Genome-scale metabolic models have proven useful for answering fundamental questions about metabolic capabilities of a variety of microorganisms, as well as informing their metabolic engineering. However, only a few models are available for oxygenic photosynthetic microorganisms, particularly in cyanobacteria in which photosynthetic and respiratory electron transport chains (ETC) share components. We addressed the complexity of cyanobacterial ETC by developing a genome-scale model for the diazotrophic cyanobacterium, Cyanothece sp. ATCC 51142. The resulting metabolic reconstruction, iCce806, consists of 806 genes associated with 667 metabolic reactions and includes a detailed representation of the ETC and a biomass equation based on experimental measurements. Both computational and experimental approaches were used to investigate light-driven metabolism in Cyanothece sp. ATCC 51142, with a particular focus on reductant production and partitioning within the ETC. The simulation results suggest that growth and metabolic flux distributions are substantially impacted by the relative amounts of light going into the individual photosystems. When growth is limited by the flux through photosystem I, terminal respiratory oxidases are predicted to be an important mechanism for removing excess reductant. Similarly, under photosystem II flux limitation, excess electron carriers must be removed via cyclic electron transport. Furthermore, in silico calculations were in good quantitative agreement with the measured growth rates whereas predictions of reaction usage were qualitatively consistent with protein and mRNA expression data, which we used to further improve the resolution of intracellular flux values.
Cyanobacteria have been promoted as platforms for biofuel production due to their useful physiological properties such as photosynthesis, relatively rapid growth rates, ability to accumulate high amounts of intracellular compounds and tolerance to extreme environments. However, development of a computational model is an important step to synthesize biochemical, physiological and regulatory understanding of photoautotrophic metabolism (either qualitatively or quantitatively) at a systems level, to make metabolic engineering of these organisms tractable. When integrated with other genome-scale data (e.g., expression data), numerical simulations can provide experimentally testable predictions of carbon fluxes and reductant partitioning to different biosynthetic pathways and macromolecular synthesis. This work is the first to computationally explore the interactions between components of photosynthetic and respiratory systems in detail. In silico predictions obtained from model analysis provided insights into the effects of light quantity and quality upon fluxes through electron transport pathways, alternative pathways for reductant consumption and carbon metabolism. The model will not only serve as a platform to develop genome-scale metabolic models for other cyanobacteria, but also as an engineering tool for manipulation of photosynthetic microorganisms to improve biofuel production.
Citation: Vu TT, Stolyar SM, Pinchuk GE, Hill EA, Kucek LA, Brown RN, et al. (2012) Genome-Scale Modeling of Light-Driven Reductant Partitioning and Carbon Fluxes in Diazotrophic Unicellular Cyanobacterium Cyanothece sp. ATCC 51142. PLoS Comput Biol8(4): e1002460. https://doi.org/10.1371/journal.pcbi.1002460
Editor: Daniel Segrè, Boston University, United States of America
Received: September 26, 2011; Accepted: February 20, 2012; Published: April 5, 2012
Copyright: © 2012 Vu et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The research was supported by the Genomic Science Program (GSP), Office of Biological and Environmental Research (OBER), U.S. Department of Energy, and is a contribution of the PNNL Biofuels and Foundational Scientific Focus Areas (SFAs). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Cyanothece spp. are unicellular, diazotrophic cyanobacteria that temporally separate light-dependent oxygenic photosynthesis and glycogen accumulation from N2 fixation at night . When grown under nutrient excess, Cyanothece sp. strain ATCC 51142 (thereafter Cyanothece 51142) cells can accumulate significant amounts of storage polymers including glycogen, polyphosphates, and cyanophycin . The inter-thylakoid glycogen granules are significantly larger in size than those found in other cyanobacteria, which points at an unusual branching pattern and packaging of this compound. From a biotechnological perspective, this presents an intriguing theoretical possibility to accumulate substantially higher amounts of polyglucose without any significant increase in the number of granules . Cyanothece 51142 is also of interest for bioenergy applications due to its ability to evolve large quantities of H2. Remarkably, H2 production in this organism can occur under light conditions in the presence of O2 and is mediated by nitrogenase , 
Sequencing of the Cyanothece 51142 genome  has enabled application of high-throughput genomic approaches to study the unique physiological and morphological features of this organism. Transcriptomic and proteomic studies have been conducted to analyze global gene expression patterns under a variety of environmental conditions and infer regulatory pathways that govern the organism's diurnal growth , . The availability of genomic information also provides means to construct genome-scale constraint-based models of metabolism, which are powerful tools for systems-level analysis and prediction of biological systems response to environmental cues and genetic perturbations , . Such models have been developed for a variety of biological systems  but only in a few studies has this approach been applied to photosynthetic microorganisms, including Synechocystis sp. PCC 6803 –, Rhodobacter sphaeroides , and Chlamydomonas reinhardtii , . However, the modeling of metabolism in oxygenic photoautotrophs is an intriguing problem due to the complexity of photosynthetic and respiratory electron transport chains, and the potential effects of two distinct photosystems upon the generation and fate of reductant and energy that drives the remainder of metabolism.
In this work, we developed the first genome-scale metabolic model of Cyanothece 51142 and used a combination of computation and experimental approaches to investigate how photosynthetic and respiratory fluxes affect metabolism. Discrete representation of PS II and PS I and their integration with multiple respiratory pathways enabled modeling of photon fluxes and electron flux distributions under conditions of variable light quality and intensity. The predicted changes in growth rates of Cyanothece 51142 in response to changes in light input were experimentally tested using a photobioreactor with controlled sources of monochromatic 630 and 680 nm light. We also carried out computational and experimental analyses of light- and nitrogen-limited chemostat growth of Cyanothece 51142 and used mRNA and protein expression data to constrain model-predicted flux distributions. Both in silico and experimental data suggest that respiratory electron transfer plays a significant role in balancing the reductant (NADPH) and ATP pools in the cells during photoautotrophic growth. This study is a first step towards a systems-level analysis of cyanobacterial metabolism, as it integrates information into a genome-scale reconstruction to understand metabolism qualitatively and quantitatively through a constraint-based analysis . We also discuss strategies for improving internal flux distributions through integration of in silico simulations and data.
Metabolic network reconstruction and initial model validation
To build a constraint-based metabolic model of Cyanothece 51142, a genome-scale metabolic network was reconstructed using the genome annotation and data from NCBI , SEED , KEGG –, and CyanoBase , . The resulting iCce806 network contains 806 genes and 667 metabolic and transport reactions (see Dataset S1 and Tables S1, S2, S3 for network details). Most of the 42 reactions without genes associated with them were added to complete metabolic pathways needed for biomass production. The final reconstruction encompasses central metabolic pathways such as the Calvin-Benson cycle, the pentose phosphate pathway (PPP), reactions within the tricarboxylic acid (TCA) cycle, as well as, the complete set of anabolic pathways involved in biosynthesis of glycogen, cyanophycin, amino acids, lipids, nucleotides, vitamins, and cofactors. Pathways for glycolate synthesis (via ribulose-1,5-bisphosphate carboxylase/oxygenase, i.e., photorespiration), glycolate conversion to serine, and glycerol catabolism are also included. Photosynthetic electron transfer associated with the thylakoid membrane is represented as a set of four separate reactions, including light capture by photosystem II (PS II) and photosystem I (PS I), electron transfer between the two photosystems, and cyclic electron transfer around PS I. Similarly, respiratory electron transfer is represented by reactions catalyzed by terminal cytochrome c oxidase (COX), quinol oxidases (QOX, both bd- and bo-types), NADH dehydrogenases (NDH, type 1 and 2), and succinate dehydrogenase. In addition, two reactions (NADP+- and ferredoxin- requiring) for flavin-dependent reduction of O2 (i.e., Mehler reactions) were included. A simplified scheme of the photosynthetic and respiratory electron transfer reactions in iCce806 is shown in Figure 1.
