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Accepted Manuscript
Gene regulatory network models in response to sugars in the plant
circadian system
Takayuki Ohara , Timothy J. Hearn , Alex A.R. Webb ,
Akiko Satake
PII:
DOI:
Reference:
S0022-5193(18)30401-6
https://doi.org/10.1016/j.jtbi.2018.08.020
YJTBI 9585
To appear in:
Journal of Theoretical Biology
Received date:
Revised date:
Accepted date:
13 March 2018
1 August 2018
16 August 2018
Please cite this article as: Takayuki Ohara , Timothy J. Hearn , Alex A.R. Webb , Akiko Satake ,
Gene regulatory network models in response to sugars in the plant circadian system, Journal of
Theoretical Biology (2018), doi: https://doi.org/10.1016/j.jtbi.2018.08.020
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Highlights
● This study investigated mechanisms by which sucrose regulates plant
circadian clocks.
● We introduced effects of sucrose into circadian gene-regulatory network
models.
● The model predicted target genes of sucrose realizing the observed phase
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response.
● The model revealed how the potential target genes should be regulated by
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sucrose.
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Title: Gene regulatory network models in response to sugars in the plant circadian
system
Authors: Takayuki Ohara
a, b, 1, *
, Timothy J. Hearn c, Alex A. R. Webb c, Akiko
Satake b
Affiliations;
a
Graduate School of Environmental Science, Hokkaido University,
b
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Sapporo, 060-0810, Japan
Department of Biology, Faculty of Science, Kyushu University, Fukuoka, 819-0395,
Japan
c
Department of Plant Sciences, University of Cambridge, Cambridge, CB2 3EA,
United Kingdom
Current address: Department of Mechanical Engineering, Ritsumeikan University,
Kusatsu, 525-8577, Japan
*
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1
Corresponding author at: Department of Mechanical Engineering, Ritsumeikan
University, Kusatsu, 525-8577, Japan
Abstract: Circadian entrainment is the process by which internal circadian oscillators
staying in synchronization with the local environmental rhythms. Circadian clocks are
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entrained by adjusting phase and period in response to environmental and metabolic
signals. In Arabidopsis thaliana, light and sugar signals differentially affect the
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circadian phase; the former advances the phase in the late of the subjective night and
delays around dusk, while the latter advances the phase mainly in the morning, which is
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optimal to maintain sucrose homeostasis. We have proposed that the phase adjustment
of the A. thaliana circadian oscillator by sugar signals contributes to the realization of
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carbon homeostasis and the increase of plant growth under fluctuating day-night cycles.
However, which genes in the circadian oscillator are targets of sucrose signals and how
the potential target genes should be regulated by sucrose to realize sucrose homeostasis
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has not been studied from the theoretical perspective. Here we investigate the effect of
sugar on the phase response property of the plant circadian oscillator using clock
gene-regulatory network models. We simulated phase response curves (PRCs) to
sucrose pulses, which were compared with an experimental PRC. Our analyses of the
gene-regulatory network model demonstrated that target genes of the sugar signal could
be members of the PSEUDO-RESPONSE REGULATOR gene family and the evening
complex components. We also examined the phase response property using a single
feedback-loop model and elucidated how phase advance is induced in the subjective
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morning under certain conditions of a target clock gene of sucrose and its regulatory
property.
Keywords: Arabidopsis thaliana; circadian rhythm; clock; sucrose; sugar signaling;
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entrainment
1. Introduction
The circadian clock is an endogenous timekeeper generating approximately 24-h
rhythmicity of a wide range of biological processes. The circadian clock allows
organisms to coordinate their physiology and behavior under periodic environmental
fluctuations. The circadian oscillator in Arabidopsis thaliana consists of interlocking
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transcriptional feedback loops and regulates important processes such as metabolism
and growth (Hsu and Harmer, 2014). Metabolites such as photosynthetic sugars and
nitrogen in turn modulate the circadian properties (Haydon et al., 2013; Yuan et al.,
2016), forming further feedback loops between the circadian oscillator and metabolic
status to improve fitness (Sanchez and Kay, 2016).
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To keep the appropriate phase relationship between the circadian oscillator and
day-night environmental cycles, the circadian phase needs to be adjusted in response to
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external environmental signals (Johnson et al., 2003). The magnitude and direction of
the phase shift of the circadian oscillator in response to the signal is dependent on the
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timing when the signal is perceived as represented by a phase response curve (PRC).
Previous studies in A. thaliana mainly focused on the PRC in response to light signals.
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Light pulses have been reported to advance and delay the phase during the latter and
former half of the subjective night, respectively (Covington et al., 2001; Locke et al.,
2005b; Ohara et al., 2015a). When the circadian clock was appropriately entrained to
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external light-dark cycles, plant biomass was increased, suggesting that entrainment is
advantageous to plant fitness (Dodd et al., 2005; Graf et al., 2010).
Besides the signals from external environments, endogenous signals such as
photosynthetic sugars also affect the circadian phase (Haydon et al., 2013; Seki et al.,
2017). Interestingly, the A. thaliana circadian oscillator differentially responds to sugar
and light signals—the PRC for sucrose signals has phase advances in the subjective
morning (Fig. 1; Haydon et al., 2013; Seki et al., 2017). Recent theoretical studies have
revealed the importance of circadian clock entrainment by endogenous sugar on sucrose
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homeostasis and growth (Feugier and Satake 2013, 2014; Webb and Satake 2015; Seki
et al. 2017; Ohara and Satake 2017). Using an integrated model of starch metabolism
and phase dynamics of the circadian clock, Seki et al. (2017) predicted that fluctuation
of sucrose level was minimized when the circadian phase was advanced in the morning
in response to sucrose signals. Another theoretical study demonstrated that adjustment
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of circadian phase to maintain carbon homeostasis is advantageous for plant growth
(Ohara and Satake 2017). These studies based on the phase oscillator models unraveled
a non-intuitive relationship between starch metabolism, the circadian oscillator, and
growth. However, these models did not contain mechanistic detail about how sugars
adjust the phase of the circadian oscillator.
Computational approaches using clock-gene regulatory network models have been
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useful to understand the mechanisms underlying the phase response to light in the plant
circadian system. Based on a clock model with a detailed structure of the regulatory
network, Pokhilko et al. (2012) have predicted the important process that could cause
discontinuous changes of phase shifts in the A. thaliana circadian oscillator in response
to red light pulses. Ohara et al. (2015b) have developed a model including multiple
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photoreceptors and predicted the essential receptor for the oscillator to properly respond
to light-to-dark transition. However, there has been no trial in silico that evaluates the
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effect of clock gene regulation by sugar on the phase response property of the plant
circadian oscillator. A previous experimental study (Haydon et al., 2013) identified that
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the mutant in which a morning-phased clock gene PSEUDO-RESPONSE REGULATOR
7 (PRR7) is not functional (prr7-11) is insensitive to the shortening of circadian period
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by sucrose under low light conditions. This study demonstrated experimentally that
sucrose entrains the circadian clock and suggested that PRR7 is necessary for
entrainment to sugars based on the observation that low sugar status increased PRR7
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expression and there was no phase response to sucrose in prr7-11. Due to the high
degree of inter-regulation and feedback between oscillator components it can be
difficult to test directly through experimentation the hypothesis that changes in PRR7
abundance are causal for the regulation of the circadian oscillator by sugars.
Computational studies can help in the interpretation of the experimental data by
providing comprehensive predictions about which circadian clock genes can be a target
of sugar signals and also what is the mechanism generating significant phase advance of
the circadian oscillator in the subjective morning. The overlap in results between
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experimental and computational studies gives strong support to the proposed
mechanisms.
Here we took a theoretical approach to test the hypothesis that changes in PRR7 activity
contribute to the entrainment of the circadian oscillator to sugars. We extended a
circadian clock-gene regulatory network model (De Caluwé et al., 2016) by
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incorporating the effect of sugar on the circadian clock genes and simulated phase
response dynamics of the system to sucrose signals to address the following two
questions: (1) which genes in the circadian oscillator are targets of sucrose signals? and
(2) how the potential target genes should be regulated by sucrose (e.g. activation or
repression) to realize observed phase advance in the subjective morning? We
additionally examined the effect of sucrose on free-running period using various
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regulatory relationships, because it has been experimentally observed that the circadian
period of clock gene expression is shortened in the presence of sucrose (Haydon et al.,
2013). We therefore looked to see if, in agreement with the experimental study, we
could identify the same components computationally for regulating period shortening
and phase adjustment. We also repurposed a single positive-negative feedback loop
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model (Locke et al., 2005a) to investigate how the activator-repressor relationship might
contribute to the phase response to perturbation. The analyses of the repurposed model
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were used to help the interpretation of the results of the realistic model.
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2. Models and Methods
2.1. Circadian clock-gene network models
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To identify the target circadian oscillator gene(s) and regulatory properties (activation or
repression) of sugar signals that generate the phase advance in the subjective morning,
we used two types of gene-regulatory network models with different complexities.
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Comparison of these models enables us to unravel both realistic and common
mechanisms underlying the phase advance of the circadian oscillator in the subjective
morning.
2.1.1. Interconnected feedback loop model
The first model (De Caluwé et al., 2016; hereafter referred to as DC2016) describes the
dynamics of mRNA and protein of eight circadian clock genes: two redundant
MYB-like transcription factors CIRCADIAN CLOCK ASSOCIATED 1 (CCA1) and
LATE ELONGATED HYPOCOTYL (LHY), which peak around dawn; four members of
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PRR gene family PRR9, PRR7, PRR5, and TIMING OF CAB EXPRESSION 1 (TOC1;
also known as PRR1), which sequentially express from morning to afternoon; and
EARLY FLOWERING 4 (ELF4) and LUX ARRHYTHMO (LUX), which peak around
dusk and are constituents of the evening complex (Nusinow et al., 2011). In the model,
dynamics of the eight clock genes were reduced by merging two genes (CCA1/LHY,
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PRR9/PRR7, PRR5/TOC1, ELF4/LUX, respectively) into a single variable (CL, P97,
P51, EL, respectively) based on the similarities of their roles and expression patterns
(Fig. 2a). The model is capable of reproducing key features of the A. thaliana circadian
clock such as phenotypes of clock mutants and light responses (De Caluwé et al., 2016)
despite its relatively compact network structure compared to highly intricate models
(Pokhilko et al., 2012; Fogelmark and Troein, 2014). The model describes the mRNA
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dynamics of CCA1/LHY (CL), PRR9/PRR7 (P97), PRR5/TOC1 (P51), and ELF4/LUX
(EL) as follows;
[]

