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Tài liệu Báo cáo khoa học: A systems biology approach for the analysis of carbohydrate dynamics during acclimation to low temperature in Arabidopsis thaliana doc

A systems biology approach for the analysis of
carbohydrate dynamics during acclimation to low
temperature in Arabidopsis thaliana
Thomas Na
gele, Benjamin A. Kandel*, Sabine Frana*, Meike Meißner and Arnd G. Heyer
Biologisches Institut, Abteilung Pflanzenbiotechnologie, Universita
t Stuttgart, Germany
Low temperature is an important environmental factor
affecting plant growth, and constraining crop produc-
tivity and species distribution [1,2]. Whereas many
tropical and subtropical species have only limited
capacities to cope with low temperature, plants from
temperate climates, such as Arabidopsis thaliana, grow
at low temperature and can increase their freezing tol-
erance when exposed to low but nonfreezing tempera-
tures, in a process termed cold acclimation [3]. The
acclimation process is a very complex phenomenon
comprising numerous changes in metabolism and

affecting gene expression, membrane structure, and the
composition of proteins and primary and secondary
metabolites [4–7]. In this context, many studies have
shown a strong correlation between changes in the
regulation of central carbohydrate metabolism and
freezing tolerance [4,8]. In Arabidopsis, the development
of leaves at low temperature causes reprogramming of
acclimation dynamics; Arabidopsis;
carbohydrate metabolism; freezing
tolerance; mathematical modelling
T. Na
gele, Biologisches Institut, Abteilung
Pflanzenbiotechnologie, Universita
Stuttgart, Pfaffenwaldring 57, D-70550
Stuttgart, Germany
Fax: +49 711 685 65096
Tel: +49 711 685 69141
E-mail: Thomas.Naegele@bio.uni-stuttgart.de
*These authors contributed equally to this
(Received 11 August 2010, revised 22 Sep-
tember 2010, accepted 22 November 2010)
Low temperature is an important environmental factor affecting the perfor-
mance and distribution of plants. During the so-called process of cold
acclimation, many plants are able to develop low-temperature tolerance,
associated with the reprogramming of a large part of their metabolism. In
this study, we present a systems biology approach based on mathematical
modelling to determine interactions between the reprogramming of central
carbohydrate metabolism and the development of freezing tolerance in two
accessions of Arabidopsis thaliana. Different regulation strategies were
observed for (a) photosynthesis, (b) soluble carbohydrate metabolism and
(c) enzyme activities of central metabolite interconversions. Metabolism of
the storage compound starch was found to be independent of accession-
specific reprogramming of soluble sugar metabolism in the cold. Mathemati-

cal modelling and simulation of cold-induced metabolic reprogramming
indicated major differences in the rates of interconversion between the
pools of hexoses and sucrose, as well as the rate of assimilate export to
sink organs. A comprehensive overview of interconversion rates is pre-
sented, from which accession-specific regulation strategies during exposure
to low temperature can be derived. We propose this concept as a tool for
predicting metabolic engineering strategies to optimize plant freezing toler-
ance. We confirm that a significant improvement in freezing tolerance in
plants involves multiple regulatory instances in sucrose metabolism, and
provide evidence for a pivotal role of sucrose–hexose interconversion in
increasing the cold acclimation output.
eInv, extracellular invertase; FrcK, fructokinase; FW, fresh weight; GlcK, glucokinase; LT
, 50% lethality temperature; nInv, neutral
invertase; Rsch, Rschew; SD, standard deviation; SPS, sucrose phosphate synthase; vInv, vacuolar invertase.
506 FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS
carbon metabolism, with a shift in partitioning of
newly fixed carbon into sucrose rather than starch
[9,10], indicating cold-induced selective stimulation of
sucrose synthesis, which could be the reason for the
elevated cellular sucrose content that is found in many
plants upon cold exposure. Sucrose may act directly as
a cryoprotectant, as has been shown in vitro with
artificial membrane systems [11], or serve as a sub-
strate for the synthesis of other cryoprotective
compounds, such as raffinose, the level of which has
been found to correlate with freezing tolerance in species
as diverse as A. thaliana [12], grape vines [13] and woody
conifers [14].
As already outlined [12], direct correlation of a mul-
tigenic trait such as freezing tolerance with the concen-
tration of only one or a few metabolites may not be
what one would expect. This was demonstrated by
work [15] showing that, despite the correlation of
freezing tolerance with raffinose levels in natural acces-
sions of Arabidopsis, varying raffinose concentrations
in accession Col-0 by overexpression of galactinol syn-
thase or knockout of raffinose synthase did not affect
freezing tolerance. Considering the complexity of the
metabolic and regulatory networks, indicated by the
schematic and very simplified structure of primary car-
bohydrate metabolism in Fig. 1, it becomes obvious
that, to investigate such nonintuitive networks, an
approach is needed that incorporates multiple and, in
part, circular metabolite interconversions and regula-
tion strategies. This is provided by systems biology
techniques, which have rapidly become integrated into
metabolic research, driven by the need to study com-
plex interactions among components of biological sys-
tems [16]. Basically, the intention of systems biology is
to resolve the relationship between individual entities,
e.g. molecules or genes, that are parts of highly inter-
connected networks, in order to understand the result-
ing system behaviour, e.g. a phenotype of an
organism. To handle complex networks, formal repre-
sentation by mathematical models is indispensable.