Linear photosynthetic electron transfer: electrons from photosystem II (PS II) to photosystem I (PS I) are transferred through plastoquinone (Pq), cytochrome b6f complex (Cyt b6f), plastocyanin (Pc) and cytochrome c6 (Cyt c6). From PS I electrons can be transferred to ferredoxin (Fd) via ferredoxin:NADP+ reductase (FNR) and subsequently to generate reductant in the form of NADPH. Cyclic photosynthetic electron transport: electrons can flow from Fd to Pq (FdPq reaction). Respiratory electron transfer: includes two cytochrome oxidases (COX), two cytochrome-quinol oxidases (QOX), and two types of NADH dehydrogenases (NDH-1 and NDH-2). Alternative sinks for reductant beyond CO2 fixation: reduced Fd can be used by the nitrogenase (Nif) and by Mehler reactions to reduce O2. Bidirectional hydrogenase (Hox) can reversibly produce H2 using NAD(P)H as an electron donor, while the uptake hydrogenase (Hup) consumes H2 using Fd as an electron acceptor. Protons transferred across the thylakoid membrane are used by the ATPase to drive ATP synthesis.
For initial testing, we examined the ability of the constraint-based model of iCce806 to predict growth under photoautotrophic (using light and fixing CO2), heterotrophic (using glycerol in the dark), and photoheterotrophic (using glycerol and light) conditions with different nitrogen sources. In silico calculated biomass yields, which simulated carbon or light- limited growth (Figure S1), qualitatively agreed with previously reported growth data for Cyanothece 51142 , , . Other non-growth conditions that were simulated with the model, included nitrogen fixation as occurs during the dark phase of Cyanothece's ciracadian cycle . In this case, the oxidation of glycogen provides reductant and ATP for nitrogenase, and we examined the model's ability to quantitatively predict the amount of nitrogen (N2) that could be fixed and stored in the dark, by maximizing cyanophycin production from glycogen. Although H2 is an obligate co-product of the nitrogenase reaction, no H2 was produced in the initial simulations under dark N2-fixing conditions, contradicting experimental observations. Model examination revealed that all of the nitrogenase-generated H2 was utilized by hydrogenases to reduce NAD(P) and ferredoxin, which ultimately increased cyanophycin production. When the three hydrogenase reactions (HDH_1, HDH_2, and UPHYDR) were eliminated from the model, the predicted ratio of fixed N2 to consumed glycogen depended on the non-growth associated ATP requirement (NGAR), and was estimated to be 0.3 (NGAR = 2.8) or 0.67 (NGAR = 0) mole N2/mole glycogen, which was in accordance with an experimentally measured value of 0.51 . Under this condition, the model predicted that H2 production would have same yields as fixed N2 (0.3 to 0.67 mole H2/mole glycogen) due to the stoichiometry of the nitrogenase reaction.
We also evaluated how fluxes through electron transfer reactions are affected by the nitrogenase flux under N2-fixing dark conditions. With glycogen being the sole source of reductant for both ATP-generating oxidative phosphorylation and N2 reduction, a balance between fluxes through respiratory pathways and nitrogenase reaction is needed. In the absence of the hydrogenase reactions, the model predicted that O2 reduction via COX, QOX, or Mehler reactions are required to consume NADH resulting from glycogen catabolism (Figure S2). The model predicts that the COX reaction is required to achieve the maximum N2 fixation rate since it generates more ATP than the QOX or Mehler pathways (∼9 O2 are needed per N2 fixed). This is consistent with the results from recent proteomic studies showing the CoxB1 (cce_1977) subunit of COX is more predominant during the dark , . These results suggest terminal oxidases are important under dark N2-fixing conditions not only to generate an intracellular anaerobic environment for nitrogenase, but also to provide ATP for nitrogenase activity.
As photosynthesis and respiratory electron transport chains are interconnected in cyanobacteria , these pathways were allowed to interact in the iCce806 model. To perform model robustness analysis, we computationally explored the impact of key photosynthetic and respiratory pathways on growth rate and intracellular flux distributions under varying photon uptake flux for PS I, while the photon uptake flux for PS II was fixed at 20 mmol·g−1 AFDW·h−1 (Figure 2). First, the model was evaluated assuming only linear photosynthetic electron transfer. In this case, all alternative reductant sinks including the proton and O2 reduction as well as cyclic photosynthetic reactions around PS I were eliminated from the model (Figure 2A). Under this condition, growth only occurred at one value of photon uptake flux for PS I and extracellular organic products (ethanol, lactate and/or alanine with trace amounts of formate) would have to be secreted in order to generate enough ATP to support biomass production. Second, when cyclic photosynthetic reactions were added back, the photon uptake flux for PS I could vary with a fixed photon uptake flux for PS II, but significant amounts of extracellular products were still formed until the photon uptake flux for PS I exceeded ∼85 mmol·g−1 AFDW·h−1 (Figure 2B). No growth occurred unless PS I photon uptake flux was greater than or equal to the photon uptake flux for PS II. Only when the model was allowed to use both cyclic photosynthesis and O2 reduction reactions were no extracellular products predicted and the photon uptake flux for PS I could be less than that for PS II (Figure 2C). Since experimental data does not indicate that any by-products including H2 or organic acids are produced by Cyanothece 51142 at a detectable level during photoautotrophic growth with excess ammonium, a plausible mechanism for balancing growth through the generation of additional ATP may involve activity of the cytochrome oxidases.
(A) Effects of removing cyclic photosynthesis (via NDH-1, NDH-2, FdPq, G3PD_PQ, and SUCD_PQ) and alternative reductant sinks (H2 production, COX, QOX, and Mehler reactions). (B) Effect of removing alternative reductant sinks but including all routes for cyclic photosynthesis. Shaded regions indicate that multiple flux values can achieve maximal growth rate. (C) All photosynthetic and respiratory electron flow routes operate, except H2 production.
Effect of light quality on cellular growth and pathway utilization
The discrete representation of PS II- and PS I-mediated reactions and their interactions with multiple respiratory reactions in iCce806 enabled further in silico analysis of growth and electron flux distributions under photoautotrophic conditions of variable light quality and intensity. In this case, the complete model was used to explore which reactions would be used to support maximal photoautotrophic growth rates for different levels of PS II and PS I photon uptake fluxes. To predict the corresponding growth rates under light-limited conditions, we constrained the photon uptake fluxes (ranging from 0 to 60 mmol·g−1 AFDW·h−1) through each photosystem. The resulting phenotypic phase plane (PhPP) contained three distinct regions (Figure 3A): in two regions growth was limited only by fluxes through PS II (region 1) or PS I (region 3), while in region 2 growth was limited by both PS II and PS I photon uptake fluxes (i.e., increases in either flux would improve growth rate). By adding artificial ATP or NADPH generating reactions (ADP+HPO4+H→ATP+H2O and NADP+H→NADPH) to the model and analyzing changes in predicted maximal growth rates, we were able to identify that in regions 1 and 3 growth was NADPH/reductant-limited, while in region 2 it was limited by energy supply (Figure 3A).
(A) 2-D phenotypic phase plane (PhPP) displaying maximum growth rates for varying photon uptake rates. The PhPP has 3 distinct regions – in regions 1 and 3, flux through a single photosystem limit growth rates, whereas in region 2 flux increases through either photosystem will increase growth rate. (B) Pathway maps of electron transfer reactions in different PhPP regions. PhPP flux variability analysis was performed to see which flux is always required (red arrows), optional (green arrows), and blocked (blue arrows) across each of the three PhPP regions.