=
1 +1 ∗∗[]
[97] 2
[51] 2
) +(
)
1+(
1
2
− (1 ∗  + 1 ∗ (1 − )) ∗ [] ,
[]2


=
3
[] 2
[51] 2
) +(
)
1+(
6
7
− 3 ∗ [51] ,
(3)
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[]
=
∗4
[] 2
[51] 2
[] 2
) +(
) +(
)
1+(
8
9
10
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− 2 ∗ [97] ,
(2)
[51] 2
[] 2
) +(
)
4
5
1+(
[51]

=
M
[97]
2 ∗∗[]+2 +2 ∗ 2
3 +[]2

(1)
− 4 ∗ [] ,
(4)
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where [X]m and [X]p represent mRNA and protein levels of component X (X
corresponds to CL, P97, P51, and EL), respectively. [P] represents the protein level of a
putative light-effect mediator P, L represents the light condition (defined as 1 under
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light and 0 under dark), and vi, Ki, and ki are constants. The temporal dynamics of
circadian clock proteins and P have been formalized by ordinary differential equations
(De Caluwé et al., 2016) and we used the same formalism in this study. The parameters
for the model were set to the optimized values fitted to experimental data reported in the
original paper (De Caluwé et al., 2016).
2.1.2. Single feedback loop model
To investigate the mechanisms generating phase advances in the morning, we first
examined the potential for an early-phased activator and late-phased repressor
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relationship in a circadian oscillator, like that between CCA1 and PRR7. To this end we
repurposed an abstracted positive-negative feedback loop model (Locke et al., 2005a;
hereafter referred to as L2005 model). L2005 was one of the first models to describe the
biochemical relationships within the plant circadian clock. Further modelling and
experimentation demonstrate that L2005 does not accurately describe the basis of the
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circadian oscillator. However, L2005 provided an excellent basis for repurposing to
consider how a positive-negative feedback loop, such as that between CCA1 and PRR7,
might result in phase advance and delay in response to perturbation. Therefore, the
purpose to use the repurposed model, which we call Early Activator Late Repressor
(EALR), was not for deriving conclusions about the regulatory relationships between
sucrose and actual circadian clock genes, but for investigating how activators and
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repressors might contribute to phase responses. Findings from analyses of EALR model
were used to interpret the results of the realistic DC2016 model. In our repurposing of
L2005 to EALR there is an activator and a repressor. The phase of the activator is about
6 hours ahead of the repressor and thus the activator is designated as EA (early-phased
activator) and the repressor as LR (late-phased repressor; Fig. 2b). These designations
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indicate that we recognize that EALR does not describe the biochemical complexities of
the circadian oscillator. However, EALR provides a reduced framework to understand
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how relationships between differently phased repressor and activator activities might
contribute to phase changes. The mRNA dynamics of EA and LR are formalized as;

2
 ∗[]

4
(5)

 ∗[]
 ∗[]
= 1 ∗ [] ∗  + 1+[] −  1+[] ,
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[]

 ∗
2 2
4

= +[]
,
 −  +[]
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[]
1

1

(6)
where [X]n represents the protein level in the nucleus of component X (X corresponds
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to LR and EA), and a, b, qi, ni, gi, mi, and ki are constant. [P] and L are the same as in
the DC2016 model. Note that Locke et al. (2005a) separately formalized the
clock-protein level in the cytoplasm and nucleus, and we used the similar formalism.
Locke et al. (2005a) reported two parameter sets for the model; one is optimally fitted to
experimental data and is accompanied with damped oscillation and the other yields the
suboptimal solution with limit cycle oscillation. Because the DC2016 model displays
sustained oscillation, we adopted the latter parameter sets to facilitate the comparison of
the results between two models.
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It should be noted that the rate of the change in the mRNA level is defined by the
balance between its production and degradation in both models. Therefore, the peak
timing of mRNA, which corresponds to the transition from the rising stage to the
declining stage of mRNA, is advanced either when production becomes low or
degradation becomes high, and vice versa. The peak timing of mRNA was used to
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quantify the level of phase-shift of the oscillator in response to sugar signals as
explained later.
2.2. Modeling regulation of circadian oscillator by sucrose
We extended the DC2016 and EALR (see Appendix A) models by incorporating the
effects of sucrose on circadian oscillator gene expression or on the mRNA degradation
activity because there is strong experimental evidence that sucrose affects transcript
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levels of several oscillator genes (Haydon et al., 2013). We considered three situations
by which sucrose might regulate the A. thaliana circadian oscillator.
Case (1): Sucrose directly affects circadian oscillator gene expression
Sucrose directly activates or represses the expression of an oscillator gene. If
dynamics (Eq. (1)) become;
[]

=
1 +1 ∗∗[]+()
[97] 2
[51] 2
) +(
)
1
2
− (1 ∗  + 1 ∗ (1 − )) ∗ [] ,
(7)
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1+(
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CCA1/LHY (CL) is the target of sucrose that activates the gene expression, its mRNA
where S(t) stands for sucrose input defined later. When sucrose represses the gene
[]
=
1 +1 ∗∗[]
[97] 2
[51] 2
) +(
) +()
1+(
1
2
− (1 ∗  + 1 ∗ (1 − )) ∗ [] .
(8)
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expression, Eq. (1) is modified as;
If other oscillator components (P97, P51, EL) are assumed to be the target of sucrose,
S(t) is similarly added to numerator or denominator of the first term in the right-hand
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side of Eqs. (2)–(4). Sucrose input S(t) is defined as;
() = {
pulse
0
onset ≤  < onset + dur
,
otherwise
(9)
where Spulse stands for the intensity of a sucrose pulse, and tonset and tdur indicate the
onset time and duration of the pulse, respectively. In the DC2016 model, there are eight
situations to examine because two regulatory relationships (active or repressive) are
possible between sucrose and each of the four clock components (Fig. 3).
Case (2): Sucrose indirectly affects oscillator gene expression through modulation
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of clock protein activity
Sucrose status modulates the activity of a circadian clock protein (e.g. by affecting its
phosphorylation state), resulting in the alteration of the expression of its target oscillator
gene. The effect of sucrose on the gene expression depends on the abundance of the
clock protein that is modulated by sucrose. If sucrose affects the expression level of
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CCA1/LHY (CL) through interaction with the PRR9/PRR7 (P97) protein, mRNA
dynamics of CL become;
[]

1 +1 ∗∗[]
=
[97] 2
[51] 2
) +(
)
1
2
1+(()∗
− (1 ∗  + 1 ∗ (1 − )) ∗ [] .
(10)
In general, when sucrose affects the expression of component X through interaction
with the protein Y, the effect of sucrose is formalized by replacing [Y]p with S(t)[Y]p in
Here sucrose input S(t) is defined as;
() = {
pulse
∗
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the equation for mRNA dynamics of X (X and Y correspond to CL, P97, P51, and EL).
onset ≤  < onset + dur
,
otherwise
(11)
where S* is constant that stands for the effects of sucrose on a clock protein in the
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absence of external sucrose pulse. We considered the following two situations: (i) Spulse
> S*; a clock protein is up-regulated by the sucrose pulse. (ii) Spulse < S*; a clock protein
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is down-regulated by the sucrose pulse. The value of S* was chosen so that the systems
show the self-sustained oscillation and is listed in Table 1. In the DC2016 model, there
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are twenty situations to examine because two regulatory relationships (up- or
down-regulation) are possible between sucrose and clock proteins (Fig. 5): PRR9/PRR7
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and PRR5/TOC1 proteins for CCA1/LHY; CCA1/LHY, PRR5/TOC1, and ELF4/LUX
proteins for PRR9/PRR7; CCA1/LHY and PRR5/TOC1 proteins for PRR5/TOC1;
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CCA1/LHY, PRR5/TOC1, and ELF4/LUX proteins for ELF4/LUX.
Case (3): Sucrose affects mRNA stability
Sucrose activates or represses degradation of mRNA. If sucrose affects mRNA
degradation of CCA1/LHY (CL), its mRNA dynamics become;
[]

