Identification of a metabolic bottleneck for cold acclimation in Arabidopsis thaliana

Identification of a metabolic bottleneck for cold acclimation inArabidopsis thaliana

Thomas Nagele†, Simon Stutz†,*, Imke I. Hormiller and Arnd G. Heyer

Institute of Biology, Department of Plant Biotechnology, University of Stuttgart, D-70569 Stuttgart, Germany

Received 9 January 2012; revised 11 May 2012; accepted 23 May 2012.

*For correspondence (e-mail [email protected]).†These authors contributed equally to this work.

SUMMARY

Central carbohydrate metabolism of Arabidopsis thaliana is known to play a crucial role during cold

acclimation and the acquisition of freezing tolerance. During cold exposure, many carbohydrates accumulate

and a new metabolic homeostasis evolves. In the present study, we analyse the diurnal dynamics of

carbohydrate homeostasis before and after cold exposure in three natural accessions showing distinct cold

acclimation capacity. Diurnal dynamics of soluble carbohydrates were found to be significantly different in

cold-sensitive and cold-tolerant accessions. Although experimentally determined maximum turnover rates for

sucrose phosphate synthase in cold-acclimated leaves were higher for cold-tolerant accessions, model

simulations of diurnal carbohydrate dynamics revealed similar fluxes. This implied a significantly higher

capacity for sucrose synthesis in cold-tolerant than cold-sensitive accessions. Based on this implication

resulting from mathematical model simulation, a critical temperature for sucrose synthesis was calculated

using the Arrhenius equation and experimentally validated in the cold-sensitive accession C24. At the critical

temperature suggested by model simulation, an imbalance in photosynthetic carbon fixation ultimately

resulting in oxidative stress was observed. It is therefore concluded that metabolic capacities at least in part

determine the ability of accessions of Arabidopsis thaliana to cope with changes in environmental conditions.

Keywords: Arabidopsis thaliana, carbohydrate metabolism, cold acclimation, mathematical modeling,

sucrose synthesis.

INTRODUCTION

As sessile organisms, plants have to adapt to environmental

changes that affect their performance, growth and distribu-

tion. Low temperature plays a key role in this context, and

thus has a great impact on crop productivity (Janska et al.,

2010).

Upon exposure to low non-freezing temperatures, Arabi-

dopsis thaliana, like many other plants, is able to increase its

freezing tolerance during a complex process termed cold

acclimation. Low temperature influences enzyme-catalysed

reactions via thermodynamic effects, slows down transport

processes across membranes through reduction of mem-

brane fluidity, and influences various other cellular events.

As a consequence, cold acclimation incorporates numerous

physiological and biochemical changes (Xin and Browse,

2000; Stitt and Hurry, 2002), and the reorganization of

cellular metabolism affects gene expression, protein com-

position and membrane structure as well as the metabolite

profile (Gilmour et al., 2000; Kaplan et al., 2007).

In several studies, it has been shown that acquisition of

freezing tolerance is closely linked to changes in the

regulation of primary carbohydrate metabolism (Guy et al.,

1992; Sasaki et al., 2001; Klotke et al., 2004). During devel-

opment of A. thaliana leaves in the cold, re-direction of

newly fixed carbon towards sucrose synthesis rather than

starch accumulation was observed (Strand et al., 1997,

1999), and the resulting higher content of sucrose in cold-

acclimated leaves has also been found in various other

plants. Sucrose may play a direct role as a cryoprotectant of

membranes or more indirectly as a substrate for other

cryoprotectants such as raffinose, which was shown to

protect the photosynthetic machinery from freezing damage

(Knaupp et al., 2011). Because of the complex nature of cold

acclimation, a simple correlation between development of

freezing tolerance and changes in metabolism cannot be

expected (Hannah et al., 2006). Multigenic traits such as cold

acclimation thus cannot be explained intuitively based on

ª 2012 The Authors 1The Plant Journal ª 2012 Blackwell Publishing Ltd

The Plant Journal (2012) doi: 10.1111/j.1365-313X.2012.05064.x

changes in concentrations of a single or only a few

metabolites.

In this context, systems biology offers the possibility of

investigating interactions among components of complex

biological networks, and helps in elucidating the underlying

regulatory mechanisms (Yuan et al., 2008). To study meta-

bolic pathways, representation of enzyme-catalysed reac-

tions by ordinary differential equations has proved to be a

versatile tool. In a system of equations representing a

metabolic pathway, incorporation of experimentally deter-

mined concentrations of metabolites and enzyme para-

meters can be used not only to validate the model but also to

predict the effects that modifications of enzymatic parame-

ters would have on metabolism (Nagele et al., 2010).

In the present study, the behaviour of three accessions of

A. thaliana during exposure to low temperatures was

examined. Low temperatures have direct thermodynamic

effects on metabolism on the one hand, but on the other

hand they also trigger cold acclimation. The acclimation

capacity of European accessions of Arabidopsis was dem-

onstrated to correlate with minimum habitat temperatures

(Hannah et al., 2006). Therefore, we used accessions varying

in acclimation capacity in order to allow separation of

thermodynamic from acclimation effects. To analyse tem-

perature effects on metabolic regulation, a simplified model

of primary carbohydrate metabolism was constructed,

comprising interconversions of the most abundant soluble

sugars in mesophyll cells (Figure 1). Identification of kinetic

parameters for metabolic reactions of primary carbohydrate

metabolism was based on metabolite concentrations

recorded over complete diurnal cycles. Model simulations

revealed significant differences in the capacity for sucrose

and raffinose synthesis during cold acclimation. Sucrose

synthesis was found to be a metabolic bottleneck under

challenging environmental conditions.

RESULTS

Net carbon uptake and enzyme activities of central

metabolite interconversions

Rates of net photosynthesis were recorded for the three

Arabidopsis accessions C24, Col and Rsch over a complete

diurnal cycle before and after cold acclimation (Figure 2).

Mean rates of CO2 exchange of non-acclimated plants were

recorded at 22�C in a greenhouse with natural light supple-

mented to a minimum of 80 lmol photons m)2 sec)1. The

accessions showed similar diurnal dynamics, with a steep

increase in CO2 assimilation during the first 3–5 h of the light

phase, followed by a decline in the afternoon and a constant

nocturnal rate of respiration. Rates of net photosynthesis of

cold-acclimated plants were determined at 4�C in a growth

chamber with a light intensity of 50 lmol pho-

tons m)2 sec)1. A steep increase of CO2 fixation during the

first hour of the light phase was followed by a plateau at

25–35 lmol CO2 h)1 g FW)1 until the end of the light period.