To analyze the effect of photon uptake rates on electron flux distributions, we calculated the flux ranges using flux variance analysis (FVA) for all photosynthetic and respiration reactions within each PhPP region (Figure 3B). In this instance, PhPP FVA was run with constraints that restrict the model to a given region and to the maximum growth for each point in the region (in contrast, standard FVA is used at a single point in a region). Using PhPP FVA, we identified active (both minimum and maximum flux values are positive or negative), inactive/blocked (minimum and maximum fluxes are both zero), and optional (which could have at least one zero and one non-zero flux value somewhere in the region) reactions leading to optimal solutions in each PhPP region. This new analysis technique allowed classification of reaction usage across entire regions of the PhPP and is not restricted to fixed points within a region. While linear photosynthesis was active and Mehler reactions were blocked across the entire PhPP, there were differences in the usage of photosynthetic and respiratory reactions observed within all three regions (Figure 3B). Surprisingly, while generation of NADPH from reduced ferredoxin via linear photosynthesis is the key source of reductant, ferredoxin-NADP+ oxidoreductase (FNR) was predicted to be active in region 2, but optional in regions 1 and 3. Closer examination of in silico calculated electron flux distributions revealed that, in addition to FNR, the model utilized a cycle involving glutamine synthetase, glutamate synthase and transhydrogenase, resulting in ATP-driven NADPH production. In regions 1 and 3, the model predicts there is excess ATP, and so this cycle can be used instead of FNR to move electrons from ferredoxin to NADPH. However, this cycle is unlikely to be of any physiological relevance since there has been no experimental data supporting this route for making NADPH, and FNR is essential for photoautotrophic growth in unicellular cyanobacteria such as Synechococcus 7002 . Differences in the predicted usage of respiratory reactions were also found. In region 1, where growth is limited by the flux through PS I, at least one of the COX and QOX reactions must be active to oxidize excess electron carriers (Pc, Cyt c6, or Pq) generated from PS II. Similarly, in region 3 under PS II flux limitation, excess electron carriers (Pq, Fd) must be reduced via NDH-1 or –2 or ferredoxin-dependent cyclic electron transfer (FdPq). Conversely, due to ATP limitation in region 2, the model favored reactions with higher proton pumping capacities and so both the QOX and FdPq reactions were inactive. The usage of COX was optional in region 2 and depended on photon uptake rates (e.g., COX reaction was inactive at the boundary between regions 2 and 3).
The model predictions (Figure 3A) were compared to batch growth experiments in the LED-photobioreactor which allowed instantaneous measurements of initial growth and photon uptake rates by Cyanothece 51142 cells exposed to different intensities and ratios of 630 and 680 nm light (Table 1). When Cyanothece 51142 cultures were illuminated with both 630 nm and 680 nm light, initial growth rates generally correlated with the total photon flux through PS II and PS I, with higher growth rates observed at 80 mmol·g−1 AFDW·h−1 total photon flux and 630 nm∶680 nm light ratio of 2∶1. When cultures were exposed to only a single wavelength of light (batch experiments 6–10), i.e., either 630 or 680 nm, Cyanothece 51142 cells displayed a similar trend with higher growth rates observed at higher photon flux intensities. The predicted growth rates were within 7% of the experimentally measured values, except for the two cases where single 630 nm wavelength irradiances were used (Table 1). The reasons for this are unclear but may be due to other physiological and/or biochemical phenomena such as state transitions that are not contained within the model but are operating in vivo.
Data from these batch experiments (batch experiments 1–5, Table 1) were also used to estimate the growth (GAR) and non-growth (NGAR) associated ATP requirements. NGAR is the amount of energy spent to maintain the cell (i.e., maintenance energy). GAR is defined as energy expenditures used on protein and mRNA turnover or repair, proton leakage, and maintenance of membrane integrity; it does not include ATP spent on polymerization reactions, which are already accounted for in the macromolecular synthesis pathways of the network. The time-averaged growth and photon uptake rates were used to constrain the model and the maximal amount of ATP hydrolysis was calculated (Figure S3) for each batch experiment. A plot of growth rate versus maximum ATP hydrolysis flux was generated and a linear fit used to estimate the GAR and NGAR values . Specifically, the slope of the fitted line is the GAR (544 mmol·g−1 AFDW·h−1), and the y-intercept is NGAR (2.8 mmol·g−1 AFDW·h−1). The estimated GAR value is significantly higher than those reported from other bacteria ; however, these model estimates assume that all absorbed photons lead to photosynthetic fluxes (100% quantum efficiency) and that the overall efficiency of ATP production via all electron transfer reactions (photosynthetic and respiratory) are accurate. Depending on the growth condition the quantum yields can change, and for Cyanothece 51142 this value was reported to be between ∼70–100% for photoautotrophic growth . Upon further analysis, we found the estimated Cyanothece ATP requirements were most sensitive to reductions in quantum efficiency and the amount of ATP generated by photosynthesis and respiration (Table S4). Since neither quantum efficiency nor combined photosynthetic and respiratory ATP production were experimentally measured for Cyanothece 51142, the original estimates, GAR = 544 and NGAR = 2.8 were used in all growth simulations.
Experimental analysis of ammonium- and light-limited growth
Chemostat cultures grown under light and ammonium limitations were used to calculate metabolic fluxes and further understand reductant partitioning pathways in Cyanothece 51142. The differences in biomass composition between these growth conditions indicated a major shift in carbon partitioning pathways (Figure 4; and Table S5). In ammonium limited cultures, carbohydrates comprised almost half of cell biomass; in contrast, under light limitation, Cyanothece 51142 cells contained higher amounts of protein, nucleic acids, and approximately 10% cyanophycin. The quantitative biomass composition measurements were used to generate two separate biomass equations for the metabolic model; experimentally measured growth rate, photon uptake rates, and O2 production rates were included as additional model constraints (Table S6, in this case no mRNA or protein expression data is used by the model). Using FBA and through minimization of the overall flux magnitude, we calculated representative flux distributions under light and ammonium limitations (values listed in Table S1). As expected, changes in flux values were consistent with differences in measured biomass compositions used in the simulations: under light limitation, fluxes increased for reactions involved in biosynthesis of amino acids, nucleotides and cyanophycin, while ammonium limitation resulted in flux increases for glycogen biosynthesis.
Comparisons of global transcriptome profiles displayed by Cyanothece 51142 during ammonium- and light-limited chemostat growth also reflected the rewiring of cellular metabolism (Table S7). Under ammonium limitation, significant increase in relative mRNA abundances was observed for genes involved in N2 fixation (cce_0198, cce_0545–0579), iron acquisition (cce_0032–0033, cce_1951, cce_2632–2635), respiratory electron transport (cce_1665, cce_3410–3411, cce_4108–4111, cce_4814–4815) as well as peptide transport, synthesis, and protein repair (cce_0392, cce_1720, cce_3033, cce_3054–3055, cce_3073–3075). Among the most highly expressed genes in ammonium-limited Cyanothece 51142 cells was the one encoding 6-phosphogluconate dehydrogenase (cce_3746), a key PPP enzyme. Under light limitation, the major changes in the transcriptome of Cyanothece 51142 included upregulation of genes encoding: components of the photosynthetic apparatus and electron transport chain (cce_0776, cce_0989–0990, cce_1289, cce_2485, cce_2959, cce_3176, cce_3963); pigment biosynthesis (cce_0920, cce_1954, cce_2652–2656, cce_2908, cce_4532–4534); CO2 uptake and fixation machinery (cce_0605, cce_3164–3166, cce_4279–4281); ATP synthase (cce_2812, cce_ 4485–4489), and protein synthesis machinery (cce_ 4016–4030) (Table S7).
Global proteome profiles of Cyanothece 51142 corroborated the shifts in gene expression (Table S8). The abundance of proteins from central metabolism (glycolysis, TCA, and pentose phosphate pathway) all had significant differences between cells grown under ammonium- and light-limited conditions. Enzymes of the oxidative PPP branch, namely glucose-6-phosphate dehydrogenase (cce_2535–2536), 6-phosphogluconolactonase (cce_4743) and 6-phosphogluconate dehydrogenase (cce_3746), showed increased abundances under ammonium limited conditions. Similarly, two-fold increase in abundance levels was observed for gluconeogenesis proteins, including fructose 1,6-bisphosphatase (cce_4758), glucose-6-phosphate isomerase (cce_0666), glyceraldehyde-3-phosphate dehydrogenase (cce_3612), and phosphoglycerate kinase (cce_4219). In contrast, relative abundances of proteins catalyzing the conversion of glycerate-3P to pyruvate (cce_1789 and cce_2454) were unchanged or up-regulated (pyruvate kinase cce_3420) in light-limited cells. Consistent with the results from global mRNA profiles was the up-regulation of Cyanothece 51142 proteins involved in photosynthesis and carbon fixation under light-limited conditions (Table S8). Notably, two key components involved in the electron transfer to PS I, namely plastocyanin (cce_0590) and cytochrome b6 (cce_1383), displayed elevated peptide abundances in light-limited cells.