=
1 +1 ∗∗[]
[97] 2
[51] 2
) +(
)
1+(
1
2
− (1 ∗  + 1 ∗ (1 − )) ∗ () ∗ [] ,
(12)
where S(t) is defined as;
() = {
pulse
1
onset ≤  < onset + dur
.
otherwise
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When Spulse > 1, degradation of mRNA is activated by sucrose. On the contrary, when
Spulse < 1, sucrose suppresses mRNA degradation. If other oscillator component X (X
corresponds to P97, P51, and EL) is assumed to be the target of sucrose, the effect of
sucrose is similarly formalized by replacing [X]m in the second term in the right-hand
side of Eqs. (2)–(4) with S(t)[X]m. Similar to the Case 1, in the DC2016 model, there are
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eight situations to examine (Fig. 7).
The EALR model was extended similar to the DC2016 model by incorporating the
effects of sucrose on the oscillator gene expression or on the mRNA degradation
activity (see Appendix A).
2.3. Phase response curve and free-running circadian period
The PRC was generated in the similar way used in a previous study (Ohara et al.,
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2015b). We mainly used 3-h sucrose pulse to stimulate the circadian oscillator. The
value of Spulse is listed in Table 1. The sucrose pulse was added in the continuous light
condition after the system converges to the limit cycle. We used the peak mRNA timing
of CCA1/LHY as an indicator of phase-shift determination and considered it as the
subjective dawn in the DC2016 model. Because LR in the EALR model corresponds to
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LHY in the original study (Locke et al., 2005a), we considered the peak mRNA timing
of LR as the subjective dawn and used to estimate phase shifts. We call the former half
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of one circadian cycle subjective morning and the latter half subjective night. The phase
shifts were evaluated at six circadian cycles after the pulse perturbations to avoid the
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transient phase.
In order to quantify how dominant the phase advance is in the subjective morning, we
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introduced an index of advancement (hereafter referred to as IA) calculated as;
∑0≤ <12 ∆ + ( )

