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Interplay between the circadian clock and metabolism: important reminders
Biological rhythms
Earth is a highly periodic environment. Indeed, Earth rotation around its axis and around the sun has important consequences including day-night alternations, succession of seasons and tidal movements. All these cyclic phenomena have a strong impact on life : some animals migrate; others hibernate while some marine species entirely adapted their metabolism to cope with tides. Human societies also have to cope with periodicity such seasonal variations in flu epidemies for example that strongly affects society’s functioning. Rhythmicity is thus present in almost every aspects of life! Let’s just think about heart beating, respiration, ovulation, about the cell cycle and sleep-wake cycles to name just a few. The next section constitutes a general overview of the main biological rhythms, about their roles and about some mechanisms that generate them.
Rhythms arise on many time-scales in living systems
Rhythmic processes are found in many species and can also appear on many time-scales with periods ranging from seconds to years (see Fig. 2.1) [46]. Circadian rhythms are among the most ubiquitous rhythms. Indeed, these 24-hour rhythms are found in eukaryotes as well as in bacteria. They control many physiological processes and will be the subject of this work. Rhythms with a period smaller than 24 h are called ultradian while rhythms with a period above 24 h are called infradian. Infradian rhythms include ovulation rhythms, reproduction rhythms, migration, hibernation, plant flowering rhythms,… But many rhythms are ultradian with periods from a fraction to several hours. For example, electrical rhythms such as neural and cardiac rhythms have a small period from a fraction of to a few seconds. The period of cytosolic calcium oscillations ranges from seconds to minutes. Rhythm in the transport of the transcription factor Msn2 in and out the nucleus occur with a period of 6 min [80]. A segmentation clock has been shown to control somitogenesis. Its period is about 90 min
[48]. The transcription factor NF-kB, involved in the inflammatory response, can oscillate with a period of several hours, as well as the tumour suppressor p53 [103], [75]. Hormonal secretion can also be pulsatile with periods ranging from several minutes to 24 h when the process is controlled by the circadian clock [87] [48].
Fig. 2.1 Non exhaustive list of important biological rhythms. The asterisk indicates rhythms that occur at the cellular level [46].
All these examples of oscillatory behaviours may seem paradoxical. Indeed, the Second Law of thermodynamics tells us that the entropy of an isolated system can only increase [72]. That means that disorder will always increase and that the system will evolve to an equilibrium steady state. So, how is it possible for living systems to be highly organized in space and time ? Indeed, oscillations are a form of temporal organization. This is because living systems such as cells for example, are not isolated systems. They are open systems that take energy from their environment to stay far away from the thermodynamical equilibrium. This has first been highlighted by Prigogyne and its work about dissipative structures in the seventies [128]. Even open systems normally evolves to a stable steady state in course of time. But Prigogyne and his co-workers have shown that this steady state can become unstable when the system evolve far from equilibrium and when it is nonlinear enough. It is what happens for living systems. Regulation of gene expression, nuclear-cytoplasmic transport as well as regulation of the activity of receptors, enzymes or ion channels associated with feedback mechanisms and/ or cooperativity give rise to instabilities and subsequent periodic behaviours [47]. In particular, it has been shown that the presence of a negative feedback loop in a biochemical system is a necessary condition to generate self-sustained oscillations.
Indeed, most of the above mentioned cellular rhythms rely on a negative feedback loop. Interestingly, an oscillatory dynamics can have different functional roles. One of these roles is to enable frequency-encoded information transmission [48]: the temporal pattern of an input signal (high or low frequency pulses, constant level) determines which cellular response is triggered (see Fig. 2.2). The frequency encoded transmission is quite common and occurs inter alia in the case of calcium oscillations or p53 oscillations as well as in the NF-κB pathway [48]. Frequency-encoded information transmission in the NF-κB signalling pathway is described here for the sake of example. Ultradian oscillations have been observed in the activity of NF-κB in the nucleus and these can be explained by a negative feedback loop between NF-κB and its partner IκBα [75]. Indeed, under unstimulated conditions, the binding between NF-κB and IκBα sequestrates NF-κB in the cytoplasm. Then, a stimulation of the cell by the tumour necrosis factor (TNFα) triggers a signalling cascade that activates the IκB kinase (IKK). The latter promotes then the degradation of IκBα. This enables NF-κB to enter the nucleus where it activates the transcription of genes involved in the innate inflammatory response. Among them, IκBα which sequestrates once again NF-κB in the cytoplasm which creates a negative feedback loop enabling an oscillatory behaviour [75]. Single-cell experiments have shown that the pattern (high frequency, low frequency or constant level) of the stimulation by an external signal (TNFα or LPS) results in a given dynamics of NF-κB nuclear entry which determines the set of target genes that are activated [6], [158].
