A systems biology approach for the analysis of carbohydrate dynamics during acclimation to low temperature in Arabidopsis thaliana Thomas Nagele, Benjamin A Kandel*, Sabine Frana*, Meike Meißner and Arnd G Heyer ă Biologisches Institut, Abteilung Panzenbiotechnologie, Universitat Stuttgart, Germany ă Keywords acclimation dynamics; Arabidopsis; carbohydrate metabolism; freezing tolerance; mathematical modelling Correspondence T Na ăgele, Biologisches Institut, Abteilung Panzenbiotechnologie, Universitat ă 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 work (Received 11 August 2010, revised 22 September 2010, accepted 22 November 2010) doi:10.1111/j.1742-4658.2010.07971.x Low temperature is an important environmental factor affecting the performance 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 accessionspecific reprogramming of soluble sugar metabolism in the cold Mathematical 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 presented, 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 tolerance 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 Introduction Low temperature is an important environmental factor affecting plant growth, and constraining crop productivity 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 tolerance when exposed to low but nonfreezing temperatures, 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 Abbreviations eInv, extracellular invertase; FrcK, fructokinase; FW, fresh weight; GlcK, glucokinase; LT50, 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 T Nagele et al ¨ 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 substrate 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 multigenic trait such as freezing tolerance with the concentration 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 accessions of Arabidopsis, varying raffinose concentrations in accession Col-0 by overexpression of galactinol synthase 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 carbohydrate 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 regulation strategies This is provided by systems biology techniques, which have rapidly become integrated into metabolic research, driven by the need to study complex interactions among components of biological systems [16] Basically, the intention of systems biology is Fig Schematic representation of central carbohydrate metabolism in leaf cells of Arabidopsis thaliana Reaction rates (r) represent central processes of carbon input, output and interconversion Systems biology of cold acclimation in A thaliana to resolve the relationship between individual entities, e.g molecules or genes, that are parts of highly interconnected networks, in order to understand the resulting system behaviour, e.g a phenotype of an organism To handle complex networks, formal representation 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 modularity, optimality and robustness, promise to advance our system-wide understanding of complex biological networks [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 accessions of different origin, i.e Rschew (Rsch), originating from Russia, and C24, originating from southern Europe, which show significantly different cold-acclimation capacities, we prove that mathematical modelling 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 days of exposure to cold (4 °C) was analysed with the well-established electrolyte leakage method, as described in Experimental procedures, with measurements at days 0, 1, and (Fig 2) The 50% lethality Fig Freezing tolerance of Rsch (black, continuous line) and C24 (grey, dotted line) over time of exposure to °C Closed circles represent means ± SD (n = 6) of LT50 FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS 507 Systems biology of cold acclimation in A thaliana T Nagele et al ă temperature (LT50) values of both accessions were significantly different at all time points during acclimation, 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 LT50 between and days, whereas the gain in tolerance was only minor during the first 24 h of cold exposure and between days and In contrast, LT50 decreased almost continuously in C24 until day 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 interconversions As enzyme activities represent crucial points of regulation in metabolic networks, we analysed the maximum activities (Vmax) of prominent enzymes in central carbohydrate metabolism with respect to different durations of exposure to °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 Vmax between Rsch and C24 were found for vInv (Fig 3A) and SPS (Fig 3D) Whereas SPS activities were consistently higher in Rsch, C24 showed significantly higher activities of vInv at 0, and days of cold exposure The activity of vInv in Rsch increased continuously during cold exposure, and became significantly higher than in C24 after days at °C As compared with that of vInv, the activities of nInv and eInv were low, and became noticeably higher only in Rsch after days of cold exposure (Fig 3B,C) However, in both accessions, values of Vmax for eInv increased