 = ∑
0≤ <24 ∆
+ (
)
,
(14)
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where Δφ+(φi) indicates the value of phase advance at the phase of ith sucrose pulse φi (i
∈ {1,…,N}; N is the number of times the pulse is injected in one circadian cycle). IA is
1 when PRCs show phase advance solely in the subjective morning and is 0 when there
is no phase advance in the subjective morning. We interpreted that phase advance is
dominant in the subjective morning when IA is larger than a threshold value. Because
phase
advance
is
detected
mainly
in
the
subjective
morning
in
the
experimentally-observed PRCs (Fig. 1), we set the threshold to a relatively high value
0.85.
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Free-running period was estimated under continuous light condition by setting Spulse in
Eqs. (9), (11), and (13) to some finite values (Table 1) throughout the simulation.
Numerical integration of the ordinary differential equations was performed with the
fourth-order Runge-Kutta method using Mathematica (version10; Wolfram Research).
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3. Results
3.1. Potential target genes of sucrose signal are PRR5/TOC1, ELF4/LUX, and
PRR9/PRR7
3.1.1 The direct effect of sucrose on oscillator gene expression in the DC2016 model
When sucrose directly affects the oscillator gene expression, among the eight possible
situations examined, phase advance was predicted to dominate in the subjective
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morning when sucrose activates PRR5/TOC1 or ELF4/LUX (Fig. 3c, d) or represses
PRR9/PRR7 (Fig. 3f). Phase advance was detected only around the dawn when the
CCA1/LHY expression was repressed (Fig. 3e). Even when signal intensity (Spulse) and
duration (Sdur) were altered, the PRCs had phase advance and delay at similar phases of
the pulse (Fig. 3; Fig. A.1), suggesting that the major determinant of the direction of
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phase shifts (i.e. advance or delay) is the timing of the sucrose pulse. In contrast, the
magnitude of phase shifts was strongly affected by the signal intensity and duration (Fig.
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3; Fig. A.1). Experimentally derived PRCs sometimes have a dead-zone in which the
oscillator has no significant response to a phase changing stimulus (Johnson et al.,
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2003). In the case of sucrose this dead zone appears to be around ZT6–12h (Fig. 1).
Among the PRCs showing phase advance in the subjective morning, the one in which
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sucrose represses PRR9/PRR7 expression contained a dead-zone (Fig. 3f).
Free-running period was shortened when sucrose was assumed to repress any of four
oscillator genes (Fig. 4). Interestingly, the period was also shortened under the
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assumption that sucrose activates PRR9/PRR7, although activation of other three genes
resulted in period lengthening (Fig. 4). Both phase advance in the subjective morning
and the period-shortening effect were observed under the assumption that sucrose
represses PRR9/PRR7.
3.1.2 The effect of sucrose on regulation of circadian clock protein activity in the
DC2016 model
When sucrose regulates the activity of clock proteins, among the twenty situations
examined, phase advance was predicted in most part of the subjective morning if
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sucrose indirectly activates PRR5/TOC1 (Fig. 5f, g) or ELF4/LUX (Fig. 5h–j) or
represses PRR9/PRR7 (Fig. 5c–e). These results support our findings in the Case 1 that
phase advance in the subjective morning is possible when sucrose up-regulates
PRR5/TOC1 or ELF4/LUX or down-regulates PRR9/PRR7. In addition, phase advance
around dawn was also detected when the CCA1/LHY expression was indirectly
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repressed (Fig. 5a, b), that is similar to the result from the Case 1 (Fig. 3e).
Several kinds of regulatory relationships made free-running period shorter (Fig. 6). The
period-shortening effect was accompanied by phase-advancing effect in the subjective
morning under the assumption that sucrose down-regulates CCA1/LHY protein and
then activates PRR5/TOC1 or ELF4/LUX expression. These regulatory relationships
also realized the PRCs with a dead-zone (Fig. 5f, h). It should be noted that in some
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conditions the effect of sucrose on the period was very weak (Fig. 6). We confirmed that
the period-shortening or lengthening effect becomes stronger when larger value of Spulse
is used, although the system displays damped oscillation when the very high value is
used (data not shown).
3.1.3 The effect of sucrose on mRNA degradation in the DC2016 model
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Similar results were obtained when sucrose regulates the mRNA degradation. Among
the eight situations examined, phase advance was predicted to dominate in the
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subjective morning when the mRNA degradation of PRR9/PRR7 is activated (Fig. 7b)
or that of PRR5/TOC1 or ELF4/LUX is repressed (Fig. 7c, d). When sucrose activates
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mRNA degradation of CCA1/LHY, phase advance was also predicted in the subjective
morning as well as in the later night (Fig. 7a). In all situations the PRCs did not contain
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a clear dead-zone.
Free-running period was shortened when mRNA degradation of any of four oscillator
genes is activated by sucrose (Fig. 8). Both phase advance in the subjective morning
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and the period-shortening effect were observed only when sucrose activates mRNA
degradation of PRR9/PRR7.
Our analyses demonstrated that there are commonly three possible circadian clock
regulations by sucrose for the phase advance in most of the subjective morning––
sucrose up-regulates PRR5/TOC1 or ELF4/LUX mRNA or down-regulates PRR9/PRR7
mRNA. Phase advance was also induced, but was not dominant, in the morning when
CCA1/LHY mRNA was down-regulated by sucrose pulse. Overall, the effects of signal
intensity and duration on the PRCs observed in Case 1 were similar between Cases 1–3
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(data not shown).
3.2. Mechanisms underlying the phase advance in the subjective morning
We investigated the mechanisms generating phase advance in the morning by reducing
the problem through focusing only on the activator-repressor loop in the EALR model.
The analyses in the EALR model were used to interpret the results derived from a
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complicated loop-structure of the realistic DC2016 model.