Frequency-encoded information transmission is not the only possible functional role of cellular oscillations. Indeed, in other biological rhythms such as circadian rhythms, the frequency is stable and an important functional role of circadian clocks seems to be to keep internal physiological processes in synchrony with the external periodic environment [132],
[10]. As we will see just below, this is notably enabled by the three fundamental properties of circadian systems: these rhythms are endogenous (relying on a negative transcriptional feedback loop) but are entrainable by external periodic signals and their period is robust against temperature fluctuations [136]. From now on, we will only focus on the study of these fascinating clocks !
8 Interplay between the circadian clock and metabolism: important reminders
Fig. 2.2 Frequency-encoded information transmisssion in the NF-κB signalling pathway. Left panel: a negative feedback loop between NF-κB its partner IκBα is at the core of the this network (Left panel) and enables the onset of an oscillatory behaviour. Right panel: the temporal pattern of the external stimulation (oscillation, constant level) determines the kind of gene transcription program that is triggered ([79] .
Circadian clocks
Fundamental properties of circadian systems
Circadian oscillations are self-sustained rhythms that can be entrained by ex-ternal periodic cues
The term circadian comes from the Latin, circa (around) and diem (a day). Circadian rhythms are thus rhythms with a period of approximatively 24 h. The most obvious circadian rhythms are the sleep-wake cycles [70]. Locomotor activity is also an overt circadian rhythm for many animals, from Drosophila to rodents. Circadian rhythms were first observed in plants, many centuries ago. Indeed, in the middle of the eighteenth century, the french scientist de Mairan observed daily rhythms in the leaf movements of the plant mimosa [49]. He noticed that these daily leaf movements still persisted under constant darkness. In the first part of the twentieth century, researchers studied the locomotor activity of rodents [49]. Typically, animals were placed in a running wheel and their activity was recorded on an actogram. In natural conditions, that is under day-night alternation, animals display rhythmic activities of exactly 24 h. As for plant leaf movements, rhythms in animal locomotor activity persist under constant conditions Nevertheless, their period is slightly different from 24h. These rhythms are thus endogenous: they are generated by internal mechanisms with a free-running period that is close to 24 h (see Fig. 2.3) [49]. The exact duration of the free-running period depends on species and there is even some variability between “individuals” of the same species [146]. Furthermore, the free-running period is not totally the same in DD (constant darkness) and LL (constant light) conditions. Thus, these studies have highlighted two of the fundamental properties of circadian rhythms [136]: they are self-sustained with a free-running period τ but can be entrained by an external periodic cue called zeitgeber (« time giver » in German) such as the light-dark cycle to a period T.
A circadian system is thus composed of three elements: an input device that is able to convey photic information about the local external time to the internal clock, an internal clock system generating self-sustained oscillations and driving rhythmic outputs resulting in overt circadian rhythms such as the locomotor activity rhythms but also rhythms in body temperature or hormone secretion (see Fig. 2.4.A). The scheme is of course a simplified view. Some circadian systems are more complex: the output rhythms can be driven by both the zeitgeber and the clock [49] and the output can also feedback on the clock or influence the effect of the zeitgeber on the clock (see Fig. 2.4.B) [49]. Moreover, as we will see later (in section 2.2.3.3.1), some organisms such as mammals have multiple clocks throughout the body [183].
The entrainment of internal clocks by zeitgeber cues informs organisms about the external local time and allows them to schedule their activities to an appropriate time of the day [10]. Entrainment not only implies that the period of the oscillator matches the one of the zeitgeber: it also entails a fixed phase relationship between the clock and the external cue. The latter depends on the amplitude and on the period of the zeitgeber, on the free running period and on the photoperiod, that is the illumination time [146]. The light-dark cycle is not the only zeitgeber; in particular, we will see (in section 2.2.3.4.2) that the feeding-fasting cycle is also an important zeitgeber [28].