Dark respiration at 4�C was significantly decreased in all

accessions when compared to greenhouse plants (P < 0.05).

C24 displayed the highest dark respiration rate (5.7 �0.5 lmol CO2 h)1 g FW)1), followed by Rsch (4.8 �0.4 lmol CO2 h)1 g FW)1) and Col (4.4 � 0.1 lmol

CO2 h)1 g FW)1).

Enzyme activities catalysing central metabolite intercon-

versions in sucrose and raffinose metabolism were deter-

mined every 4 h over a diurnal cycle starting at 06:00

(Figure 3). Activities were determined for non-acclimated

and cold-acclimated plants. To enable simulation of bio-

chemical reactions at 4�C, enzyme activities of cold-accli-

mated plants were determined at 4�C. For non-acclimated

plants, sucrose phosphate synthase (SPS), catalysing the

synthesis of sucrose-6-phosphate from UDP-glucose and

fructose-6-phosphate, showed an increase during the first

4 h in the light, a plateau during the afternoon and a slight

decrease during the night in all three accessions (Figure 3a–

c). Peak values of approximately 75 lmol fructose-6-phos-

phate h)1 g FW)1 were reached in Col between 10:00 and

14:00. At 4�C, SPS activities were significantly decreased. Col

showed a significantly higher SPS activity than C24 during

almost the entire diurnal cycle, while SPS activity in Rsch

was significantly higher than in C24 at all time points.

Hydrolytic sucrose cleavage in leaves is catalysed by differ-

ent isoforms of invertase with neutral or acidic pH optima.

As all contribute to sucrose cleavage, the sum of neutral,

acid vacuolar and cell wall-bound acid invertase activity was

determined (Figure 3d–f). C24 showed a mean invertase

activity of approximately 300 lmol sucrose h)1 g FW)1,

while Col and Rsch displayed invertase activities of

200 lmol sucrose h)1 g FW)1. At 4�C, invertase activity

was significantly higher in C24 when compared to Col and

Figure 1. Reaction network of the primary carbohydrate metabolism in leaves

of Arabidopsis thaliana.

Reaction rates (r) represent central enzymatic steps of carbon assimilation,

metabolite interconversion and carbon export.

2 Thomas Nagele et al.

ª 2012 The AuthorsThe Plant Journal ª 2012 Blackwell Publishing Ltd, The Plant Journal, (2012), doi: 10.1111/j.1365-313X.2012.05064.x

Rsch (P < 0.05). The hexose phosphorylation capacity was

determined by measuring activities of glucokinase and

fructokinase (Figure 3g–l). In non-acclimated plants, hexoki-

nase activities in Col and Rsch increased during the first 8 h

of the light phase and declined until 02:00, while activities in

C24 were not significantly altered during the diurnal cycle. At

4�C, activities in C24, Col and Rsch decreased to 30–50% and

showed a slight dampening of diurnal dynamics. In addition

to these central enzyme activities of sucrose metabolism,

raffinose metabolism was characterized by measuring

activities of raffinose synthase and melibiase, which cleaves

off the galactosyl unit from either raffinose or melibiose, i.e.

before or after removal of the fructose by invertase. These

activities showed very low dynamics and were at least

tenfold lower when compared to other enzymes of sucrose

metabolism (Figure 3m–r). Activities were similar for all

accessions before acclimation, reaching values of 0.05–

0.1 lmol sucrose h)1 g FW)1 for raffinose synthase and 0.2–

0.3 lmol melibiose h)1 g FW)1 for melibiase, respectively.

Melibiase activities further decreased at 4�C to 0.01–

0.025 lmol melibiose h)1 g FW)1. Raffinose synthase

activity in Rsch at 4�C was higher than in C24 and Col,

reaching peak values of 0.05–0.075 lmol sucrose h)1 g FW)1

between 10:00 and 14:00, but did not significantly differ from

C24 and Col over the whole diurnal cycle.

Diurnal metabolite dynamics

In contrast to a mathematical model developed for non-

acclimated Col plants that focussed on sucrose metabolism

(Nagele et al., 2010), the model presented here also

accounts for raffinose metabolism in leaves of Arabidopsis

starting from galactinol, which is the first metabolite exclu-

sively dedicated to raffinose synthesis and is easy to mea-

sure. This model extension is indispensable for modelling

carbohydrate metabolism during cold exposure, because

raffinose plays an important role in the metabolic cold

response of Arabidopsis thaliana (Klotke et al., 2004; Kaplan

et al., 2007; Knaupp et al., 2011). Thus, the extended model

comprises ten ordinary differential equations describing

time-dependent changes of central metabolites (Figure 1).

Except for synthesis and degradation of starch, all metabo-

lite interconversions were described using the Michaelis–

Menten equation that represents the dominating rate law in

biochemical networks. Raffinose synthesis, catalysed by

raffinose synthase, was modelled using a bi-substrate

kinetic including concentrations of sucrose and galactinol

(Kaplan et al., 2007). The rate of raffinose degradation was

determined by allowing two alternative reactions, both

involving invertase and melibiase but with different

sequential arrangement (Kaplan et al., 2007). Rates of

sucrose synthesis, sucrose degradation and hexose phos-

phorylation were assumed to follow the kinetics of the rate-

limiting enzymes sucrose phosphate synthase, invertase

and glucokinase/fructokinase, respectively (Sturm, 1999;

Strand et al., 2003; Claeyssen and Rivoal, 2007). Experi-

mentally determined Vmax values for these enzymes were

used to constrain identification of kinetic parameter sets,

which were determined by a process of parameter identifi-

cation based on diurnal metabolite data (Tables S1–S6). The

calculated sets of kinetic parameters and a starting concen-

tration of each of the considered metabolites, pre-set to the

experimentaly determined concentrations at timepoint 6:00,

were then used to simulate entire diurnal dynamics of

metabolite concentrations. This simulation yielded virtual

µmol

CO

2h–1

gFW

–1µm

olC

O2

h–1gF

W–1

µmol

CO

2h–1

gFW

–1

Time

C24(a)

(b)

(c)

06:00 10:00 14:00 18:00 22:00 02:00 06:00–40

–20

0

20

40

60

80

100

120

140

Time

Col

06:00 10:00 14:00 18:00 22:00 02:00 06:00–40

–20

–40

–20

0

20

40

60

80

100

120

140

Time

Rsch

06:00 10:00 14:00 18:00 22:00 02:00 06:00

0

20

40

60

80

100

120

140

Figure 2. Rates of net photosynthesis.

