### Culture conditions and sample analysis

*S. platensis* strain C1 was used in this study. Cells were grown at 35 °C in 1,000 ml Erlenmeyer flasks with a culture volume of 500 ml and continuous stirring. Autotrophic and mixotrophic cultures were grown under fluorescent light at 100 μEinstein/m^{2}/s. Zarrouk’s medium [47] was used for autotrophic growth and Zarrouk’s medium with glucose at a final concentration of 20 mM was used for the mixotrophic cultures. For the aerobic-dark cultures (heterotrophic), the flasks were wrapped with aluminum foil and incubated in the dark and sodium bicarbonate in Zarrouk’s medium was substituted by 20 mM of glucose. The control culture was not provided with a carbon source. In this heterotrophic cultivation using various organic or inorganic compounds as a carbon source, the cultures were cultivated in 250 ml flasks containing 100 ml of each tested medium, with three replicates.

The maximum growth rates under autotrophic, heterotrophic, and mixotrophic growth conditions were measured by the optical density at 560 nm and compared with the standard curve. The results from these three conditions are shown in Table 4. For autotrophic growth, the amount of bicarbonate was determined by titration with 0.1 N H_{2}SO_{4}[48]. The level of phosphate was measured as described elsewhere [49]. The maximum uptake rates of both substrates were calculated as 0.20 and 0.0056 mmol/mmol dry cell/h, respectively, in the exponential phase.

### Metabolic network reconstruction

A metabolic network of *S. platensis* C1 was formulated using a combination of two procedures: automatic and manual reconstruction (see Fig. 1). In order to accelerate the process of metabolic network reconstruction, the annotated data of the draft genome sequence of *S. platensis* C1 (NCBI ID 67617) [24] were used as the input for the Pathway Tools software version 13.0 [26, 27], which can automatically generate a preliminary gene-protein-reaction (GPR) association in the network. The PathoLogic algorithm embedded in the software performs the inference process from the entire sequence and functional annotations of *S. platensis* C1 by comparing the data to the MetaCyc database [31] as a key reference. The initial metabolic network consists of connections between the gene sequences, enzymes, metabolites, reactions, and biochemical pathways. Then, the manual reconstruction procedure was performed. Biochemical information related to *Spirulina* from the literature, books and published databases, such as KEGG [32], Brenda [33], CyanoBase [50] and updated Metacyc [31], were used as manually curated data for each pathway, reaction and gene product (enzyme): i) presence/absence pathway and reaction, ii) metabolite and cofactor specificity, iii) directionality of reactions, and iv) GPR association and location. The exchange reactions that allow specific molecules through the system and environment were included in the model according to TransportDB [51]. The Pathway Tools software cannot automatically provide information about protein complexes or isoenzymes. Published information must be used to determine the type of enzyme relationship, which is assumed to be an AND or OR relationship, where the AND relationship indicates cooperation between subunits in protein complexes and the OR relationship indicates the existence of isoenzymes. BLAST [28, 29] was used for assigning enzymatic functions of the missing genes by searching nucleotide sequences against NCBI’s database using the expectation value (E-value) of less than e-5 and the similarity and identity score of 50 %. The top best hits were taken to check for the protein domain against pfam database [30] , if it contains the conserved domain, gene are assumed to be functional orthologues. However, the no gene-association reactions were presented in the refined network, although we could not annotate the corresponding gene sequence in the *S. platensis* C1 genome via the homology search because of its physiological evidence. During the manual curation, iterative modeling was performed using FBA for checking the completeness and consistency of the model and experiment. Some reactions were added to fulfill the system connection based on reactions present in closed organisms. The process of curation is iterative until the gaps in a draft metabolic network are filled [52, 53]. An accepted metabolic network of *S. platensis* C1 was further used to predict growth behavior under autotrophic, heterotrophic, and mixotrophic conditions. Since no biomass composition data for *S. platensis* C1 are available, the stoichiometry of the biomass formation reaction used in this study was obtained from the work of Cogne *et al*[23].

### Topology analysis

In order to analyze the metabolites connected within the network, we formulated a stoichiometric matrix S, derived from reaction lists of *S. platensis* C1. The column and row represent a reaction and a metabolite, respectively; each element is a stoichiometric coefficient. For each network, metabolite connectivity is defined as the number of metabolites that participate in any given reaction. The number of occurrences of each metabolite was calculated to reveal the highly connected metabolites of the reconstructed network. We also compared the metabolite connectivity pattern between the published genome-scale metabolic networks of *Synechocystis* sp. PCC6803 (*i*Syn669) [20], *E. coli (i*AF1260*)*[36], and yeast (*i*FF708) [37].

### Flux balance analysis (FBA)

Flux balance analysis is a modeling technique that requires a developed stoichiometric metabolic network and a list of constraint parameters of biochemical reactions [11, 12]. A set of metabolic reactions are converted into a mathematical stoichiometric format or an S (m × n) matrix, where the rows indicate the metabolites, m, and the columns represent the reactions, n. Based on a pseudo-steady state assumption, the change in growth rate is much smaller than the change in metabolite concentration and flux. Thus, the model could be written as S x v = 0, where v corresponds to a vector of all reaction fluxes in the network. Since the metabolic networks usually possess higher the number of independent reactions than the number of metabolites, the rank of a developed stoichiometric matrix is thus less than the number of reactions fluxes, giving rise to an underdetermined system. Using linear programming, the flux vector can be found by specifying an objective function (*z*) that can be minimized or maximized. In the case of minimization, the linear equation can be written as min *z* = c^{T}v , where c is a row vector representing the influence of individual fluxes on the objective function. The metabolic flux distributions of the network are estimated under given conditions. In addition, the constraint parameters indicate the allowable range of flux values and are needed for convex solution space. The constraints for the upper and lower boundaries of reversible and irreversible reactions were defined as -∞ ≤ v_{i} ≤ ∞ and 0 ≤ v_{i} ≤ ∞, respectively. More details on the FBA approach have been described elsewhere [54, 55].