Integration of data on, for example, gene expression,
protein abundance, metabolite concentration and other
biological parameters with an iterative model, and
exploration of model characteristics such as modular-
ity, optimality and robustness, promise to advance our
system-wide understanding of complex biological net-
works [17].
In this work, we present a systems biology approach
focused on the dynamic modelling of cold-induced
reprogramming of central carbohydrate metabolism in
A. thaliana. Performing experiments with two acces-
sions of different origin, i.e. Rschew (Rsch), originat-
ing from Russia, and C24, originating from southern
Europe, which show significantly different cold-accli-
mation capacities, we prove that mathematical model-
ling of metabolism and validation by experimental
data offers an attractive possibility for the study of
complex system–environment interactions.
Freezing tolerance
Changes in freezing tolerance of Rsch and C24 during
7 days of exposure to cold (4 °C) was analysed with
the well-established electrolyte leakage method, as
described in Experimental procedures, with measure-
ments at days 0, 1, 3 and 7 (Fig. 2). The 50% lethality
Fig. 1. Schematic representation of central carbohydrate metabo-
lism in leaf cells of Arabidopsis thaliana. Reaction rates (r) represent
central processes of carbon input, output and interconversion.
Fig. 2. Freezing tolerance of Rsch (black, continuous line) and C24
(grey, dotted line) over time of exposure to 4 °C. Closed circles rep-
resent means ± SD (n =6)ofLT
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FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS 507
temperature (LT
) values of both accessions were sig-
nificantly different at all time points during acclima-
tion, confirming that Rsch is more tolerant to freezing
than C24, and has a higher acclimation capacity, as
previously outlined [6]. The basic tolerance of C24
was ) 3.3 ± 0.07 °C, whereas that of Rsch was
) 4.9 ± 0.09 °C. Rsch showed the strongest reduction
in LT
between 1 and 3 days, whereas the gain in tol-
erance was only minor during the first 24 h of cold
exposure and between days 3 and 7. In contrast, LT
decreased almost continuously in C24 until day 3 and
did not change thereafter, resulting in final freezing
tolerances of ) 5.4 ± 0.12 °C in C24 and ) 9.1 ±
0.16 °C in Rsch.
Enzyme activites of central carbohydrate
As enzyme activities represent crucial points of regula-
tion in metabolic networks, we analysed the maximum
activities (V
) of prominent enzymes in central car-
bohydrate metabolism with respect to different dura-
tions of exposure to 4 °C (Fig. 3). The enzymes
analysed included vacuolar invertase (vInv), neutral
invertase (nInv), extracellular invertase (eInv), sucrose
phosphate synthase (SPS), fructokinase (FrcK) and
glucokinase (GlcK). Significant differences in V
between Rsch and C24 were found for vInv (Fig. 3A)
and SPS (Fig. 3D). Whereas SPS activities were consis-
tently higher in Rsch, C24 showed significantly higher
activities of vInv at 0, 1 and 3 days of cold exposure.
The activity of vInv in Rsch increased continuously
during cold exposure, and became significantly higher
than in C24 after 7 days at 4 °C. As compared with
that of vInv, the activities of nInv and eInv were low,
and became noticeably higher only in Rsch after
7 days of cold exposure (Fig. 3B,C). However, in both
accessions, values of V
for eInv increased continu-
ously from 0 to 3 days of cold exposure.
Maximum activities of the hexose-phosphorylating
FrcK and GlcK showed similar patterns in both acces-
sions over the whole period of cold exposure
(Fig. 3E,F). The V
of GlcK rose sharply in both
accessions by a factor of $ 1.5 during the first day of
cold exposure (Fig. 3F).
Cold-induced changes in net carbon uptake and
sink export
To obtain a quantitative measure of how exposure to
4 °C influenced the process of photosynthesis, gas
exchange of plants was measured by infrared gas anal-
ysis. Measurements were performed during the first 8 h
of the light phase, representing the time period of pho-
tosynthetic activity until plants were harvested for
analysis of metabolites (see below). The rate of net car-
bon uptake was integrated and divided by the time
period of measurement to obtain the mean uptake rate
per hour (Fig. 4A). Mean net carbon uptake was not
significantly influenced by cold exposure in Rsch, but
showing a slight decrease during the first day at 4 °C
and stabilization over the following time period. C24
showed slightly lower mean rates of carbon uptake
before and during the first day of cold acclimation.
