1
Circadian Systems: Progress towards Systemlevel Understanding of Circadian Rhythms
Jeffrey J. Kang

Abstract—Circadian rhythms manifest in the physiology and
behaviour of many organisms, from bacteria to humans. Using
the systems biology approach, cellular systems that generate
circadian rhythms are systematically perturbed and
characterized. Models of the relevant molecular mechanisms in
Drosophila have been formulated and serve as roadmaps in the
modeling of circadian systems in mammals. Numerical
simulations are used to validate molecular models and provide
insight into the behaviour of circadian systems. These models are
constantly evolving as progress is made towards a system-level
understanding of circadian rhythms.
Index Terms—circadian, Drosophila, systems biology, clock
genes.
I. INTRODUCTION
B
iological clocks have been studied by scientists since the
seventeenth century when it was observed that the leaves
of the heliotrope plant open and close in adherence to a daynight rhythm even in the absence of light stimuli [1]. Since
then, research has shown that endogenous rhythms with a
period of approximately 24 hours manifest in almost all
eukaryotic organisms as well as some bacteria. Named
circadian clocks for the Latin term circa dies, meaning about
one day, these biological rhythms effect changes in physiology
and behaviour that allow organisms to anticipate and adapt to
environmental changes brought about by the day-night cycle.
In recent years, the application of systems biology
techniques has provided new insight into the inner workings of
circadian clocks, revealing a cellular oscillator comprised of a
network of interlocking positive and negative transcriptional
feedback loops [2]. Characterization of the clock circuitry has
been performed by systematically perturbing circadian systems
using genetic manipulation. By using targeted gene deletions,
the behaviour of circadian rhythms in mutants can be observed
to infer gene function and interaction. Advancements in highthroughput gene manipulation and gene expression
measurement techniques have increased the efficiency of these
experiments. These mutagenesis studies have led to the
identification of clock genes and the roles they play in
generating circadian rhythms. Models of circadian systems on
the molecular levels for several organisms have been created
and refined. Although these models are not yet complete, they
will improve as the complexities of circadian circuitry are
unravelled.
Circadian systems are well suited to study using the systems
biology approach. The emergence of systems biology theory
and its associated tools have greatly benefited research in this
field and aided progress towards a system-level understanding
of circadian rhythms, whereby circadian systems may be
controlled and designed. Such an understanding may lead to
treatments for sleep-related ailments and certain neurological
disorders in humans.
II. THE CIRCADIAN SYSTEM
In terms of classic systems theory, the circadian clock can
be modelled as a system that receives input consisting of
environmental light-dark signals and produces output in the
form of a biological rhythm expressed in physiology and
behaviour. The system can be thought of as an autonomous
oscillator producing a signal of fixed frequency with phase
changes determined by the input. Although some elements of
the system’s molecular mechanisms have been discovered, the
exact structure of the system is still unknown.
The molecular basis of circadian systems has been studied
in the most detail in the fruitfly Drosophila melanogaster, the
organism in which the first clock gene per was isolated in
1984. It was observed that transcription of the per gene is
induced when levels of its own product, the PER protein, are
reduced [3]. This forms a negative autoregulatory feedback
loop creating oscillations in transcription of the per gene, thus
providing an early model for the circadian oscillator. However,
as experimental advancements have been made, this model has
undergone many changes, reflecting the need in systems
biology to improve the system model iteratively.
III. CIRCADIAN STRUCTURE IN DROSOPHILA
Current models of circadian oscillators in Drosophila
consist of multiple interlocking feedback loops. Both negative
and positive feedback mechanisms are believed to exist. The
negative feedback mechanism is based on two transcriptional
activators, dCLK and CYC, and two repressors, PER and
TIM. Fig. 1 shows a diagram of the molecular model proposed
in [4]. The proteins dCLK and CYC form a heterodimer which
bids to E-boxes in the regulatory regions of the per and tim
genes, enhancing their transcription. After PER and TIM have
reached a threshold concentration, they associate and enter the
nucleus and bind to the dCLK-CYC heterodimers, thereby
2
IV. COMPUTATIONAL MODELING AND ANALYSIS
Fig. 1. Molecular model of Drosophila circadian system.
repressing per and tim transcription. Positive feedback is seen
in the dCLK protein which represses dclk gene transcription. If
dclk expression is slightly activated then the formation of
dCLK-CYC heterodimers enhances per and tim transcription.
As PER and TIM bind to dCLK-CYC, the repression of dclk
by dCLK is relieved. This further increases dCLK levels, and
hence a positive feedback loop is formed [5].
