Temperature-amplitude coupling for stable biological rhythms at different temperatures

The clock in growing hyphae and their synchronization in Neurospora crassa

Utilizing a microfluidic chip with serpentine channels, we inoculated the chip with an agar plug with Neurospora crassa mycelium and successfully captured individual hyphae in channels. For the first time, we report the presence of an autonomous clock in hyphae. Fluorescence of a mCherry reporter gene driven by a clock-controlled gene-2 promoter (ccg-2p) was measured simultaneously along hyphae every half an hour for at least 6 days. We entrained single hyphae to light over a wide range of day lengths, including 6,12, 24, and 36 h days. Hyphae tracked in individual serpentine channels were highly synchronized (K = 0.60-0.78). Furthermore, hyphae also displayed temperature compensation properties, where the oscillation period was stable over a physiological range of temperatures from 24 °C to 30 °C (Q10 = 1.00-1.10). A Clock Tube Model developed could mimic hyphal growth observed in the serpentine chip and provides a mechanism for the stable banding patterns seen in race tubes at the macroscopic scale and synchronization through molecules riding the growth wave in the device.

Temperature compensation through kinetic regulation in biochemical oscillators

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

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, 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.

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).

Systematic analysis of negative and positive feedback loops for robustness and temperature compensation in circadian rhythms

Temperature compensation and robustness to biological noise are two key characteristics of the circadian clock. These features allow the circadian pacemaker to maintain a steady oscillation in a wide range of environmental conditions. The presence of a time-delayed negative feedback loop in the regulatory network generates autonomous circadian oscillations in eukaryotic systems. In comparison, the circadian clock of cyanobacteria is controlled by a strong positive feedback loop. Positive feedback loops with substrate depletion can also generate oscillations, inspiring other circadian clock models. What makes a circadian oscillatory network robust to extrinsic noise is unclear. We investigated four basic circadian oscillators with negative, positive, and combinations of positive and negative feedback loops to explore network features necessary for circadian clock resilience. We discovered that the negative feedback loop system performs the best in compensating temperature changes. We also show that a positive feedback loop can reduce extrinsic noise in periods of circadian oscillators, while intrinsic noise is reduced by negative feedback loops.

Artificial temperature-compensated biological clock using temperature-sensitive Belousov-Zhabotinsky gels

The circadian rhythm is a fundamental physiological function for a wide range of organisms. The molecular machinery for generating rhythms has been elucidated over the last few decades. Nevertheless, the mechanism for temperature compensation of the oscillation period, which is a prominent property of the circadian rhythm, is still controversial. In this study, we propose a new mechanism through a chemically synthetic approach (i.e., we realized temperature compensation by the Belousov-Zhabotinsky (BZ) gels). The BZ gels are prepared by embedding a metal catalyst of the BZ reaction into the gel polymer. We made the body of BZ gels using a temperature-sensitive polymer gel, which enabled temperature compensation of the oscillation by using temperature dependence of volume. Moreover, we constructed a simple mathematical model for the BZ oscillation in temperature-sensitive gels. The model can reproduce temperature compensation of BZ gels, even though all reactions are temperature sensitive according to the Arrhenius rule. Our finding hints that a soft body coupling may be underlying temperature-compensated biological functions, including circadian rhythms.

Insights about circadian clock in glioma: From molecular pathways to therapeutic drugs

Glioma is characterized as the most aggressive brain tumor that occurred in the central nervous system. The circadian rhythm is an essential cyclic change system generated by the endogenous circadian clock. Current studies found that the circadian clock affects glioma pathophysiology. It is still controversial whether the circadian rhythm disruption is a cause or an effect of tumorigenesis. This review discussed the association between cell cycle and circadian clock and provided a prominent molecular theoretical basis for tumor therapy. We illustrated the external factors affecting the circadian clock including thermodynamics, hypoxia, post-translation, and microRNA, while the internal characteristics concerning the circadian clock in glioma involve stemness, metabolism, radiotherapy sensitivity, and chemotherapy sensitivity. We also summarized the molecular pathways and the therapeutic drugs involved in the glioma circadian rhythm. There are still many questions in this field waiting for further investigation. The results of glioma chronotherapy in sensitizing radiation therapy and chemotherapy have shown great therapeutic potential in improving clinical outcomes. These findings will help us further understand the characteristics of glioma pathophysiology.

Role of the reaction-structure coupling in temperature compensation of the KaiABC circadian rhythm

When the mixture solution of cyanobacterial proteins, KaiA, KaiB, and KaiC, is incubated with ATP in vitro, the phosphorylation level of KaiC shows stable oscillations with the temperature-compensated circadian period. Elucidating this temperature compensation is essential for understanding the KaiABC circadian clock, but its mechanism has remained a mystery. We analyzed the KaiABC temperature compensation by developing a theoretical model describing the feedback relations among reactions and structural transitions in the KaiC molecule. The model showed that the reduced structural cooperativity should weaken the negative feedback coupling among reactions and structural transitions, which enlarges the oscillation amplitude and period, explaining the observed significant period extension upon single amino-acid residue substitution. We propose that an increase in thermal fluctuations similarly attenuates the reaction-structure feedback, explaining the temperature compensation in the KaiABC clock. The model explained the experimentally observed responses of the oscillation phase to the temperature shift or the ADP-concentration change and suggested that the ATPase reactions in the CI domain of KaiC affect the period depending on how the reaction rates are modulated. The KaiABC clock provides a unique opportunity to analyze how the reaction-structure coupling regulates the system-level synchronized oscillations of molecules.

