Vol. 280, Issue 4, R1206-R1212, April 2001
A molecular explanation for the long-term suppression of
circadian rhythms by a single light pulse
Jean-Christophe
Leloup and
Albert
Goldbeter
Unité de Chronobiologie théorique, Faculté des
Sciences, Université Libre de Bruxelles, Campus Plaine, C.P.
231, B-1050 Brussels, Belgium
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ABSTRACT |
With the use of a
molecular model for circadian rhythms in Drosophila based on
transcriptional regulation, we show how a single, critical pulse of
light can permanently suppress circadian rhythmicity, whereas a second
light pulse can restore the abolished rhythm. The phenomena occur via
the pulsatile induction of either protein degradation or gene
expression in conditions in which a stable steady state coexists with
stable circadian oscillations of the limit cycle type. The model
indicates that suppression by a light pulse can only be accounted for
by assuming that the biochemical effects of such a pulse much outlast
its actual duration. We determine the characteristics of critical
pulses suppressing the oscillations as a function of the phase at which
the rhythm is perturbed. The model predicts how the amplitude and
duration of the biochemical changes induced by critical pulses vary
with this phase. The results provide a molecular, dynamic explanation
for the long-term suppression of circadian rhythms observed in a
variety of organisms in response to a single light pulse and for the
subsequent restoration of the rhythms by a second light pulse.
circadian clock; rhythm suppression; singularity; Drosophila; model
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INTRODUCTION |
ONE OF THE MOST
INTRIGUING observations on circadian rhythms is that they can be
suppressed in a prolonged manner by a single pulse of light. Long-term
suppression has been reported for a variety of organisms including
insects (33), plants (7), and mammals
(12, 16, 19). The abolished rhythm can often be restored
by a second light pulse (7, 12). These puzzling observations bear on the very nature of the circadian clock mechanism. Physical models of a nonmolecular nature have been used to account for
suppression in terms of return of a limit cycle oscillator to its
singularity (7, 17, 18, 34). To get deeper insight into
the molecular bases of the phenomenon, it is crucial to account for
prolonged suppression in a realistic biochemical model in which the
effect of light is incorporated explicitly. We report here that a
molecular model for the circadian clock, taking into account the
triggering by light of either protein degradation or gene expression,
can explain the long-term suppression of circadian rhythms by a single,
critical light pulse and the restoration of rhythmicity by another such
pulse. The model predicts how the duration and amplitude of the
biochemical changes induced by critical pulses vary with the phase at
which the rhythm is perturbed.
The most detailed model available for the circadian clock
(23-25) is based on experimental observations
collected for Drosophila; this model (schematized in Fig. 1)
relies on negative autoregulation of gene expression (10).
A similar feedback mechanism underlies circadian rhythms in other
organisms (5) such as Neurospora (2), mammals (21, 30), plants
(11), and cyanobacteria (14). For
definiteness, we will focus on the Drosophila clock model,
but we shall primarily take it as a tool to assess how a single light
pulse can trigger long-term suppression of circadian rhythmicity. Thus
we shall consider the cases in which light acts by inducing protein
degradation, as in Drosophila, or gene expression, as in
Neurospora and mammals.
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Fig. 1.
Scheme of the model for circadian oscillations in
Drosophila involving negative regulation of gene expression
by PER and TIM (23). per
(MP) and tim
(MT) mRNAs are synthesized in the nucleus and
transferred into the cytosol, where they accumulate at the maximum
rates vsP and vsT,
respectively; there they are degraded enzymatically at the maximum
rates vmP and vmT. The
rates of synthesis of the PER and TIM proteins, proportional to
MP and MT, are
characterized by the apparent first-order rate constants
ksP and ksT. Parameters
ViP (ViT) (i = 1, ...4) denote the maximum rate of the kinase(s) and phosphatase(s)
involved in the reversible phosphorylation of P0
(T0) into P1
(T1) and P1
(T1) into P2
(T2), respectively. The fully phosphorylated
forms (P2 and T2) are
degraded by enzymes of maximum rate vdP,
vdT, and reversibly form a complex C
with association and dissociation rate constants
k3, k4. Complex
C is transported into the nucleus at a rate characterized by
the apparent first-order rate constant k1.