Using experimental measurements and in silico mutagenesis to restrict the range of predicted flux distributions
Since there may be more than one flux distribution that is consistent with the experimentally measured rates of growth, photon uptake, and O2 production we used FVA to identify required (flux must be non-zero), optional (flux may or may not be zero), or inactive (flux must be zero) reactions under light- and ammonium-limited growth conditions. As our initial simulations (Table 2) produced a large number of optional reactions (170 out of 667 for both growth conditions), that represent uncertainty regarding usage, we subsequently used the transcriptome and proteome data (TPD) to further constrain the model. Using a modification to a previously developed approach , we obtained a flux distribution that was consistent with measured rates and TPD while reducing the overall flux magnitude (Table S1). In this analysis, flux was favored through reactions for which proteins were detected and disfavored through reactions associated with undetected proteins and transcriptome data less than a given threshold (e.g., log2 of mRNA expression level is less than 8). The model constrained by TPD predicted that the majority of reactions in central metabolism would be active under both chemostat conditions (Figure 5). In addition, we subsequently applied FVA employing additional constraints arising from the TPD. Comparison between FVA results with and without TPD constraints demonstrated a significant decrease in the number of ambiguities (the optional reaction set) when TPD is used (Table 2).
The flux values (mmol·g−1 AFDW·h−1) are those where the flux distribution best matches the transcriptome and proteome data (TPD) while also minimizing the magnitude of all fluxes in the network. The flux values in red and green represent ammonia-limited (AL) and light-limited (LL) conditions, respectively. Arrow colors indicate relative flux ratios between AL and LL conditions.
While the number of optional reactions was reduced by incorporating TPD into the model, the flux spans (difference between maximum and minimum values) of individual fluxes was still large (>30 mmol·g−1 AFDW·h−1 for some central metabolic reactions, Table S1). These large flux spans could arise from cycles or alternative pathways in the model, and deleting these features from the model could subsequently reduce the flux spans. FVA was repeated using measured growth, photon uptake, and O2 release rates under light-limited conditions as constraints and with optional reactions were deleted (similar results were found for ammonia limited conditions, data not shown). Flux spans for reactions in central metabolism (Figure 5) were then calculated for a series of single or double reaction deletions in silico. The purpose of this analysis was to identify those reactions that exert the greatest impact on the flux span in central metabolism (Figure 6A). Single deletions of glyceraldehyde-3-phosphate dehydrogenase (GAPD or GAPD_NADP) or hydrogenase (HDH_1) reduced the average central metabolic flux span the most (from 74 to 22 mmol·g−1 AFDW·h−1). Other single deletions with significant effects included FNR and NDH-1, which are involved in photosynthesis and respiration. The reaction deletions shown in Figure 6A all had a larger impact on reducing average central metabolic flux span than did imposition of constraints based on TPD. There were cases where single deletions had large effects on other specific reactions, but only modest effects on overall central metabolic flux spans. For example, a single deletion in phosphogluconate dehydrogenase (PGDHr) reduced the span for glucose-6-phosphate isomerase flux (PGI) to 0 (Figure 6B), but only reduced the average central metabolic flux span by ∼0.7 mmol·g−1 AFDW·h−1. The in silico analysis of double reaction deletions did not yield any new double deletions that would reduce the average central metabolic flux span significantly. However, some double deletions strategies did reduce flux spans of individual reactions.
(A) Effects of deletions are compared to the cases where no reactions were deleted (red bar), or TPD were used as constraints (green bar). The values represent the average flux span across all reactions in central metabolism. Only deletions which lower the flux span by at least >1 mmol·g−1 AFDW·h−1 are presented. (B) Changes in flux spans for specific reactions catalyzed by ribulose bisphosphate carboxylase (RBC) and phosphoglucose isomerase (PGI) between simulations that (i) use TPD data as a constraint (green bars), (ii) delete single reactions (blue and purple bars), (iii) delete two reactions (yellow bar) or (iv) impose no additional constraints (red bars). Reaction abbreviations match those listed in Table S1.
Several cyanobacterial metabolic models (all for Synechocystis PCC 6803) have been published, which represented photosynthesis as two lumped reactions ,  for linear (PSII, Cyt b6f, PSI, and FNR) and cyclic (PS I and Cyt b6f) pathways. In this study, we modeled photosynthesis as a larger set of separate reactions  as this structuring allowed analysis of the effects of different illumination on the production and partitioning of reductant through photosynthetic and respiratory reactions, as well as the contribution of different electron transfer pathways to growth. Our PhPP FVA results showed how different photosynthetic and respiratory electron transport chain components are used to maximize biomass production under different lighting regimes. It was not surprising that linear photosynthesis was active in all three regions because the cell needs photons from both PSI and PSII to grow under photoautotrophic conditions. However, the Mehler reactions were inactive in all three regions when we only consider maximal growth rate solutions. In regions 1 and 3, reducing equivalents (e.g., NADPH) limit growth and the Mehler reactions would lower the amount of reducing equivalents available for growth. The Mehler reactions are less energetically efficient than NADH dehydrogenase and cytochrome oxidase so the model would not use them in region 2, where ATP is limiting. So while the Mehler reactions can carry flux in the model, using these reactions lowers the maximum growth rate making them inactive (blocked reactions) in our PhPP analysis. A recent study showed that the Mehler reactions are operational in Synechocystis sp. PCC 6803, serving as a sink for excess electrons . These reactions are also likely to be active in Cyanothece 51142, since the associated proteins were detected in the proteomic data (Table S8). As a result the model only predicted non-zero Mehler fluxes when the proteomic data were used to constrain the model (Table S1).
In the absence of cyclic photosynthesis, other products including water (produced by COX, QOX or Mehler reactions), H2 (via hydrogenase), or small organic compounds (alanine, ethanol, lactate and formate) were predicted to be necessary in order to balance the electrons and ATP needed to support growth. In the presence of linear and cyclic photosynthesis reactions, these products must also be produced unless significant amounts of cyclic photosynthesis occurs (>3 times the amount of linear photosynthesis). Since H2 and small organic compounds are not generally produced under photoautotrophic conditions with excess ammonium, any additional energy is most likely supplied by cytochrome oxidase activities that reduce photosynthetically produced O2. Interestingly, in the absence of cytochrome oxidase activities in the model, the PS I fluxes must always be greater than or equal to the PS II fluxes. It was shown that the marine cyanobacteriium Synechococcus has a PS I/PS II protein ratio >1, which has been explained as a mechanism to protect PS II from photo-damage . Under conditions with high levels of PS II activity, cytochrome oxidase activity may ensure an adequate supply of oxidized plastoquinone (needed for PS II) and reduce O2 concentrations to limit photorespiration.
