Different strategies of metabolic regulation in cyanobacteria: from transcriptional to biochemical control

Cyanobacteria Synechococcus sp. PCC 7942 and Synechocystis sp. PCC 6803 show similar changes in the metabolic response to changed CO2 conditions but exhibit significant differences at the transcriptomic level. This study employs a systems biology approach to investigate the difference in metabolic regulation of Synechococcus sp. PCC 7942 and Synechocystis sp. PCC 6803. Presented multi-level kinetic model for Synechocystis sp. PCC 6803 is a new approach integrating and analysing metabolomic, transcriptomic and fluxomics data obtained under high and ambient CO2 levels. Modelling analysis revealed that higher number of different isozymes in Synechocystis 6803 improves homeostatic stability of several metabolites, especially 3PGA by 275%, against changes in gene expression, compared to Synechococcus sp. PCC 7942. Furthermore, both cyanobacteria have the same amount of phosphoglycerate mutases but Synechocystis 6803 exhibits only ~20% differences in their mRNA levels after shifts from high to ambient CO2 level, in comparison to ~500% differences in the case of Synechococcus sp. PCC 7942. These and other data imply that the biochemical control dominates over transcriptional regulation in Synechocystis 6803 to acclimate central carbon metabolism in the environment of variable inorganic carbon availability without extra cost carried by large changes in the proteome.

However, the handling of large data sets from "omics" experiments, such as transcriptomics, remains challenging. In the frame of systems biology, attempts were initiated to integrate those data into mathematical models [13][14][15] . These approaches not only support the handling of complex data sets but also allow analysis of those data sets to reveal metabolic and regulatory networks.
The current standard method for mathematical analysis of metabolism, functions of particular pathways or the effects of specific gene knock outs is stoichiometric modelling 16 . This method is suitable for large metabolic networks and is based on enforcing constraints on the metabolic fluxes, such as CO 2 fixation and glycogen synthesis, allowing to predict the flux distribution. Common method employed within stoichiometric modelling is flux balance analysis (FBA) 17 , proved to be valuable for the evaluation of the metabolism of Synechocystis 6803 5, [18][19][20][21] . However, FBA is a static approach and its advanced derivatives, e.g., regulatory FBA (rFBA) 22 , provide only limited information regarding dynamics and system regulation. Alternatively, kinetic models [23][24][25] can be used for the description of cellular functions in photosynthetic organisms. These models require more knowledge and data input than the stoichiometric models, but they allow the description and analysis of different cellular states.
We have extended the traditional kinetic model, based on metabolic data from one steady state, to multi-level kinetic model (various omics data and several steady states) and applied this approach to analyse the metabolic regulation of cyanobacterium Synechococcus 7942 14,26 . This multi-level kinetic modelling approach combines enzymatic data from the literature and experimentally obtained metabolic, fluxomic and transcriptomics data from several steady states to describe central carbon metabolism in this organism. Gene expression data served as a proxy to estimate changes in the amount of specific enzyme in cells grown under different CO 2 conditions 14 .
The gene expression analysis revealed that the cyanobacterium Synechococcus 7942 exhibits major changes in expression of genes for many enzymes involved in central carbon metabolism after a shift from HC to AC 9 .
Here, we report on a multi-level kinetic model for the cyanobacterium Synechocystis 6803 and its application to analyse metabolic alterations in cells shifted from HC (high CO 2 ) to AC (ambient CO 2 ) conditions. In contrast to Synechococcus 7942, Synechocystis 6803 cells did not show significant changes in the expression of enzymes involved in central carbon metabolism 27,28 , whereas the principal changes in the metabolome were similar in both cyanobacteria during the AC shift response 29 . These findings may indicate that in Synechocystis 6803 carbon metabolism is rather regulated at the posttranslational, i.e. biochemical, level during the acclimation to different CO 2 levels. In this study, we focus on three major topics: 1) differences in the metabolic regulation between Synechococcus 7942 and Synechocystis 6803, 2) the role of additional isozymes in Synechocystis 6803, and 3) the influence of gene expression on metabolic fluxes.