Transport of the nuclear form of the PER-TIM complex
(CN) into the cytosol is characterized by the
apparent first-order rate constant k2. The
nuclear PER-TIM complex exerts a negative feedback on per
and tim transcription (see Ref. 23 for further details and
for a list of the kinetic equations). In Drosophila, light
controls the rhythm by enhancing the rate of TIM degradation
(vdT). In mammals, in which homologous clock
genes are at work and in which a similar model might apply, light acts
by enhancing the rate of per expression
(vsP).
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RESULTS |
Molecular model for the circadian clock.
Extending a previous version based on the regulation of per
alone (8), the clock model (Fig.
1) takes into account nuclear transcription of the per and tim genes and
transport of per and tim mRNAs into the cytosol,
where they are translated into the PER and TIM proteins; the latter are
multiply phosphorylated (6, 36) and form a complex that
enters the nucleus and represses per and tim
transcription (13, 22, 27, 35, 36). The model incorporates
degradation of the PER and TIM proteins and their mRNAs. Negative
regulation by the PER-TIM complex involves interaction with the CYC
(28) and CLOCK (1) proteins, which are not
considered explicitly in this model; incorporation of these two
proteins in an extended model preserves oscillatory behavior. Light
controls the Drosophila clock by triggering TIM degradation
(13, 22, 27, 35, 36); the maximum rate of TIM degradation
(vdT) increases with light, accordingly. In
mammals, where per and tim genes are also found
(20, 32), light acts by enhancing the rate of
per expression (vsP)
(31). The model is described by a set of 10 differential equations that govern the time evolution of the
concentrations of per and tim mRNAs and of the
various forms of PER and TIM proteins and PER-TIM complex (23,
25). This model accounts for circadian oscillations in continuous darkness, entrainment by light-dark cycles, and phase shifting by light pulses (23-25). Phase shifting by a
brief light pulse can only be accounted for by assuming that the
biochemical effects triggered by the pulse much outlast its actual duration.
Coexistence of a stable rhythm with a stable steady state.
Here, we focus on the long-term suppression of circadian rhythmicity by
critical light pulses. We will not consider explicitly the light pulse
itself. Instead, we will investigate the effect of the pulsatile
increase in the light-controlled parameters vdT or vsP that is triggered by the light pulse. Of
key importance for suppression is the bifurcation diagram showing the
dynamic behavior of the circadian regulatory system as a function of
parameters vdT (Fig.
2A) or
vsP (Fig. 2B). The diagram of Fig.
2A pertains to the case in which light acts by triggering
protein degradation. It represents the dynamic behavior of the
oscillatory system by a single state variable, the fully phosphorylated
form of the TIM protein (T2), as a function of
vdT. At low values of
vdT, a stable steady state is obtained. As
vdT increases, the steady state becomes unstable, and
sustained oscillations of the limit cycle type occur. Shown in Fig.
2A is the envelope of oscillations giving the minimum and
maximum levels of T2 at different values of
vdT. Beyond a second bifurcation value, the
steady state recovers its stability. For the set of parameter values
considered, over a sizeable range of vdT values
both to the left and to the right of the steady-state instability
domain in Fig. 2A, a stable steady state coexists with a
stable limit cycle. These two stable regimes are separated by an
unstable limit cycle. Such a situation is referred to as hard
excitation (26), because the system in the stable steady
state has to be excited by a finite perturbation to evolve to the
stable limit cycle. In contrast, when the steady state is unstable, an
infinitesimal perturbation suffices to drive the system away from
steady state toward the limit cycle (soft excitation). A similar type
of bifurcation diagram is obtained as a function of parameter
vsP (Fig. 2B), for the case in which light acts by triggering gene expression.
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Fig. 2.
Bifurcation diagram showing the domain of sustained
oscillations as a function of the light-controlled parameter in the
molecular model for the circadian clock. The diagrams represent the
stable (solid line) or unstable (dashed line) steady-state value of a
state variable [the concentration of the phosphorylated TIM form
(A) or of per mRNA (B), in nM], as
well as its envelope [maximum (Max) and minimum (Min)] in the course
of stable (solid line) or unstable (dotted line) sustained
oscillations, as a function of vdT
(A) or vsP (B). In
A, the 1st (vdT = 1.3 nM/h) and
2nd arrow (vdT = 2.2 nM/h) correspond to
conditions exemplifying hard and soft excitation, respectively. In the
domain of hard excitation, a stable limit cycle (see Fig.
