Positive Feedback Promotes Oscillations in Negative Feedback Loops

A simple three-component negative feedback loop is a recurring motif in biochemical oscillators. This motif oscillates as it has the three necessary ingredients for oscillations: a three-step delay, negative feedback, and nonlinearity in the loop. However, to oscillate, this motif under the common Goodwin formulation requires a high degree of cooperativity (a measure of nonlinearity) in the feedback that is biologically “unlikely.” Moreover, this recurring negative feedback motif is commonly observed augmented by positive feedback interactions. Here we show that these positive feedback interactions promote oscillation at lower degrees of cooperativity, and we can thus unify several common kinetic mechanisms that facilitate oscillations, such as self- activation and Michaelis-Menten degradation. The positive feedback loops are most beneficial when acting on the shortest lived component, where they function by balancing the lifetimes of the different components. The benefits of multiple positive feedback interactions are cumulative for a majority of situations considered, when benefits are measured by the reduction in the cooperativity required to oscillate. These positive feedback motifs also allow oscillations with longer periods than that determined by the lifetimes of the components alone. We can therefore conjecture that these positive feedback loops have evolved to facilitate oscillations at lower, kinetically achievable, degrees of cooperativity. Finally, we discuss the implications of our conclusions on the mammalian molecular clock, a system modeled extensively based on the three-component negative feedback loop

Mining for novel candidate clock genes in the circadian regulatory network

Background Most physiological processes in mammals are temporally regulated by means of a master circadian clock in the brain and peripheral oscillators in most other tissues. A transcriptional-translation feedback network of clock genes produces near 24 h oscillations in clock gene and protein expression. Here, we aim to identify novel additions to the clock network using a meta- analysis of public chromatin immunoprecipitation sequencing (ChIP-seq), proteomics and protein-protein interaction data starting from a published list of 1000 genes with robust transcriptional rhythms and circadian phenotypes of knockdowns. Results We identified 20 candidate genes including nine known clock genes that received significantly high scores and were also robust to the relative weights assigned to different data types. Our scoring was consistent with the original ranking of the 1000 genes, but also provided novel complementary insights. Candidate genes were enriched for genes expressed in a circadian manner in multiple tissues with regulation driven mainly by transcription factors BMAL1 and REV-ERB α,β. Moreover, peak transcription of candidate genes was remarkably consistent across tissues. While peaks of the 1000 genes were distributed uniformly throughout the day, candidate gene peaks were strongly concentrated around dusk. Finally, we showed that binding of specific transcription factors to a gene promoter was predictive of peak transcription at a certain time of day and discuss combinatorial phase regulation. Conclusions Combining complementary publicly- available data targeting different levels of regulation within the circadian network, we filtered the original list and found 11 novel robust candidate clock genes. Using the criteria of circadian proteomic expression, circadian expression in multiple tissues and independent gene knockdown data, we propose six genes (Por, Mtss1, Dgat2, Pim3, Ppp1r3b, Upp2) involved in metabolism and cancer for further experimental investigation. The availability of public high-throughput databases makes such meta-analysis a promising approach to test consistency between sources and tap their entire potential

Seasonal reproduction in a fluctuating energy environment: Insolation-driven synchronized broadcast spawning in corals

*Background/Question/Methods:* Colonies of spawning corals reproduce in mass-spawning events, in which polyps within each colony release sperm and eggs for fertilization in the water column, with fertilization occurring only between gametes from different colonies. Participating colonies synchronize their gamete release to a window of a few hours once a year (for the species Acropora digitifera we study experimentally). This remarkable synchrony is essential for successful coral reproduction and thus, maintenance of the coral reef ecosystem that is currently under threat from local and global environmental effects such as pollution, global warming and ocean acidification. The mechanisms determining this tight synchrony in reproduction are not well understood, although several influences have been hypothesized and studied including lunar phase, solar insolation, and influences of temperature and tides. Moreover, most corals are in a symbiotic relationship with photosynthetic algae (Symbiodinium spp.) that live within the host tissue. Experiments supported by detailed bioenergetic modeling of the coral-algae symbiosis have shown that corals receive >90% of their energy needs from these symbionts. We develop a bioenergetic integrate-and-fire model in order to investigate whether annual insolation rhythms can entrain the gametogenetic cycles that produce mature gametes to the appropriate spawning season, since photosynthate is their primary source of energy. We solve the integrate-and-fire bioenergetic model numerically using the Fokker-Planck equation and use analytical tools such as rotation number to study entrainment.

