drugs.

Coupling protocol of interlocked feedback oscillators in circadian clocks

Circadian rhythms (approx. 24 h) show the robustness of key oscillatory features such as phase, period and amplitude against external and internal variations. The robustness of Drosophila circadian clocks can be generated by interlocked transcriptional-translational feedback loops, where two negative feedback loops are coupled through mutual activations. The mechanisms by which such coupling protocols have survived out of many possible protocols remain to be revealed. To address this question, we investigated two distinct coupling protocols: activator-coupled oscillators (ACO) and repressor-coupled oscillators (RCO). We focused on the two coupling parameters: coupling dissociation constant and coupling time-delay. Interestingly, the ACO was able to produce anti-phase or morning-evening cycles, whereas the RCO produced in-phase ones. Deterministic and stochastic analyses demonstrated that the anti-phase ACO provided greater fluctuations in amplitude not only with respect to changes in coupling parameters but also to random parameter perturbations than the in-phase RCO. Moreover, the ACO deteriorated the entrainability to the day-night master clock, whereas the RCO produced high entrainability. Considering that the real, interlocked feedback loops have evolved as the ACO, instead of the RCO, we first proposed a hypothesis that the morning-evening or anti-phase cycle is more essential for Drosophila than achieving robustness and entrainability.

Transcription-based circadian mechanism controls the duration of molecular clock states in response to signaling inputs

The molecular oscillator of the mammalian circadian clock consists in a dynamical network of genes and proteins whose main regulatory mechanisms occur at the transcriptional level. From a dynamical point of view, the mechanisms leading to an oscillatory solution with an orderly protein peak expression and a clear day/night phase distinction remain unclear. Our goal is to identify the essential interactions needed to generate phase opposition between the activating CLOCK:BMAL1 and the repressing PER:CRY complexes and to better distinguish these two main clock molecular phases relating to rest/activity and fast/feeding cycles. To do this, we develop a transcription-based mathematical model centered on linear combinations of the clock controlled elements (CCEs): E-box, R-box and D-box. Each CCE is responsive to activators and repressors. After model calibration with single-cell data, we explore entrainment and period tuning via interplay with metabolism. Variation of the PER degradation rate γ_p, relating to the tau mutation, results in asymmetric changes in the duration of the different clock molecular phases. Time spent at the state of high PER/PER:CRY decreases with γ_p, while time spent at the state of high BMAL1 and CRY1, both proteins with activity in promoting insulin sensitivity, remains constant. This result suggests a possible mechanism behind the altered metabolism of tau mutation animals. Furthermore, we expose the clock system to two regulatory inputs, one relating to the fast/feeding cycle and the other to the light-dependent synchronization signaling. We observe the phase difference between these signals to also affect the relative duration of molecular clock states. Simulated circadian misalignment, known to correlate with insulin resistance, leads to decreased duration of BMAL1 expression. Our results reveal a possible mechanism for clock-controlled metabolic homeostasis, whereby the circadian clock controls the relative duration of different molecular (and metabolic) states in response to signaling inputs.

Weak coupling between intracellular feedback loops explains dissociation of clock gene dynamics

Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described in recent experimental studies that applied various perturbations such as slice preparations, light pulses, jet-lag, and culture medium exchange. In this paper, we provide evidence that this "presumably transient" dissociation of circadian gene expression oscillations may occur at the single-cell level. Conceptual and detailed mechanistic mathematical modeling suggests that such dissociation is due to a weak interaction between multiple feedback loops present within a single cell. The dissociable loops provide insights into underlying mechanisms and general design principles of the molecular circadian clock.

Computational modeling and analysis of the impacts of sleep deprivation on glucose stimulated insulin secretion

Circadian clock is an exquisite internal biological clock functioning in all living organisms. Lifestyle changes such as shift work or frequent travelling might result in malfunctioning of the central and consequently the peripheral clocks leading to different metabolic disorders. Disruptions in β cell clock have been found to be a potential reason behind β cell failure that makes a person prone towards developing type 2 diabetes (T2DM). In this study, a Petri net model for β cell circadian clock has been developed, followed by analysis of the negative impacts of sleep deprivation conditions on the process of glucose stimulated insulin secretion (GSIS) through misalignment of circadian clock. The analysis of structural properties of the Petri net model reveals robustness of the circadian system. The simulation results predict that sleep loss negatively affects the expression of circadian genes which eventually leads to impaired GSIS and β cell failure. These results suggest that sleep/wake cycle is a vital contributor for the entrainment of the circadian clock and normal functioning of β cell.