4A) coexists with a stable steady state; these 2 attractors
are separated by an unstable limit cycle. The diagrams are established
by determining, by means of the AUTO program (4), the
steady state and periodic solutions of the kinetic equations of the
model listed as equations 1a-1j in Ref.
23. Parameter values are as in Ref. 23,
except vsP = 1.1 (for
A), vdT = 1.3 (for
B), vmP = 1.0, vdP = 2.2 (all in nM/h), and
k1 = 0.8/h.
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Circadian rhythm suppression by a single light pulse via
light-induced protein degradation.
In the simulations, we first consider that a pulse of light results in
a pulsatile increase in parameter vdT during a
time that generally outlasts the duration of the light pulse itself. The light pulse may indeed trigger the pulsatile synthesis or activation of an enzyme involved in the proteolytic pathway. This enzyme may remain active long after the light stimulus has ended. In
the range of vdT values, in which a stable limit
cycle surrounds an unstable steady state (for example, for the value
indicated by the second arrow in Fig. 2A), a pulse of light
applied at the appropriate phase with the appropriate duration and
magnitude can only suppress the rhythm transiently. Then, indeed, if
the finely tuned pulse succeeds in bringing the oscillator in the close
vicinity of the singularity (i.e., the steady state), the system will
skip a variable number of peaks before returning spontaneously to the
limit cycle; the closer the system approaches the steady state, the
more delayed is this return.
In contrast, suppression of the rhythm becomes permanent in conditions
of hard excitation. Then, as shown in Fig.
3, which corresponds to the
vdT value indicated by the first arrow in Fig. 2A, when applied at the appropriate phase of the
oscillations with appropriate duration and magnitude, a critical light
pulse can permanently abolish circadian rhythmicity (Fig. 3, first
arrow). Suppression of the rhythm results from the light-induced
degradation of TIM that causes a decrease in the protein below a
critical level, which drives the oscillator into the basin of
attraction of the stable steady state. An identical pulse (Fig. 3,
second arrow) restores the suppressed rhythm; here, the decrease in TIM beyond a critical level brings the system back into the basin of
attraction of the stable limit cycle.
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Fig. 3.
Permanent rhythm suppression by a single, critical pulse
of light in the circadian clock model and restoration of the rhythm by
a similar pulse. At the time indicated by the 1st arrow, to mimick the
effect of a light pulse, parameter vdT is
increased during 2 h from the basal value of 1.3 nM/h up to 4.0 nM/h. Initial conditions correspond to point 4 in Fig. 4,
A and B. At the time indicated by a 2nd arrow, a
similar change in vdT, mimicking a 2nd light
pulse, is initiated. The curve is obtained by numerical integration of
the model equations (23) for the parameter values of Fig.
2.
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To permanently suppress the rhythm by a single light pulse, neither the
phase at which it is applied nor the characteristics of the critical
perturbation are uniquely defined. As indicated in Fig.
4A, the
model predicts that permanent suppression by a light pulse can be
observed over a large portion of the limit cycle, corresponding roughly
to the rising phase of the TIM protein (Fig. 4B), between
the two black dots. At each of the phases in this portion of the limit
cycle, several combinations of the duration and amplitude of the
light-induced rise in parameter vdT are capable of permanent suppression. Thus, at a given phase of the cycle, in the
amplitude-duration plane for the effect of the light pulse, there
exists a domain (rather than a point corresponding to a unique pair of
values) in which single critical pulses can abolish the rhythm. The
shape of this domain changes as a function of phase: the model predicts
(Fig. 4C) that as the oscillations progress in the
permissive range from the minimum to the maximum level of TIM, the
pulses capable of permanently suppressing the rhythm are, at first,
those that produce a relatively long but small-amplitude increase in
TIM degradation, whereas near the maximum of TIM, successful pulses are
those that cause a large-amplitude but briefer increase in this
parameter. Relating these predictions to experiments in
Drosophila will require the quantitative determination of
the effect of light pulses of varying intensity and duration on the rate of TIM degradation.
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Fig. 4.