continuously from to days of cold exposure Maximum activities of the hexose-phosphorylating FrcK and GlcK showed similar patterns in both accessions over the whole period of cold exposure (Fig 3E,F) The Vmax 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 °C influenced the process of photosynthesis, gas exchange of plants was measured by infrared gas analysis Measurements were performed during the first h 508 of the light phase, representing the time period of photosynthetic activity until plants were harvested for analysis of metabolites (see below) The rate of net carbon 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 °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 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 days at °C, when the mean uptake rate [21.5 ± 1.03 lmol C1Ỉh)1Ỉg)1 fresh weight (FW)] was almost the same as in Rsch (24.7 ± 1.8 lmol C1Ỉh)1Ỉg)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 Experimental procedures, the rate of assimilate export from photosynthetically active source organs to consuming sink organs or metabolic pathways other than carbohydrate pathways was calculated as the difference between net carbon uptake and changes in cellular carbohydrate 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 °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 accessions reached almost the same export rate after days of cold exposure Discontinuities in the calculated export rate after day and days result from the sharp increase in carbohydrate content (starch and soluble carbohydrates) 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 day of cold exposure (Fig 5A), but showed a significant increase between day and days (PRsch < 0.0001; PC24 < 0.0001), coinciding with the main increase in freezing tolerance (see Fig 2) The starch content of C24 decreased nonsignificantly until FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS T Nagele et al ă Systems biology of cold acclimation in A thaliana A D B E C F Fig Maximum activities of enzymes in central carbohydrate metabolism during cold exposure (A–C) Vmax values of three invertase isoforms: vInv, nInv and eInv (D) Vmax of SPS (E, F) Vmax 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) days of cold exposure, reaching 16.2 ± 7.07 lmol C6Ỉg)1 FW, whereas Rsch had a starch level of 23 ± 7.4 lmol C6Ỉg)1 FW after the cold acclimation period Over the time course of acclimation, changes in concentrations of soluble carbohydrates during cold exposure displayed some similarities with respect to dynamics, but differed greatly in absolute values FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS 509 Systems biology of cold acclimation in A thaliana T Nagele et al ă A B Fig Rates of net photosynthesis (A) and simulated sink export (B) during cold exposure in Rsch (black) and C24 (grey) Open circles represent 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 A B C D Fig Cold-induced dynamics of central carbohydrates in Rsch (black) and C24 (grey) Open circles represent means of measurements ± SD (n = 5) Continuous lines represent means of model simulations (n = 50) In (B) (sucrose) and (C) (hexoses), dotted lines represent the results of model simulations with lower and top values of kinetic parameters (Fig 5B–D) Sucrose content increased significantly and reached peak values after days of cold exposure: 7.1 ± 2.3 lmolỈg)1 FW in Rsch and ± 0.8 lmolỈg)1 510 FW in C24 (Fig 5B) This was followed by a slight but nonsignificant decrease until days of cold exposure Concentrations of free hexoses, calculated as the FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS T Nagele et al ă sum of fructose and glucose equivalents, were similar in both accessions at the beginning of cold exposure (Fig 5C) However, after days of cold exposure, Rsch (67.1 ± 9.3 lmol C6Ỉg)1 FW) accumulated almost three times as much hexose as C24 (28.1 ± 2.8 lmol C6Ỉg)1 FW), and it maintained this level until days, whereas C24 showed a significant decrease in hexose level to 15.1 ± 3.7 lmol C6Ỉg)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 significantly from 0.13 ± 0.04 to 2.25 ± 0.6 lmolỈg)1 FW after 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 lmolỈg)1 FW (P < 0.01; Fig 5D) Simulation of metabolic levels and rates of interconversion Identification of parameters used to describe the metabolic network as represented in Fig was performed by applying a constraint-based approach (for the explicit 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 °C were used as lower and upper bounds in the process of parameter identification The resulting model simulation using identified parameters was successful in describing cold exposure-dependent changes in carbohydrate 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 varying initial carbohydrate levels were performed, yielding means with corresponding SDs of estimated kinetic parameters Identified values of Vmax matched the values from experiments, and comparison of identified Km and Ki values agreed with values from the literature (Table 1) Rate constants and corresponding