The circadian rhythm is produced by the alternating cycles
of activation and repression of per and tim. A sustained
oscillation is generated by separating the intervals of activation
and repression [6]. The kinase DBT plays an important role in
generating these delays by phosphorylating and destabilizing
PER. Thus, DBT retards the accumulation of PER. Each
activation-repression cycle lasts approximately 24 hours. Light
input affects the system via the CRY protein which acts as a
photoreceptor. When exposed to light, CRY associates with
TIM, which promotes rapid TIM degradation. This reduction
in TIM levels causes a phase delay in the circadian cycle. Two
genes not shown in Fig. 1 are sgg and vr, whose roles are not
fully understood, but appear to be ancillary. The heterodimer
dCLK-CYC activates vri transcription in the same manner as it
activates per and tim. High levels of VRI subsequently repress
per and tim expression, though the mechanism by which this
occurs is unknown. SGG plays a role in determining the timing
of PER-TIM translocation to the nucleus by phosphorylating
TIM.
The multiple negative and positive transcription regulatory
factors within circadian systems are necessary to ensure
reliable oscillation with relatively constant periods in the
presence of stochastic biochemical noise and under varying
cellular conditions. The stochastic nature of reaction events is
important when the number of molecules is small as is the case
in many cellular systems. This behaviour can be regarded as
internal noise of the system. Cellular conditions such as
transcription and translation rates may vary with changes in
temperature, nutrition or growth conditions [7]. The complex
feedback loops present within the regulatory mechanisms
create a robust periodicity, reducing the sensitivity of the
system to noise and changes in cellular conditions.
Computational models of circadian rhythms can be
developed based on the molecular model. Computational
analysis can then offer theoretical predictions based on
simulations of the system’s molecular mechanisms. In [8], a
procedure for developing a computational model of biological
rhythms is proposed. This procedure can be summarized in
four steps.
1) Variable identification: The key variables of the
phenomenon to be modeled are identified. Additionally, the
nature of the interactions between variables forming the
relevant feedback loops is characterized.
2) Mathematical description: A system of differential
equations describing the time evolution of the system is
formulated. For spatially homogenous conditions, these
equations are ordinary differential equations. Otherwise, as is
the case in the presence of diffusion, partial differential
equations are used to describe the system’s evolution in both
the spatial and temporal domains.
3) Calculation of steady states: The steady states of the
system, as determined by the differential equations, are solved
using analytical methods or by numerical integration.
4) Steady state analysis: The stability properties of the
steady states are determined using a method such as linear
stability analysis. If a steady state is deemed to be unstable
then the evolution of the system to either a stable steady state
or sustained oscillations is calculated. In the case of sustained
oscillations, the period and amplitude are described as
functions of the system parameters.
A computational model allows predictions of system
behaviour to be obtained via numerical simulations using
known or assumed parameter values. Theoretical predictions
can then be compared to experimental observations to evaluate
the accuracy of the model. The model is then modified if
incongruity between prediction and experimental observations
exists, or when additional information regarding the modeled
variables and interactions is discovered.
The first computation models for circadian rhythms were
proposed for Drosophila. An early model based on the
negative control of the PER protein on per expression
consisting of only five kinetic equations was developed using
the procedure detailed above [8]. Numerical simulations
produced the desired sustained oscillations, but the steady state
became unstable for some parameter values. As understanding
of the system structure improved, a ten-variable model was
proposed based on the negative control exerted by the PERTIM heterodimer. This model also accounted for the effects of
light in entraining the circadian system. Simulations showed
sustained oscillations in complete darkness with phase shifts
induced by light pulses. However, models based on continuous
differential equations are deterministic and only approximate
reaction kinetics. If the number of molecules in a system is
small, the model does not accurately portray the stochastic
effects of biochemical noise. When the discrete nature of
reaction events is taken into account, the simulated oscillations
3
Fig. 2. Comparison of simulated and experimental PER concentrations.
persist but with widely fluctuating periods and amplitudes [7].
Thus a flaw is exposed in the molecular model upon which the
computation model was formulated.
In [7], an alternative model incorporating hysteresis in the
negative regulation of transcription produces more accurate
results when consideration is given to noise in reaction
kinetics. Simulations show that even with as few as ten
molecules per cell, the standard deviation of the period
remains less than 10%. While this hysteresis model may not
accurately portray the molecular mechanisms at work in the
Drosophila circadian system, it illustrates the need for models
to be robust to stochastic noise. It has been hypothesized that
the addition of positive feedback elements to existing models
may improve their sensitivity to noise [9]. A more recent 23variable model includes both positive and negative feedback
loops. Simulation of this model suggests that positive feedback
elements are not necessary to generate circadian rhythms [5],
but no evaluation of their effect on the robustness of the model
was made. The true importance of these positive feedback
elements remains unclear.