Introduction to Biological Rhythms: A Brief History of Chronobiology and its Relevance to Parasite Immunology

Almost every living organism on Earth is exposed to a fluctuating environment e.g., light:dark cycles, food availability, seasonal photoperiods. Most species have therefore evolved internal timing mechanisms allowing them to anticipate these rhythmic environmental changes, obtaining a survival advantage. Circadian (24 h) rhythms, in particular, regulate multiple aspects of physiology, including sleep/wake activity, feeding rhythms, and immune function. Recent studies have identified circadian rhythms in symptoms of parasite infections, rhythms in parasite schizogony, and evidence that certain parasites can manipulate host rhythms. Furthermore, efficacy of anti-parasite medications can also be modulated by timing of drug administration. Understanding the interactions between host rhythms, parasite rhythms, and disease severity is crucial to fully understand how to combat infections and reduce pathology. The aim of this review is, therefore, to provide an introduction to the field of biological rhythms, give a brief history of chronobiology research, and discuss the relevance of biological rhythms to parasite immunology.

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

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

A Robust and Self-Sustained Peripheral Circadian Oscillator Reveals Differences in Temperature Compensation Properties with Central Brain Clocks

Circadian clocks are characterized by three properties: they run in constant conditions with a period of ∼24 h, synchronize to the environmental cycles of light and temperature, and are temperature compensated, meaning they do not speed up with temperature. Central brain clocks regulate daily activity rhythms, whereas peripheral clocks are dispersed throughout the body of insects and vertebrates. Using a set of luciferase reporter genes, we show that Drosophila peripheral clocks are self-sustained but over-compensated, i.e., they slow down with increasing temperature. In contrast, central clock neurons in the fly brain, both in intact flies and in cultured brains, show accurate temperature compensation. Although this suggests that neural network properties contribute to temperature compensation, the circadian neuropeptide Pigment Dispersing Factor (PDF) is not required for temperature-compensated oscillations in brain clock neurons. Our findings reveal a fundamental difference between central and peripheral clocks, which likely also applies for vertebrate clocks.

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Drosophila halteres contain a robust circadian oscillator

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Circadian clocks of halteres and antennae are over-compensated

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The Drosophila central brain clock is temperature compensated

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The neuropeptide PDF is not required for temperature compensation of clock neurons

Theoretical study on the regulation of circadian rhythms by RNA methylation

Messenger RNAs are often destabilized by methylation, suggesting that mRNA methylation alters mRNA and protein dynamics. This may indicate that the gene regulatory system is reflected by the metabolic system through mRNA methylation because methylation substrates are components of the metabolic system. Elucidating the mechanisms by which mRNA methylation regulates gene regulatory systems has posed considerable challenges due to the numerous targets of mRNA methylation. Recent studies have demonstrated that inhibition of mRNA N6-methyladenosine methylation elongates circadian periods. The aim of this study was to understand the mechanisms by which mRNA methylation regulates circadian rhythms. Using a detailed realistic model and a simple model, we demonstrated that period elongation of circadian rhythms by decreasing mRNA methylation can be achieved by two possibilities, i.e., decreasing mRNA methylation stabilizes nonoscillatory mRNAs such as Ck1δ and/or stabilizes oscillatory mRNAs of clock genes such as Per and Cry. In addition, we predicted that period elongation by stabilizing nonoscillatory mRNA (Ck1δ) should always be accompanied by the distortion of the circadian waveform. Finally, we discuss the validity of the two possible mechanisms on the regulation of circadian rhythms by mRNA methylation by quantifying waveform distortion of circadian gene activity data with or without mRNA methylation inhibitors.

Development and Optimization of Expression, Purification, and ATPase Assay of KaiC for Medium-Throughput Screening of Circadian Clock Mutants in Cyanobacteria

The slow but temperature-insensitive adenosine triphosphate (ATP) hydrolysis reaction in KaiC is considered as one of the factors determining the temperature-compensated period length of the cyanobacterial circadian clock system. Structural units responsible for this low but temperature-compensated ATPase have remained unclear. Although whole-KaiC scanning mutagenesis can be a promising experimental strategy, producing KaiC mutants and assaying those ATPase activities consume considerable time and effort. To overcome these bottlenecks for in vitro screening, we optimized protocols for expressing and purifying the KaiC mutants and then designed a high-performance liquid chromatography system equipped with a multi-channel high-precision temperature controller to assay the ATPase activity of multiple KaiC mutants simultaneously at different temperatures. Through the present protocol, the time required for one KaiC mutant is reduced by approximately 80% (six-fold throughput) relative to the conventional protocol with reasonable reproducibility. For validation purposes, we picked up three representatives from 86 alanine-scanning KaiC mutants preliminarily investigated thus far and characterized those clock functions in detail.