rates of sucrose synthesis were compared with Vmax 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 experimental results (Fig 5A–D), thus proving reproducibility of the obtained parameters and of simulation results Systems biology of cold acclimation in A thaliana Mean values of accession-specific parameter sets were used to analyse low-temperature effects on interconversion rates during the 7-day cold acclimation period Rates of sucrose–hexose interconversions showed significant differences between Rsch and C24 after days of exposure to °C (Fig 6A,B), but were the same for the first days of cold exposure, except for a small peak in sucrose cleavage rate in Rsch on day (Fig 6A) In order to obtain a comprehensive overview of all simulated rates of metabolite interconversions, a three-dimensional surface plot was created (Fig 7A,B) that allowed (a) assessment of the trajectory 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 of exposure to °C, the corresponding flux in Rsch was reduced only during the first 24 h of cold exposure (Fig 7A,B, CO2 to sucrose) A similar pattern was observed for rates of CO2 uptake and export of sucrose to sink organs, but not for starch synthesis As already illustrated in Fig 6, sucrose cleavage and hexose-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 Vmax 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 day at °C was predicted to be higher than the experimental value, whereas the simulated hexose content was lowered Performance of a further in silico experiment in which the Vmax and k values of C24 were applied to the Rsch model confirmed that the main differences in reprogramming of carbohydrate metabolism occur during the first days of exposure to low temperature (Fig S2) In particular, the sucrose content after day at °C was underestimated and, simultaneously, the hexose content showed a faster increase than in the corresponding experimental data FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS 511 512 Hexoses fi sucrose (Hxk, SPS) Sucrose fi hexoses (invertase) Vmax Km Ki r k r 62.1 10.5 1.7 2.33 0.33 0.29 17.3 11.9 4.1 0.91 1.1 0.85 ± ± ± ± ± ± ± ± ± ± ± ± 9.8 2.7 0.3 0.1 0.08 0.08 7.7 2.9 0.8 0.43 0.3 0.24 Parameter estimation GT, genotype; Hxk, hexokinase (glucokinase + fructokinase) C24 Vmax Km Ki r k r Sucrose fi hexoses (invertase) Rsch Hexoses fi sucrose (Hxk, SPS) Parameter Reaction GT 22.2 ± 11.7 5–12 [35] 2.5 [36] – – Hxk: 3.73 ± 0.97 SPS: 22.1 ± 7.0 64.6 ± 18.3 5–12 [35] 2.5 [36] – – Hxk: 3.3 ± 1.0 SPS: 6.3 ± 2.6 Experiment ⁄ literature Time of exposure to °C (days) 36.6 12.1 1.7 0.58 0.05 0.72 11.0 10.4 4.1 0.76 0.04 0.61 ± ± ± ± ± ± ± ± ± ± ± ± 3.1 1.9 0.3 0.06 0.01 0.1 2.5 2.6 0.8 0.14 0.02 0.22 Parameter estimation 16.0 ± 11.9 – – – – Hxk: 0.51 ± 0.13 SPS: 2.4 ± 0.5 28.9 ± 12.6 – – – – Hxk: 0.54 ± 0.09 SPS: 0.73 ± 0.54 Experiment ⁄ literature 42.2 12.1 1.7 0.48 0.03 0.88 41.4 10.4 4.1 0.99 0.02 1.21 ± ± ± ± ± ± ± ± ± ± ± ± 5.0 1.9 0.3 0.06 0.004 0.12 4.7 2.6 0.8 0.27 0.009 0.58 Parameter estimation 21.1 ± 17.3 – – – – Hxk: 0.42 ± 0.1 SPS: 3.2 ± 1.7 34.7 ± 19.6 – – – – Hxk: 0.59 ± 0.2 SPS: 1.2 ± 0.61 Experiment ⁄ literature 12.8 12.1 1.7 0.12 0.04 0.67 75.9 10.4 4.1 1.24 0.04 2.63 ± ± ± ± ± ± ± ± ± ± ± ± 2.1 1.9 0.3 0.02 0.002 0.04 36.4 2.6 0.8 0.45 0.016 0.76 Parameter estimation 85.1 ± 59.1 – – – – Hxk: 0.51 ± 0.18 SPS: 4.7 ± 1.2 10.8 ± 6.1 – – – – Hxk: 0.66 ± 0.16 SPS: 1.4 ± 0.8 Experiment ⁄ literature Table Validation of enzyme parameters determined by parameter estimation Values of Km and Ki are given in mM The unit of maximum enzyme activity (Vmax) and rate of metabolite interconversion (r) is lmol substrath)1Ỉg)1 FW Rate constants (k) are given in h)1 The results of parameter estimation for Km and Ki are compared with values from the literature Identified values of Vmax are compared with experimental data obtained at 22 °C (0 days at °C) and °C (1 day, days and days at °C), respectively The results of parameter estimation represent means ± SD (n = 50) Experimental data represent means ± SDs (n = 7) Systems biology of cold acclimation in A thaliana T Nagele et al ă FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ê 2010 FEBS T Nagele et al ă Systems biology of cold acclimation in A thaliana A B Fig Dynamics of rates of sucrose cleavage (A) and hexose-based sucrose synthesis (B) during exposure to °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 A B Fig Surface plot of simulated rates of metabolite interconversion for accessions C24 (A) and Rsch (B) For comparison, all fluxes are represented in lmol C6Ỉh)1Ỉg)1 FW In addition to surface topography, quantities of fluxes are indicated by colour as defined in the colour bar Discussion 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] FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS 513 Systems biology of cold acclimation in A thaliana T Nagele et al ă However, the complex interactions of metabolic pathways 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 °C, thus capturing different stages of metabolic adjustment to low temperature As indicated by the