After 3 days of cold exposure, the mean rate of carbon
uptake was significantly lower for C24 than for Rsch
(P = 0.03), and this was followed by recovery until
7 days at 4 °C, when the mean uptake rate
[21.5 ± 1.03 lmol C
fresh weight (FW)] was
almost the same as in Rsch (24.7 ± 1.8 lmol
Calculated means of uptake rates were fed into the
mathematical model, and standard deviations (SDs)
were set as boundaries in the estimation process for
model parameters (Fig. 4A). As described in Experi-
mental procedures, the rate of assimilate export from
photosynthetically active source organs to consuming
sink organs or metabolic pathways other than carbo-
hydrate pathways was calculated as the difference
between net carbon uptake and changes in cellular car-
bohydrate content. The resulting surplus of carbon
equivalents (Fig. 4B) was regarded as being exported
to sink organs or other pathways. The time courses of
simulated export rate during the first day of exposure to
4 °C were very similar in both accessions, showing a
slight decrease, which was also found for net carbon
uptake (see above). During the following days of cold
exposure, Rsch showed a noticeably faster regeneration
of sink export rate than did C24, although both acces-
sions reached almost the same export rate after 7 days
of cold exposure. Discontinuities in the calculated
export rate after 1 day and 3 days result from the sharp
increase in carbohydrate content (starch and soluble car-
bohydrates) during that time period of cold exposure.
Effect of cold exposure on levels of soluble
carbohydrates and starch
Contents of leaf starch, sucrose, hexoses and raffinose
were determined over the course of cold exposure
(Fig. 5). In both accessions, starch content was not
altered at 1 day of cold exposure (Fig. 5A), but
showed a significant increase between 1 day and 3 days
< 0.0001; P
< 0.0001), coinciding with the
main increase in freezing tolerance (see Fig. 2). The
starch content of C24 decreased nonsignificantly until
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7 days of cold exposure, reaching 16.2 ± 7.07 lmol -
FW, whereas Rsch had a starch level of
23 ± 7.4 lmol C
FW after the cold acclimation
Over the time course of acclimation, changes in con-
centrations of soluble carbohydrates during cold expo-
sure displayed some similarities with respect to
dynamics, but differed greatly in absolute values
Fig. 3. Maximum activities of enzymes in central carbohydrate metabolism during cold exposure. (A–C) V
values of three invertase iso-
forms: vInv, nInv and eInv. (D) V
of SPS. (E, F) V
values of FrcK and GlcK. Significant differences between the ecotypes Rsch (black)
and C24 (grey) are indicated by asterisks (P < 0.05). Bars represent means ± SD (n = 7).
T. Na
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FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS 509
(Fig. 5B–D). Sucrose content increased significantly
and reached peak values after 3 days of cold exposure:
7.1 ± 2.3 lmolÆg
FW in Rsch and 3 ± 0.8 lmolÆg
FW in C24 (Fig. 5B). This was followed by a slight
but nonsignificant decrease until 7 days of cold expo-
sure. Concentrations of free hexoses, calculated as the
Fig. 4. Rates of net photosynthesis (A) and simulated sink export (B) during cold exposure in Rsch (black) and C24 (grey). Open circles rep-
resent means of measurements ± SD (n = 3). Continuous lines represent means of model simulations (n = 50). Dotted lines represent
results of model simulations with lower and top values of kinetic parameters.
Fig. 5. Cold-induced dynamics of central carbohydrates in Rsch (black) and C24 (grey). Open circles represent means of measure-
ments ± SD (n = 5). Continuous lines represent means of model simulations (n = 50). In (B) (sucrose) and (C) (hexoses), dotted lines repre-
sent the results of model simulations with lower and top values of kinetic parameters.
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510 FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS
sum of fructose and glucose equivalents, were similar
in both accessions at the beginning of cold exposure
(Fig. 5C). However, after 3 days of cold exposure,
Rsch (67.1 ± 9.3 lmol C
FW) accumulated
almost three times as much hexose as C24
(28.1 ± 2.8 lmol C
FW), and it maintained this
level until 7 days, whereas C24 showed a significant
decrease in hexose level to 15.1 ± 3.7 lmol C
(P < 0.001). The raffinose concentration increased
almost linearly with time of cold exposure in both
accessions. In Rsch, the raffinose content increased sig-
nificantly from 0.13 ± 0.04 to 2.25 ± 0.6 lmolÆg
FW after 7 days of cold exposure (P < 0.01), and was
about twice as high as in C24, which showed an
increase from 0.09 ± 0.02 to 0.96 ± 0.39 lmolÆg
FW (P < 0.01; Fig. 5D).
Simulation of metabolic levels and rates of
Identification of parameters used to describe the meta-
bolic network as represented in Fig. 1 was performed
by applying a constraint-based approach (for the expli-
cit model structure, see Experimental procedures).