Results and Discussion
Comparison of two cyanobacteria revealed the dominant role of isozymes in metabolic regulation in Synechocystis 6803. The model of Synechocystis 6803 was used to compare central carbon metabolism and its acclimation to varying Ci conditions with that of Synechococcus 7942. These two unicellular cyanobacterial strains are often used as models to investigate molecular aspects of carbon acclimation 30,31 . Compared with Synechocystis 6803, Synechococcus 7942 has an approximately 40% smaller genome (http://genome.microbedb.jp/cyanobase) and is strictly photoautotrophic. Hence, the metabolism of Synechocystis 6803 is more complex and flexible, thus making it more difficult to elucidate. The different genomic capacity also resulted in significant differences within the metabolic network between these cyanobacteria. In particular, Synechocystis 6803 runs an active OPP cycle under phototrophic conditions 11 and harbours more isozymes of fructose-1,6-bisphosphatase, phosphofructokinase, ribose-5-phosphate isomerase, phosphoglycolate phosphatase and phosphoketolase 32 . With the exception of ribose-5-phosphate isomerase and phosphoglycolate phosphatase, the position of these additional isozymes in the metabolic network potentially allows them to regulate the flux of fructose-6-phosphate among the Calvin-Benson cycle, glycolysis, OPP and/or glycolytic bypass, see Fig. 1. However, Synechocystis 6803 also lacks some enzymes compared with Synechococcus 7942, such as the glycerate 3-phosphate kinase in the photorespiratory pathway, which is replaced by a glycerate 2-phosphate kinase 33 , and one of the glycolytic glyceraldehyde-3-phosphate dehydrogenases.
As previously mentioned, Synechocystis 6803 cells did not show significant changes in the expression of genes for enzymes of central carbon metabolism triggered by changing CO 2 conditions 27,28 , whereas in Synechococcus 7942 those changes mainly explained the observed changes in the carbon metabolism in HC compared to AC cells 9,26 . It is notable that the mean value of transcriptional changes of the enzymes implemented into the model is 1.01 between HC and AC cells, whereas it was 1.36 in Synechococcus 7942. Despite the unchanged expression, Synechocystis 6803 exhibited marked differences in metabolites under different Ci conditions (see Table 1), which are comparable to those reported from Synechococcus 7942 9,26 . Hence, the major difference between Synechocystis 6803 and Synechococcus 7942 seems to be based on different ranges of transcriptional regulation and the amount of isozymes for crucial metabolic nodes. This raises the question if isozymes play a key role in the metabolic regulation of Synechocystis 6803.
To test this hypothesis, we assessed the role of transcriptional control over metabolism. To do that, measured changes in the transcriptome of Synechocystis 6803 cells shifted from HC to AC were obtained from the literature 29 and then shuffled and randomly redistributed as weight factors of enzymatic activities. Randomized distribution of transcriptome data was employed in other studies for different reasons, for instance, to elucidate the role of particular metabolic pathway in a genomic model 34 . In our case, the varying transcriptional changes were applied to the complete model with all isozymes occurring in Synechocystis 6803 and to a model, in which all the isozymes that are missing in Synechococcus 7942 were not considered (see Fig. 1, blue colour labels these enzymes). We note that the deletion of isozymes, i.e., keeping only one isozyme per reaction in the model, would dramatically affect the results of the simulations obtained with and without isozymes, because the kinetic parameters of all isozymes, including the remaining isozyme, were initially estimated for two or more isozymes. Therefore, the kinetic parameters of the remaining single isozymes (Fig. 1, blue color) were rebalanced to obtain a good match with experimental data for cells grown in HC and AC. The manual rebalancing of kinetic parameters of the each remaining single isozyme started with shifting the k M_single value to the mean of k M values or original isozymes followed by adjusting the V max_single accordingly to match the measured metabolic levels. More information about the parameter space for k M of isozymes can be found in our previous study 14 . After the rebalancing procedure, we repeated the simulation, based on shuffled and each time randomly redistributed weight factors, of metabolic changes in Ci-shifted cells 30-times for both scenarios. Yellow indicates the newly added oxidative phase of the oxidative pentose phosphate pathway, which is active also during the day (HC condition) in Synechocystis 6803, in contrast to Synechococcus 7942. Transaldolase was omitted due to low flux 11 , and phosphogluconolactonase was neglected for simplicity. White indicates the metabolites whose concentrations are available in the metabolome data set. The model includes the Calvin-Benson cycle, glycogen synthesis (sink from glucose-6-phosphate), photorespiratory pathways, glycolysis, the oxidative pentose pathway and sink reactions (representing the adjacent pathway and the calculation of biomass production). The reversibility of a particular reaction is indicated by two small arrows. Red squares