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.
Mammalian circadian clocks have a hierarchical organization, governed by the suprachiasmatic nucleus (SCN) in the hypothalamus. The brain itself contains multiple loci that maintain autonomous ...circadian rhythmicity, but the contribution of the non-SCN clocks to this hierarchy remains unclear. We examine circadian oscillations of clock gene expression in various brain loci and discovered that in mouse, robust, higher amplitude, relatively faster oscillations occur in the choroid plexus (CP) compared to the SCN. Our computational analysis and modeling show that the CP achieves these properties by synchronization of "twist" circadian oscillators via gap-junctional connections. Using an in vitro tissue coculture model and in vivo targeted deletion of the Bmal1 gene to silence the CP circadian clock, we demonstrate that the CP clock adjusts the SCN clock likely via circulation of cerebrospinal fluid, thus finely tuning behavioral circadian rhythms.
Abstract 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.
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.
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.
Modern imaging techniques allow the monitoring of circadian rhythms of single cells. Coupling between these single cellular circadian oscillators can generate coherent periodic signals on the tissue ...level that subsequently orchestrate physiological outputs. The strength of coupling in such systems of oscillators is often unclear. In particular, effects on coupling strength by varying cell densities, by knockouts, and by inhibitor applications are debated.
In this study, we suggest to quantify the relative coupling strength via analyzing period, phase, and amplitude distributions in ensembles of individual circadian oscillators. Simulations of different oscillator networks show that period and phase distributions become narrower with increasing coupling strength. Moreover, amplitudes can increase due to resonance effects. Variances of periods and phases decay monotonically with coupling strength, and can serve therefore as measures of relative coupling strength.
Our theoretical predictions are confirmed by studying recently published experimental data from PERIOD2 expression in slices of the suprachiasmatic nucleus during and after the application of tetrodotoxin (TTX). On analyzing the corresponding period, phase, and amplitude distributions, we can show that treatment with TTX can be associated with a reduced coupling strength in the system of coupled oscillators. Analysis of an oscillator network derived directly from the data confirms our conclusions.
We suggest that our approach is also applicable to quantify coupling in fibroblast cultures and hepatocyte networks, and for social synchronization of circadian rhythmicity in rodents, flies, and bees.
Lymphocytes circulate through lymph nodes (LN) in search for antigen in what is believed to be a continuous process. Here, we show that lymphocyte migration through lymph nodes and lymph occurred in ...a non-continuous, circadian manner. Lymphocyte homing to lymph nodes peaked at night onset, with cells leaving the tissue during the day. This resulted in strong oscillations in lymphocyte cellularity in lymph nodes and efferent lymphatic fluid. Using lineage-specific genetic ablation of circadian clock function, we demonstrated this to be dependent on rhythmic expression of promigratory factors on lymphocytes. Dendritic cell numbers peaked in phase with lymphocytes, with diurnal oscillations being present in disease severity after immunization to induce experimental autoimmune encephalomyelitis (EAE). These rhythms were abolished by genetic disruption of T cell clocks, demonstrating a circadian regulation of lymphocyte migration through lymph nodes with time-of-day of immunization being critical for adaptive immune responses weeks later.
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•Lymphocyte numbers in lymph nodes and lymph oscillate over the course of the day•Rhythmic Ccr7 and S1pr1 expression drives rhythmic lymphocyte homing and egress•Adaptive immune responses to immunization and pathogens are time-of-day dependent•Loss of circadian clocks in lymphocytes ablates rhythmic adaptive immune responses
Lymphocyte trafficking through lymph nodes and lymph is an important immune surveillance mechanism of the body. Druzd et al. (2017) demonstrate that this trafficking occurs in a circadian manner and that adaptive immune responses are also time-of-day dependent and are ablated when circadian clock function is lost in T cells.
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.
The circadian clock is a fundamental and pervasive biological program that coordinates 24-hour rhythms in physiology, metabolism, and behavior, and it is essential to health. Whereas therapy adapted ...to time of day is increasingly reported to be highly successful, it needs to be personalized, since internal circadian time is different for each individual. In addition, internal time is not a stable trait, but is influenced by many factors, including genetic predisposition, age, sex, environmental light levels, and season. An easy and convenient diagnostic tool is currently missing.
To establish a validated test, we followed a 3-stage biomarker development strategy: (a) using circadian transcriptomics of blood monocytes from 12 individuals in a constant routine protocol combined with machine learning approaches, we identified biomarkers for internal time; and these biomarkers (b) were migrated to a clinically relevant gene expression profiling platform (NanoString) and (c) were externally validated using an independent study with 28 early or late chronotypes.
We developed a highly accurate and simple assay (BodyTime) to estimate the internal circadian time in humans from a single blood sample. Our assay needs only a small set of blood-based transcript biomarkers and is as accurate as the current gold standard method, dim-light melatonin onset, at smaller monetary, time, and sample-number cost.
The BodyTime assay provides a new diagnostic tool for personalization of health care according to the patient's circadian clock.
This study was supported by the Bundesministerium für Bildung und Forschung, Germany (FKZ: 13N13160 and 13N13162) and Intellux GmbH, Germany.
Neural activities of the brain occur through the formation of spatio-temporal patterns. In recent years, macroscopic neural imaging techniques have produced a large body of data on these patterned ...activities, yet a numerical measure of spatio-temporal coherence has often been reduced to the global order parameter, which does not uncover the degree of spatial correlation. Here, we propose to use the spatial autocorrelation measure Moran's I, which can be applied to capture dynamic signatures of spatial organization. We demonstrate the application of this technique to collective cellular circadian clock activities measured in the small network of the suprachiasmatic nucleus (SCN) in the hypothalamus.
We found that Moran's I is a practical quantitative measure of the degree of spatial coherence in neural imaging data. Initially developed with a geographical context in mind, Moran's I accounts for the spatial organization of any interacting units. Moran's I can be modified in accordance with the characteristic length scale of a neural activity pattern. It allows a quantification of statistical significance levels for the observed patterns. We describe the technique applied to synthetic datasets and various experimental imaging time-series from cultured SCN explants. It is demonstrated that major characteristics of the collective state can be described by Moran's I and the traditional Kuramoto order parameter R in a complementary fashion.
Python 2.7 code of illustrative examples can be found in the Supplementary Material.
christoph.schmal@charite.de or grigory.bordyugov@hu-berlin.de.
Supplementary data are available at Bioinformatics online.
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