Model constraints were set by experimental data on
net carbon uptake, metabolite levels and maximum
enzyme activities, which gave a provisional estimation
of the maximum flux capacity of the corresponding
pathway. Experimental data on maximum enzyme
activities of SPS, GlcK, FrcK and invertase at 4 °C
were used as lower and upper bounds in the process of
parameter identification. The resulting model simula-
tion using identified parameters was successful in
describing cold exposure-dependent changes in carbo-
hydrate levels (Fig. 5A–D, continuous lines). To test
the statistical robustness of the identified model
parameters and to validate them with experimental
data, 50 independent identification processes with vary-
ing initial carbohydrate levels were performed, yielding
means with corresponding SDs of estimated kinetic
parameters. Identified values of V
matched the val-
ues from experiments, and comparison of identified K
and K
values agreed with values from the literature
(Table 1). Rate constants and corresponding rates of
sucrose synthesis were compared with V
values for
both hexokinase activity (GlcK and FrcK) and SPS
activity, as both enzymes contribute to hexose-based
sucrose synthesis (see also ‘Model documentation’ in
Doc. S3). Simulations resulting from upper, lower and
mean values of parameter sets described metabolic
changes during cold exposure within the SDs of experi-
mental results (Fig. 5A–D), thus proving reproducibility
of the obtained parameters and of simulation results.
Mean values of accession-specific parameter sets
were used to analyse low-temperature effects on inter-
conversion rates during the 7-day cold acclimation per-
iod. Rates of sucrose–hexose interconversions showed
significant differences between Rsch and C24 after
7 days of exposure to 4 °C (Fig. 6A,B), but were the
same for the first 3 days of cold exposure, except for a
small peak in sucrose cleavage rate in Rsch on day 2
(Fig. 6A). In order to obtain a comprehensive over-
view of all simulated rates of metabolite interconver-
sions, a three-dimensional surface plot was created
(Fig. 7A,B) that allowed (a) assessment of the trajec-
tory of interconversion rates as a function of time of
cold exposure, (b) comparison of the magnitudes of
the various interconversion rates, and (c) lineup of the
accessions with respect to their metabolic acclimation
strategies. Major differences in sucrose metabolism
between the accessions were identified. Whereas C24
showed a cold-induced reduction of carbon channelling
into sucrose synthesis from the start until day 3 of
exposure to 4 °C, the corresponding flux in Rsch was
reduced only during the first 24 h of cold exposure
(Fig. 7A,B, CO
to sucrose). A similar pattern was
observed for rates of CO
uptake and export of
sucrose to sink organs, but not for starch synthesis. As
already illustrated in Fig. 6, sucrose cleavage and hex-
ose-based resynthesis were increased in Rsch, whereas
C24 showed a significant reduction in sucrose cycling
during cold exposure (Fig. 7A,B, sucrose to hexoses,
hexoses to sucrose).
In silico experiments
To estimate the metabolic impact of differences
between Rsch and C24 concerning sucrose cycling, we
performed in silico experiments, using the validated
mathematical model in terms of predictive metabolic
engineering [18]. Replacing V
values and k values
in the C24 model with the identified values for Rsch
resulted in simulations that were not successful in
describing the whole experimental dataset on sucrose
and hexoses (Fig. S1). The sucrose content after 1 day
at 4 °C was predicted to be higher than the experimen-
tal value, whereas the simulated hexose content was
lowered. Performance of a further in silico experiment
in which the V
and k values of C24 were applied to
the Rsch model confirmed that the main differences in
reprogramming of carbohydrate metabolism occur dur-
ing the first 3 days of exposure to low temperature
(Fig. S2). In particular, the sucrose content after 1 day
at 4 °C was underestimated and, simultaneously, the
hexose content showed a faster increase than in the
corresponding experimental data.
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Table 1. Validation of enzyme parameters determined by parameter estimation. Values of K
and K
are given in mM. The unit of maximum enzyme activity (V
) and rate of metabolite
interconversion (r)islmol substrateÆh
FW. Rate constants (k) are given in h
. The results of parameter estimation for K
and K
are compared with values from the literature. Identi-
fied values of V
are compared with experimental data obtained at 22 °C (0 days at 4 °C) and 4 °C (1 day, 3 days and 7 days at 4 °C), respectively. The results of parameter estimation
represent means ± SD (n = 50). Experimental data represent means ± SDs (n = 7).