Non-sinusoidal Waveform in Temperature-Compensated Circadian Oscillations

Time series of biological rhythms are of various shapes. Here, we investigated the waveforms of circadian rhythms in gene-protein dynamics using a newly developed, to our knowledge, index to quantify the degree of distortion from a sinusoidal waveform. In general, most biochemical reactions accelerate with increasing temperature, but the period of circadian rhythms remains relatively stable with temperature change, a phenomenon known as "temperature compensation." Despite extensive research, the mechanism underlying this remains unclear. To understand the mechanism, we used transcriptional-translational oscillator models for circadian rhythms in the fruit fly Drosophila and mammals. Given the assumption that reaction rates increase with temperature, mathematical analyses revealed that temperature compensation required waveforms that are more nonsinusoidal at higher temperatures. We then analyzed a post-translational oscillator (PTO) model of cyanobacteria circadian rhythms. Because the structure of the PTO is different from that of the transcriptional-translational oscillator, the condition for temperature compensation would be expected to differ. Unexpectedly, the computational analysis again showed that temperature compensation in the PTO model required a more nonsinusoidal waveform at higher temperatures. This finding held for both models even with a milder assumption that some reaction rates do not change with temperature, which is consistent with experimental evidence. Together, our theoretical analyses predict that the waveform of circadian gene-activity and/or protein phosphorylation rhythms would be more nonsinusoidal at higher temperatures, even when there are differences in the network structures.

Period-amplitude co-variation in biomolecular oscillators

The period and amplitude of biomolecular oscillators are functionally important properties in multiple contexts. For a biomolecular oscillator, the overall constraints in how tuning of amplitude affects period, and vice versa, are generally unclear. Here, the authors investigate this co-variation of the period and amplitude in mathematical models of biomolecular oscillators using both simulations and analytical approximations. The authors computed the amplitude-period co-variation of 11 benchmark biomolecular oscillators as their parameters were individually varied around a nominal value, classifying the various co-variation patterns such as a simultaneous increase/decrease in period and amplitude. Next, the authors repeated the classification using a power norm-based amplitude metric, to account for the amplitudes of the many biomolecular species that may be part of the oscillations, finding largely similar trends. Finally, the authors calculate 'scaling laws' of period-amplitude co-variation for a subset of these benchmark oscillators finding that as the approximated period increases, the upper bound of the amplitude increases, or reaches a constant value. Based on these results, the authors discuss the effect of different parameters on the type of period-amplitude co-variation as well as the difficulty in achieving an oscillation with large amplitude and small period.

Co-existing feedback loops generate tissue-specific circadian rhythms

The analysis of tissue-specific data-based models of the gene regulatory network of the mammalian circadian clock reveals organ-specific synergies of feedback loops.

Gene regulatory feedback loops generate autonomous circadian rhythms in mammalian tissues. The well-studied core clock network contains many negative and positive regulations. Multiple feedback loops have been discussed as primary rhythm generators but the design principles of the core clock and differences between tissues are still under debate. Here we use global optimization techniques to fit mathematical models to circadian gene expression profiles for different mammalian tissues. It turns out that for every investigated tissue multiple model parameter sets reproduce the experimental data. We extract for all model versions the most essential feedback loops and find auto-inhibitions of period and cryptochrome genes, Bmal1–Rev-erb-α loops, and repressilator motifs as possible rhythm generators. Interestingly, the essential feedback loops differ between tissues, pointing to specific design principles within the hierarchy of mammalian tissue clocks. Self-inhibitions of Per and Cry genes are characteristic for models of suprachiasmatic nucleus clocks, whereas in liver models many loops act in synergy and are connected by a repressilator motif. Tissue-specific use of a network of co-existing synergistic feedback loops could account for functional differences between organs.

Long negative feedback loop enhances period tunability of biological oscillators

Oscillatory phenomena play a major role in organisms. In some biological oscillations such as cell cycles and heartbeats, the period can be tuned without significant changes in the amplitude. This property is called (period) tunability, one of the prominent features of biological oscillations. However, how biological oscillators produce tunable oscillations remains largely unexplored. We tackle this question using computational experiments. It has been reported that positive-plus-negative feedback oscillators produce tunable oscillations through the hysteresis-based mechanism. First, in this study, we confirmed that positive-plus-negative feedback oscillators generate tunable oscillations. Second, we found that tunability is positively correlated with the dynamic range of oscillations. Third, we showed that long negative feedback oscillators without any additional positive feedback loops can produce tunable oscillations. Finally, we computationally demonstrated that by lengthening the negative feedback loop, the Repressilator, known as a non-tunable synthetic gene oscillator, can be converted into a tunable oscillator. This work provides synthetic biologists with clues to design tunable gene oscillators.