LT50 values, the freezing tolerances 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 metabolic responses on the improvement in freezing tolerance Comparison of changes in metabolism between day and 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 This coincides with the time point of maximal tolerance acquisition, thus proving the importance of photosynthesis and long-distance transport for acclimation The requirement for photosynthetic activity 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 significantly enhanced in plants with increased SPS activity, 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 and 7, had the capacity to assimilate at least about lmol C6Ỉh)1Ỉg)1 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 tolerance [23] It appears that the major difference between Rsch and C24 is the capacity to re-establish homeostasis in carbon allocation This is supported by the observation that Arabidopsis plants with SPS overexpression, 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 514 the phloem loading transporter AtSUC2 [20,24] However, 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-containing 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 content 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 correlation 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 regulation 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 metabolic 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 carbohydrate 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 metabolism of Rsch and C24 In particular, rates of sucrose cleavage and hexose-based sucrose resynthesis showed significant differences with respect to both their absolute 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 days in the cold Regarding the question of FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS T Nagele et al ă 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 simultanous reduction in hexose concentration, particularly during the initial period of cold exposure Using RNA interference-mediated inhibition of the dominating vacuolar 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 coldinduced 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 represents 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 process incorporating environmental changes Furthermore, we suggest that successful metabolic engineering of freezing tolerance in plants should include such an analysis of the dynamics of metabolism to gain comprehensive information about the effects of individual overexpression or knockout events on the whole acclimation 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 Systems biology of cold acclimation in A thaliana plants per 10-cm pot in a growth chamber at h of light (50 lmolỈm)2Ỉs)1; 22 °C) ⁄ 16 h of dark (16 °C) for weeks, and then transferred to a growth chamber with a temperature regime of 22 °C in the day (16 °h) and 16 °C at night (8 h) The light intensity was 50 lmolỈm)2Ỉs)1, and the relative humidity was 70% Plants were watered daily, and fertilized every weeks with standard NPK fertilizer After 42 days, plants were shifted to a 16-h ⁄ 8-h light ⁄ dark regime of ⁄ °C and a light intensity of 50 lmolỈm)2Ỉs)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 day, days and days of exposure to °C Samples were taken after a light period of h At that stage, the aerial part of the plant is exclusively composed of rosette leaves, allowing a direct comparison of metabolite with CO2 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 °C ⁄ h, and samples were taken at °C intervals over a temperature range of to ) 18 °C Conductivity was measured with an inoLab740 conductivity meter (WTW GmbH, Weilheim, Germany) and multilabpilot software The LT50 values were calculated as the log EC50 values of sigmoidal dose– response curves, fitted to the measured leakage values with graphpad prism software Gas exchange measurement Exchange rates of CO2 were measured with an infrared gas analysis system (Uras G; Hartmann & Braun AG, Frankfurt 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 Retsch MM20 ball mill (Retsch, Haan, Germany) The homogenate was extracted twice in 400 lL of 80% ethanol 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 CarboPac PA-1 column on a Dionex (Sunnyvale, CA, USA) FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS 515 Systems biology of cold acclimation in A thaliana T Nagele et al ă 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 °C in 0.5 m NaOH for 30 After acidification with m CH3COOH, the suspension was digested for h with amyloglucosidase The glucose content of the supernatant was then determined 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), mm MgCl2, mm EDTA, mm EGTA, mm phenylmethanesulfonyl fluoride, mm dithiothreitol, 0.1% Triton X-100 and 10% glycerin Suspensions were centrifuged at 3500 g for 25 at °C, and invertase activities were assayed in the supernatants Soluble 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 wallbound invertase was determined as described for soluble acid invertase, but