GT Reaction Parameter
Time of exposure to 4 °C (days)
01 3 7
Experiment ⁄
Experiment ⁄
Experiment ⁄
Experiment ⁄
Rsch Sucrose fi hexoses
17.3 ± 7.7 22.2 ± 11.7 11.0 ± 2.5 16.0 ± 11.9 41.4 ± 4.7 21.1 ± 17.3 75.9 ± 36.4 85.1 ± 59.1
11.9 ± 2.9 5–12 [35] 10.4 ± 2.6 – 10.4 ± 2.6 – 10.4 ± 2.6 –
4.1 ± 0.8 2.5 [36] 4.1 ± 0.8 – 4.1 ± 0.8 – 4.1 ± 0.8 –
r 0.91 ± 0.43 – 0.76 ± 0.14 – 0.99 ± 0.27 – 1.24 ± 0.45 –
Hexoses fi sucrose
(Hxk, SPS)
k 1.1 ± 0.3 – 0.04 ± 0.02 – 0.02 ± 0.009 – 0.04 ± 0.016 –
r 0.85 ± 0.24 Hxk: 3.73 ± 0.97
SPS: 22.1 ± 7.0
0.61 ± 0.22 Hxk: 0.51 ± 0.13
SPS: 2.4 ± 0.5
1.21 ± 0.58 Hxk: 0.42 ± 0.1
SPS: 3.2 ± 1.7
2.63 ± 0.76 Hxk: 0.51 ± 0.18
SPS: 4.7 ± 1.2
C24 Sucrose fi hexoses
62.1 ± 9.8 64.6 ± 18.3 36.6 ± 3.1 28.9 ± 12.6 42.2 ± 5.0 34.7 ± 19.6 12.8 ± 2.1 10.8 ± 6.1
10.5 ± 2.7 5–12 [35] 12.1 ± 1.9 – 12.1 ± 1.9 – 12.1 ± 1.9 –
1.7 ± 0.3 2.5 [36] 1.7 ± 0.3 – 1.7 ± 0.3 – 1.7 ± 0.3 –
r 2.33 ± 0.1 – 0.58 ± 0.06 – 0.48 ± 0.06 – 0.12 ± 0.02 –
Hexoses fi sucrose
(Hxk, SPS)
k 0.33 ± 0.08 – 0.05 ± 0.01 – 0.03 ± 0.004 – 0.04 ± 0.002 –
r 0.29 ± 0.08 Hxk: 3.3 ± 1.0
SPS: 6.3 ± 2.6
0.72 ± 0.1 Hxk: 0.54 ± 0.09
SPS: 0.73 ± 0.54
0.88 ± 0.12 Hxk: 0.59 ± 0.2
SPS: 1.2 ± 0.61
0.67 ± 0.04 Hxk: 0.66 ± 0.16
SPS: 1.4 ± 0.8
GT, genotype; Hxk, hexokinase (glucokinase + fructokinase).
Systems biology of cold acclimation in A. thaliana T. Na
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512 FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS
Cold acclimation of plants involves a large number of
metabolic changes as well as readjustments in other
cellular processes. Numerous studies have emphasized
the importance of primary carbohydrate metabolism
during cold acclimation, and have identified regulatory
instances with significant influence [9,10,12,15,19,20].
Fig. 7. Surface plot of simulated rates of
metabolite interconversion for accessions
C24 (A) and Rsch (B). For comparison, all
fluxes are represented in lmol C
FW. In addition to surface topography,
quantities of fluxes are indicated by colour
as defined in the colour bar.
Fig. 6. Dynamics of rates of sucrose cleavage (A) and hexose-based sucrose synthesis (B) during exposure to 4 °C. Lines represent means
of simulation (n = 50) for Rsch (black) and C24 (grey). Dotted lines represent results of model simulations with lower and top values of
kinetic parameters.
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However, the complex interactions of metabolic path-
ways precludes the generation of a full picture of
cold acclimation through assembly of reaction details.
In the present study, a systems biology approach with
dynamic modelling was developed and validated by
experimental data on two Arabidopsis accessions, Rsch
and C24, with different cold acclimation capacities.
Dynamics were generated by varying the time periods
for which plants were exposed to 4 °C, thus capturing
different stages of metabolic adjustment to low temper-
ature. As indicated by the LT
values, the freezing tol-
erances of the accessions differed not only in terms of
the absolute values but also in the progression of the
acclimation process. This is an important outcome, as
it allows estimation of the impact of different meta-
bolic responses on the improvement in freezing toler-
ance. Comparison of changes in metabolism between
1 day and 3 days of cold exposure revealed significant
differences in net carbon uptake and sink export rate
between Rsch and C24. Whereas net carbon uptake
and rate of sink export were constantly reduced in C24
over the entire exposure time, Rsch almost completely
compensated for the low-temperature effects at day 3.
This coincides with the time point of maximal toler-
ance acquisition, thus proving the importance of pho-
tosynthesis and long-distance transport for
acclimation. The requirement for photosynthetic activ-
ity has also been demonstrated [21], and it was shown
that acclimation does not take place in total darkness.