indicate the major carbon reallocation nodes for changing CO 2 levels. Purple indicates the involved enzymes: RuBisCOribulose-1,5-bisphosphate carboxylase oxygenase, PGK-phosphoglycerate kinase, GAP-glyceraldehyde-3-phosphate dehydrogenase, TPI-triose-phosphate isomerase, ALDO-aldolase, FBPase-fructose-1,6 bisphosphatase, PFK-phosphofructokinase, TKT-transketolase, SBPase-sedoheptulose-1,7 bisphosphatase, RPI -phosphopentose isomerase, PPE-phosphopentose epimerase, PRK -phosphoribulokinase, GPI-glucose-6-phosphate isomerase, G6PD-glucose-6-phosphate dehydrogenase, PGD-phosphogluconate dehydrogenase, PGPase-phosphoglycolate phosphatase, PKET-phosphoketolase, GOX -glycolate oxidase, SGATserineglyoxylate transaminase, HPR -hydroxypyruvate reductase, GLYK -glycerate kinase, AGT-alanineglyoxylate transaminase, TSS -tartronatesemialdehyde synthase, TSR-tartronatesemialdehyde reductase, SHMT-serine hydroxymethyltransferase, GLOX -glyoxylate oxidase, PSAT*-phosphoserine transaminase (3-phosphoglycerate dehydrogenase is, for simplicity, not implemented), PGM-phosphoglycerate mutase, ENO-enolase. Open book symbol indicates an involvement of metabolite in other reaction(s). This analysis of the metabolic levels in AC-grown cells revealed that the higher number of isozymes present in Synechocystis 6803 (but absent in Synechococcus 7942) affect the behaviour of many metabolites. This effect is particularly visible in the homeostatic stability of 3PGA and 2PG, which increased by 275% and 215%, respectively (Fig. 2). Similar positive impact on homeostatic stability of F6P, FBP and Ri5P (substrates of additional isozymes) is approximately 20% (Fig. 2), but was lower in the case of other metabolites, e.g., + 2.1% for DHAP or + 2.5% for E4P. The homeostatic stability for these metabolic concentrations is here defined as a ratio of standard deviations from series of simulations with randomly redistributed measured transcriptomic changes (see above) between results without and with additional isozymes. In other words, homeostatic stability for particular metabolite describes the precision of maintaining aimed steady state concentrations in changing environments such as different CO 2 levels. The high sensitivity of 2PG towards changes in the expression of corresponding genes ( Fig. 2) correlates with the existence of additional 2PG phosphatase in Synechocystis to maintain the concentration of this toxic intermediate in changing environment, in contrast to the situation in Synechococcus 7942 with only two genes encoding for 2PG phosphatases 32 . In addition to the lowered homeostatic stability of 2PG in the case without additional isozymes, we observed also 50% higher mean concentration of 2PG which may inhibits certain enzymes of the Calvin-Benson cycle 12 ; thus further explaining the existence of third phosphoglycolate phosphatase in Synechocystis 6803.  Another interesting finding of the simulations was an increased homeostatic stability of 3PGA by 275% due to more isozymes in Synechocystis (Fig. 2). 3PGA is neither substrate nor product of these isozymes and phosphoglycerate mutase isozymes (PGMs) are present in the same number in Synechococcus 7942 and Synechocystis 6803 32 . 3PGA acts on the crucial metabolic crossroad between the Calvin-Benson cycle and glycolysis, hence its concentration seems to have a significant impact on growth 26 . We recently showed that primary regulatory role of isozymes not necessarily aims at the catalysed reaction 26 , which seems be also the case of fructose-1,6-bisphosphatases, phosphofructokinases, ribose-5-phosphate isomerases and phosphoketolases. Finally, it is evident that comparable metabolic regulation of 3PGA levels can be achieved either with additional isozymes and almost unchanged expression of 3 PGMs (approximately 20% differences in mRNA levels) in Synechocystis after shifts from HC to AC 29 or lower number of isozymes and high expression changes of PGMs (approximately 500% differences in mRNA levels) in Synechococcus after HC to AC shifts 9 . Finally, we have shown before that an extra PGM does not improve the homeostatic stability of 3PGA 14 ; incorrect annotation of fourth PGM in Synechococcus 7942 and Synechocystis 6803 was identified by our multi-level kinetic modelling approach 14 and recently experimentally confirmed as phosphoserine phosphatase in Synechocystis 6803 35 .
These results support the notion that the biochemical control, i.e., control provided by posttranslational level and isozymes, dominates over transcriptional regulation to acclimate central carbon metabolism from HC toward AC conditions in Synechocystis 6803 compared to Synechococcus 7942. Furthermore, the simulations showed that it is possible to describe the metabolic levels under different CO 2 conditions using only one set of kinetic parameters, implying a minor role of posttranslational modifications. Finally, this finding may also explain why Synechocystis 6803 with its higher enzyme coding capacity does not strongly depend on the regulation of gene expression. Regulation via increased number of specific isozymes is sufficient to maintain the robust homeostasis at metabolic level without extra cost carried by large changes in the transcriptome and thus in the proteome, even in the environment of variable inorganic carbon availability.