Similarly, cyclic electron flow via NADH dehydrogenase- or ferredoxin-dependent routes have also been experimentally demonstrated to play important roles in balancing the amount of NADPH and ATP produced via photosynthesis. Synechocystis 6803 mutants lacking ndhD genes (encoding subunits of NDH-1) had significantly lower cyclic photosynthesis activity . Although the mechanism of electron transfer from ferredoxin to the plastoquinone pool (without using NDH) is still unclear, its activity has been demonstrated in green algae  and higher plants . Our computational simulations also showed that, under light-limited photoautotrophic conditions, cyclic electron transfer involving NADH dehydrogenase (NDH-1) is needed for maximal growth if ATP (rather than NADPH) is limiting. In an environment where PS I photon availability is high relative to PS II, cyclic electron transport is needed (Figure 2) to increase availability of PS I substrates (reduced PC or Cyt c6) and protect against photo-damage. Cyclic electron flow has been experimentally shown to help protect the photosynthetic apparatus from photo-damage –
In addition to studying the interactions between components of the photosynthetic and respiratory components computationally, we also experimentally evaluated cells grown under continuous light conditions in light- and ammonia-limited chemostats. The measured 630 nm and 680 nm photon uptake and O2 production rates suggests that reductant was being directed towards O2 via the Mehler, QOX, and/or COX reactions. In both chemostat conditions, the model predicted that steady-state growth rate could have been achieved using lower photon uptake rates by decreasing the amount of reductant generated by PS II that was predicted to reduce O2.
A limitation to flux balance analysis is that a wide range of flux values may be consistent with the constraints in the computational model. An iterative application of computational and experimental methods is an important strategy to improve the comprehensive understanding of cyanobacterial metabolism. We have begun to apply this iterative approach, by including mRNA and protein expression datasets as additional constraints beyond biomass composition and physiological rate measurements. Experimentally-measured TPD were successfully used to further constrain the model, and thereby reduce uncertainty and increase the number of required (that is, metabolically active) reactions (Table 2). However, there remained discrepancies in that the model did not predict flux through all reactions for which proteins were experimentally detected. Such discrepancies can be used to subsequently improve the model with previously developed approaches –. For example, an earlier version of the model did not predict flux through proline oxidase, even though proteome data demonstrated that proline oxidase was synthesized. This prediction arose because the model did not contain a reaction in which FADH2 (a product of the proline oxidase reaction) could be reoxidized to FAD. After experimental confirmation that proline can be used as a nitrogen source (implying activity of proline oxidase) by Cyanothece 51142 (data not shown), a FADH2 recycling reaction was included in the final iCce806 model.
Even with these additional TPD constraints, a wide range of flux values remained feasible (Figure 6). We should note that we did not take real enzymatic activities into account (which can be affected by post-translational modifications), as we did not have this type of data for the two conditions examined. Such data, if available, could be used as additional factors for determining whether to favor or disfavor fluxes through associated reactions (See Material and Methods). Other constraint-based methods for incorporating gene expression data use similar Boolean on/off type of constraints to restrict fluxes , ,  and would be expected to yield results similar to those described herein. Thus, novel computational methods which can more quantitatively constrain the metabolic flux values are still needed. The strategy of evaluating fluxes for reaction deletions in silico can be used to identify knockout mutants that can potentially improve the resolution of intracellular flux distributions. A flux that is well resolved would have a small span meaning we can more definitively state its value. If the mutants show no growth defects then the corresponding reactions may not be used under the conditions tested, or alternative pathways not included in the model may occur. Either way, this information could be used to better resolve the intracellular flux distribution or improve the metabolic model. For Cyanothece 51142, this would require development of a genetic system (such a system already exists for another Cyanothece strain ) as experiments with mutants would have the most potential to improve resolution of central metabolic fluxes during photoautotrophic growth. Also, as a complement to the in silico reaction knockouts that our simulations predict would reduce the flux spans associated with central metabolic reactions, the photobioreactor employed here provides a system whereby cultivation conditions can be rigorously controlled and some aspects of physiological state monitored continuously. In addition, cells from steady-state or perturbed cultures can be interrogated via physiological or biochemical analyses to experimentally test the predictions of the computational models for wild type or mutants. As the number of available cyanobacterial models continues to grow, cross-species physiological, genomic, and metabolic comparisons will enable the identification of core networks and contribute towards improving our understanding of metabolic processes in cyanobacteria.
Material and Methods
Culture and growth conditions
Cyanothece 51142 was grown in modified ASP2 medium  amended with 0.75 mM K2HPO4, 0.03 mM FeCl3•6H2O, and 17 mM NH4Cl which substituted NaNO3 as the nitrogen source. Routinely, the cells were maintained under continuous white light illumination (50 µmol photons·m−2·s−1) in 1-L Roux bottles sparged with CO2-enriched air (0.3% vol/vol). Culture purity was confirmed by plating on DIFCO Bacto Tryptic Soy Broth and DIFCO Luria-Bertani solid media (BD Diagnostic Systems, Franklin Lakes, NJ) as well as by phase contrast or acridine orange fluorescent microscopy.
Controlled batch and chemostat cultures of Cyanothece 51142 were grown in a 7.5-L borosilicate glass vessel operated at 5.5-L working volume under the control of New Brunswick Bioflo 3000 bench-top bioreactor (New Brunswick Scientific, Edison, NJ). The vessel was housed in a custom-made black anodized aluminum enclosure equipped with light-emitting diodes (LED) generating 680 nm and 630 nm light for the preferential excitation of chlorophyll a and phycobilin pigments, respectively. Built-in sensors allowed for automatic adjustment of incident and transmitted light intensities using custom-designed control module. Both hardware and software components of the LED enclosure and the control module were developed at Pacific Northwest National Laboratory (US Patent Application # 20100062483; http://appft1.uspto.gov). All experiments were carried out under continuous illumination in modified ASP2 medium sparged with CO2-enriched argon (Ar) (0.2% vol/vol). Agitation, temperature, pH, and gas flow rates were maintained at 250 rpm, 30°C, 7.4, and 2.8 L/min, respectively. Incoming and off-gas composition was constantly monitored by an in-line mass spectrometry based gas analyzer MGA iSCAN (Hamilton Sundstrand, Pomona CA). Cell density was monitored spectrophotometrically at 625, 678, and 730 nm.
To establish a light-limited chemostat culture, the photobioreactor was inoculated with 10 mL of mid-log phase Cyanothece 51142 cells and maintained as a batch culture under 630 nm and 680 nm illumination at 40 and 70 µmol photon·m−2·s−1, respectively, until the culture reached late logarithmic stage. Chemostat mode was initiated by continuous inflow of medium at a dilution rate of 0.05 hr−1 that resulted in a steady-state optical density (OD730) of 0.20. Similarly, a nitrogen-limited continuous culture of Cyanothece 51142 was established using low-nitrogen ASP medium containing 0.75 mM NH4+. The ammonium-limited chemostat was maintained under identical operating conditions in regard to the culture dilution rate and optical density under incident light at 38.5 and 73.5 µmol photon·m−2·s−1 for 630 nm and 680 nm wave lengths, respectively).
The light uptake fluxes (mmol·g−1 AFDW·h−1) were determined by multiplying the light consumption rates (µmol photon m−2s−1) by the surface area of cell culture exposed to light (m2) and dividing by the amount of biomass in the reactor (g AFDW). The light consumption rates were determined by subtracting the transmitted light intensity from the values of incident light intensity after corrections were made for the abiotic consumption of light to account for the gas bubbles and probes in the reactor. Cells in the 5.5 L working volume were assumed to be equally exposed to the light at all times. Based on the inner diameter and height of the liquid culture at working volume, the surface area was 0.1403 m2. The amount of biomass in the reactor was determined from the working volume and biomass concentrations.
Biomass ash-free dry weight (AFDW) was measured using centrifuged (11,000× g, 4°C) cell pellets as described previously . Total protein, reducing carbohydrates, RNA, and DNA were assayed using standard analytical techniques –. The total lipid fraction was measured gravimetrically after an extraction from a known volume of freeze-dried culture using previously published methodology . Total reducing carbohydrates were quantified using the anthrone method  with glycogen as the standard. Chlorophyll concentrations were measured as described elsewhere , . Amino acid composition was analyzed in acid-phenol hydrolyzed samples prepared using Eldex hydrolysis/derivatization station (Eldex Laboratories, Inc., Napa, CA) . The derivatized samples were resolved on a 4-µm AccQ-Tag Nova-Pak C-18 column (3.9 mm×150 mm, Waters Corp., Milford, MA, USA), eluted using a linear gradient of acetonitrile (from 1.2% to 4.2% over 15 min.; from 4.2% to 6% over 4 min.; from 6% to 20% over 12 min.; at 20% over 1 min.; from 20% to 60% over 1 min.) with a flow rate of 1.0 ml/min at 37°C, and detected at 254 nm (HPLC system and UV detector by Shimadzu, Tokyo, Japan). Cyanophycin was estimated based on relative amino acid values and total protein measurements (see Text S1 for details).