Because we defined the peak mRNA timing of LR as the subjective dawn in the EALR
model, declining and rising stages of LR mRNA correspond to the subjective morning
and night, respectively (Fig. 9a, d). When sucrose directly represses LR expression,
sucrose pulse added in the subjective morning advanced the phase (Fig. 9a, b). In
contrast, the pulse in the subjective night delayed the phase (Fig. 9d, e). This is because
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during the subjective morning the pulse-induced decrease of LR mRNA (Fig. 9a) was
followed by the premature rise of EA mRNA (Fig. 9b), leading to the advanced phase of
the oscillator (Fig. 9a, b). When the pulse was added during the subjective night, the
pulse-induced decrease of LR mRNA (Fig. 9d) was followed by the slow decline of EA
mRNA (Fig. 9e), resulting in the delayed phase of the oscillator (Fig. 9d, e).
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These results can be explained intuitively using the phase plane representations (Fig. 9c,
f). The sucrose perturbation to the system during the subjective morning moved state
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points toward the subjective dusk (Fig. 9c), resulting in the advancement of the phase of
the oscillator. During the night, the pulse caused state points to take a longer path to the
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subjective morning (Fig. 9f), shifting the phase of the oscillator backward. The resultant
PRC showed clear phase advance in the subjective morning and delay in the subjective
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night (Fig. 10a).
When sucrose directly activates LR expression, opposite phase response was predicted
based on the same argument, namely phase delay in the subjective morning and phase
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advance in the subjective night (Fig. A.2a; Fig. 10a). The results from the Case 2 (Fig.
A.2b; Fig. 10c) and Case 3 (Fig. A.2c; Fig. 10e) were similar to those in the Case 1 (Fig.
9c) because of the same effect of perturbation to the system. We also examined the
situation where sucrose directly represses EA expression and found that phase advance
was induced in the subjective morning (Fig. A.2d; Fig. 10b). Again, the results from the
Case 2 (Fig. 10d) and Case 3 (Fig. 10f) were similar to those in the Case 1 (Fig. 10b)
when the sucrose stimuli have the same effect of perturbation to the system.
The phase plane analyses were also useful to interpret the results of the DC2016 model.
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When sucrose represses PRR9/PRR7 expression, state points perturbed during the
subjective morning took a shorter path to the subjective dusk (Fig. 11a), resulting in the
advancement of the phase of the oscillator (Fig. 3f). In contrast, the sucrose perturbation
during the subjective night caused state points to make a detour (Fig. 11b), delaying the
phase of the oscillator (Fig. 3f). Both of these observations were in line with those in the
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EALR model above. Similar explanations were possible even when we observe other
subspaces of the limit cycle (Fig. A.3). When sucrose activates PRR5/TOC1 (Fig. 11c)
or ELF4/LUX (Fig. 11d), the sucrose perturbation during the subjective morning caused
state points to take a shorter path to the subjective dusk, advancing the phase of the
oscillator (Fig. 3c, d). Because PRR5/TOC1 and ELF4/LUX are repressors of
PRR9/PRR7 (Fig. 2a), state points were similarly perturbed when sucrose represses
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PRR9/PRR7 (Fig. 11a) or sucrose activates PRR5/TOC1 or ELF4/LUX (Fig. 11c, d).
4. Discussion
Our analyses of the realistic gene-regulatory network model (the DC2016 model)
demonstrated that target genes of sugar signals could be PRR5/TOC1, ELF4/LUX, and
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PRR9/PRR7. We predicted that either sugar-induced down-regulation of PRR9/PRR7
mRNA (Fig. 3f; Fig. 5c–e; Fig. 7b) or up-regulation of PRR5/TOC1 (Fig. 3c; Fig. 5f, g;
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Fig. 7c) or ELF4/LUX (Fig. 3d; Fig. 5h–j; Fig. 7d) mRNA is necessary to induce phase
advance consistently in the subjective morning. The following four regulatory
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relationships realized not only phase-advancing effect in the subjective morning but also
the period-shortening effect in the presence of sucrose; activation of mRNA degradation
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or direct repression of gene expression of PRR9/PRR7, or indirect activation of
PRR5/TOC1 or ELF4/LUX through down-regulation of CCA1/LHY protein. In the
latter three, PRCs contained a similar dead-zone (Fig. 3f; Fig. 5f, h) to that in the
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experimentally derived PRCs (Fig. 1). Among these possibilities, the regulation of
PRR9/PRR7 by sucrose is of great interest because of rich experimental data. Haydon et
al. (2013) showed that photosynthetically derived sugars decrease transcript levels of
PRR7 and PRR5 and does not affect PRR9. The prr7-11 mutant is deficient in the clear
phase response to sugars (Haydon et al., 2013). These results suggest that suppression
of PRR7 would be sufficient to realize phase advance in the subjective morning.
The timing of expression of PRR7 might make it suited to regulation by metabolic
signals such as sugars. PRR7 expression peaks in the middle of the photoperiod and as
14
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such its timing is not locked as rigidly to the transitions of the external light-dark cycle
as some other oscillator components. The timings of expression of CCA1 and LHY are
tightly locked to dawn, whereas the timing of TOC1 is associated with dusk. Therefore,
unlike CCA1, LHY and TOC1 the timing of PRR7 expression might be more plastic,
suited to regulation by sugar signals, which in part are associated with photosynthesis in
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the photoperiod.
The contribution of the evening components to the circadian clock response to sugars
have not been empirically investigated partly because mutations of LUX (Hazen et al.,
2005; Onai and Ishiura, 2005), ELF4 (Doyle et al., 2002; McWatters et al., 2007), and
another member of the evening complex ELF3 (Hicks et al., 1996; Covington et al.,
2001; Thines and Harmon, 2010) cause arrhythmic or very weak circadian oscillation in
AN
US
continuous light or dark condition. Therefore, it is difficult to examine whether they are
target for sugar signals by measuring e.g. phase shifts of the mutant clock in response to
sucrose pulse in the constant light condition.
Among the potential regulatory-relationships between circadian clock genes and sucrose,