Is carbon metabolism scalable in response to a changing environment? At this point, we have analysed two major inputs to our model: metabolic and transcriptomic data. However, estimations of the steady state levels of metabolites cannot be directly translated into carbon flux. This gap can be filled when data from 13 C-labelling experiments, which directly estimate the metabolic fluxes, are considered as alternative input data 11,12 . Fluxes in cyanobacteria are commonly analysed by stoichiometric modelling, which is based on FBA (flux balance analysis) via genome-scale reconstruction of metabolic networks 5,18-21 . However, fluxes can also be calculated within kinetic models, e.g., the rates of reactions based on Michaelis-Menten kinetics are equal to fluxes in units of mmol s −1 36 . Such data can then be normalized to the measured flux, typically provided in units of mmol h −1 g DW −1 11 . Moreover, the use of fluxes as input data provides additional constraints for parameter fitting in kinetic modelling.
Accordingly, we compared the calculated fluxes from our multi-level kinetic model of Synechocystis 6803 with the normalized estimated fluxes from a labelling experiment performed at HC conditions 11 and those obtained from published calculations based on FBA 20 . This analysis reveals a good match between the fluxes calculated via our model and those measured in the labelling experiment (Table 2). This match was better than that between the fluxes calculated via our multi-level kinetic model here and stoichiometric FBA model 20 . In the latter case, we observed two major discrepancies, namely a 2.9-fold difference in glycogen synthesis (considered as G6P sink, see Fig. 1) and an 8.3-fold difference in phosphoketolase flux in cells grown in HC (Table 2). Comparing the HC fluxes between phosphoketolase and G6PD ( Table 2) indicates that stoichiometric model opted for more beneficial flux via phosphoketolase that preserves carbon molecules in comparison to the route via glycolysis, which could explain the 8.3-fold difference. Although we do not have data from 13 C labeling for the flux through phosphoketolase (PKET), we could calculate an estimate from other fluxes involving F6P. The maximal flux via PKET could not be higher than 5 10 −2 mmol h −1 g DW −1 . This estimation is based on the mass conversation law of reactions included within the model. In reality the flux could be lower, since the model is not considering   20 . For this purpose, we considered a ratio of 3.6 based on difference in growth rates and corresponding ribulose synthesis fluxes between HC and AC resulting from our model. Using this rescaling factor, we divided all fluxes from the original Knoop stoichiometric model 20 by a constant 3.6 to translate the HC values into normalized AC fluxes.
This attempt resulted in a good match for glycogen synthesis and a 4-fold improvement for phosphoketolase-driven flux under AC conditions (Table 2). Furthermore, the comparison of the fluxes based on our multi-level kinetic model and the rescaled values of Knoop model 20 in AC revealed a better match than the same comparison for HC, see Table 2. These findings imply that the stoichiometric model 20 describes rather the situation of Synechocystis 6803 under AC conditions. On this basis, the majority of fluxes are scalable for cells in changing CO 2 conditions. We note that the stoichiometric model 20 was designed for HC allowing to adjust HCO 3 − uptake as necessary for optimal growth yield. However, there are three exceptions to scalable metabolism: phosphoglycerate mutase (and following reactions), glycogen synthesis and phosphoketolase. Phosphoglycerate mutase regulates the crucial flux of carbon between the Calvin-Benson cycle and glycolysis (Fig. 1) and it plays a major role in biomass production 26 . A vast difference is noted in glycogen synthesis between HC and AC. HC grown cells of Synechocystis 6803 contain about 20-fold more glycogen than AC cells (9.1 versus 0.4 μ g glycogen OD 750 −1 ml −1 ; own unpublished results). Furthermore, phosphoketolase allows by passing of glycolysis and thus prevents the loss of CO 2 due to pyruvate dehydrogenase, a feature not required in HC. These differences suggest that the redistribution of carbon sources at different CO 2 level exclusively occurs in a few cardinal nodes of metabolic crossroads such as phosphoglycerate mutase, glycogen synthesis and phosphoketolase, see Fig. 1 (red squares), whereas the vast majority of other fluxes is simply maintained at a constant ratio corresponding to changes in overall growth.