Strand et al. [22] found that cold acclimation was sig-
nificantly enhanced in plants with increased SPS activ-
ity, leading to higher photosynthetic performance at
low temperatures. Interestingly, model simulations for
C24 and Rsch revealed that synthesis of soluble sugar
was never limited by photosynthetic capacity. Even
C24, which displayed a reduction in photosynthesis at
days 3 and 7, had the capacity to assimilate at least
about 3 lmol C
FW, which would have been
sufficient to bring about much higher sugar levels than
those determined. Therefore, we suggest that assimilate
allocation within the plant may become limiting in the
cold. This was also demonstrated for cucumber, in
which the sucrose supply to sink organs rather than
source capacity correlated with low-temperature toler-
ance [23]. It appears that the major difference between
Rsch and C24 is the capacity to re-establish homeosta-
sis in carbon allocation. This is supported by the
observation that Arabidopsis plants with SPS overex-
pression, which show a significant increase in freezing
tolerance as compared with the wild type, not only
accumulate sucrose in their leaves, but also specifically
increase the expression of the high-affinity sucrose
transporter AtSUC1, which is highly homologous to
the phloem loading transporter AtSUC2 [20,24]. How-
ever, it has to be kept in mind that the sink export rate
in our model is composed of assimilate export to sink
organs and flux into further pools of carbon-contain-
ing metabolites and structural components, e.g. amino
acids and cell wall components. Therefore, the real
rates of export of carbohydrates to sink organs might
be smaller than predicted by our model.
In contrast to soluble carbohydrates, the starch con-
tent of plants did not show significant differences
between the accessions over the whole period of cold
exposure, even though net carbon uptake rates varied
strongly. This suggests that starch metabolism was
directly correlated neither with photosynthesis nor with
the cold acclimation process. This may explain why
we, using C24 and Rsch, did not find a negative corre-
lation of freezing tolerance with channelling of carbon
into starch, whereas Klotke et al. [12] reported such a
correlation for C24 and Col-0, which has a freezing
tolerance similar to that of [6]. Given that starch plays
an important role as a major integrator in the regula-
tion of plant growth [25], it is noticeable that, at least
in Rsch, the most significant changes in starch content
occurred simultaneously with the largest increase in
freezing tolerance. Considering that rates of rosette
biomass increase are negatively correlated with starch
levels [25], our data confirm the observation that the
acquisition of freezing tolerance is coupled to a meta-
bolic state in which growth is suspended [26].
Major changes in pools of free hexoses and sucrose
took place until the third day of cold exposure, but
after this no further significant changes could be
observed. Therefore, we conclude that the process of
cold acclimation is divisible into three consecutive
stages: (a) immediate response to displacement of
homeostasis; (b) reprogramming of central carbohy-
drate metabolism; and (c) stabilization of a new state
of metabolic homeostasis with respect to carbohydrate
metabolism. Simulation of metabolite interconversion
rates revealed a distinct difference in sucrose metabo-
lism of Rsch and C24. In particular, rates of sucrose
cleavage and hexose-based sucrose resynthesis showed
significant differences with respect to both their abso-
lute values and the time course. From the simulations,
it appears that the ability to sustain the cycling of
sucrose, which has been postulated to function in the
stabilization of mesophyll sugar metabolism [27–29],
positively correlates with low-temperature acclimation
capacity. Additional support for this hypothesis arises
from experimental data on enzyme activities, which
show that invertase activity is increased during cold
exposure in Rsch, whereas acitivity is reduced in C24
after 7 days in the cold. Regarding the question of
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how to engineer plant metabolism in order to improve
freezing tolerance, one could suggest increasing the
maximum activities of enzymes participating in sucrose
cycling. Assuming that Rsch is optimized for cold
acclimation, we suggest, on the basis of the results of
the in silico experiments (Figs S1 and S2), that the
metabolism of C24 has to be changed in a way that
leads to an increased sucrose content and a simulta-
nous reduction in hexose concentration, particularly
during the initial period of cold exposure. Using RNA
interference-mediated inhibition of the dominating vac-
uolar invertase ATbFRUCT4 (At1g12240), we have
already demonstrated this [12]. However, it was shown
that fully cold-acclimated transformants of C24 did
not differ from the wild type with regard to freezing
tolerance and, at the same time, differences in sucrose
concentration between the C24 genotypes were lost.
Therefore, we suggest that inhibition of invertase must
be linked with overexpression of SPS, as described in
[22], to achieve sucrose accumulation, a decrease in
hexose content and, in consequence, a significant
increase in freezing tolerance.
The present study elucidates differences in cold-
induced reprogramming of central carbohydrate
metabolism. Mathematical modelling of metabolism
with respect to the dynamics of freezing tolerance
revealed a significant correlation of sucrose synthesis
and degradation with the process of cold acclimation.
We conclude that acclimation to low temperature rep-
resents a dynamic process, the investigation of which
therefore requires approaches that take into account
metabolic dynamics and interdependencies rather than
simple steady-state concentrations. We present a
method based on dynamic modelling that allows for
the quantification and visualization of cellular rates of
metabolite interconversion during an acclimation pro-
cess incorporating environmental changes. Further-
more, we suggest that successful metabolic engineering
of freezing tolerance in plants should include such an
analysis of the dynamics of metabolism to gain com-
prehensive information about the effects of individual
overexpression or knockout events on the whole accli-
mation process.