Effects of phase on rhythm suppression through
light-induced TIM degradation. A: single critical pulses can
permanently suppress the rhythm when applied over the portion of the
limit cycle (closed arrowed curve shown as projection onto the plane
formed by the concentrations of phosphorylated TIM and tim
mRNA) bounded by the 2 black dots. As shown in B, this
portion corresponds to the rising phase of TIM. The trajectory starting
from point 4 corresponds to the rhythm suppression by a
critical light pulse, shown in Fig. 3. The other trajectory starts at a
point ( ) located after the TIM maximum; the same
stimulus used in Fig. 3 fails to suppress the rhythm, and the system
returns to the limit cycle. Shown in A and B are
5 points of the limit cycle, marked 1-5, for which characteristics
of suppressing pulses were determined. The 5 domains in C,
within which permanent suppression is observed, correspond to these
points. The domains, determined by numerical simulations using the
parameter values of Fig. 2A (1st arrow), show the amplitude
and duration of the light-induced increase in
vdT, which cause permanent suppression of the
rhythm. Qualitatively similar results were obtained for other basal
values of vdT in the domain of hard excitation
in Fig. 2A. Amplitude is defined as the ratio of the
light-induced value of vdT divided by the basal
value (i.e., the value before the pulse). Concentrations in
A and B are in nM.
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The reason why the suppressive range corresponds roughly to the rise in
TIM becomes clearer when comparing the effect of the same pulse given
either in the suppressive range (e.g., starting from point 4 in Fig. 4A) or outside this range, after the maximum in TIM
(see trajectory starting from the black square in Fig. 4A).
In the former case, the effect of the pulse goes against the flow as it
tends to reduce TIM at a time when the protein level is increasing. The
system is thus pulled back and, as a result, evolves toward the inside
of the limit cycle where it is captured by the attracting stable steady
state. The level of tim mRNA, although high at the beginning
of the pulse, cannot counteract the light-induced decrease in TIM and
is also pulled to its steady-state value (see Fig. 4A). When
the same pulse is given after the maximum in TIM, when the protein
level has started to decrease, its effect accompanies the flow so that
the decrease in TIM is larger than in the previous case; the system
moves out of the limit cycle but returns to it asymptotically. In such
a case, the perturbation does not suppress the rhythm but merely causes
a phase shift.
Circadian rhythm suppression via light-induced gene expression.
In view of experimental observations (31), circadian
rhythm suppression by light pulses in mammals probably involves
light-induced transcription rather than protein degradation. To address
such a possibility in the present model, assuming that it holds for mammals, in which the same clock genes are present (20,
32), we have checked whether permanent suppression can occur in
conditions of hard excitation in Fig. 2B, solely as a result
of a transient increase in per transcription in response to
a light pulse (31), in the absence of light-induced TIM
degradation. Here, in the simulations, we implement the effect of a
light pulse by increasing parameter vsP in a
pulsatile manner during a time that may exceed the duration of the
triggering light pulse. The suppression of circadian oscillations of
per mRNA by a critical pulse of per expression is
demonstrated in Fig. 5A (1st
arrow); restoration of the rhythm by a second such pulse can also occur
(Fig. 5A, 2nd arrow). The changes in T2
associated with the suppression and subsequent restoration of circadian
rhythmicity by critical pulses of per expression are shown
in Fig. 5B (1st and 2nd arrow, respectively).
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Fig. 5.
Long-term suppression of circadian rhythmicity by
pulsatile gene expression. In A, the oscillations in
per mRNA are suppressed by a critical pulse in
per expression (1st arrow) effected by a pulsatile increase
in parameter vsP, which is increased from a
basal value of 1.1 nM/h up to 2.2 nM/h during 7.5 h. The initial
conditions correspond to point 3 in the 3 panels of Fig. 6.
A second, similar pulse (2nd arrow) restores the oscillations. The
associated time variation in TIM protein (T2) is shown in
B. Parameter values are as in Fig. 3 with
vdP = 1.3 nM/h.
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Permanent suppression of the rhythm resulting from the pulsatile
expression of per can occur over a wide range of phases, corresponding to the portion of the limit cycle bounded by the two
empty circles in Fig.
6A, that
extends from the maximum of per mRNA to a point located
beyond the trough (Fig. 6B). The shape of the domain of
suppressing pulses in the amplitude-duration plane again changes with
phase (Fig. 6C). Compared with Fig. 4C, however,
as the phase changes, the duration of these pulses varies more than
their amplitude. The domains of suppressing pulses in Fig.