Another interesting result was found for the flux via glucose-6-phosphate dehydrogenase (G6PD), see Table 2. This flux is considered zero in published stoichiometric model 20 because the involvement of G6PD does not allow a maximum efficiency of metabolism. It has been shown that the flux through G6PD leads to approximately 13% loss of total fixed carbon 11 . The flux via G6PD of approximately 16·10 −2 mmol h −1 gDW −1 measured in HC 11 indicates that this flux is not regulated by changes in gene expression in AC-shifted cells, because the weight factors for enzymatic activity based on the measured changes in the transcriptome are + 8% for G6PD and + 37% for phosphogluconate dehydrogenase 29 . These transcriptional changes directly translated into G6PD activity would result in simulated flux 10.3·10 −2 mmol h −1 gDW −1 via G6PD at AC conditions. This hypothetical high flux is very unlikely, since it did not allow to match the observed metabolic levels and it would led to further 34% decrease of the growth rate in AC. To obtain a good match between observed metabolite and growth changes with flux, it was necessary to modify the two values of weight factors from the transcriptional changes by newly estimated values of only 8% of the HC V max for G6PD (i.e., 13.5-fold down-regulation) and 7% for phosphogluconate dehydrogenase (i.e., 19.6-fold down-regulation) (see Table 2) at AC. Because the previous study reported no reduction in enzymatic activities of G6PD or phosphogluconate dehydrogenase under photoautotrophic compared to heterotrophic conditions 37 , our findings support the idea that OPP cycle is primarily regulated by post-translational modifications. Finally, our model provided significantly lower fluxes via phosphoglycerate mutase isozymes and the following part of glycolysis in AC cells compared with the published stoichiometric model 20 . This difference can be explained by taking into consideration that the stoichiometric model assumes zero flux via OPP cycle under this conditions 20 (Table 2) and by the different goals of both approaches. Our multi-level kinetic modelling approach aims to match the experimental data, whereas stoichiometric modelling calculates the fluxes to achieve the theoretical maximal growth efficiency of cyanobacterial cells living in a steady state at never changing environment. Nevertheless, the complexity and vast amount of experimental data required for the multi-level kinetic model makes this approach extremely difficult and prone to error. Thus, a comparison with existing stoichiometric models is valuable and future combinations of the multi-level kinetic modelling and stoichiometric modelling should become a standard approach.

Influence of gene expression on metabolic fluxes.
Modelling metabolic levels is sensitive to changes of the kinetic parameters within the model. However, fluxes must also fulfil the mass conservation law-fluxes in linear chains of reactions are the same or lower and split in the branching points in dependence of the kinetic properties of enzymes. Therefore the question arises to what degree are the fluxes influenced by the network topology and how transcriptomic changes influence the kinetic parameters (V max ). We have addressed this question by testing the sensitivity of fluxes against changes of the transcriptome for Synechocystis 6803 and Synechococcus 7942. For this purpose, we collected the measured changes in transcriptome 9,29 , for enzymes involved in our metabolic network, then shuffling them and randomly redistributing them as weight factors of enzymatic activities. Please note that analysis for Synechococcus 7942 was carried out by previous kinetic model 26 with newly implemented calculation of fluxes as described here for model of Synechocystis 6803.
To this end, our in silico experiment for Synechocystis 6803 reveals that randomly redistributed changes (20 independent simulations) in gene expression yield almost identical results in fluxes for intermediates within the Calvin-Benson cycle after shifts from HC to AC conditions (Fig. 3A) as found before using the measured changes in gene expression 29 . Moreover, if we focus on the fluxes out of the Calvin-Benson cycle, we observed some deviations among measured and calculated fluxes. In particular, the fluxes via phosphoglycerate mutase Scientific RepoRts | 6:33024 | DOI: 10.1038/srep33024 and phosphoketolase are affected. They became slightly lower after randomized gene expression changes compared with the fluxes based on measured mRNA levels (Fig. 3A). On the other hand, we can observe an opposite trend for glucose-6-phosphate sink (simplified synthesis of glycogen). All these differences correspond with expected redirection of carbon flux in cells at AC conditions. That means that gene expression changes can contribute to enhance the fluxes via phosphoglycerate mutase or phosphoketolase and to reduce the flux via glucose-6-phosphate sink (Fig. 3A). Taken together, the differences between both scenarios imply a potential minor impact of transcriptional regulation on carbon reallocation and major regulatory role of biochemical control for carbon metabolism in Synechocystis 6803.
