Robustness from flexibility in the fungal circadian clock

Background Robustness is a central property of living systems, enabling function to be maintained against environmental perturbations. A key challenge is to identify the structures in biological circuits that confer system-level properties such as robustness. Circadian clocks allow organisms to adapt to the predictable changes of the 24-hour day/night cycle by generating endogenous rhythms that can be entrained to the external cycle. In all organisms, the clock circuits typically comprise multiple interlocked feedback loops controlling the rhythmic expression of key genes. Previously, we showed that such architectures increase the flexibility of the clock's rhythmic behaviour. We now test the relationship between flexibility and robustness, using a mathematical model of the circuit controlling conidiation in the fungus Neurospora crassa. Results The circuit modelled in this work consists of a central negative feedback loop, in which the frequency (frq) gene inhibits its transcriptional activator white collar-1 (wc-1), interlocked with a positive feedback loop in which FRQ protein upregulates WC-1 production. Importantly, our model reproduces the observed entrainment of this circuit under light/dark cycles with varying photoperiod and cycle duration. Our simulations show that whilst the level of frq mRNA is driven directly by the light input, the falling phase of FRQ protein, a molecular correlate of conidiation, maintains a constant phase that is uncoupled from the times of dawn and dusk. The model predicts the behaviour of mutants that uncouple WC-1 production from FRQ's positive feedback, and shows that the positive loop enhances the buffering of conidiation phase against seasonal photoperiod changes. This property is quantified using Kitano's measure for the overall robustness of a regulated system output. Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure. Conclusions Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator. More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators

Synchronization and entrainment of coupled circadian oscillators

Circadian rhythms in mammals are controlled by the neurons located in the suprachiasmatic nucleus of the hypothalamus. In physiological conditions, the system of neurons is very efficiently entrained by the 24-hour light-dark cycle. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light dark cycle in neuronal synchronization. Nevertheless, heterogeneity as a natural and permanent ingredient of these cellular interactions is seemingly to play a major role in these biochemical processes. In this paper we use a model that considers the neurons of the suprachiasmatic nucleus as chemically-coupled modified Goodwin oscillators, and introduce non-negligible heterogeneity in the periods of all neurons in the form of quenched noise. The system response to the light-dark cycle periodicity is studied as a function of the interneuronal coupling strength, external forcing amplitude and neuronal heterogeneity. Our results indicate that the right amount of heterogeneity helps the extended system to respond globally in a more coherent way to the external forcing. Our proposed mechanism for neuronal synchronization under external periodic forcing is based on heterogeneity-induced oscillators death, damped oscillators being more entrainable by the external forcing than the self-oscillating neurons with different periods.Comment: 17 pages, 7 figure

Prediction of photoperiodic regulators from quantitative gene circuit models

Photoperiod sensors allow physiological adaptation to the changing seasons. The external coincidence hypothesis postulates that a light-responsive regulator is modulated by a circadian rhythm. Sufficient data are available to test this quantitatively in plants, though not yet in animals. In Arabidopsis, the clock-regulated genes CONSTANS (CO) and FLAVIN, KELCH, F-BOX (FKF1) and their lightsensitive proteins are thought to form an external coincidence sensor. We use 40 timeseries of molecular data to model the integration of light and timing information by CO, its target gene FLOWERING LOCUS T (FT), and the circadian clock. Among other predictions, the models show that FKF1 activates FT. We demonstrate experimentally that this effect is independent of the known activation of CO by FKF1, thus we locate a major, novel controller of photoperiodism. External coincidence is part of a complex photoperiod sensor: modelling makes this complexity explicit and may thus contribute to crop improvement

Interaction between the Circadian Clock and Regulators of Heat Stress Responses in Plants.

The circadian clock is found ubiquitously in nature, and helps organisms coordinate internal biological processes with environmental cues that inform the time of the day or year. Both temperature stress and the clock affect many important biological processes in plants. Specifically, clock-controlled gene regulation and growth are impacted by a compromised clock or heat stress. The interactions linking these two regulatory pathways include several rhythmic transcription factors that are important for coordinating the appropriate response to temperature stress. Here we review the current understanding of clock control of the regulators involved in heat stress responses in plants

Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems

Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for phase-response curves, a fundamental one-dimensional phase reduction of oscillator models. The proposed theoretical and numerical analysis tools are illustrated on several system-theoretic questions and models arising in the biology of cellular rhythms

Circadian rhythms and hormonal homeostasis: Pathophysiological implications

Over recent years, a deeper comprehension of the molecular mechanisms that control biological clocks and circadian rhythms has been achieved. In fact, many studies have contributed to unravelling the importance of the molecular clock for the regulation of our physiology, including hormonal and metabolic homeostasis. Here we will review the structure, organisation and molecular machinery that make our circadian clock work, and its relevance for the proper functioning of physiological processes. We will also describe the interconnections between circadian rhythms and endocrine homeostasis, as well as the underlying consequences that circadian dysregulations might have in the development of several pathologic affections. Finally, we will discuss how a better knowledge of such relationships might prove helpful in designing new therapeutic approaches for endocrine and metabolic diseases