Net carbon uptake was recorded for non-acclimated (grey) and cold-

acclimated (black) plants of the Arabidopsis accessions C24 (a), Col (b) and

Rsch (c). Day/night transitions are indicated by the bars at the top. Solid lines

represent means of three measurements � SD. Day/night transitions are

indicated by the bars at the top.

A metabolic bottleneck for cold acclimation 3


metabolite concentration courses that remained within the

standard deviations for most of the experimentally deter-

mined concentrations (Figures 4 and 5).

Diurnal dynamics and concentrations of hexose phos-

phates were successfully described by the model for all

accessions, and were found to be similar in non-acclimated

and cold-acclimated plants (Figure 4a–c). In contrast to

hexose phosphates, sucrose content increased significantly

in cold-acclimated plants, and simulations as well as exper-

imental data showed elevated levels of sucrose in Rsch and

Col compared to C24 (Figure 4d–f). Like sucrose, concentra-

tions of glucose and fructose were significantly increased in

all accessions after cold acclimation (Figure 4g–l). Mean

levels of hexoses were highest in Rsch (glucose, approxi-

mately 12.5 lmol g FW)1; fructose, approximately 8 lmol

g FW)1) followed by Col (glucose, approximately 7.5 lmol

g FW)1; fructose, approximately 2.5 lmol g FW)1) and C24

(glucose, approximately 2.5 lmol g FW)1; fructose, approx-

imately 1.5 lmol g FW)1).

Levels of starch were significantly elevated during the

light phase, reaching peak mean values of 50–60 lmol

C6 g FW)1 in cold-acclimated Rsch (Figure 4m–o). During

the night, starch levels decreased to basal levels of

5–10 lmol C6 g FW)1 in both non-acclimated and cold-

acclimated plants. As an immediate product of photosyn-

thesis, transitory leaf starch is only synthesized during the

light phase and degraded during the subsequent night to

sustain respiration and nocturnal carbohydrate metabolism.

As this is a stand-alone bi-directional pathway, we did not

perform kinetic modelling of starch metabolism, and instead

calculated rates of synthesis (06:00–22:00) and degradation

(22:00–06:00) to match the experimentally determined starch

levels. Because dark respiration was reduced in cold-accli-

mating leaves at 4�C, an accumulation of starch would have

µmol

Frc

–6–P

hgF

W–1

–1µm

olS

ucro

seh

gFW

–1–1

µmol

Glu

cose

hgF

W–1

–1µm

olF

ruct

ose

hgF

W–1

–1µm

olS

ucro

seh

gFW

–1–1

µmol

Mel

ibio

seh

gFW

–1–1

Sucrose Phosphate Synthase

Invertase

Glucokinase

Fructokinase

Raffinose Synthase

Melibiase

C24 Col Rsch

0

20

40

60

80

100

(a)

0

2

4

5

1

3

(g)

0

2

4

65

3

1

(j)

0

0.05

0.1

0.15

0.2

0.25

(m)

(h)

(k)

(e)

(q)

(n)

(b)

0

200

400

600(d) (f)

(i)

(l)

(r)

(o)

(c)

00.10.20.30.40.5 (p)

06:00 14:00 22:00 06:00Time

06:00 14:00 22:00 06:00Time

06:00 14:00 22:00 06:00Time

Figure 3. Diurnal dynamics of central enzyme

activities.

Maximum enzyme activities were experimentally

determined for non-acclimated plants (green

error bars; n > 3) and for cold-acclimated plants

at 4�C (blue error bars; n > 3): sucrose phosphate

synthase (a–c), invertase (d–f), glucokinase (g–i),

fructokinase (j–l), raffinose synthase (m–o),

melibiase (p–r). Green and blue crosses inter-

linked by dashed lines represent the enzyme

activities that yielded the best simulation result

for metabolite dynamics in non-acclimated and

cold-acclimated plants. Maximum invertase

activity was used to simulate degradation of

sucrose and raffinose (d–f). Green (22�C) and

blue (4�C) error bars represent experimentally

determined maximum activities. Dashed lines

interlinking green crosses (22�C, sucrose degra-

dation) and blue crosses (4�C, sucrose degrada-

tion) yielded the best simulation result for

metabolite dynamics. Orange crosses (22�C)

and pink crosses (4�C) yielded the best simula-

tion result for metabolite dynamics with respect

to raffinose degradation. Day/night transitions

are indicated by the bars at the top.



resulted at low temperature, possibly influencing soluble

sugar metabolism (Guy et al., 2008). To minimize such a

starch suppression effect, which would not have been

accessible to mathematical modelling, light intensities at

20�C and 4�C were adjusted in such a way that differences in

diurnal starch content were minimized (see Experimental

procedures). Hexose phosphates, representing the output of

the Calvin–Benson cycle, were taken as substrates of starch

synthesis, while degradation was modelled in two ways,

yielding either glucose or hexose phosphates (Zeeman

et al., 2007).

Raffinose and galactinol, which have been implicated in

cold acclimation in many studies, were significantly

increased during cold acclimation in all accessions (Fig-

ure 5a–f). Raffinose levels were highest in the cold-tolerant

accession Rsch, followed by Col and C24. Galactinol was

also most elevated in Rsch. Melibiose, resulting from

raffinose degradation by invertase, was most significantly

elevated in C24, but Col did not show an increase after cold

acclimation. Galactose produced by melibiase-driven deg-

radation of raffinose was significantly elevated after cold

acclimation in all accessions, reaching values of 0.2 lmol

g FW)1 in Rsch.