Deciphering the Dynamics of Interlocked Feedback Loops in a Model of the Mammalian Circadian Clock

Mathematical models of fundamental biological processes play an important role in consolidating theory and experiments, especially if they are systematically developed, thoroughly characterized, and well tested by experimental data. In this work, we report a detailed bifurcation analysis of a mathematical model of the mammalian circadian clock network developed by Relógio et al., noteworthy for its consistency with available data. Using one- and two-parameter bifurcation diagrams, we explore how oscillations in the model depend on the expression levels of its constituent genes and the activities of their encoded proteins. These bifurcation diagrams allow us to decipher the dynamics of interlocked feedback loops by parametric variation of genes and proteins in the model. Among other results, we find that REV-ERB, a member of a subfamily of orphan nuclear receptors, plays a critical role in the intertwined dynamics of Relógio's model. The bifurcation diagrams reported here can be used for predicting how the core clock network responds-in terms of period, amplitude and phases of oscillations-to different perturbations.

Protein sequestration versus Hill-type repression in circadian clock models

Circadian (∼24 h) clocks are self-sustained endogenous oscillators with which organisms keep track of daily and seasonal time. Circadian clocks frequently rely on interlocked transcriptional-translational feedback loops to generate rhythms that are robust against intrinsic and extrinsic perturbations. To investigate the dynamics and mechanisms of the intracellular feedback loops in circadian clocks, a number of mathematical models have been developed. The majority of the models use Hill functions to describe transcriptional repression in a way that is similar to the Goodwin model. Recently, a new class of models with protein sequestration-based repression has been introduced. Here, the author discusses how this new class of models differs dramatically from those based on Hill-type repression in several fundamental aspects: conditions for rhythm generation, robust network designs and the periods of coupled oscillators. Consistently, these fundamental properties of circadian clocks also differ among Neurospora, Drosophila, and mammals depending on their key transcriptional repression mechanisms (Hill-type repression or protein sequestration). Based on both theoretical and experimental studies, this review highlights the importance of careful modelling of transcriptional repression mechanisms in molecular circadian clocks.

Entrainment of a cellular circadian oscillator by light in the presence of molecular noise

In this paper, we consider a stochastic molecular circadian oscillator described by a sequence of biological reactions and its deterministic kinetics governed by a system of ordinary differential equations in the limit of large numbers of molecules. The oscillations in the model are generated by negative feedback regulation of a gene. The focus of this paper is the entrainment of the oscillator by a periodic light signal that affects the maximal transcription rate of the gene. We introduce two scalings of the model parameters that provide independent control over the natural frequency of the oscillator and the relative noise level. We study entrainment in two ways: by visualizing the stochastic limit cycle in various projections of the discrete phase space of the system and by evaluating the maximum of the normalized cross correlation of the light signal with the number of protein molecules in the cell. The visualization method ignores the phase of the oscillator, and we find in this way that entrainment has a subtle organizing effect on the limit cycle as a whole. The cross correlation results reveal an interval of natural frequencies of the oscillator surrounding the frequency of the light signal within which maximal entrainment occurs with rather sharp drops in entrainment at the edges of this interval. The width of the interval of maximal entrainment increases with the amplitude of the light signal. These statements are applicable both to the stochastic oscillator and to its deterministic limit, but the results are most clear-cut in the deterministic case and degrade from there as the relative noise level increases.

Modeling transcriptional co-regulation of mammalian circadian clock

The circadian clock is a self-sustaining oscillator that has a period of about 24 hours at the molecular level. The oscillator is a transcription-translation feedback loop system composed of several genes. In this paper, a scalar nonlinear differential equation with two delays, modeling the transcriptional co-regulation in mammalian circadian clock, is proposed and analyzed. Sufficient conditions are established for the asymptotic stability of the unique nontrivial positive equilibrium point of the model by studying an exponential polynomial characteristic equation with delay-dependent coefficients. The existence of the Hopf bifurcations can be also obtained. Numerical simulations of the model with proper parameter values coincide with the theoretical result.

Modeling the interactions of sense and antisense Period transcripts in the mammalian circadian clock network