### Minimization of metabolic adjustment (MOMA)

The algorithm of minimization of metabolic adjustment was introduced by Segre *et al*[46]. This approach uses quadratic programming to search for a point in the feasible solution space of the mutant, which is nearest to an optimal point in the wild-type feasible solution space. The minimal distance is evaluated from the closest point and defined as the Euclidian distance. MOMA is also based on the same stoichiometric constraints as FBA, but it relaxes the assumption of optimal growth flux for the mutants. This method displays a suboptimal flux distribution that is intermediate between wild-type optimum and mutant optimum. In this study, we used the MOMA algorithm available in the COBRA toolbox [13, 14] to carry out the gene essentiality analysis.

### Model simulation

In this work, we used the COBRA toolbox [13, 14] with the Systems Biology Markup Language (SBML) Toolbox v2 [56] on MATLAB to automatically construct the stoichiometric matrix of the reconstructed metabolic network. This tool uses FBA, which uses glpk (http://www.gnu.org/software/glpk/) as the linear programming solver to estimate the optimal flux distributions under the maximized biomass objective. Simulations of three different growth conditions: heterotrophic (with glucose, aerobically in the dark), autotrophic (without glucose in the light) and mixotrophic (with glucose in the light) were performed according to the minimal growth-dependent medium. The uptake rates of carbon, nitrogen, phosphate, and sulfate sources were set and varied under each condition as shown in Table 4. The minimal medium of heterotrophic and mixotrophic growth was supplemented with glucose as the other carbon source. The light reaction was lumped and the photon flux was constrained between zero and 100 μEinstein/m^{2}/s for autotrophic and mixotrophic conditions, while it was set to zero for heterotrophic cell growth. The other external metabolites involved in transport reactions such as H_{2}O, Na^{+}, Mg^{2+}, H^{+}, Zn^{2+}, and Fe^{2+} (see Addition file 1), except for the substrates, were allowed to freely enter or leave the system. The uptake rates of all metabolites absent in the medium were set to zero. The flux values were expressed in mmol/mmol dry cell/h. All the three models in SBML format are provided in Additional files 5-7.

### Active reaction determination

In order to investigate the system-level change in response to the growth conditions we identified modes of metabolic operation under autotrophy and mixotrophy in terms of active reaction presented the non-zero flux value of the simulations. The different *in silico* constraints of the simulation were set according to the carbon source utilized, as described above.

### Flux variability analysis (FVA)

Flux variability analysis is used to examine the full range of numerical values for each reaction flux in the metabolic system while still satisfying the given constraints set and optimizing for a particular objective [44]. Determining the range of flux values (v) through each reaction, maximum value of the biomass objective function (*z*) is first computed and is used as s further constraint with multiple optimizations to minimize and maximize flux values of every reaction through FBA. The mathematical equation can be written as max(*z*
^{T}v). The difference between the calculated minimum and maximum values for each flux defines the flux variability of that reaction. In this study, we used the COBRA toolbox [13, 14] to perform FVA.

### Gene essentiality analysis

The effect of genetic changes such as gene deletion can be simulated by constraining reactions associated to gene of interest to be zero [45]. To determine the effect of genetic perturbation, all reactions associated with each gene in the *i*AK692 model were individually removed while still optimizing the growth rate. This *in silico* analysis was performed using the MOMA algorithm running through the COBRA toolbox [13, 14] under autotrophic and mixotrophic conditions. An essential gene (lethal gene) was defined if no positive flux value for biomass formation could be obtained for a given mutant.

### Phenotypic phase plane (PhPP)

A robustness analysis was performed to determine the sensitivity of the predicted growth in changing the fluxes through a pre-defined range. Phenotypic phase plane is the method which has been used to obtain the sensitivity analysis as a function of dual variables [25]. PhPP analysis was done by varying two particular reactions of interest and iteratively calculating the objective function. The shadow prices of the dual fluxes were evaluated for each solution. In metabolic network, a shadow prices is the rate at which the objective function (*z*) changes in response to an increase availability of each metabolite. Mathematically equation used to calculate the shadow price can be written as: γ_{i} = d*z*/db_{i} where γ_{i} is the *i*th shadow price and b_{i} is the *i*th metabolite of the metabolic network. In this study, we performed PhPP using the COBRA toolbox [13, 14]. The simulation was carried out with autotrophy by setting the boundaries of the absorbed photon fluxes between zero to 100 μEinstein/m^{2}/s; and of the bicarbonate uptake rates between zero to 0.4 mmol/mmol dry cell/h. For mixotrophy, PhPP analysis was performed by varying the boundaries of the glucose uptake rates between zero to 0.034 mmol/mmol dry cell/h and the bicarbonate uptake rates between zero to 0.4 mmol/ mmol dry cell/h.