down-regulation of PRR9/PRR7 might have an advantage for plant growth. It has been
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experimentally suggested that PRR7 and 5 (Nakamichi et al., 2012; Liu et al., 2013) and
the evening complex (Nusinow et al., 2011) repress the expression of PHYTOCHROME
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INTERACTING FACTOR4 (PIF4) and PIF5, both of which encode the basic helix–
loop–helix transcription factor that is essential for hypocotyl elongation growth in A.
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thaliana seedlings. Because sucrose pulse in the phase-response-curve experiments
transiently increases carbon availability for A. thaliana seedlings, sucrose-induced
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down-regulation of PRR7 followed by increased expressions of PIF4 and PIF5 (Liu et
al., 2011) would be advantageous for effective usage of excess carbon and facilitating
plant growth.
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In conclusion, we have theoretically elucidated the regulatory mechanisms by which
endogenous sugar signals regulate the plant circadian oscillator. Although the previous
theoretical studies have revealed the importance of the dynamical feedback from
sucrose to the plant circadian clock for flexible regulation of carbon metabolism and
optimization of sink growth (Feugier and Satake, 2013; Seki et al., 2017; Ohara and
Satake, 2017), how the circadian phase is shifted in response to sucrose has been elusive
due to the lack of a comprehensive study using computational approaches. The current
study using the clock-gene regulatory network models elucidated possible regulatory
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relationships between oscillator genes and sucrose stimuli that induce significant phase
advance during the subjective morning. Our computational approaches can be applied to
investigate how sugar signaling works at a whole plant scale to realize carbon
homeostasis. A previous experimental study has suggested that the circadian oscillator
in A. thaliana roots have distinct network structure from that in shoots, and can be
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entrained by photosynthetic sugars transported from the source leaf (James et al., 2008).
Although the effects of sugar signals on carbon homeostasis have been examined
mainly in the photosynthetic leaves (Seki et al., 2017), it would be possible that the
translocated sucrose also affects homeostatic regulation of carbon metabolism in roots.
The circadian clock model with the modified network structure will predict how the
phase of the root clock can be shifted by the sucrose stimulus. This knowledge will be
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incorporated into the previous model describing sucrose translocation from the source to
sink (Ohara and Satake, 2017) in order to explicitly formalize the circadian-phase
regulation by sugar in roots. Such extended model will be useful to investigate the
impact of the circadian entrainment by sugar signaling at a whole plant scale.
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Acknowledgments
TO was supported by Grant-in-Aid for JSPS Fellows Number 16J04492. AS was funded
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by JSPS KAKENHI (JP17H06478). TJH and AARW were supported by BBSRC grant
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Fig. 1. Phase response curves for sucrose pulses experimentally observed in
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Arabidopsis thaliana. Data from (a) Haydon et al. (2013) and (b) Seki et al. (2017).
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Fig. 2. Circadian clock-gene network structures of the (a) DC2016 and (b) EALR
models. The DC2016 model includes a positive-negative feedback loop consisting of
CCA1/LHY (activator) and PRR9/PRR7 (repressor) and a negative-negative feedback
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loop between CCA1/LHY (repressor) and PRR5/TOC1 (repressor).
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Suc
1.0
b
I
A
= 0.0889
0.5
1
0.0
Strong
Moderate
Weak
- 1.0
- 1.5
- 2.0
2
4
6
8
10
12
14
16
0
-1
18
20
22
-2
24
0.0
0
-1
- 1.0
12
14
16
18
20
22
24
E
L
F
4
/
L
U
X
AN
US
I
A
= 0.9357
-3
-4
2
4
6
8
10
12
14
16
18
20
22
24
C
C
A
1
/
L
H
Y
Suc
2
4
6
8
10
f
I
A
= 0.2365
2
12
14
16
18
20
22
24
P
R
R
9
/
P
R
R
7
Suc
I
A
= 0.9984
2
M
1
1
0
0
-1
ED
Phase shift (h)
10
-2
I
A
= 0.9756
- 2.0
-2
2
4
6
8
10
Suc
12
14
16
18
20
22
-1
4
6
8
10
12
14
16
18
20
22
24
E
L
F
4
/
L
U
X
I
A
= 0.0099
CE
3
2
0.2
1
0.0
0
- 0.2
-1
AC
4
Suc
h
0.4
- 0.4
2
2
P
R
R
5
/
T
O
C
1
I
A
= 0.0021
0.6
-2
24
PT
0.8
Phase shift (h)
8
1
- 0.5
g
6
Suc
0.5
3
4
d2
1.0
- 1.5
2
P
R
R
5
/
T
O
C
1
Suc
c
Phase shift (h)
I
A
= 0.0196
2
- 0.5
e
P
R
R
9
/
P
R
R
7
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Phase shift (h)
a
Suc
C
C
A
1
/
L
H
Y
-2
4
6
8
10
12
14
16
18
20
22
24
2
Phase of pulse (h)
4
6
8
10
12
14
16
18
20
22
24
Phase of pulse (h)
Fig. 3. Phase response curves simulated by the DC2016 model. Circadian clock gene
expression is directly (a)–(d) activated or (e)–(h) repressed by sucrose stimulus. Target
genes are (a), (e) CCA1/LHY, (b), (f) PRR9/PRR7, (c), (g) PRR5/TOC1, and (d), (h)
ELF4/LUX. Different colors correspond to different stimulation strengths. The values of
Spulse for strong and weak stimulations are the double and half of that for moderate
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stimulation, respectively (Table 1). Illustrations above the PRCs display the stimulation
schemes where rectangles represent the clock genes and solid lines with arrows and bars
represent activation and repression effects, respectively. The values of IA calculated for
moderate stimulation are shown. Stars indicate the conditions that yield phase advance
AC
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PT
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M
AN
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in most part of the subjective morning.
23
Suc
4
C
C
A
1
/
L
H
Y
Suc
3
P
R
R
9
/
P
R
R
7
Suc
2
P
R
R
5
/
T
O
C
1
Suc
E
L
F
4
/
L
U
X
1
21
22
23
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24
25
26
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Free-running period (h)
Fig. 4. Free-running period in the case that sucrose directly activates (red) or represses
(blue) oscillator gene expression. The period in the absence of the effect of sucrose is
also represented (black). Stars indicate the conditions under which the period is
AC
CE
PT
ED
M
shortened. The values of Spulse are listed in Table 1.
24
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PT
ED
M
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Fig. 5. Circadian clock gene expression influenced by sucrose though up- (red) or
down-regulation (blue) of the activity of circadian clock proteins in the DC2016 model.