Recently proposed models provide simulated output of
protein levels that closely match experimental data. Fig. 2
shows a comparison between simulated levels of gene product
in the Drosophila circadian system obtained using the model
proposed in [5] compared to experimental observations. In this
diagram, “PER” refers to an average of PER and TIM protein
levels. The peak, minimum and shape of the protein level
progression over the course of the circadian cycle are similar
in the simulated and experimental cases. The period of
simulated cycle is approximately 24 hours. Simulations such as
this one show that current understanding of the molecular
mechanism governing circadian rhythms, while incomplete,
accurately describes the key elements of the circadian system.
V. CIRCADIAN RHYTHM IN MAMMALS
The study of model organisms is useful in inferring the
function of human genes. These organisms have been
described as the Rosetta Stones for deciphering human
biological systems [11]. In the study of human circadian
systems, Drosophila serves as an excellent model organism.
Understanding of the molecular mechanisms in the Drosophila
circadian clock has greatly assisted the study of their
counterparts in mammals. Homologues of most Drosophila
clock genes have been identified in mammals [3]. The
transcriptional feedback loops that generate oscillations in
mammalian circadian systems are more complex than those
found in Drosophila and the key proteins are different, but
important similarities exist.
Models of mammalian circadian systems have been
developed based on various mutagenesis studies conducted on
mice. As in Drosophila, the rhythm is based on a core negative
feedback loop. The two transcription factors CLOCK and
BMAL1 (MOP3) form a heterodimer that binds to the E-boxes
in the promoter regions of mPer1, mPer2, mPer3, mCry1 and
mCry2, thereby stimulating the transcription of the three mPer
and two mCry genes [4]. This is analogous to the effect of the
dCLK-CYC heterodimer on PER in Drosophila. The mPer
and mCry genes are the respective homologues of per and cry.
The mCRY proteins act as the transcription repressors instead
of TIM and PER in Drosophila. By entering the nucleus and
interfering with the activation of the CLOCK-BMAL1
heterodimer, the mCRY proteins repress the transcription of
the mPer and mCry genes. Some mechanisms of the
mammalian circadian system are still unclear. While mPER2
is believed to assist in the transcription of the bmal gene, the
functions of mPER1 and mPER3 are unknown. To date, no
homologue for tim has been discovered for mammals;
however, genome-wide complex trait analysis in mice
indicates the presence of undiscovered clock genes [2].
In addition to understanding how circadian rhythms are
generated at the cellular level, it is also important to
understand how the circadian system operates on an organism
level to induce changes in physiology and behaviour. In
organisms such as birds, reptiles and fish, the circadian clock
is localized in specific areas of the central nervous system such
as the pineal gland. However, the mammalian circadian system
consists of a hierarchy of dispersed oscillators [1]. The center
of this system is located in the suprachiasmatic nucleus (SCN)
of the anterior hypothalamus of the brain. In mice, destruction
of the SCN renders the animal behaviourally and
physiologically
arrhythmic.
In
humans
with
craniopharyngioma, the tumour can constrict the SCN region
of the brain, leading to severe disruption of sleep-wake cycles
[10]. The SCN can be regarded as a master clock that
coordinates the timing of slave clocks in other areas of the
brain and in peripheral organs such as the liver and the kidney.
Synchronized slave clocks then regulate local rhythms that
govern physiology and behaviour.
Unlike the master clock, slave clocks are unable to produce
self-sustaining oscillations and require periodic input from the
master clock. SCN cells in culture produce circadian rhythm
for weeks, but the rhythm produced by liver cells in culture
dampen and disappear in under one week [2]. The differences
4
between the oscillation mechanisms within cells comprising
the master clock and slave clocks are unknown. Genetic
studies show that the molecular compositions of the master
clock and slave clocks are very similar. One hypothesis states
that the master clock benefits from global differences in the
levels and kinetics of clock proteins rather than from the
existence of dissimilar genes or proteins in the SCN [2].
The SCN contains approximately 10,000 to 20,000 neurons.
Each neuron exhibits its own circadian rhythm with varying
periods, though the mechanism of how individual oscillations
are coordinated to generate a single overt rhythm is unknown.
The SCN is often modeled as a single oscillator for the sake of
simplicity. However, this simple model is not always valid as
spatially inhomogeneous rhythms have been observed within
regions of the SCN. One study has attempted to reconcile this
observation by modelling the SCN as a system of 10,000
neurons behaving as locally-coupled, self-sustained oscillators
[12]. Simulation of this system showed that a global rhythm
emerged due to local coupling between oscillators leading to
synchronization. The period of the global output corresponded
to the average periods of the individual oscillators. The period
of the rhythm was found to be stable for low amplitudes as
well as amplitude transients. This model presents one possible
explanation for SCN rhythm generation, though molecularlevel understanding of neuron synchronization is lacking.