Simulated rates of metabolite interconversion

Enzymatic parameters identified in model simulations were

used to calculate metabolic flux rates of reactions in sucrose

and raffinose metabolism (Figures 6 and 7). The calculated

rate of sucrose synthesis as well as export to sink organs and

other metabolic pathways were the most dynamic fluxes in

both non-acclimated and cold-acclimated plants (Figure 6, r3

and r9). In the three accessions C24, Col and Rsch, both

fluxes significantly increased during the first 4 h of the light

phase, followed by a constant decline until the end of the

night (Figure 6a–c). In Rsch, r3 and r9 were significantly

increased between 22:00 and 02:00 before declining until the

end of the night (Figure 6c). Particularly in non-acclimated

plants, r9 became negative at the end of the night, indicating

0

5

10

15Fructose

µmol

gFW

–1

06:00 14:00 22:00 06:00Time

06:0006:00 14:00 22:00Time

Starch

06:00 14:00 22:00 06:000

20

40

60

80

100

Time

µmol

gFW

–1

0

5

10

15

20Glucose

µmol

gFW

–10

2

4

6

8

10Sucrose

µmol

gFW

–1

C24 Col

(b)

Rsch

(c)

0

0.5

1

1.5

2 (a)

(e) (f)(d)

(h) (i)(g)

(k) (l)(j)

(n) (o)(m)

Hexose phosphates

µmol

gFW

–1

Figure 4. Diurnal concentration changes in

sucrose and starch metabolism.

Concentrations of hexose phosphates (a–c), as

well as sucrose (d–f), glucose (g–i) and fructose

(j–l) were experimentally determined for Rsch,

Col and C24. Starch content was also determined

for a whole diurnal cycle (m–o). Closed circles

with error bars represent means of five measure-

ments � SD. Solid lines indicate the best simu-

lation results for metabolite concentrations for

non-acclimated (grey lines) and cold-acclimated

plants (black lines). Day/night transitions are




a flux of carbon from other metabolic pathways into soluble

sugar metabolism. Rates of sucrose cleavage (r6) showed a

significant increase during the first 8 h of the light phase,

reaching a peak of 4.5 lmol C6 h)1 g FW)1 in the second half

of the day, followed by a subsequent decline until the end of

the night (Figure 6b). In contrast to Col, such dynamics were

not observed in C24 and Rsch, which had rather constant

rates of 3 and 4 lmol C6 h)1 g FW)1, respectively, with non-

significant oscillations during the night (Figure 6a,c). In all

three accessions, the rate of sucrose cleavage exceeded

sucrose synthesis at the end of the night, and rates of

sucrose synthesis became similar to those of hexose phos-

phorylation (r7 and r8). Compared to non-acclimated plants,

fluxes of sucrose cleavage and hexose phosphorylation

were significantly decreased at 4�C (Figure 6d–f). In Col and

C24, rates of sucrose synthesis were significantly decreased

during the light phase, while nocturnal rates were similar to

those of non-acclimated plants. In Rsch, a cold-induced

significant decrease was only detectable during the first 4 h

of the day (Figure 6f).

In comparison to flux rates of sucrose metabolism, those

involved in raffinose synthesis and degradation were at least

20 times lower in non-acclimated plants and 5–10 times

lower in cold-acclimated plants (Figure 7a–f). Except for

Rsch, most fluxes were rather constant during the whole

diurnal cycle. The highest values of and most significant

changes in rates of raffinose synthesis (r4 and r10) were

observed in both non-acclimated and cold-acclimated Rsch

plants (Figure 7c,f). As indicated by simulation results, rates

of raffinose synthesis were up to 10 times higher in cold-

acclimated Rsch plants than in C24 and Col plants.

Simulation of SPS activity at freezing temperatures

To evaluate possible relationships between cold tolerance

and regulation of primary carbon metabolism, we compared

calculated flux rates for the various accessions using the

Vmax values determined for cold-acclimated plants. While

flux rates were very similar among the accessions, the pro-

portion of Vmax differed between the cold-sensitive C24

plants and the two tolerant accessions Col and Rsch in the

case of SPS, reaching extreme values of 0.5 in C24 and 0.25

in Rsch at 4�C (Figure 8a,b). Because SPS activity in photo-

synthetically active leaves represents a rate-limiting step in

carbon fixation, we thus assumed C24 to be more sensitive

towards environmental changes that either cause a reduc-

tion in SPS activity or an increase in photosynthetic input of

carbon into primary metabolism. A limitation in the capacity

of SPS to catalyse sucrose synthesis would result in accu-

mulation of phosphorylated intermediates and cause a dis-

equilibrium between primary and secondary reactions of

photosynthesis, promoting generation of reactive oxygen

species. To test this hypothesis, we first assessed the impact

C24 Col Rsch

Melibiose

0

0.4

0.8

1.2

µmol

gFW

–1

Galactinol

0

0.4

0.8

1.2

1.6

µmol

gFW

–1

06:00 14:00 22:00 06:00Time

06:0006:00 14:00 22:00Time

Galactose

µmol

gFW

–1

06:00 14:00 22:00 06:00Time

0

0.1

0.2

0.3

0.4

Raffinose

µmol

gFW

–1

0

2

4

5

3

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

1

Figure 5. Diurnal concentration changes in the

central raffinose metabolism.

Concentrations of raffinose (a–c) as well as

galactinol (d–f), melibiose (g–i) and galactose

(j–l) were determined for Rsch, Col and C24.

Closed circles with error bars represent means of

five measurements � SD. Solid lines indicate the

best simulation results for metabolite concentra-

tions for non-acclimated (grey lines) and

cold-acclimated plants (black lines). Day/night

transitions are indicated by the bars at the top.



that a change in temperature would have on the ratio of

photosynthetic input and maximum SPS activity by calcu-

lating enzyme activities at different temperatures according

to the Arrhenius equation (Figure 8c,d). The temperature at

which Vmax of SPS would become rate-limiting for carbon

fixation was found to be )3 to )5�C in C24, but not in Rsch, at a

light intensity of 50 lmol m)2 sec)1 (Figure 8c,d). As

reported by Strand et al. (2003), an increase of irradiance

from 50 to 200 lmol m)2 sec)1 should result in an increase of

CO2 uptake by approximately 25% in cold-acclimated plants.

Assuming that the increase of 25% in CO2 uptake affects the

rate of sucrose synthesis to the same extent, this would ex-

ceed the capacity of SPS in C24, but not in Rsch. Therefore, we

exposed plants to temperatures of 4�C and )4�C and light

intensities of both 50 and 200 lmol m)2 sec)1 for a period of

4 h (Figure 9). As an indicator of a redox disequilibrium that

would trigger an increase in reactive oxygen species scav-

enging activities, we determined activity of peroxidase that

catalyses the disproportionation of H2O2. Although there was

no significant difference in peroxidase activity in control

experiments at 4�C for both accessions (Figure 9a,b), a sig-

nificant elevation of peroxidase activity was detected for C24

when the irradiance was elevated at )4�C (P < 0.01; Fig-

ure 9c,d). Peroxidase activity in Rsch was not affected by

irradiance and was significantly lower at )4�C and

200 lmol m)2 sec)1 than in C24 (P < 0.01).