Microarray expression analysis
Previously developed whole-genome oligonucleotide microarrays of Cyanothece 51142  were manufactured by Agilent Technologies (Santa Clara, CA). RNA isolation, labeling, hybridization, and data analysis were performed by MOgene, LC (St. Louis, MO) using published protocols .
Cell lysis and tryptic digestion followed a previously described “global protein preparation” scheme . A reference peptide database was prepared using strong cation exchange fractionation (10 fractions) of a portion of each global digest, as previously reported –. The methods for capillary liquid chromatography and mass spectrometry have been described in detail elsewhere , , . Here, the HPLC mobile phase was 0.1% formic acid in water (A) and 0.1% formic acid in acetonitrile (B). A Finnigan LTQ ion trap mass spectrometer (ThermoFinnigan, San Jose, CA) was used for MS/MS analysis of SCX fractions and an LTQ-Orbitrap (Thermo) was used for high-resolution MS analysis of the global unfractionated samples. Each of the 10 SCX fractions was analyzed once, while each global digest was injected four times.
To build an accurate mass and time (AMT) tag database, SEQUEST analysis software was used to match the MS/MS fragmentation spectra to sequences from the annotation of the Cyanothece 51142 proteome . Peptide identifications from the SCX fractions were combined with identifications from unfractionated samples to create a reference database of calculated mass and normalized elution time for each identified peptide. This database was used for subsequent high-sensitivity, high-throughput analysis of Cyanothece 51142 samples using the AMT tag approach . LC-MS features from the unfractionated global samples were matched to the rich database built from the fractionated samples to give accurate peptide IDs. The area of each LC elution peak was used as a measure of peptide abundance.
Data from the AMT output were imported into the software MDART (Burnum et al., unpublished results), for filtering using a mass error tolerance of <5 parts per million, delta match score >0 (a measure of peptide uniqueness), match score >−1, and absolute normalized elution time error <10,000. The resulting 7450 peptides were imported into the software tool DAnTE  for further filtering and analysis. Peptide abundances were transformed to log base 2 and mean-centered. A linear regression-based normalization method available in DAnTE was then applied within each replicate category. Peptide abundances were used to infer the corresponding protein abundances through the ‘Rrollup’ algorithm in DAnTE . During the Rrollup step, peptides were excluded if not present in at least 3 of the eight datasets, and Grubbs' outlier test was applied with a P-value cutoff of 0.05 to further remove outlying peptides. For increased confidence in protein identifications, each protein was required to be identified by at least 2 unique peptides, resulting in a total of 865 proteins. The minimum observed relative protein abundance value (14,465) was imputed as a crude surrogate for missing data for statistical calculations. Statistical differences between the two samples (4 technical replicates of each) were determined using ANOVA with a P-value cutoff of 0.05 (q<0.03) in DAnTE .
Metabolic network reconstruction: iCce806
A draft metabolic network of Cyanothece 51142 was reconstructed in SimPheny (Genomatica, San Diego, CA) using a previously described automated model-building process . Metabolic reactions and gene-to-protein-to-reaction (GPR) associations from other models were incorporated into the reconstruction if good BLAST hits could be found between genes in Cyanothece 51142 and genes in other modeled organisms. Additional reactions were added as necessary to produce known biomass constituents or utilize known nutrients; detailed literature, database, and BLAST searches were then carried out to find genes encoding these reactions in Cyanothece 51142 genome. This resulted in several new GPR associations that were incorporated into the reconstruction.
Constraint-based analysis of flux distributions
Based on the metabolic reconstruction, a constraint-based metabolic model for Cyanothece 51142 was developed as described in . Fluxes are limited based on several different types of constraints: steady-state mass balance constraints (Eq. 1), enzyme capacity and thermodynamic constraints (Eq. 2) , given by:(1)(2)where S is a stoichiometric matrix for the reaction network, v is a flux vector, and α and β are parameters that limit the capacity and directionality of individual reactions. Flux balance analysis (FBA) uses these constraints to identify a flux distribution which maximizes or minimizes an objective function, such as growth rate . Flux variability analysis (FVA) can also be used to determine the range of values each flux can take that are consistent with Eq. 1 and 2, by maximizing and minimizing each flux individually .
To further constrain the models based on mRNA or protein expression data, a modified version of the method developed by Shlomi et al.  was used. Here, we identified a single flux distribution that best agreed with measured transcriptome and proteome data (TPD) and minimized flux usage. Reactions with experimentally measured fluxes belong to set RE (which included biomass production and exchange fluxes for oxygen, 630 nm and 680 nm photons) and were constrained to their measured values. Reactions associated with detected proteins were included in the high reaction set (RH). Reactions associated with undetected proteins and genes with low mRNA expression levels (whose mRNA expression was less than the lowest mRNA expression of detected proteins) were included in the low reaction set (RL). The method finds a flux distribution that maximizes the number of active reactions (v≠0) and inactive reactions (v = 0) in reaction sets RH and RL, respectively. For reactions in set RH, binary variables x and y indicate whether a reaction is active, meaning its flux is greater than a positive threshold ε (x = 0 and y = 1), or smaller than a negative threshold -ε (x = 1 and y = 0) for reversible reactions. If both x and y are zero then the reaction is inactive and its flux value is zero. Likewise, a binary variable z is used for reactions in set RL such that if z = 1 then the reaction is inactive (v = 0). The original method  has alternate solutions, which can contain unrealistically high flux values due to the presence of cycles (e.g., futile cycles and circulations) in the network. To identify a solution that minimizes the use of these cycles, the objective function was modified to also minimize the sum of squared fluxes through the network.
The mixed integer quadratic programming formulation to identify a flux distribution that best matches TPD while minimizing flux magnitude is given below (Eq. 3).(3)Additionally, to find the flux ranges consistent with the TPD, flux variability analysis (FVA) was performed by minimizing and maximizing the flux through each reaction in the network. In these FVA simulations, the same constraints described above were included and the binary variables (x, y, and z) were further constrained by their optimal values (xopt, yopt, and zopt) found in the original problem (formulation below, Eq. 4). In this study, all model simulations were performed in GAMS software (General Algebraic Modeling System, GAMS Development Corporation, Washington, D.C.(4)
SBML file of the model i Cce806 which stores reactions and GPR associations.
In silico predictions for biomass yields under photoautotrophic, heterotrophic and photoheterotrophic conditions. Comparison of maximal biomass yields per g of C substrate when different nitrogen sources are used. Under photoautotrophic conditions CO2 uptake flux was fixed at 1 mmol.g−1 AFDW.h−1 and photon uptake fluxes at PSI and PSII were fixed at 10 mmol•g−1 AFDW•h−1. In the heterotrophic simulations glycerol was the limiting nutrient. Glycerol uptake was fixed at 1 mmol•g−1 AFDW•h−1 and maximal biomass yields were calculated under dark conditions. In photoheterotrophic simulations both glycerol and light were limiting (so an increase in either would improve growth rates). In this case, glycerol uptake rate was fixed at 1 mmol•g−1 AFDW•h−1, while photon uptake fluxes for PSI and PSII were both fixed at 10 mmol•g−1 AFDW•h−1. Since light was limiting in the photoheterotrophic condition CO2 was predicted to be secreted and not used as an additional carbon source.