Experimental procedures
Plant material
A. thaliana plants of the accessions Rsch and C24 were
grown in GS90 soil and vermiculite (1 : 1), with three
plants per 10-cm pot in a growth chamber at 8 h of light
(50 lmolÆm
;22°C) ⁄ 16 h of dark (16 °C) for 4 weeks,
and then transferred to a growth chamber with a tempera-
ture regime of 22 °C in the day (16 °h) and 16 °C at night
(8 h). The light intensity was 50 lmolÆm
, and the rela-
tive humidity was 70%. Plants were watered daily, and fer-
tilized every 2 weeks with standard NPK fertilizer. After
42 days, plants were shifted to a 16-h ⁄ 8-h light ⁄ dark regime
of 4 ⁄ 4 °C and a light intensity of 50 lmolÆm
. Leaf
samples consisting of two rosette leaves each were taken
from nine individual plants grown in three different pots
in a random design before and after 1 day, 3 days and
7 days of exposure to 4 °C. Samples were taken after a
light period of 8 h. At that stage, the aerial part of the
plant is exclusively composed of rosette leaves, allowing
a direct comparison of metabolite with CO
data. Leaf samples were weighed, immediately frozen in
liquid nitrogen and stored at ) 80 °C until metabolite
Electrolyte leakage measurement
Freezing tolerance was tested according to the electrolyte
leakage method as previously described [30], with a few
modifications. The cooling rate was set to 4 °C ⁄ h, and sam-
ples were taken at 2 °C intervals over a temperature range
of 0 to ) 18 °C. Conductivity was measured with an ino-
Lab740 conductivity meter (WTW GmbH, Weilheim, Ger-
many) and multilabpilot software. The LT
values were
calculated as the log EC
values of sigmoidal dose–
response curves, fitted to the measured leakage values with
graphpad prism 3 software.
Gas exchange measurement
Exchange rates of CO
were measured with an infrared gas
analysis system (Uras 3 G; Hartmann & Braun AG, Frank-
furt am Main, Germany). A whole-rosette cuvette design
was used as described in [31]. Gas exchange was measured
in the growth chamber shortly before plant harvesting.
Means of raw data for gas exchange were converted to flux
rates per gram of FW obtained at the end of the exposure
by weighing complete rosettes.
Carbohydrate analysis
Frozen leaf samples were homogenized with a Rets-
ch MM20 ball mill (Retsch, Haan, Germany). The
homogenate was extracted twice in 400 lL of 80% etha-
nol at 80 °C. Extracts were dried and dissolved in
500 lL of distilled water. Contents of glucose, fructose,
sucrose and raffinose were analysed by high-performance
anion exchange chromatography (HPAEC) with a Carb-
oPac PA-1 column on a Dionex (Sunnyvale, CA, USA)
T. Na
gele et al. Systems biology of cold acclimation in A. thaliana
FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS 515
DX-500 gradient chromatography system coupled with a
pulsed amperometric detection by a gold electrode. For
starch extraction, pellets for ethanol extraction were
solubilized by heating them to 95 °Cin0.5m NaOH
for 30 min. After acidification with 1 m CH
COOH, the
suspension was digested for 2 h with amyloglucosidase.
The glucose content of the supernatant was then deter-
mined and used to assess the starch content of the
Measurement of enzyme activities
Enzyme activities were determined in crude extracts of leaf
samples. For assessment of acitivities of soluble acid
invertase, cell wall-bound invertase and nInv, about
100 mg of frozen leaf tissue was homogenized in 50 mm
Hepes ⁄ KOH (pH 7.4), 5 mm MgCl
,1mm EDTA, 1 mm
EGTA, 1 mm phenylmethanesulfonyl fluoride, 5 mm dith-
iothreitol, 0.1% Triton X-100 and 10% glycerin. Suspen-
sions were centrifuged at 3500 g for 25 min at 4 °C, and
invertase activities were assayed in the supernatants. Solu-
ble acid invertase was assayed in 20 mm sodium acetate
buffer (pH 4.7) with 100 mm sucrose as a substrate. nInv
was assayed in 20 mm Hepes ⁄ KOH (pH 7.5), also with
100 mm sucrose as substrate. The activity of cell wall-
bound invertase was determined as described for soluble
acid invertase, but without centrifugation of the homoge-
nized suspension and subsequent subtraction of soluble
acid invertase activity. The control of each assay was
boiled for 3 min after addition of enzyme extract. Reac-
tions were incubated for 60 min at 30 and 4 °C, and
stopped by boiling for 3 min; the concentration of glucose
was determined photometrically.
The activity of SPS was determined after homogeniza-
tion of frozen leaf tissue in 50 mm Hepes ⁄ KOH (pH 7.5),
15 mm MgCl
,1mm EDTA, 2.5 mm dithiothreitol and
0.1% Triton X-100. Suspensions were centrifuged at
16 200 g for 5 min at 4 °C, and SPS activity was assayed
in the supernatant with a reaction buffer consisting of
50 mm Hepes ⁄ KOH (pH 7.5), 15 mm MgCl
, 2.5 mm
dithiothreitol, 10 mm UDP-glucose, 10 mm fructose 6-
phosphate and 40 mm glucose 6-phosphate; 30% KOH
was added to the control of each assay. Reactions were
incubated for 30 min at 25 and 4 °C, and then at 10 min
at 95 °C. Anthrone 0.2% in 95% H
was added, and
the samples were incubated for 8 min at 90 °C. Absorp-
tion at 620 nm was determined photometrically.