DISCUSSION

A mathematical model is presented that, using ordinary

differential equations, can simulate diurnal dynamics of

central carbohydrate metabolism under non-acclimating

and acclimating conditions based on identified kinetic

enzyme parameters and pre-set starting concentrations of

metabolites. The model was used to simulate diurnal

dynamics of metabolite concentrations and enzyme activi-

ties (Figures 6 and 7), and the simulations were compared

with experimental data (Figures 3–5) recorded at six time

points during a complete diurnal cycle in three accessions of

Arabidopsis that have been shown to represent different

cold-acclimation capacities (Hannah et al., 2006). Diurnal

profiles of net photosynthesis, i.e. the carbon input function

into the model, revealed a significantly higher rate of noc-

turnal leaf respiration in the cold-sensitive accession C24

compared to rates in Col and Rsch (Figure 2). Although we

found a reduction in nocturnal respiration of warm-grown

leaves during a 14-day exposure to 4�C as previously

C24 non-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:00

0

5

10

15

Time

µmol

Ch

gFW

6–1

–1

Col non-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:00

0

5

10

15

Time

µmol

Ch

gFW

6–1

–1

Rsch non-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:00

0

5

10

15

Time

µmol

Ch

gFW

6–1

–1

(a)

(b)

(c)

(d)

(e)

(f)

Rsch cold-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:00Time

µmol

Ch

gFW

6–1

–10

5

10

15

Col cold-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:00Time

µmol

Ch

gFW

6–1

–1

0

5

10

15

C24 cold-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:00Time

µmol

Ch

gFW

6–1

–1

0

5

10

15

Figure 6. Diurnal dynamics of simulated fluxes

in sucrose metabolism.

Rates of sucrose synthesis (black), sucrose cleav-

age (red), sucrose export (green) and glucose/

fructose phosphorylation (pink/blue) were deter-

mined for non-acclimated (a–c) and cold-accli-

mated plants (d–f) of C24, Col and Rsch. Closed

circles with error bars represent means of 15

simulations � SD for non-acclimated plants and

20 simulations � SD for cold-acclimated plants.

Day/night transitions are indicated by the bars at

the top.



described by Talts et al. (2004), this reduction was different

for the differentially cold-tolerant accessions. The higher

rates of leaf respiration found in the cold-sensitive C24

accession cause larger maintenance costs resulting from an

increased number of mitochondria per cell and increased

enzyme activities (Miroslavov and Kravkina, 1991; Talts

C24 non-acclimated

µmol

Ch

gFW

6–1

–1

06:00 10:00 14:00 18:00 22:00 02:00 06:000

0.05

0.1

0.15

Time

(a)

C24 cold-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:00Time

µmol

Ch

gFW

6–1

–1

Time

Col non-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:000

0.05

0.1

0.15

(b)

µmol

Ch

gFW

6–1

–1

Col cold-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:00Time

(e)µm

olC

hgF

W6

–1–1

Rsch non-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:00Time

(c)

µmol

Ch

gFW

6–1

–1

Rsch cold-acclimated

06:00 10:00 14:00 18:00 22:00 02:00 06:000

0.05

0.1

0.15

0.2

0.25

Time

(f)

µmol

Ch

gFW

6–1

–1

0

0.05

0.1

0.15

0.2

0.25

0

0.05

0.1

0.15

(d)

0

0.05

0.1

0.15

Figure 7. Diurnal dynamics of simulated fluxes

in raffinose metabolism.

Rates of raffinose synthesis (black), raffinose

degradation by melibiase (red) and invertase

(pink), galactinol synthesis (blue), melibiose

degradation (green) and galactose phosphoryla-

tion (brown) were determined for non-accli-

mated (a–c) and cold-acclimated plants (d–f) of

C24, Col and Rsch. Closed circles with error bars

represent means of 15 simulations � SD for non-

acclimated plants and 20 simulations � SD for

cold-acclimated plants. Day/night transitions are


µmol

Ch

gFW

6–1

–1

C24

Time

(a) (b)

(c) (d)

06:00 10:00 14:00 18:00 22:00 02:00 06:000

5

10

15

20

25

30

35

40

Time

Rsch

06:00 10:00 14:00 18:00 22:00 02:00 06:000

5

10

15

20

25

30

35

40

µmol

Ch

gFW

6–1

–1

T [°C] T [°C]–5 –3 –10 5 10 15

0

4

8

12

16

20

24

28

µmol

Ch

gFW

6–1

–1

–5 –3 –10 5 10 150

4

8

12

16

20

24

28

µmol

Ch

gFW

6–1

–1

Figure 8. Limitation of sucrose synthesis by SPS

activity at low temperature.

Diurnal maximum SPS activities (black error

bars) were compared to simulated rates of

sucrose synthesis (grey error bars) in cold-accli-

mated plants of C24 (a) and Rsch (b). Mean rates

of diurnal sucrose synthesis at 50/

200 lmol m)2 sec)1 (grey filled circles/black

crosses) were determined for C24 (c) and Rsch

(d). Calculated sub-zero SPS activities (black

error bars, continuous line) were compared to

reaction rates, and the temperature regime at

which SPS activity cannot compensate for su-

crose synthesis was determined for C24 (black

dotted lines). Day/night transitions are indicated

by the bars at the top.



et al., 2004). Talts et al. (2004) proposed this as a mechanism

to avoid bottlenecks at near-critical temperatures, allowing

rapid reorganization of metabolism. Although C24 was not

metabolically impaired at 4�C, it appeared to be closer to a

critical temperature than the cold-tolerant accessions. The

50% lethality temperature (LT50) for C24 is only 10�C below

the treatment temperature, compared with 15�C for Rsch

(Hannah et al., 2006), which may explain the differences in

nocturnal leaf respiration rates recorded at 4�C.

Mathematical modelling and simulation of diurnal meta-

bolite dynamics represents an attractive tool for identifica-

tion of metabolic bottlenecks resulting from temperature

constrains on enzymatic turnover rates, because modelling

allows a comprehensive estimation of metabolite fluxes that

cannot be determined based on metabolite concentrations

when cycling and/or redundant pathways are involved.