Effects of distribution of fluxes through electron transport chains (ETC) on nitrogenase flux. Nitrogen fixation (nitrogenase) flux was varied while fluxes through ETC reactions were maximized and minimized under dark N2-fixing condition with all hydrogenase reactions eliminated from the model. Under this condition the amount of H2 produced is equal to the nitrogenase flux. A glycogen demand reaction was added to the model (→Glycogen; allowing for glycogen consumption) and its flux was limited to 0.171 mmol•g−1 AFDW•h−1. A) Effects of distribution of fluxes through cytochrome c oxidases (COX) and cytochrome-quinol oxidases (QOX) on nitrogenase flux. B) Effects of distribution of total flux through COX and QOX, and flux through Mehler reactions on nitrogenase flux. C) Effects of distribution of fluxes through NADH dehydrogenase reactions (NDH) and Fd-dependent cyclic reaction (FdPq) on nitrogenase flux. Shaded regions indicate ETC reactions can have multiple values for a particular nitrogenase flux.
Estimating ATP requirements from batch data. Average growth rates and photon uptake fluxes from batch experiments were used to constrain the model. The maximum ATP hydrolysis flux (flux through the ATPM reaction) was calculated using these measurement constraints. The data points represent the calculated maximal ATP hydrolysis values for different batch experiments. The growth-associated ATP requirement (GAR, slope) and non-growth associated ATP requirement (NGAR, y-intercept) were estimated by linear regression of these data.
Reactions in the genome-scale metabolic network i Cce806.
Metabolites in the genome-scale metabolic network i Cce806.
Genome-scale metabolic network statistics for iCce806. Number of genes, reactions, metabolites, and network gaps in iCce806.
Effects of changing simulation conditions on ATP requirement parameters, GAR and NGAR.
Biomass compositions under ammonia-limited (AL), and light-limited (LL) chemostat conditions.
Experimental measurements for two chemostat conditions.
Transcriptomic data. Fold change in mRNA expression levels between light-limited and ammonia-limited chemostats.
Proteomic data. Protein expression levels measured in light-limited and ammonia-limited chemostats.
Proteomic analyses were performed in the Environmental Molecular Sciences Laboratory, a DOE/BER national scientific user facility on the PNNL campus in Richland, Washington. The authors wish to acknowledge Jessica De Ingeniis (from the Burnham Institute) for her help with the amino acid analysis. We also thank Oleg Geydebrekht and Matthew Melnicki (both PNNL) for help with cultivation experiments, Janani Shutthanandan (PNNL) for help with preparation of proteomic samples, and Sebastian Jaramillo Riveri (PNNL) for his assistance with analysis of mRNA and protein expression data.
Conceived and designed the experiments: TV SMS GEP JKF AEK ASB JLR. Performed the experiments: SMS GEP EAH LAK RNB. Analyzed the data: TV SMS GEP ASB JLR. Contributed reagents/materials/analysis tools: ALO RNB MSL. Wrote the paper: TV SMS GEP JKF AEK ASB JLR. Performed the computational simulations: TV.
- 1. Reddy KJ, Haskell JB, Sherman DM, Sherman LA (1993) Unicellular, aerobic nitrogen-fixing cyanobacteria of the genus Cyanothece. J Bacteriol 175: 1284–1292.KJ ReddyJB HaskellDM ShermanLA Sherman1993Unicellular, aerobic nitrogen-fixing cyanobacteria of the genus Cyanothece.J Bacteriol17512841292
- 2. Schneegurt MA, Sherman DM, Sherman LA (1997) Growth, physiology, and ultrastructure of a diazotrophic cyanobacterium, Cyanothece sp. strain ATCC 51142, in mixotrophic and chemoheterotrophic cultures. J Phycol 33: 632–642.MA SchneegurtDM ShermanLA Sherman1997Growth, physiology, and ultrastructure of a diazotrophic cyanobacterium, Cyanothece sp. strain ATCC 51142, in mixotrophic and chemoheterotrophic cultures.J Phycol33632642
- 3. Nakamura Y, Takahashi J, Sakurai A, Inaba Y, Suzuki E, et al. (2005) Some cyanobacteria synthesize semi-amylopectin type alpha-polyglucans instead of glycogen. Plant Cell Physiol 46: 539–545.Y. NakamuraJ. TakahashiA. SakuraiY. InabaE. Suzuki2005Some cyanobacteria synthesize semi-amylopectin type alpha-polyglucans instead of glycogen.Plant Cell Physiol46539545
- 4. Bandyopadhyay A, Stockel J, Min H, Sherman LA, Pakrasi HB (2010) High rates of photobiological H2 production by a cyanobacterium under aerobic conditions. Nat Commun 1: 139.A. BandyopadhyayJ. StockelH. MinLA ShermanHB Pakrasi2010High rates of photobiological H2 production by a cyanobacterium under aerobic conditions.Nat Commun1139
- 5. Min H, Sherman LA (2010) Hydrogen production by the unicellular, diazotrophic cyanobacterium Cyanothece sp. strain ATCC 51142 under conditions of continuous light. Appl Environ Microbiol 76: 4293–4301.H. MinLA Sherman2010Hydrogen production by the unicellular, diazotrophic cyanobacterium Cyanothece sp. strain ATCC 51142 under conditions of continuous light.Appl Environ Microbiol7642934301
- 6. Welsh EA, Liberton M, Stockel J, Loh T, Elvitigala T, et al. (2008) The genome of Cyanothece 51142, a unicellular diazotrophic cyanobacterium important in the marine nitrogen cycle. Proc Natl Acad Sci U S A 105: 15094–15099.EA WelshM. LibertonJ. StockelT. LohT. Elvitigala2008The genome of Cyanothece 51142, a unicellular diazotrophic cyanobacterium important in the marine nitrogen cycle.Proc Natl Acad Sci U S A1051509415099
- 7. Stockel J, Welsh EA, Liberton M, Kunnvakkam R, Aurora R, et al. (2008) Global transcriptomic analysis of Cyanothece 51142 reveals robust diurnal oscillation of central metabolic processes. Proc Natl Acad Sci U S A 105: 6156–6161.J. StockelEA WelshM. LibertonR. KunnvakkamR. Aurora2008Global transcriptomic analysis of Cyanothece 51142 reveals robust diurnal oscillation of central metabolic processes.Proc Natl Acad Sci U S A10561566161
- 8. Toepel J, Welsh E, Summerfield TC, Pakrasi HB, Sherman LA (2008) Differential transcriptional analysis of the cyanobacterium Cyanothece sp. strain ATCC 51142 during light-dark and continuous-light growth. J Bacteriol 190: 3904–3913.J. ToepelE. WelshTC SummerfieldHB PakrasiLA Sherman2008Differential transcriptional analysis of the cyanobacterium Cyanothece sp. strain ATCC 51142 during light-dark and continuous-light growth.J Bacteriol19039043913
- 9. Oberhardt MA, Palsson BO, Papin JA (2009) Applications of genome-scale metabolic reconstructions. Mol Syst Biol 5: 320.MA OberhardtBO PalssonJA Papin2009Applications of genome-scale metabolic reconstructions.Mol Syst Biol5320
- 10. Price ND, Reed JL, Palsson BO (2004) Genome-scale models of microbial cells: evaluating the consequences of constraints. Nat Rev Microbiol 2: 886–897.ND PriceJL ReedBO Palsson2004Genome-scale models of microbial cells: evaluating the consequences of constraints.Nat Rev Microbiol2886897