Finally, the same analysis showed substantially different results for Synechococcus 7942. As already discussed above, the changes in transcriptome and thus the impact of their redistribution are significantly broader in Synechococcus 7942 9 in comparison to Synechocystis 6803 29 . We observed very high standard deviations of flux rates after assuming random changes in the expression of certain enzymes (Fig. 3B). These deviations were particularly pronounced for the carbon redirection nodes: phosphoglycerate mutase, phosphoketolase and glucose-6-phosphate sink. There we observed 9.6-fold difference for phosphoketolase and 1.8-fold for glucose-6-phosphate sink between the fluxes based on measured and random changes in gene expression, respectively (Fig. 3B). The absence of similar high variability also in phosphoglycerate mutase is probably best explained by the existence of three isozymes of phosphoglycerate mutase in Synechococcus 7942 14 . Thus, these isozymes allow a robust biochemical regulation of this step in Synechococcus 7942 as was observed for many other reactions in Synechocystis 6803, which codes for corresponding more isozymes in its larger genome. Hence, we can conclude that the fluxes in AC on the metabolic crossroads, i.e., on the branching points, are mostly regulated by gene expression changes in the case of Synechococcus 7942 and by the action of different isozymes in Synechocystis 6803 (compare Fig. 3A,B).

Materials and Methods
Comparison of transcriptomic changes was performed for genes encoding enzymes involved in central carbon metabolism after HC (5% CO 2 ) to AC (0.04% CO 2 ) shift from Synechocystis 6803 and Synechococcus 7942. The data were obtained from 8 for Synechococcus 7942 and 29 for Synechocystis 6803. The cyanobacterial strains were grown under almost identical conditions in the two studies and sampling of cells after the HC to AC shifts were done at exactly the same time points. The relative metabolomic data for Synechocystis 6803 cells grown in HC and AC conditions were obtained from 7,8,38 . The consideration of two environmental conditions was necessary to understand and implement the changes in the transcriptomic level of isozymes in the model and was essential for constraining the model. The measured fluxomics data were obtained from 11 , while simulated fluxes via stoichiometric modelling were obtained from 20 . The flux from the multi-level kinetic model was assumed to be equal to the rate of the particular reaction in the steady state.
The kinetic model approach prefers the absolute concentration of metabolites on the cellular level. Therefore, we recalculated the relative cellular metabolic concentrations given in the literature 7,8,38 to absolute values from the ratios to the main CO 2 fixation product 3PGA. The cellular concentration of 3PGA was calculated as 5 mM. This value was obtained exactly as described before for Synechococcus 7942 26 and is similar to the measured concentration of 6.1 mM reported by 38 . We converted optical density as parameter reflecting biomass into cell volume via our calibration curve and assumed that 60% of the total cyanobacterial cell is represented by osmotic freely accessible cytoplasm 26 . The presented model describes the average population behavior of cyanobacteria and cannot distinguish any heterogeneity. The multi-level kinetic model of Synechocystis 6803 for both high and ambient CO 2 conditions is available in the Supplementary Model S1 (high CO 2 ) and Supplementary Model S2 (ambient CO 2 ). A summary of the V max values estimated for Synechocystis 6803 cells grown in HC together with weight factors (fold changes in transcriptome after shifting from HC to AC) is provided in the Supplementary Note S3. The list of differential equations and rate equations (required for particular flux calculations and comparison with measured flux data) is available in the Supplementary Figure S4. The model for Synechococcus 7942 was previously described 26 .
General information about the model. The multi-level kinetic model for Synechocystis 6803 was developed and simulations were executed using the SimBiology toolbox of MATLAB (The MathWorks, Inc., Natick, Massachusetts, United States of America). The routine for parameter estimation was a hybrid genetic algorithm. The model for both high and ambient CO 2 conditions is available in the Supplemental Model S1 (high CO 2 ) and Supplemental Model S2 (ambient CO 2 ) in SBML format L2V4 compatible with MATLAB 2010b and higher. We recommend to open the model either in MATLAB or user friendly COPASI (free academic license).
The final model (Supplemental Model S1 for HC and Supplemental Model S2 for AC) was constrained by metabolic fluxes in HC, growth rate ratio between HC and AC and changes in enzyme quantity using the transcriptomics as well as metabolic levels under HC and AC. The model constraint on energy charge assumed the same ATP · (ADP + ATP) −1 ratio in HC and AC cells, which was maintained in a narrow range 0.74-0.78 as previously proposed 39 . The simulated growth ratio between HC and AC was 3.5 which is similar to experimental value 3.4 reported for Synechocystis 6803, e.g. ref. 40. As shown in Table 1, the comparisons of the simulated and experimental values correspond with each other. Unfortunately, some metabolic concentrations are only available for HC cells. We included these values to further constrain the parameter estimation.