*Results/Conclusions:* In the presence of short-term fluctuations in the energy input, our model shows that a feedback regulatory mechanism is required to achieve coherence of spawning times to within one lunar cycle, in order for subsequent cues such as lunar and diurnal light cycles to unambiguously determine the “correct” night of spawning. Entrainment to the annual insolation cycle is by itself not sufficient to produce the observed coherence in spawning. The feedback mechanism can also provide robustness against population heterogeneity due to genetic and environmental effects. We also discuss how such bioenergetic, stochastic, integrate-and-fire models are also more generally applicable: for example to aquatic insect emergence, synchrony in cell division and masting in trees

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.Comparing rhythms with and without an intervention reveals the functioning of the circadian system. High‐throughput studies of clock outputs (transcripts, proteins, etc.) typically compare lists of rhythmic outputs in each condition using Venn diagrams. This approach incorrectly predicts too many altered rhythms, while also overlooking some rhythm changes. Direct comparison of amplitudes and phases using R‐package comparerhythms fixes this problem and reveals limited circadian remodeling due to metabolic changes. imageDeutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Peer Reviewe

Data integration and analysis for circadian medicine

Data integration, data sharing, and standardized analyses are important enablers for data-driven medical research. Circadian medicine is an emerging field with a particularly high need for coordinated and systematic collaboration between researchers from different disciplines. Datasets in circadian medicine are multimodal, ranging from molecular circadian profiles and clinical parameters to physiological measurements and data obtained from (wearable) sensors or reported by patients. Uniquely, data spanning both the time dimension and the spatial dimension (across tissues) are needed to obtain a holistic view of the circadian system. The study of human rhythms in the context of circadian medicine has to confront the heterogeneity of clock properties within and across subjects and our inability to repeatedly obtain relevant biosamples from one subject. This requires informatics solutions for integrating and visualizing relevant data types at various temporal resolutions ranging from milliseconds and seconds to minutes and several hours. Associated challenges range from a lack of standards that can be used to represent all required data in a common interoperable form, to challenges related to data storage, to the need to perform transformations for integrated visualizations, and to privacy issues. The downstream analysis of circadian rhythms requires specialized approaches for the identification, characterization, and discrimination of rhythms. We conclude that circadian medicine research provides an ideal environment for developing innovative methods to address challenges related to the collection, integration, visualization, and analysis of multimodal multidimensional biomedical data.Peer Reviewe

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 Charite-Universitatsmedizin 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

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.Peer Reviewe

On Localization Performance in Imaging Sensor Nets

We propose a massively scalable “imaging ” architecture for sensor networks, in which sensor nodes act as “pixels ” that electronically reflect (and possibly modulate data on top of) a beacon transmitted by a collector node. The collector employs sophisticated radar and image processing techniques to localize the responding sensor nodes, and (if data modulation is present) multiuser data demodulation techniques to extract the data sent by multiple sensors. The sensors do not need to know their own locations, do not need to communicate with each other, and can be randomly deployed. In this initial exposition, we develop basic insight into the localization capabilities of this approach, ignoring sensor data modulation. This reduces to an idealized one-bit, on-off keyed, communication model in which the the sensors are either “active ” or “inactive”, with the active sensors responding to the collector’s beacon without superimposing data modulation. We consider a moving collector, with the sensor reflections creating a Synthetic Aperture Radar (SAR)-like geometry. However, the collector must employ significant modifications to SAR signal processing for estimation of the location of the active sensors: noncoherent techniques similar to those in noncoherent radar tomography to account for the lack of carrier synchronization between sensor and collector nodes, and decision feedback mechanisms for estimation of the locations of multiple closely spaced active sensors. Measures for localization performance are defined, and the effect of system parameters such as bandwidth, beamwidth and signal-to-noise-ratio on performance is investigated