Quantification of circadian rhythms in mammalian lung tissue snapshot data.

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.

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 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, fastening 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.

Mathematical Modeling in Circadian Rhythmicity.

Circadian clocks are autonomous systems able to oscillate in a self-sustained manner in the absence of external cues, although such Zeitgebers are typically present. At the cellular level, the molecular clockwork consists of a complex network of interlocked feedback loops. This chapter discusses self-sustained circadian oscillators in the context of nonlinear dynamics theory. We suggest basic steps that can help in constructing a mathematical model and introduce how self-sustained generations can be modeled using ordinary differential equations. Moreover, we discuss how coupled oscillators synchronize among themselves or entrain to periodic signals. The development of mathematical models over the last years has helped to understand such complex network systems and to highlight the basic building blocks in which oscillating systems are built upon. We argue that, through theoretical predictions, the use of simple models can guide experimental research and is thus suitable to model biological systems qualitatively.

Synergies of Multiple Zeitgebers Tune Entrainment.

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.

Principles underlying the complex dynamics of temperature entrainment by a circadian clock.

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.