Activities of GlcK and FrcK were measured as described
in [32], at ambient temperature (22 °C) and 4 °C. Synthe-
sized glucose 6-phosphate was converted to 6-phosphogluc-
onolactone by glucose-6-phosphate dehydrogenase, and the
conversion was measured photometrically by changes in the
concentration of the reduced cosubstrate NADPH. For
isomerization of fructose 6-phosphate, phosphoglucoisom-
erase was added.
Mathematical modelling, parameter identification
and simulation
A mathematical model was developed, representing central
carbohydrate metabolism in leaves of A. thaliana. The
model was based on the following system of ordinary dif-
ferential equations describing alterations in carbohydrate
pools over time of exposure to low temperature (4 °C):
À r
À r
À r
These state equations for sucrose, starch, hexoses, raffi-
nose and sinks depended on the adjoining fluxes r(t). The
different r
A fi B
values described the respective metabolic
fluxes from metabolite A to metabolite B (see Fig. 1).
The rate of net starch synthesis (r
)was deter-
mined by interpolation of measured starch contents
(unit: C
) and calculation of the first derivative of this
function. The flux rate of CO
into sucrose synthesis
) was caclulated as the difference between the rate
of net photosynthesis and that of net starch synthesis (unit:
¼ r
Ratesof net photosynthesis (r
) were calcu-
lated as the average rate of carbon uptake during the first
half of the light phase (n = 8 h):
where xNPS
describes the integral of carbon uptake per
hour. Data points were spline-interpolated to obtain time-
continuous information on net photosynthesis during the
whole period of cold exposure. The rate of raffinose synthe-
sis, r
Suc fi Raf
, was calculated as already described for
starch, assuming that pools of raffinose and sucrose are
reversibly interconnected.
The rate of sucrose export to sink organs (r
Suc fi Sinks
was calculated as the difference between the spline-interpo-
lated rates of net photosynthesis and of changes in the
carbohydrate pool.
Systems biology of cold acclimation in A. thaliana T. Na
gele et al.
516 FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS
The rate of sucrose cleavage (r
Suc fi Hex
) was described
by an irreversible Michaelis–Menten enzyme kinetic, with
competitive inhibition by the product as described in [31]:
Á c
þ c
ðtÞÞ Â ð1 þ
The reaction rate r
A fi B
(t) depends on the substrate con-
centration c
(t), the maximum activity of the catalysing
enzyme (V
) and the enzyme specific substrate affinity,
expressed by K
. It also depends on the concentration of
the reaction product and the dissociation constant K
inhibitor binding.
The rate of hexose-based sucrose synthesis was described
by the mass action rate law:
ðtÞ¼k Á c
In this reaction kinetic, the reaction rate r
(t) depends
on the substrate concentration c
(t) and the rate constant k.
The model code and a detailed description of the model
structure are provided in Docs S1a, S1b, S2a,b and S3).
The identification of unknown parameters (V
, K
and k) was carried out by minimizing the cost function,
i.e. the sum of squared errors between simulated and mea-
sured states, by variation of the model parameters. The
identification process was performed with a particle swarm
pattern search method for bound constrained global opti-
mization, as described in [33].
The model was implemented in the numerical software
matlab (Version, R2008a) with the software
packages systems biology toolbox2 and the sbpd Exten-
sion Package as described in [34]. Both matlab and sys-
tems biology toolbox2 are necessary for the performance
of model simulations using the sbsimulate function.
ANOVAs and t-tests were performed with matlab (Ver-
sion, R2008a).
We would like to thank S. Stutz for fruitful discussions
and for helping with measurements of enzyme activi-
ties at low temperature. We would also like to thank
A. Allinger for expertise in plant cultivation, and the
rderung Baden-Wu
rttemberg at
the Universita
t Stuttgart for financial support.
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Supporting information
The following supplementary material is available:
Fig. S1. Simulation results of in silico experiment 1 for
hexoses (black) and sucrose (grey).
Fig. S2. Simulation results of in silico experiment 2 for
hexoses (black) and sucrose (grey).
Doc. S1a. Model structure of C24.
Doc. S1b. sbml format of model structure of C24.
Doc. S2a. Model structure of Rsch.
Doc. S2b. sbml format of model structure of Rsch.
Doc. S3. Documentation of the model structure.
This supplementary material can be found in the
online version of this article.
Please note: As a service to our authors and readers,
this journal provides supporting information supplied
by the authors. Such materials are peer-reviewed and
may be re-organized for online delivery, but are not
copy-edited or typeset. Technical support issues arising
from supporting information (other than missing files)
should be addressed to the authors.
Systems biology of cold acclimation in A. thaliana T. Na
gele et al.
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