In recent years, it has become increasingly apparent that antisense transcription plays an important role in the regulation of gene expression. The circadian clock is no exception: an antisense transcript of the mammalian core-clock gene PERIOD2 (PER2), which we shall refer to as Per2AS RNA, oscillates with a circadian period and a nearly 12 h phase shift from the peak expression of Per2 mRNA. In this paper, we ask whether Per2AS plays a regulatory role in the mammalian circadian clock by studying in silico the potential effects of interactions between Per2 and Per2AS RNAs on circadian rhythms. Based on the antiphasic expression pattern, we consider two hypotheses about how Per2 and Per2AS mutually interfere with each other's expression. In our pre-transcriptional model, the transcription of Per2AS RNA from the non-coding strand represses the transcription of Per2 mRNA from the coding strand and vice versa. In our post-transcriptional model, Per2 and Per2AS transcripts form a double-stranded RNA duplex, which is rapidly degraded. To study these two possible mechanisms, we have added terms describing our alternative hypotheses to a published mathematical model of the molecular regulatory network of the mammalian circadian clock. Our pre-transcriptional model predicts that transcriptional interference between Per2 and Per2AS can generate alternative modes of circadian oscillations, which we characterize in terms of the amplitude and phase of oscillation of core clock genes. In our post-transcriptional model, Per2/Per2AS duplex formation dampens the circadian rhythm. In a model that combines pre- and post-transcriptional controls, the period, amplitude and phase of circadian proteins exhibit non-monotonic dependencies on the rate of expression of Per2AS. All three models provide potential explanations of the observed antiphasic, circadian oscillations of Per2 and Per2AS RNAs. They make discordant predictions that can be tested experimentally in order to distinguish among these alternative hypotheses.

Dissociation of Per1 and Bmal1 circadian rhythms in the suprachiasmatic nucleus in parallel with behavioral outputs

The temporal order of physiology and behavior in mammals is primarily regulated by the circadian pacemaker located in the hypothalamic suprachiasmatic nucleus (SCN). Taking advantage of bioluminescence reporters, we monitored the circadian rhythms of the expression of clock genes Per1 and Bmal1 in the SCN of freely moving mice and found that the rate of phase shifts induced by a single light pulse was different in the two rhythms. The Per1-luc rhythm was phase-delayed instantaneously by the light presented at the subjective evening in parallel with the activity onset of behavioral rhythm, whereas the Bmal1-ELuc rhythm was phase-delayed gradually, similar to the activity offset. The dissociation was confirmed in cultured SCN slices of mice carrying both Per1-luc and Bmal1-ELuc reporters. The two rhythms in a single SCN slice showed significantly different periods in a long-term (3 wk) culture and were internally desynchronized. Regional specificity in the SCN was not detected for the period of Per1-luc and Bmal1-ELuc rhythms. Furthermore, neither is synchronized with circadian intracellular Ca2+ rhythms monitored by a calcium indicator, GCaMP6s, or with firing rhythms monitored on a multielectrode array dish, although the coupling between the circadian firing and Ca2+ rhythms persisted during culture. These findings indicate that the expressions of two key clock genes, Per1 and Bmal1, in the SCN are regulated in such a way that they may adopt different phases and free-running periods relative to each other and are respectively associated with the expression of activity onset and offset.

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.

Systems Biology-Derived Discoveries of Intrinsic Clocks

A systems approach to studying biology uses a variety of mathematical, computational, and engineering tools to holistically understand and model properties of cells, tissues, and organisms. Building from early biochemical, genetic, and physiological studies, systems biology became established through the development of genome-wide methods, high-throughput procedures, modern computational processing power, and bioinformatics. Here, we highlight a variety of systems approaches to the study of biological rhythms that occur with a 24-h period-circadian rhythms. We review how systems methods have helped to elucidate complex behaviors of the circadian clock including temperature compensation, rhythmicity, and robustness. Finally, we explain the contribution of systems biology to the transcription-translation feedback loop and posttranslational oscillator models of circadian rhythms and describe new technologies and "-omics" approaches to understand circadian timekeeping and neurophysiology.

Impact of time delays on oscillatory dynamics of interlinked positive and negative feedback loops

Interlinking a positive feedback loop (PFL) with a negative feedback loop (NFL) constitutes a typical motif in genetic networks, performing various functions in cell signaling. How time delay in feedback regulation affects the dynamics of such systems still remains unclear. Here, we investigate three systems of interlinked PFL and NFL with time delays: a synthetic genetic oscillator, a three-node circuit, and a simplified single-node model. The stability of steady states and the routes to oscillation in the single-node model are analyzed in detail. The amplitude and period of oscillations vary with a pointwise periodicity over a range of time delay. Larger-amplitude oscillations can be induced when the PFL has an appropriately long delay, in comparison with the PFL with no delay or short delay; this conclusion holds true for all the three systems. We unravel the underlying mechanism for the above effects via analytical derivation under a limiting condition. We also develop a stochastic algorithm for simulating a single reaction with two delays and show that robust oscillations can be maintained by the PFL with a properly long delay in the single-node system. This work presents an effective method for constructing robust large-amplitude oscillators and interprets why similar circuit architectures are engaged in timekeeping systems such as circadian clocks.