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(a), (b) CCA1/LHY expression is influenced through the regulation of (a) PRR9/PRR7
or (b) PRR5/TOC1. (c)–(e) PRR9/PRR7 expression is influenced through the regulation
of (c) CCA1/LHY, (d) PRR5/TOC1, or (e) ELF4/LUX. (f), (g) PRR5/TOC1 expression
is influenced through the regulation of (f) CCA1/LHY or (g) PRR5/TOC1. (h)–(j)
ELF4/LUX expression is influenced through the regulation of (h) CCA1/LHY, (i)
PRR5/TOC1, or (j) ELF4/LUX. Illustrations above the PRCs display the stimulation
schemes where rectangles and ellipses represent the clock genes and proteins,
respectively, and solid lines with arrows and bars represent activation and repression
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effects, respectively. Stars indicate the conditions that yield phase advance in most part
AC
CE
PT
ED
M
AN
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of the subjective morning. The values of Spulse and S* are listed in Table 1.
26
C
C
A
1
/
10
L
H
Y
Suc
PRR9/
PRR7
C
C
A
1
/
9
L
H
Y
Suc
CCA1/
LHY
P
R
R
9
/
8
P
R
R
7
Suc
PRR5/
TOC1
P
R
R
9
/
7
P
R
R
7
Suc
ELF4/
LUX
P
R
R
9
/
6
P
R
R
7
Suc
CCA1/
LHY
P
R
R
5
/
5
T
O
C
1
Suc
PRR5/
TOC1
P
R
R
5
/
4
T
O
C
1
Suc
CCA1/
LHY
E
L
F
4
/3
L
U
X
Suc
PRR5/
TOC1
E
L
F
4
/2
L
U
X
Suc
ELF4/
LUX
E
L
F
4
/1
L
U
X
AN
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PRR9/
PRR7
ED
M
Suc
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22
23
24
25
Free-running period (h)
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Fig. 6. Free-running period in the case that sucrose up- (red), or down-regulates (blue)
the activity of circadian clock proteins. The period in the absence of the effect of
sucrose is also represented (black). Stars indicate the conditions under which the period
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is shortened. The values of Spulse are listed in Table 1.
27
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ED
Fig. 7. Sucrose affects degradation of mRNA in the DC2016 model. The mRNA
degradation of (a) CCA1/LHY, (b) PRR9/PRR7, (c) PRR5/TOC1, and (d) ELF4/LUX
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are activated (red) or repressed (blue). Illustrations above the PRCs display the
stimulation schemes where diamonds represent mRNA. Stars indicate the conditions
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that yield phase advance in most part of the subjective morning. The values of Spulse are
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listed in Table 1.
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Suc
C
C
A
1
/
L
H
Y
4
Degradation
Suc
P
R
R
9
/
P
R
R
7
Degradation
3
P
R
R
5
/
T
O
C
1
Degradation
2
Suc
E
L
F
4
/
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U
X
1
Degradation
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Suc
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25
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Free-running period (h)
Fig. 8. Free-running period in the case that sucrose activates (red) or represses (blue)
mRNA degradation. The period in the absence of the effect of sucrose is also
represented (black). Stars indicate the conditions under which the period is shortened.
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The values of Spulse are listed in Table 1.
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PT
Fig. 9. Phase shifts obtained by sucrose pulse added during (a)–(c) the subjective
morning (white background) and (d)–(f) the subjective night (gray background) in the
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EALR model. LR expression is directly repressed by the pulse. (a), (d) Time series of
LR mRNA concentration. (b), (e) Time series of EA mRNA concentration. Two vertical
dashed lines represent the onset and offset of the 3-h sucrose pulse. Subjective dawn
AC
corresponds to the peak mRNA timing of LR. (c), (f) Limit cycles in phase planes, the
coordinates of which indicate the LR and EA mRNA concentrations. Arrows represent
the direction of rotation. Flashes and thick lines on the limit cycles represent the onset
and the 3-h period of sucrose stimulations, respectively. Black circles and squares
represent the subjective dawn and dusk, respectively.
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Fig. 10. Phase response curves simulated by the EALR model. (a) LR and (b) EA
AC
expressions are directly activated (red) or repressed (blue) by the sucrose pulse. (c) LR
and (d) EA expressions are influenced through up- (red) or down-regulation (blue) of
EA and LR proteins, respectively. (e) LR and (f) EA mRNA degradations are activated
(red) or repressed (blue). Illustrations above the PRCs display the stimulation schemes
where rectangles, ellipses, and diamonds represent the clock gene, protein, and mRNA
respectively. Stars indicate the conditions that yield phase advance in most part of the
subjective morning. The values of Spulse and S* are listed in Table 1.
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Fig. 11. Limit cycles in phase planes, the coordinates of which indicate the PRR9/PRR7
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and CCA1/LHY mRNA concentrations in the DC2016 model. (a), (b) Sucrose represses
PRR9/PRR7 expression. (c) Sucrose activates PRR5/TOC1 expression. (d) Sucrose
activates ELF4/LUX expression. Sucrose pulse was added during (a), (c), (d) the
subjective morning and (b) the subjective night. Details are as in the legend to Fig. 9.
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Table 1. Summary of the values used for Spulse and S*.
S*
Spulse
# of Figure
Value
# of Figure
Value
3a–d
1.0 (Moderate)
5
0.5 (Up-regulation)
2.0 (Strong)
2.0 (Down-regulation)
3e–h
8 (Moderate)
10c, d
16 (Strong)
1.0 (Activation)
2.0 (Up-regulation)
0.2 (Down-regulation)
6
1.4 (Up-regulation)
0.6 (Down-regulation)
1.2 (Activation)
0.8 (Repression)
1.2 (Activation)
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8
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7
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1.0 (Repression)
5
0.8 (Repression)
10a, b
0.1 (Activation)
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0.2 (Repression)
10c, d
1.4 (Up-regulation)
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1.0 (Down-regulation)
10e, f
1.14 (Activation)
AC
0.80 (Repression)
A.1a–d
1
A.1e–h
8
0.95 (Up-regulation)
1.50 (Down-regulation)
4 (Weak)
4
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0.5 (Weak)
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Appendix A. Formalization of the effects of sucrose in the EALR model
Here we describe the formalization of the effects of sucrose on the circadian oscillator
based on the EALR model.
Case (1): Sucrose directly affects circadian oscillator gene expression
If LR or EA is the target of sucrose that activates the gene expression, mRNA dynamics
[]