without centrifugation of the homogenized suspension and subsequent subtraction of soluble acid invertase activity The control of each assay was boiled for after addition of enzyme extract Reactions were incubated for 60 at 30 and °C, and stopped by boiling for min; the concentration of glucose was determined photometrically The activity of SPS was determined after homogenization of frozen leaf tissue in 50 mm Hepes ⁄ KOH (pH 7.5), 15 mm MgCl2, mm EDTA, 2.5 mm dithiothreitol and 0.1% Triton X-100 Suspensions were centrifuged at 16 200 g for at °C, and SPS activity was assayed in the supernatant with a reaction buffer consisting of 50 mm Hepes ⁄ KOH (pH 7.5), 15 mm MgCl2, 2.5 mm dithiothreitol, 10 mm UDP-glucose, 10 mm fructose 6phosphate and 40 mm glucose 6-phosphate; 30% KOH was added to the control of each assay Reactions were incubated for 30 at 25 and °C, and then at 10 at 95 °C Anthrone 0.2% in 95% H2SO4 was added, and the samples were incubated for at 90 °C Absorption at 620 nm was determined photometrically Activities of GlcK and FrcK were measured as described in [32], at ambient temperature (22 °C) and °C Synthesized glucose 6-phosphate was converted to 6-phosphogluconolactone 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, phosphoglucoisomerase was added 516 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 differential equations describing alterations in carbohydrate pools over time of exposure to low temperature (4 °C): d= ðSucÞ ¼ rCO !Suc À rSuc!Raf À rSuc!Hex dt 1 ỵ rHex!Suc rSuc!Sinks 2 d= Starchị ẳ rCO !Starch dt d= Hexị ẳ 2rSuc!Hex rHex!Suc dt d= Rafị ẳ rSuc!Raf dt d= Sinksị ¼ rSuc!Sinks dt These state equations for sucrose, starch, hexoses, raffinose and sinks depended on the adjoining fluxes r(t) The different rA fi B values described the respective metabolic fluxes from metabolite A to metabolite B (see Fig 1) The rate of net starch synthesis (rCO2 !Starch )was deter- mined by interpolation of measured starch contents (unit: C6) and calculation of the first derivative of this function The flux rate of CO2 into sucrose synthesis (rCO2 !Suc ) was caclulated as the difference between the rate of net photosynthesis and that of net starch synthesis (unit: C6 h)1Ỉg)1 FW): rCO2 !Suc ¼ rNetPhotosynthesis ÀrCO2 !Starch Ratesof net photosynthesis (rNetPhotosynthesis) were calculated as the average rate of carbon uptake during the first half of the light phase (n = h): n R rNetPhotosynthesis ¼ xNPSi i¼1 n ; where xNPSi describes the integral of carbon uptake per hour Data points were spline-interpolated to obtain timecontinuous information on net photosynthesis during the whole period of cold exposure The rate of raffinose synthesis, rSuc 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 (rSuc fi Sinks) was calculated as the difference between the spline-interpolated rates of net photosynthesis and of changes in the carbohydrate pool FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ê 2010 FEBS T Nagele et al ă Systems biology of cold acclimation in A thaliana The rate of sucrose cleavage (rSuc fi Hex) was described by an irreversible Michaelis–Menten enzyme kinetic, with competitive inhibition by the product as described in [31]: rA!B tị ẳ Vmax;A cA tị cB Km;A ỵ cA tịị ỵ Ki;B Þ The reaction rate rA fi B(t) depends on the substrate concentration cA(t), the maximum activity of the catalysing enzyme (Vmax,A) and the enzyme specific substrate affinity, expressed by Km,A It also depends on the concentration of the reaction product and the dissociation constant Ki,B for inhibitor binding The rate of hexose-based sucrose synthesis was described by the mass action rate law: rA!B tị ẳ k Á cA ðtÞ In this reaction kinetic, the reaction rate rAfiB(t) depends on the substrate concentration cA(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 (Vmax,A, Km,A, Ki,B and k) was carried out by minimizing the cost function, i.e the sum of squared errors between simulated and measured states, by variation of the model parameters The identification process was performed with a particle swarm pattern search method for bound constrained global optimization, as described in [33] The model was implemented in the numerical 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J Exp Bot 50, 735–743 Supporting information The following supplementary material is available: Fig S1 Simulation results of in silico experiment for hexoses (black) and sucrose (grey) Fig S2 Simulation results of in silico experiment 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 FEBS Journal 278 (2011) 506–518 ª 2010 The Authors Journal compilation ª 2010 FEBS ... in A thaliana A D B E C F Fig Maximum activities of enzymes in central carbohydrate metabolism during cold exposure (A? ??C) Vmax values of three invertase isoforms: vInv, nInv and eInv (D) Vmax of. .. 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. .. mathematical model was developed, representing central carbohydrate metabolism in leaves of A thaliana The model was based on the following system of ordinary differential equations describing alterations