Multi-level kinetic model of Synechocystis 6803. A multi-level kinetic model of the central carbon metabolism of Synechocystis 6803 was generated to analyze the regulatory events and compare these events with Synechococcus 7942. The scope of the model includes the main parts of central carbon metabolism, such as the Calvin-Benson cycle, photorespiration, glycolysis, carbohydrate synthesis, and the OPP pathway. These metabolic reactions were coupled to simplified light reactions and Ci uptake as the main input parameters. Biomass production is one of the main output parameters (see Fig. 1), which is estimated as weighted sum of sink reactions. For example, the sink from ribose-5-phosphate for nucleotides synthesis (Fig. 1) contributes with 5 carbon molecules to biomass production. This simplified approach allowed to estimate the CO 2 fixation under ambient CO 2 level by comparing to relative changes in growth rate of cyanobacteria between HC and AC. The different growth rates are mean values of published data extracted from the previous experiments on HC to AC acclimations of Synechocystis 6803 8,28 or Synechococcus 7942 9 . We assume that the biochemical composition of the two cyanobacterial species is rather similar. Moreover, the biomass in the model is supposed to be equal to the amount of fixed carbon, whereas nitrogen was not a limiting nutrient factor in the experimental setups 41 . The definition of biomass in the model is provided by following equation, based on the model content, in which upper index s stands for accumulation of respective metabolite in the sink (Fig. 1)  The model consists of 54 reactions, 36 metabolites and 182 kinetic parameters. The enzymatic reactions are described by Michaelis-Menten kinetics, except for the light reactions and Ci uptake, which are described by mass action kinetics. The equations for the Calvin-Benson cycle were obtained from previous studies on plant metabolism 23,42 , however, the kinetic parameters were changed (parameter estimation) to the specific conditions (metabolic and flux levels) of the cyanobacterial cell. All reactions, except for the import of external CO 2 , are localized in a single compartment.
The starting point of modelling Synechocystis 6803 was our existing model of Synechococcus 7942 26 , which was modified and extended because Synechocystis 6803 has an approximately 40% larger genome, including some differences in the number and specificity of enzymes for central carbon metabolism (discussed in more detail below). The initial sets of kinetic parameters were obtained from the model of carbon metabolism in C3 plants 42,43 and from our model of Synechococcus 7942 26 .
Kinetic parameters estimation. Initially, we assumed that the principal kinetic properties of the Calvin-Benson cycle are conserved among oxygenic phototrophs. However, the application of kinetic parameters from the previous models 26,42 did not result in an acceptable match (up to 34-fold differences in metabolic level) between the calculated and measured metabolic data for Synechocystis 6803 cells in HC conditions 7,8,38 . Therefore, it was necessary to search for Synechocystis 6803-specific kinetic parameters. For this purpose, we employed a routine called parameter estimation requiring the Global optimization and Optimization toolboxes within MATLAB. As a search method for parameter estimation, the genetic algorithm was used, which mimics natural selection by employing processes as inheritance, mutation, selection and crossover within a population of candidate solutions. This process runs numerous iterations to minimize the measure of the distance among the model predictions and the experimental data. However, parameter estimation can yield several kinetic parameter sets, all offering a good match with the experimental data. To substantially constrain the process of parameter estimation, we added metabolic data from Synechocystis 6803 cells grown under AC conditions 7,8 .
The essential step in identifying the optimized kinetic parameters involves implementation of the connection between both data sets (HC and AC), which, in contrast to traditional kinetic modelling, enabled estimation of one set of kinetic parameters for metabolic reactions describing both HC and AC. To connect the two data sets, Scientific RepoRts | 6:33024 | DOI: 10.1038/srep33024 we used fold changes in the mRNA levels of genes for metabolic enzymes in the model after shifting from HC to AC 29 . These fold changes were used as weight factors of the enzymatic abundances applied on V max of each reaction, assuming a 1:1 ratio between a change in transcriptome and enzymatic amount. This assumption is supported by several studies with bacterial cells, e.g., E. coli 44 and salt acclimated cells of Synechocystis 6803 45 . Further support for this assumption was obtained by our results on glucose-6-phosphate dehydrogenase, which confirmed its post-translational modification (discussed below in the section Is carbon metabolism scalable in response to a changing environment?). Because the resulting model describes two environmental conditions (HC and AC) and implements the transcriptome as well as metabolome data, we refer to it as the multi-level kinetic model of Synechocystis 6803.