 ∗[]

 ∗[]
= 1 ∗ [] ∗  + 1+[] + () −  1+[] ,
1

1
[]
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become;
 ∗
(A.1)

 ∗[]
2 2
4

= +[]
 + () −  +[] .
4

2
(A.2)

[]

 ∗[]

1
 ∗[]
= (1 ∗ [] ∗  + 1+[] ) ∗ 1+() −  1+[] ,
 ∗
1
1

1
[]
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When sucrose represses the gene expression, mRNA dynamics become;
 ∗[]
2 2
4

= +[]
 ∗ 1+() −  +[] .
2
4



(A.3)
(A.4)
There are four situations to examine because two regulatory relationships (active or
M
repressive) are possible between sucrose and each of two clock components (Fig. 10a,
b).
ED
Case (2): Sucrose indirectly affects oscillator gene expression through modulation
of clock protein activity
PT
If sucrose affects LR expression through the interaction with EA protein, mRNA
dynamics become;

 ∗()∗[]
 ∗[]
= 1 ∗ [] ∗  + 1+()∗[] −  1+[] .
CE
[]

1
1

(A.5)
If sucrose affects EA expression through the interaction with LR protein, mRNA
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dynamics become;
[]

 ∗
 ∗[]
2 2
4

= +()∗[]
 −  +[] .
2

4
(A.6)

There are four situations to examine because two regulatory relationships (up- or
down-regulation) are possible between sucrose and each of two clock proteins (Fig. 10c,
d).
Case (3): Sucrose affects mRNA stability
If sucrose affects mRNA degradation of LR or EA, mRNA dynamics become;
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[]

 ∗[]
∗
1

1
[]

 ∗[]
= 1 ∗ [] ∗  + 1+[] − () ∗  1+[] ,
(A.7)

 ∗[]
2 2
4

= +[]
 − () ∗  +[] .
2
4

(A.8)

There are four situations to examine because two regulatory relationships (active or
CR
IP
T
repressive) are possible between sucrose and mRNA degradation for each of two clock
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components (Fig. 10e, f).
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Fig. A.1. Phase response curves simulated by the DC2016 model for various pulse
durations. Circadian clock gene expression is directly (a)–(d) activated or (e)–(h)
repressed by sucrose stimulus. Target genes are (a), (e) CCA1/LHY, (b), (f) PRR9/PRR7,
(c), (g) PRR5/TOC1, and (d), (h) ELF4/LUX. Different colors correspond to different
pulse durations. The values of Spulse are listed in Table 1.
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Fig. A.2. Limit cycles in phase planes for various combinations of a target circadian
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clock gene of sucrose and its regulatory property. (a) LR expression is directly activated.
(b) LR expression is indirectly repressed through down-regulation of the EA protein. (c)
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LR mRNA degradation is activated. (d) EA expression is directly repressed. Details are
AC
CE
as in the legend to Fig. 9.
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Fig. A.3. Limit cycles in various phase planes in the DC2016 model. (a), (b) The
coordinates indicate the PRR9/PRR7 and PRR5/TOC1 mRNA concentrations. (c), (d)
The coordinates indicate the PRR9/PRR7 and ELF4/LUX mRNA concentrations.
Sucrose pulse that represses PRR9/PRR7 expression was added during (a), (c) the
subjective morning and (b), (d) the subjective night. Details are as in the legend to Fig.
9.
38
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