6C are also smaller than those observed in Fig.
4C. Permanent suppression by light-induced gene expression
might thus require finer tuning than suppression by light-induced
protein degradation.
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Fig. 6.
Effect of phase on rhythm suppression by pulsatile
light-induced transcription of per. A: single
critical pulses can permanently suppress the rhythm when applied over
the portion of the limit cycle bounded by the 2 empty circles. Shown in
this portion are 5 points marked 1-5, for which characteristics of
suppressing pulses were determined. The 5 points are within the range
extending from the maximum in per mRNA to slightly beyond
the trough in this variable (B). The 5 domains in
C, within which permanent suppression is observed,
correspond to these points. The domains, determined by numerical
simulations using the parameter values of Fig. 2B, show the
amplitude and duration of the light-induced increase in
vsP that cause permanent suppression of the
rhythm. Amplitude is defined as the ratio of the light-induced value of
vsP divided by the value (1.1 nM/h) before the
pulse. Concentrations in A and B are in
nM.
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In contrast, restoration of the abolished rhythm appears to be more
easy to achieve when the light pulse induces gene expression rather
than protein degradation. In the former case, the return to the limit
cycle occurs for changes in biochemical parameters of relatively
shorter duration and amplitude (compare curves a and b in Fig. 7). More
generally, it is less arduous to restore the rhythm than to suppress
it, because it is enough for the pulse to exceed a critical duration,
at a given suprathreshold amplitude, for the rhythm to resume.
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Fig. 7.
Duration and amplitude of pulses restoring circadian
oscillations. When the oscillations are suppressed and the system is at
steady state, return to the limit cycle via a light-induced rise in
parameter vsP measuring per
expression occurs when the pulse characteristics correspond to a point
above the lower boundary (curve a). Restoration
of rhythmicity via a light-induced rise in parameter
vdT occurs when the pulse characteristics
correspond to a point above the upper boundary (curve
b). Parameter values are as in Figs. 3-6; the amplitude
of the pulse in vdT or
vsP is defined as in Figs. 4 and 6,
respectively.
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DISCUSSION |
The present results account, in terms of a realistic molecular
mechanism, for the long-term suppression of circadian rhythms by a
single light pulse. The phenomenon has been observed for the D. pseudoobscura circadian rhythm of pupal eclosion
(33), for the circadian rhythm of petal movement in
Kalanchoe (7), and for circadian rhythms in
hamster (19), chipmunk (12), and human
(16). The results also account for the restoration of
these rhythms by a similar light pulse (7, 12). The link between suppression and the situation in which stable oscillations coexist with a stable steady state was already made when circadian rhythms were first related to limit cycle behavior (17).
The suppression phenomenon in Kalanchoe was later accounted
for in terms of hard excitation by means of the Van der Pol oscillator model borrowed from the physical literature (7). The
present report provides a first instance in which permanent rhythm
suppression by a critical light pulse occurs in a realistic molecular
model for a circadian clock. This phenomenon eludes sheer intuition and
can only be explained by means of a theoretical model.
The present explanation of long-term suppression of circadian
rhythmicity differs from the alternative explanation based on a
putative desynchronization of circadian pacemakers following perturbation by the light pulse (12, 34). Here,
suppression results from the pulse-induced transition occurring in all
pacemaker cells from a stable oscillatory regime to a stable steady
state. Ultradian illustrations of an analogous phenomenon have been
reported for squid axon membranes (9) and cardiac tissue
(15), in which repetitive firing was suppressed by a brief
depolarizing or hyperpolarizing current pulse, respectively.
The analysis of the model suggests that long-term suppression of
circadian rhythms by critical light pulses should not necessarily be
observed in all organisms. Whether suppression possesses a permanent or
only transient nature will depend on whether the regulatory network
controlling the circadian clock operates in conditions in which a
stable limit cycle coexists with a stable singularity. Transient and
permanent suppression differ in two respects. In the former case, the
rhythm resumes by itself without external intervention; in the latter,
restoration of the rhythm requires a new pulse of light. Permanent
suppression is also more robust, i.e., less difficult to achieve,
because the pulse has to bring the oscillator anywhere into the basin
of attraction of the steady state rather than in its close vicinity.