Is it possible to further constrain the kinetic parameters? Multi-level kinetic modeling approach represents a significant advancement in parameters constraining in comparison to traditional kinetic modeling. This advancement is based on using a single set of kinetic parameters for more than one system state, e.g., multiple environmental conditions. Moreover, energetic and redox limitations are usually neglected in kinetic modeling, but our approach includes these biological important parameters. Our multi-level kinetic model works with flexible concentrations of ATP and NADPH as these compounds play a crucial role in metabolic regulation within multi-level kinetic modeling 26 . Finally, we assume that prokaryotes evolved toward maximal growth efficiency (in the bounds and costs of adaptive mechanisms towards stress conditions). Thus, the maximal growth rate in HC together with growth rate ratio between HC and AC were used as additional constraining factors for parameter fits. Finally, our current approach includes fluxomic data, which revealed that the parameters estimation procedure itself is flawed in extraordinary cases. In order to match metabolic levels of F6P and G6P, fluxes via futile cycle phosphofructokinase-fructose-1,6-bisphosphatase were several times higher than physiologically possible, but could be corrected after incorporation of flux data. Therefore, including data from additional omics approaches may further improve the accuracy of kinetic parameters. Due to high constraints, we have found only one set of kinetic parameters that allowed matching the experimental data at HC and AC. However, multiple sets of parameter allowed comparable match with experiments on metabolic level after removing the constraint of maximal biomass requirement. Finally, modifications of certain parameters can be compensated to some extent by modifying other one, especially the couple of V max and K M for particular reaction if the substrate and product concentrations do not change significantly in HC and AC. Further model constraints as well as increased knowledge about metabolic regulation can be achieved by implementation of series of measurements based on single mutations (enforcing an adaptation of metabolic network), different light conditions, or other environmental factors affecting the central carbon metabolism.
Systems biology workflow. The integration of various omics data occurred in several steps. In the first step, metabolic and fluxomics data from cells grown at high CO 2 and ATP · (ADP + ATP) −1 ratio were used for identification of kinetic parameters. The next step included data from the high to ambient CO 2 shift by applying the mean values of measured transcript changes as weight factors for each V max estimated for HC. Then, the third step simulated a transition to steady state in AC, calculation of biomass and evaluates the match with metabolic data from cells grown at AC and the growth rate ratio between HC and AC states. The deviation between the simulated and experimental metabolic data could reach up to 100% at this stage. This boundary has been empirically chosen to obtain a broader set of results followed by manual curation and tuning of parameter sets. If no match was found after hundreds of parameter estimation runs made in the first step, the model was re-evaluated and missing reaction(s) or regulatory steps, e.g., isoenzyme or OPP, were implemented. Finally, if the match was improved to deviation below 100% (usually around 25%), the final tuning of kinetic parameters was initiated to improve the match between simulated and experimental data. This fine tuning was partially done by automatic parameter estimation routines and partially manually. Manual tuning and curation of kinetic parameters at the different levels of parameter estimation and data integration is an essential part of modelling, because it provides a deeper understanding of system behavior and helps to detect errors in the algorithms, routines and model structure.

Conclusions
The main goal of this study is to achieve a mathematical description of the response of the central carbon metabolism to different inorganic carbon conditions in Synechocystis 6803, which could help to identify major regulatory processes. Our multi-level kinetic model approach allowed employing the same process of parameter estimation for Synechocystis 6803 as before for Synechococcus 7942 and resulted in a good match on the metabolic level. Furthermore, we demonstrate that the higher number of isozymes present in the larger Synechocystis 6803 genome compared with Synechococcus 7942 allow higher homeostatic stability on the metabolic level against changes in gene expression suggesting the possibility of a shift in metabolic regulation from genetic control in Synechococcus 7942 to enzymatic control in Synechocystis 6803. The only exception is G6PD, an enzyme from the OPP cycle that is active in photoautotrophic conditions as well as during the night. In this case, post-translational modifications are necessary to explain the regulation of G6PD.
To support the notion that the two cyanobacteria control central carbon metabolism on different regulatory levels, we analysed the impact of random changes in gene expression on the fluxes. Our simulation revealed that the AC-induced fluxes at the branching points of the metabolic network are highly dependent on transcriptional changes in Synechococcus 7942 but not in the case of Synechocystis 6803. These findings may be relevant for future attempts to use cyanobacteria for biotechnological purposes. Host strains with greater genomes such as Synechocystis 6803 might be more difficult to engineer toward changes in carbon allocation, since the metabolic network is rather stable due to biochemical regulation. Thus, the introduction of single branches or the up-or down-regulation of specific enzymes will have lower impact than in cyanobacterial hosts with lowered genome Scientific RepoRts | 6:33024 | DOI: 10.1038/srep33024 size such as Synechococcus 7942, in which transcriptional changes via different promoter strength or the expression of additional enzymes will have a bigger impact on the cellular carbon allocation. Finally, our results indicate that the multi-level kinetic modelling of cyanobacterial central carbon metabolism can be used to analyse and optimize cellular carbon reallocation towards specific needs in green biotechnology.