Using modelling, it is possible to compare maximum

enzyme activities, which can be assessed experimentally in

a statistically robust manner, with rates of metabolite

interconversion, which are difficult to determine experimen-

tally. To identify steps in central carbohydrate metabolism

that may create bottlenecks at low temperatures, we calcu-

lated metabolic flux rates based on kinetic parameters

identified in the model simulation, and compared these flux

rates with activities of rate-limiting enzymes involved in

carbohydrate metabolism. Enzyme activities catalysing hex-

ose phosphorylation and raffinose degradation displayed

similar diurnal profiles in all three accessions. Significant

differences occurred for SPS, invertase and raffinose syn-

thase. At 4�C, the capacity for raffinose synthesis was

highest in Rsch, showing up to tenfold higher rates than

C24, and was intermediate in Col (Figure 3). Although

raffinose does not appear to contribute to protection of the

plasma membrane during freeze–thaw cycles (Zuther et al.,

2004), stabilization of the photosynthetic machinery has

been shown to play a physiological role in cold tolerance

(Knaupp et al., 2011). It has been demonstrated that, under

various abiotic stress conditions, raffinose synthesis is

stimulated by an elevation of galactinol synthase activity,

which provides the substrate for raffinose synthase (Taji

et al., 2002). Indeed, concentrations of the precursors

sucrose and galactinol were elevated in Rsch, and, under

conditions of low raffinose synthase activity, high substrate

concentrations may bring about raffinose accumulation via

high saturation of the enzyme.

Over-expression of SPS, which catalyses the rate-limiting

step of sucrose synthesis in leaves of Arabidopsis, was

demonstrated to increase freezing tolerance in the accession

Columbia (Strand et al., 2003). Consistently, we found that

differences in SPS activity contribute to the differential cold

tolerance of natural accessions of Arabidopsis, with the

cold-tolerant accession Rsch having significantly elevated

SPS activity during the entire diurnal cycle compared to C24

at 4�C (Figure 8). However, in contrast to SPS enzyme

activities, flux rates of sucrose synthesis calculated on the

basis of model simulations did not differ in cold-acclimated

plants of C24, Col and Rsch because of similar rates of net

photosynthesis and starch formation, leading to similar

concentrations of hexose phosphates, which represent the

substrate pool for sucrose synthesis. This demonstrates

that, although metabolite levels differ between cold-sensi-

tive and cold-tolerant accessions after 14 days of cold

acclimation, the metabolic dynamics are similar and appar-

ently do not correlate with cold tolerance. This is not

surprising given that all accessions are chilling-tolerant

and are able to establish a metabolic homeostasis that

enables them to grow at non-freezing temperatures. How-

ever, this finding does not exclude physiological implica-

tions of the observed difference in maximum SPS activities

of cold-sensitive and tolerant accessions. As already men-

tioned above, a high capacity of SPS would help to avoid

metabolic bottlenecks occurring under rapidly changing

environmental conditions. When sucrose synthesis

becomes limiting, phosphate limitation of triose phosphate

export from the plastids will result, and this must be

compensated for by increased starch synthesis in order to

prevent a collapse of the Calvin–Benson cycle (Poolman

et al., 2000). When starch metabolism cannot compensate

for insufficient export of triose phosphates because of low

ambient temperature, linear electron transport is impaired

(Schneider et al., 2002), and this in turn will result in a redox

disequilibrium and potentially in production of reactive

oxygen species. It has been demonstrated for Chlamydo-

monas reinhardtii that a slow down of the Calvin–Benson

cycle enhances the extent of photoinactivation of photosys-

tem II (Takahashi and Murata, 2005). This also occurs during

exposure to high light, which again causes generation of

reactive oxygen species that inhibit the repair of or

even inactivate the reaction center of photosystem II

(Murata et al., 2007). Our model simulations yielded kinetic

Per

oxid

ase

activ

ity[U

min

gFW

]–1

–1

A B C D0

20

40

60

80

100

Figure 9. Peroxidase activity as a function of temperature and irradiance in

C24 and Rsch.

Peroxidase activity was determined for C24 (black bars) and Rsch (grey bars)

at an irradiance of 50/200 lmol m)2 sec)1 at 4�C (a, b) and )4�C (c, d). The

asterisk indicates significantly different peroxidase activity in C24 and Rsch

(P < 0.01).



parameters for sucrose synthesis in C24 and Rsch that

predicted a possible enzymatic constraint at )4�C for C24 but

not Rsch. To analyse whether the predicted higher suscep-

tibility of cold-acclimated C24 plants to an overload of

photosynthetic input at low temperature could be verified

experimentally, cold-acclimated C24 and Rsch plants, which

represented the extremes of cold tolerance in this study,

were exposed to a temperature that, according to thermo-

dynamic properties, should override the capacity for sucrose

synthesis in C24, thus imposing a redox imbalance. We did

indeed determine a redox disequilibrium based on induction

of peroxidase activity in C24 at a temperature of )4�C and a

light intensity of 200 lmol m)2 sec)1, thus verifying model

predictions. It is interesting to note that a critical tempera-

ture of )4�C was also calculated for C24 based on an

independent method, i.e. fluorescence analysis of photo-

system II function (Mishra et al., 2011). In that study it was

demonstrated that, at )4�C, fluorescence transients of C24

and the tolerant accession Tenela vary significantly, again

indicating a disequilibrium of primary and secondary reac-

tions of photosynthesis in C24 at this temperature. However,

the critical temperature calculated for Rsch ()15�C) could not

be tested, because photosynthetic light reactions are com-

pletely abolished at that temperature and absorbed quanta

are disipated by fluorescence (Mishra et al., 2011). This

implies that, because of the higher enzymatic capacity, Rsch

would not encounter a metabolic limitation imposed by

sucrose synthesis.

Based on experimental results and model simulations, we

therefore conclude that a central feature of cold-tolerant

accessions of Arabidopsis is their ability to avoid bottlenecks

in central carbohydrate metabolism caused by rapid

changes of environmental conditions.