Until systematic experiments are done over a wide range of light-pulse
amplitudes and durations, the question remains as to whether permanent
suppression of the locomotor activity rhythm can occur in D. melanogaster. Suppression of circadian rhythms has been linked to
type 0 phase-response curves (PRC) associated with strong resetting to
a single phase (33, 34). Such a PRC has been obtained in
D. melanogaster for 6 h light stimuli, whereas a
low-amplitude type 1 PRC showing only moderate phase advances or delays
was obtained for a 1-h light pulse of similar intensity (29). The model can account for both types of PRC
depending on the duration and magnitude of the pulse of light-induced
TIM degradation. The fact that the experiments on the type 0 PRC showed phase shifts rather than long-term suppression of the locomotor activity rhythm in D. melanogaster (29) would
suggest that the latter phenomenon does not occur in this organism, but
the pulses used may have missed the domains of permanent suppression
shown in Fig. 4C.
Although they were obtained in a model based on the molecular mechanism
of the Drosophila clock, the results bear on light-induced suppression of circadian rhythms in other organisms. The negative autoregulatory feedback loop that forms the core of the oscillatory mechanism in Drosophila is indeed observed in mammals, in
which homologs of the Drosophila clock genes are found
(20, 32), and in Neurospora, in which the
frq gene is negatively regulated by its protein product FRQ
(2, 5). Mechanistic differences between flies, fungi, and
mammals exist: for example, the role of TIM in mammals may differ from
that seen in Drosophila (5). Moreover, in
Neurospora (3) and mammals (31),
light triggers transcription instead of protein degradation. The
general significance of our results is nevertheless supported by the
fact that hard excitation is a robust phenomenon in models for this and
other nonlinear regulatory systems and by the finding that the
long-term suppression and subsequent restoration of circadian rhythms
by a critical perturbation can occur via pulsatile protein degradation or pulsatile gene expression.
The present results also indicate that long-term suppression of
circadian rhythms should also be observable in Drosophila and other organisms by directly triggering per or
tim expression. The pulsatile perturbation silencing
rhythmicity in Fig. 6 may indeed be obtained either with light, in
organisms in which it triggers transcription, or by means of a promoter
inducing gene expression.
Perspectives
Few phenomena in physiology remain as puzzling as the long-term
suppression of circadian rhythmicity by a single light pulse and the
subsequent restoration of the rhythm by a second pulse. Explanation of
these observations escapes sheer intuition and has therefore much to
gain from a modeling approach. One commonly invoked scenario for
suppression rests on the pulse-induced desynchronization of oscillators
responsible for circadian rhythmicity. An alternative mechanism
investigated here involves the pulse-triggered transition of pacemaker
cells from a stable oscillatory regime into a stable steady state in
conditions in which these two states coexist. Restoration of the
suppressed rhythm by a second light pulse involves the reverse
transition from the stable steady state to stable oscillations.
Although the theoretical principle of such an explanation is not novel,
this study provides its first implementation based on a detailed
molecular mechanism for circadian rhythms. The effects of light pulses
are mediated through induction of either protein degradation or gene
expression. By providing an explicit mechanism in terms of complex
dynamical processes at the molecular level for a behavioral response
that largely stands as a physiological enigma, the present results
yield a striking application of concepts from nonlinear dynamics to
biology. They also give a clear-cut example of how theoretical models
closely related to experiments may contribute new, counterintuitive
insights that could not have been reached without resorting to a
modeling approach.
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ACKNOWLEDGEMENTS |
This work was supported by Grant 3.4607.99 from the Fonds de la
Recherche Scientifique Médicale (Belgium), by the programme "Actions de Recherche Concertée" (ARC 94-99/180)
launched by the Division of Scientific Research, Ministry of Science
and Education, French Community of Belgium.
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FOOTNOTES |
J.-C. Leloup is Chargé de Recherches du Fonds National de la
Recherche Scientifique.
Address for reprint requests and other correspondence: A. Goldbeter, Unité de Chronobiologie théorique, Faculté
des Sciences, Université Libre de Bruxelles, Campus Plaine, C.P.
231, B-1050 Brussels, Belgium (E-mail:
agoldbet{at}ulb.ac.be).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 13 July 2000; accepted in final form 13 November 2000.
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