Table of contents :
1 Introduction
2 Interplay between the circadian clock and metabolism: important reminders
2.1 Biological rhythms
2.1.1 Rhythms arise on many time-scales in living systems
2.2 Circadian clocks
2.2.1 Fundamental properties of circadian systems
2.2.1.1 Circadian oscillations are self-sustained rhythms that can be entrained by external periodic cues
2.2.1.2 Temperature compensation
2.2.2 Circadian clocks allow fitness to changing environments
2.2.3 Organisation of the mammalian clock
2.2.3.1 Circadian rhythms are generated by the SCN
2.2.3.2 Circadian oscillations are cell autonomous
2.2.3.2.1 Transcriptional and translational feedback loops
2.2.3.2.2 Post-transcriptional and post-translational modifications
2.2.3.3 Secondary clocks in peripheral tissues
2.2.3.3.1 Clock genes are rhythmically expressed in multiple tissues
2.2.3.3.2 Circadian gene expression is largely tissue-specific
2.2.3.4 Entrainment properties of peripheral clocks
2.2.3.4.1 The SCN drives peripheral clocks through neuroendocrine cues
2.2.3.4.2 Food is the dominant zeitgeber for peripheral clocks
2.3 Clock and metabolism
2.3.1 Evidences for the coupling between clock and metabolism
2.3.1.1 Nuclear receptors are implicated in both clock and metabolic pathways
2.3.1.2 Defects in the clock lead to metabolic disorders
2.3.1.3 Disturbed feeding-fasting cycles lead to altered clock gene expression
2.3.2 Interplay between clock and metabolic pathways at the tissue-level
2.3.2.1 Energy producing processes: Cellular respiration
2.3.2.2 Energy consuming processes: Storage processes and gluconeogenesis
2.3.2.2.1 Glucose storage and gluconeogenesis
2.3.2.2.2 Fat storage
2.3.2.3 The nutrient sensors and their interactions with the clock
2.3.2.3.1 AMPK
2.3.2.3.1.1 AMPK as a nutrient sensor
2.3.2.3.1.2 AMPK and the clock
2.3.2.3.2 Sirtuins
2.3.2.3.2.1 Sirtuins as nutrient sensors
2.3.2.3.2.2 SIRT1 and the clock
2.3.2.3.2.3 SIRT3 and the clock
2.3.2.3.3 Crosstalks between AMPK and SIRT1
2.3.2.3.3.1 AMPK increases NAD+ levels, thereby enhancing SIRT1 activity
2.3.2.3.3.2 SIRT1 deacetylates LBK1
2.3.3 Interplay between clock and metabolism at the level of the whole organism
2.4 Chronotherapy
2.4.1 Generalities about chronotherapy
2.4.2 Rev-Erb agonists
3 Mathematical modelling in biology
3.1 Roles of modelling in the study of circadian clocks
3.2 Steps of a mathematical modelling process
3.2.1 Construction of a mathematical model: case of the Goodwin model and of a related clock model
3.2.1.1 The Goodwin model
3.2.1.2 A toy model for the mammalian clock
3.2.2 Considerations about parameter estimation methods
4 A detailed model describing entrainment of the liver clock by metabolism
4.1 Construction of the mathematical model
4.1.1 Model for the core clock
4.1.1.1 Equations
4.1.2 Addition of the action of the nutrient sensors AMPK and SIRT1 on the clock
4.1.2.1 Incorporation of the Nampt-NAD+-SIRT1 loop
4.1.2.2 Incorporation of AMPK and its interactions with the clock
4.1.2.3 Incorporation of PGC1-α
4.1.3 Summary of the construction of our model
4.2 Parameter estimation
4.2.1 Choice of experimental data
4.2.2 Reproduction of expression time profiles from wild-type animals
4.2.3 Reproduction of knockout phenotypes
4.3 Effect of perturbations of AMPK rhythms on the clock
4.4 Targeting the clock to rescue physiological expression profiles
4.4.1 Rescue of clock oscillations amplitude in Cry1 mutants following a dampening in AMPK rhythm
4.4.2 Pharmacological rescue of physiological expression profiles after disruption of AMPK rhythm
4.5 Conclusion
5 Preliminary results and Perspectives
5.1 Preliminary results
5.1.1 Relative importance of the different feedback loops
5.2 Perspectives
5.2.1 Improvement of our present model
5.2.1.1 Include the circadian variations of PGC1α mRNA
5.2.1.2 Represent the positive feedback loop between AMPK and SIRT1
5.2.1.3 Consideration of the effect of neuro-endocrine cues from SCN on the liver clock: Effect of glucocorticoid signalling
5.2.2 Build a global model connecting our model to major metabolic pathways
5.2.2.1 Model A: glycolytic model
5.2.2.2 Model B: modelling of the switch between glycolysis and fatty acid oxidation
5.2.2.3 Model C: addition of storage processes and gluconeogenesi
5.2.2.4 Model D: taking into consideration the control of the feeding-fasting cycle by the SCN
6 Supplementary Information
6.1 Kinetic Equations
6.2 Forcing Function
6.3 List of Parameters
7 Résumé en français
7.1 Introduction: couplage entre horloge circadienne et métabolisme
7.1.1 Horloge circadienne
7.1.2 Horloge et métabolisme
7.2 Résultats: modèle mathématique décrivant l’entrainement de l’horloge du foie par le métabolisme
7.2.1 Construction du modèle
7.2.2 Estimation de paramètres
7.2.3 Effet des perturbations du rythme d’AMPK sur l’horloge
7.2.4 Approche pharmacologique: rétablissement du bon fonctionnement de l’horloge par l’administration d’un agoniste de l’horloge
7.3 Conclusions
References