EXPERIMENTAL PROCEDURES

Plant material

Arabidopsis thaliana plants of the accessions used in this study weregrown in a 1:1 mixture of GS90 soil and vermiculite (Gebr. PatzerGmbH, www.einheitserde.de). Three plants each were raised in10 cm pots in a growth chamber under 8 h light (50 lmol m)2 sec)1;22�C)/16 h dark (16�C) for 4 weeks, and then transferred to a green-house with a temperature of 22�C during the day (16 h) and 16�Cduring the night (8 h). In the greenhouse, natural light was supple-mented to an intensity of at least 80 lmol m)2 sec)1. The relativehumidity was 70%. Plants were watered daily and fertilized every2 weeks with standard nitrogen/phosphorus/potassium fertilizer.After 42 days, a set of plants was harvested. Leaf samples consistingof one or two rosette leaves (corresponding to approximately100 mg fresh weight) were randomly taken from nine individualplants grown in three different pots every 4 h during a full day.

Another set of greenhouse-grown plants was shifted after42 days to a growth chamber with a 16 h/8 h light/dark phase at4�C, and a light intensity of 50 lmol m)2 sec)1 for 14 days prior toharvesting. Leaf samples were then taken as described above.

At harvesting, the aerial part of the plant was exclusivelycomposed of rosette leaves, allowing direct comparison ofmetabolite with CO2 exchange data. Leaf samples were weighed,

immediately frozen in liquid nitrogen and stored at )80�C untilfurther processing.

Gas exchange measurement

Exchange rates of CO2 were measured using an infra-red gas anal-ysis system (Uras 3 G, Hartmann & Braun AG, Hartmann & BraunAG, www.abb.com). A whole-rosette cuvette design was used asdescribed by Nagele et al. (2010). Gas exchange was measured inthe respective growth chambers shortly before plant harvest.Means of raw data for gas exchange were converted to flux rates perg FW (obtained at the end of the exposure by weighing completerosettes). Experiments were repeated three times for each accessionand condition.

Analysis of metabolite concentrations

Frozen leaf samples were homogenized using an MM20 ball mill(Retsch, Retsch GmbH, www.retsch.de). The homogenate wasextracted twice in 400 ll of 80% ethanol at 80�C. Extracts were thendried and dissolved in 500 ll water. Contents of glucose, fructose,sucrose and raffinose, as well as galactose, galactinol and meli-biose, were analysed via high-performance anion exchange chro-matography (HPAEC). A CarboPac PA1 column (glucose, fructose,sucrose, raffinose) or CarboPac MA1 column (galactose, galactinol,melibiose) on a DX-500 gradient chromatography system (Dionex,Sunnyvale, CA, USA, www.dionex.com) coupled with pulsedamperometric detection by a gold electrode was applied.

For starch extraction, pellets from the ethanol extraction weresolubilized by incubation in 0.5 M NaOH at 95�C for 30 min. Afteracidification with 1 M CH3COOH, the suspension was digested withamyloglucosidase for 2 h at 55�C. The glucose content of thesupernatant that was subsequently used to assess the starchcontent of the sample was determined as described below.

Glucose-6-phosphate and fructose-6-phosphate were measuredas described previously (Jelitto et al., 1992; Gibon et al., 2002).

Measurement of enzyme activities

Enzyme activities were determined in crude extracts of leaf samples.For determination of the activities of soluble acid invertase and

neutral invertase as well as cell wall-bound invertase, frozen leaftissue was homogenized in 50 mM HEPES/KOH (pH 7.4), 5 mM

MgCl2, 1 mM EDTA, 1 mM EGTA, 1 mM phenylmethanesulfonylfluoride, 0.1% Triton X-100 and 10% glycerol. Suspensions werecentrifuged for 25 min at 17 000 g and 4�C. The supernatants wereused to determine acid and neutral invertase activities as previouslydescribed (Nagele et al., 2010).

Activity of sucrose phosphate synthase (SPS) was determined inhomogenates of frozen leaf tissue in 50 mM HEPES/KOH (pH 7.5),15 mM MgCl2, 1 mM EDTA, 2.5 mM dithiothreitol, 1 mM phen-ylmethanesulfonyl fluoride and 0.1% Triton X-100. Suspensions werecentrifuged at 17 000 g and 4�C for 5 min. SPS activity was assayed insupernatants as described previously (Nagele et al., 2010).

Activity of glucokinase and fructokinase was measured asdescribed previously (Wiese et al., 1999) at ambient temperature(22�C) and 4�C.

Activity of raffinose synthase and melibiase was determined inhomogenates of frozen leaf tissue in 50 mM HEPES/KOH (pH 7.5),5 mM MgCl2, 1 mM EDTA, 0.1% Triton X-100, 1 mM phen-ylmethanesulfonyl fluoride and 0.5 mM dithiothreitol. Suspensionswere centrifuged at 17 000 g and 4�C for 5 min. Four volumes of50 mM HEPES/KOH (pH 7.5), 5 mM MgCl2, 25 mM sucrose, 25 mM

galactinol and 0.5 mM dithiothreitol (raffinose synthase), or 50 mM

citrate phosphate buffer (pH 5.0), 5 mM MgCl2, 25 mM melibioseand 0.5 mM dithiothreitol (melibiase), were added to samples. After



incubation for 20 h at 30�C or 48 h at 4�C, the reaction was stoppedby adding 500 ll 100% ethanol. Controls were stopped directly afteraddition of the extract. The samples were dried and dissolved in500 ll water. The changes in myo-inositol (in the case of raffinosesynthase) and galactose (melibiase) contents were analysed viaHPAEC on a DX-500 gradient chromatography system using aCarboPac MA1 column as described above.

Activity of peroxidase was determined in homogenates of frozenleaf tissue in phosphate buffer (pH 7). Homogenates were centri-fuged at 1500 g and 4�C for 10 min and 500 ll of the supernatantwas incubated with 250 ll of 1% v/v guaiacol. The reaction wasstarted by addition of 125 ll of 0.066% v/v H2O2, and the change inabsorption was determined photometrically at 470 nm for 10 min.