The input and output pathways of the mammalian circadian
system have also been a focus of study. Input pathways
provide external stimulation to the system in the form of
environmental inputs that entrain the circadian rhythm. In
humans, it has been observed that the daily cycles of sleeping,
waking, activity and hunger conform to a period of about 23
hours if the body is deprived of environmental cues associated
with the day-night cycle [1]. Therefore, environmental
information, primarily taking the form of observed light and
dark, is required to extend this period to 24 hours. In
mammals, the signalling pathway that carries entraining signals
to the SCN has been identified as the retinohypothalamic tract
(RHT) [2]. The RHT delivers photic input from retinal
ganglion cells to SCN neurons. These visual cues are believed
to be necessary and sufficient to synchronize circadian
rhythms to 24 hour day-night cycles. The output pathways by
which the SCN master clock synchronizes slave clocks are
believed to the hormonal in nature. Neurons secrete several
neuropeptides such as the hormone vasopressin based on a
circadian rhythm [1]. Additionally, neurons send signals to the
pineal gland, resulting in production of melatonin, another
hormone.
VI. CONCLUSION
Circadian rhythms and their manifestation in physiology and
behaviour have long been observed. In recent years, advances
in genetics have allowed the molecular mechanisms—the so
called clockwork—of circadian rhythms to be studied. Models
of circadian systems of organisms such as Drosophila emerged
first from these studies. These models have been invaluable in
the modeling of circadian systems of more complex organisms
such as mammals thanks to similarities in the circadian
systems of disparate species at the molecular level. Current
models are constantly evolving as new experimental
observations are made and fresh insight is gained.
The role played by systems biology in the study of circadian
systems is crucial. Systems biology provides a strategy to deal
with the immense complexity of circadian systems. Through
the use of incrementally improving models and systematic
perturbations of circadian systems, an understanding of the
relationships between the various genes and proteins that form
the core of the circadian systems has been gained.
Computational models and simulations have been used to
confirm or invalidate hypotheses regarding the structure and
kinetics of the molecular mechanisms of circadian systems.
Simulations are also used to make predictions of system
behaviour, providing insights that are sometimes
counterintuitive and difficult to obtain by other means.
The culmination of these studies will be a system-level
understanding of circadian systems in not just Drosophila and
mice, but also humans. Such an understanding would enable
circadian systems to be characterized, controlled and perhaps
even created. This may lead to new avenues for
pharmacological treatments for conditions such as jetlag and
ailments afflicting shift workers, as well as sleep-related
psychiatric disorders and SCN-based neurological disorders.
REFERENCES
P. Sassone-Corsi, “Molecular clocks: mastering time by gene
regulation,” Nature, vol. 392, pp. 871-874, April 1998.
[2] S. M. Reppert and D. R. Weaver, “Coordination of circadian timing in
mammals,” Nature, vol. 418, pp. 935-941, August 2002.
[3] H. Okamura, S. Yamaguchi, and K. Yagita, “Molecular machinery of
the circadian clock in mammals,” Cellular Tissue Research, vol. 309,
pp. 47-56, July 2002.
[4] J. A. Ripperger and U. Schibler, “Circadian regulation of gene
expression in animals,” Current Opinion in Cell Biology, vol. 13,
pp.357-362, June 2001.
[5] P. Smolen, D. A. Baxter, and J. H. Bryne, “Modeling circadian
oscillations with interlocking positive and negative feedback loops,”
Journal of Neuroscience, vol. 21, pp. 6644-6656, September 2001.
[6] M. W. Young and S. A. Kay, “Time zones: a comparative genetics of
circadian clocks,” Nature Reviews Genetics, vol. 2, pp. 702-715,
September 2001.
[7] N. Barkai and S. Leibler, “Circadian clocks limited by noise,” Nature,
vol. 403, pp. 267-268, January 1999.
[8] A. Goldbeter, “Computational approaches to cellular rhythms,” Nature,
vol. 420, pp. 238-245, November 2002.
[9] M. H. Hastings, “Circadian clockwork: two loops are better than one,”
Nature Reviews Neuroscience, vol. 1, pp.143-146, November 2000.
[10] H. D. Piggins, “Human clock genes,” Annals of Medicine, vol. 34, pp.
394-400, May 2002.
[11] T. Ideker, T. Galitski, and L. Hood, “A new approach to decoding life:
systems biology,” Annual Review of Genomics and Human Genetics,
vol. 2, pp. 343-372, September 2001.
[12] H. Kunz and P. Achermann, “Simulation of circadian rhythm generation
in the suprachiasmatic nucleus with locally coupled self-sustained
oscillators,” Journal of Theoretical Biology, vol. 224, pp 63-78,
September 2003.
[1]
5