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
Introduction
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
Keywords
acclimation dynamics; Arabidopsis;
carbohydrate metabolism; freezing

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.
Abbreviations
eInv, extracellular invertase; FrcK, fructokinase; FW, fresh weight; GlcK, glucokinase; LT
50
, 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].

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.
Results
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
50
.

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
max
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
max
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
max
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

Æh
)1
Æg
)1
FW).
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

sure displayed some similarities with respect to
dynamics, but differed greatly in absolute values
A
B
C
D
E
F
Fig. 3. Maximum activities of enzymes in central carbohydrate metabolism during cold exposure. (A–C) V
max
values of three invertase iso-
forms: vInv, nInv and eInv. (D) V
max
of SPS. (E, F) V
max
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
¨
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 509
(Fig. 5B–D). Sucrose content increased significantly
and reached peak values after 3 days of cold exposure:
7.1 ± 2.3 lmolÆg
)1
FW in Rsch and 3 ± 0.8 lmolÆg
)1
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

Æg
)1
FW
(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
)1
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
)1
FW (P < 0.01; Fig. 5D).
Simulation of metabolic levels and rates of
interconversion
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

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
2
to sucrose). A similar pattern was
observed for rates of CO
2
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

and K
i
are given in mM. The unit of maximum enzyme activity (V
max
) and rate of metabolite
interconversion (r)islmol substrateÆh
)1
Æg
)1
FW. Rate constants (k) are given in h
)1
. The results of parameter estimation for K
m
and K
i
are compared with values from the literature. Identi-
fied values of V
max
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
Parameter
estimation
Experiment ⁄
literature
Parameter
estimation
Experiment ⁄

2.63 ± 0.76 Hxk: 0.51 ± 0.18
SPS: 4.7 ± 1.2
C24 Sucrose fi hexoses
(invertase)
V
max
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
K
m
10.5 ± 2.7 5–12 [35] 12.1 ± 1.9 – 12.1 ± 1.9 – 12.1 ± 1.9 –
K
i
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
¨
gele et al.
512 FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS

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
50
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.

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

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.
Conclusions
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

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
)2
Æs
)1
. 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
2
exchange
data. Leaf samples were weighed, immediately frozen in
liquid nitrogen and stored at ) 80 °C until metabolite
extraction.
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
50
values were
calculated as the log EC
50

solubilized by heating them to 95 °Cin0.5m NaOH
for 30 min. After acidification with 1 m CH
3
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
sample.
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
2
,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

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):
d
=
dt
ðSucÞ¼
1
2
r
CO
2
!Suc
À r
Suc!Raf
À r
Suc!Hex
þ
1
2
r
Hex!Suc
À
1

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
CO
2
!Starch
)was deter-
mined by interpolation of measured starch contents
(unit: C
6
) and calculation of the first derivative of this
function. The flux rate of CO
2
into sucrose synthesis
(r
CO
2
!Suc
) was caclulated as the difference between the rate
of net photosynthesis and that of net starch synthesis (unit:
C
6
h
)1
Æg
)1
FW):
r
CO

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]:
r
A!B
ðtÞ¼
V
max;A
Á c
A
ðtÞ
ðK
m;A
þ c

In this reaction kinetic, the reaction rate r
AfiB
(t) depends
on the substrate concentration c
A
(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
max,A
, K
m,A
,
K
i,B
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 7.6.0.324, 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.
Statistics
ANOVAs and t-tests were performed with matlab (Ver-
sion 7.6.0.324, R2008a).

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Supporting information
The following supplementary material is available:
Fig. S1. Simulation results of in silico experiment 1 for