Mathematical modelling, parameter identification and

simulation

A mathematical model was developed, representing the centralsucrose and raffinose metabolism in leaves of Arabidopsis thaliana.The model was based on the following system of ordinary differ-ential equations describing time-dependent alterations in carbohy-drate pools and the rate of carbohydrate export to sink organs andother metabolic pathways:

d

dtðHPÞ ¼ 1

6

� �r1 � r2a � 2r3 þ r7 þ r8 � r10 þ r12 � br2b ð1Þ

d

dtðSucÞ ¼ r3 � r4 � r6 �

1

2r9 þ r5a ð2Þ

d

dtðRafÞ ¼ r4 � r5a � r5b ð3Þ

d

dtðGlcÞ ¼ r6 � r7 þ r11 � ar2b ð4Þ

d

dtðFrcÞ ¼ r6 � r8 þ r5b ð5Þ

d

dtðGalÞ ¼ r11 þ r5a � r12 ð6Þ

d

dtðGolÞ ¼ r10 � r4 ð7Þ

d

dtðMelÞ ¼ r5b � r11 ð8Þ

d

dtðStarchÞ ¼ r2a þ r2b ð9Þ

d

dtðSinksÞ ¼ r9: ð10Þ

The rate of net photosynthesis (r1) was approximated by asmoothing spline interpolation of measurements over whole diur-nal cycles. It was calculated in units of lmol C1 h)1 g FW)1, and wasincluded in the differential equation for hexose phosphates (HP)with a stoichiometric factor of 1/6 (Eqn 1). Rates of starch synthesisand degradation (r2a and r2b) were determined by identification ofinterpolation parameters. Interpolation was performed using acubic spline. Although starch synthesis was unambiguously derivedfrom the pool of hexose phosphates, nocturnal starch degradationwas modelled by two alternative pathways yielding either glucose(ar2b) or hexose phosphates (br2b) where a + b = 1. The rate of su-crose export (r9) leaving the system to either sink organs or othermetabolic pathways was calculated as the difference between car-bon equivalents entering the system by net photosynthesis and therate of concentration changes of carbohydrate pools.

Alterations of hexose phosphates (HP), sucrose (Suc), raffinose(Raf), glucose (Glc), fructose (Frc), galactose (Gal), galactinol (Gol),melibiose (Mel) depended on the rates of metabolite interconver-sion ri(t) catalysed by rate-limiting enzymes. Reaction rates weremodelled by Michaelis–Menten kinetics. A possible diurnal modu-lation of substrate affinity in the reactions catalysed by invertase (r5b

and r6), glucokinase (r7) and fructokinase (r8) was incorporated viaconcentration changes of allosteric effectors, which were consid-ered as follows. The reaction rate of sucrose cleavage (enzymeinvertase) was modelled as an irreversible Michaelis–Mentenenzyme kinetic incorporating mixed inhibition by the productsglucose and fructose. Glucose was modelled as a non-competitiveinhibitor and fructose as a competitive inhibitor (Sturm, 1999).Reaction rates of glucose and fructose phosphorylation (enzymehexokinase) were modelled as Michaelis–Menten enzyme kineticsnon-competitively inhibited by hexose phosphates (Claeyssen andRivoal, 2007). The synthesis of raffinose was modelled by abi-substrate kinetic describing a double-displacement catalyticmechanism as suggested by Peterbauer et al. (2002) for stachyosesynthesis A detailed description of reaction kinetics as well ascomplete model structures are given in Files S1 and S2.

Values of Vmax were considered adjustable during diurnal cycleswithin the standard deviation of measurements, whereas values ofKm were defined as constant. Identification of unknown parameterswas performed by minimizing the cost function, i.e. the sum ofsquared errors between simulated and measured states, by varia-tion of the model parameters. The identification process wasperformed using a particle swarm pattern search method for boundconstrained global optimization as described previously (Vaz andVicente, 2007).

The model was implemented in the numerical software MATLAB

(version 7.9.0, R2009b) using the software packages ‘SYSTEMS BIOL-

OGY TOOLBOX2’ and the ‘SBPD EXTENSION PACKAGE’ as describedpreviously (Schmidt and Jirstrand, 2006).

Statistics

To determine the minimum number of parameter identificationruns needed for a reliable mean value of simulation results, weapplied an approach of randomly choosing k out of n calculated fluxrates at each of the time points at which metabolite concentrationsand enzyme activities were measured. We calculated the mean ofthe chosen flux rates and repeated the procedure n

k

� �times. Then we

built the variance of the nk

� �mean values. During the next steps, we

chose (k + 1), (k + 2), …, n out of n flux rates. Identification runswere performed until variances did not differ significantly any more.t tests were performed using the MATLAB software (version 7.9.0,R2009b).

Calculation of sub-zero SPS activities using the Arrhenius

equation

The Arrhenius equation describes the relationship of temperatureand the rate of a (bio)chemical reaction as follows:

v ¼ C � e�EART ð11Þ

The reaction rate v depends on a constant C and an exponentialterm defined by the reaction enthalpy EA, the gas constant R(8.31451 J mol)1 K)1) and the reaction temperature T (K). EA can beestimated from logarithmic plotting of measured reaction ratesagainst the reciprocal of the reaction temperature (Atkins et al.,2006). The slope of this plot is equal to )EA/R, and it follows that

EA ¼ R � EA

Rð12Þ



Using the results of enzyme activity measurements of cold-accli-mated plants at 25�C and 4�C (298.15 and 277.15 K), we calculated amean activation enthalpy of 55.25 kJ mol)1 for SPS. The reactionconstant C was then calculated for the experimentally determinedmean value of Vmax at 25�C as follows:

C ¼ Vmax

.e�

EART ð13Þ

Using these values of C and EA, we calculated SPS activities bysolving Eqn 11 for a temperature regime of 25�C (298.15 K) to )5�C(268.15 K).

ACKNOWLEDGEMENTS

We would like to thank Annika Allinger for excellent plant cultiva-tion.

SUPPORTING INFORMATION

Additional Supporting Information may be found in the onlineversion of this article:Table S1. Diurnal dynamics of identified kinetic parameters in themodel of C24, non-acclimated.Table S2. Diurnal dynamics of identified kinetic parameters in themodel of Col, non-acclimated.Table S3. Diurnal dynamics of identified kinetic parameters in themodel of Rsch, non-acclimated.Table S4. Diurnal dynamics of identified kinetic parameters in themodel of C24, cold-acclimated.Table S5. Diurnal dynamics of identified kinetic parameters in themodel of Col, cold-acclimated.Table S6. Diurnal dynamics of identified kinetic parameters in themodel of Rsch, cold-acclimated.File S1. Detailed description of the reaction kinetics.File S2. Model structure for simulation of diurnal carbohydratemetabolism in A. thaliana.Please note: As a service to our authors and readers, this journalprovides supporting information supplied by the authors. Suchmaterials are peer-reviewed and may be re-organized for onlinedelivery, but are not copy-edited or typeset. Technical supportissues arising from supporting information (other than missingfiles) should be addressed to the authors.

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Identification of a metabolic bottleneck for cold acclimation in Arabidopsis thaliana