- 11. Fu P (2009) Genome-scale modeling of Synechocystis sp. PCC 6803 and prediction of pathway insertion. J Chem Technol Biotechnol 84: 473–483.P. Fu2009Genome-scale modeling of Synechocystis sp. PCC 6803 and prediction of pathway insertion.J Chem Technol Biotechnol84473483
- 12. Knoop H, Zilliges Y, Lockau W, Steuer R (2010) The metabolic network of Synechocystis sp. PCC 6803: systemic properties of autotrophic growth. Plant Physiol 154: 410–422.H. KnoopY. ZilligesW. LockauR. Steuer2010The metabolic network of Synechocystis sp. PCC 6803: systemic properties of autotrophic growth.Plant Physiol154410422
- 13. Montagud A, Navarro E, Fernandez de Cordoba P, Urchueguia JF, Patil KR (2010) Reconstruction and analysis of genome-scale metabolic model of a photosynthetic bacterium. BMC Syst Biol 4: 156.A. MontagudE. NavarroP. Fernandez de CordobaJF UrchueguiaKR Patil2010Reconstruction and analysis of genome-scale metabolic model of a photosynthetic bacterium.BMC Syst Biol4156
- 14. Imam S, Yilmaz S, Sohmen U, Gorzalski AS, Reed JL, et al. (2011) iRsp1095: a genome-scale reconstruction of the Rhodobacter sphaeroides metabolic network. BMC Syst Biol 5: 116.S. ImamS. YilmazU. SohmenAS GorzalskiJL Reed2011iRsp1095: a genome-scale reconstruction of the Rhodobacter sphaeroides metabolic network.BMC Syst Biol5116
- 15. Boyle NR, Morgan JA (2009) Flux balance analysis of primary metabolism in Chlamydomonas reinhardtii. BMC Syst Biol 3: 4.NR BoyleJA Morgan2009Flux balance analysis of primary metabolism in Chlamydomonas reinhardtii.BMC Syst Biol34
- 16. Chang RL, Ghamsari L, Manichaikul A, Hom EF, Balaji S, et al. (2011) Metabolic network reconstruction of Chlamydomonas offers insight into light-driven algal metabolism. Mol Syst Biol 7: 518.RL ChangL. GhamsariA. ManichaikulEF HomS. Balaji2011Metabolic network reconstruction of Chlamydomonas offers insight into light-driven algal metabolism.Mol Syst Biol7518
- 17. Overbeek R, Begley T, Butler RM, Choudhuri JV, Chuang HY, et al. (2005) The subsystems approach to genome annotation and its use in the project to annotate 1000 genomes. Nucleic Acids Res 33: 5691–5702.R. OverbeekT. BegleyRM ButlerJV ChoudhuriHY Chuang2005The subsystems approach to genome annotation and its use in the project to annotate 1000 genomes.Nucleic Acids Res3356915702
- 18. Kanehisa M, Goto S (2000) KEGG: kyoto encyclopedia of genes and genomes. Nucleic Acids Res 28: 27–30.M. KanehisaS. Goto2000KEGG: kyoto encyclopedia of genes and genomes.Nucleic Acids Res282730
- 19. Kanehisa M, Goto S, Hattori M, Aoki-Kinoshita KF, Itoh M, et al. (2006) From genomics to chemical genomics: new developments in KEGG. Nucleic Acids Res 34: D354–357.M. KanehisaS. GotoM. HattoriKF Aoki-KinoshitaM. Itoh2006From genomics to chemical genomics: new developments in KEGG.Nucleic Acids Res34D354357
- 20. Kanehisa M, Araki M, Goto S, Hattori M, Hirakawa M, et al. (2008) KEGG for linking genomes to life and the environment. Nucleic Acids Res 36: D480–484.M. KanehisaM. ArakiS. GotoM. HattoriM. Hirakawa2008KEGG for linking genomes to life and the environment.Nucleic Acids Res36D480484
- 21. Nakamura Y, Kaneko T, Hirosawa M, Miyajima N, Tabata S (1998) CyanoBase, a www database containing the complete nucleotide sequence of the genome of Synechocystis sp. strain PCC6803. Nucleic Acids Res 26: 63–67.Y. NakamuraT. KanekoM. HirosawaN. MiyajimaS. Tabata1998CyanoBase, a www database containing the complete nucleotide sequence of the genome of Synechocystis sp. strain PCC6803.Nucleic Acids Res266367
- 22. Nakao M, Okamoto S, Kohara M, Fujishiro T, Fujisawa T, et al. (2010) CyanoBase: the cyanobacteria genome database update 2010. Nucleic Acids Res 38: D379–381.M. NakaoS. OkamotoM. KoharaT. FujishiroT. Fujisawa2010CyanoBase: the cyanobacteria genome database update 2010.Nucleic Acids Res38D379381
- 23. Feng X, Bandyopadhyay A, Berla B, Page L, Wu B, et al. (2010) Mixotrophic and photoheterotrophic metabolism in Cyanothece sp. ATCC 51142 under continuous light. Microbiology 156: 2566–2574.X. FengA. BandyopadhyayB. BerlaL. PageB. Wu2010Mixotrophic and photoheterotrophic metabolism in Cyanothece sp. ATCC 51142 under continuous light.Microbiology15625662574
- 24. Aryal UK, Stockel J, Krovvidi RK, Gritsenko MA, Monroe ME, et al. (2011) Dynamic proteomic profiling of a unicellular cyanobacterium Cyanothece ATCC51142 across light-dark diurnal cycles. BMC Syst Biol 5: 194.UK AryalJ. StockelRK KrovvidiMA GritsenkoME Monroe2011Dynamic proteomic profiling of a unicellular cyanobacterium Cyanothece ATCC51142 across light-dark diurnal cycles.BMC Syst Biol5194
- 25. Stockel J, Jacobs JM, Elvitigala TR, Liberton M, Welsh EA, et al. (2011) Diurnal rhythms result in significant changes in the cellular protein complement in the cyanobacterium Cyanothece 51142. PLoS One 6: e16680.J. StockelJM JacobsTR ElvitigalaM. LibertonEA Welsh2011Diurnal rhythms result in significant changes in the cellular protein complement in the cyanobacterium Cyanothece 51142.PLoS One6e16680
- 26. Vermaas WF (2001) Photosynthesis and respiration in cyanobacteria. WF Vermaas2001Photosynthesis and respiration in cyanobacteria.In: eLS: John Wiley and Sons: Chichester. Available: http://www.els.net/.
- 27. Schluchter WM, Bryant DA (1992) Molecular characterization of ferredoxin-NADP+ oxidoreductase in cyanobacteria: cloning and sequence of the petH gene of Synechococcus sp. PCC 7002 and studies on the gene product. Biochemistry 31: 3092–3102.WM SchluchterDA Bryant1992Molecular characterization of ferredoxin-NADP+ oxidoreductase in cyanobacteria: cloning and sequence of the petH gene of Synechococcus sp. PCC 7002 and studies on the gene product.Biochemistry3130923102
- 28. Teusink B, Wiersma A, Molenaar D, Francke C, de Vos WM, et al. (2006) Analysis of growth of Lactobacillus plantarum WCFS1 on a complex medium using a genome-scale metabolic model. J Biol Chem 281: 40041–40048.B. TeusinkA. WiersmaD. MolenaarC. FranckeWM de Vos2006Analysis of growth of Lactobacillus plantarum WCFS1 on a complex medium using a genome-scale metabolic model.J Biol Chem2814004140048
- 29. Pinchuk GE, Hill EA, Geydebrekht OV, De Ingeniis J, Zhang X, et al. (2010) Constraint-based model of Shewanella oneidensis MR-1 metabolism: a tool for data analysis and hypothesis generation. PLoS Comput Biol 6: e1000822.GE PinchukEA HillOV GeydebrekhtJ. De IngeniisX. Zhang2010Constraint-based model of Shewanella oneidensis MR-1 metabolism: a tool for data analysis and hypothesis generation.PLoS Comput Biol6e1000822
- 30. Shlomi T, Cabili MN, Herrgard MJ, Palsson BO, Ruppin E (2008) Network-based prediction of human tissue-specific metabolism. Nat Biotechnol 26: 1003–1010.T. ShlomiMN CabiliMJ HerrgardBO PalssonE. Ruppin2008Network-based prediction of human tissue-specific metabolism.Nat Biotechnol2610031010
- 31. Shastri AA, Morgan JA (2005) Flux balance analysis of photoautotrophic metabolism. Biotechnol Prog 21: 1617–1626.AA ShastriJA Morgan2005Flux balance analysis of photoautotrophic metabolism.Biotechnol Prog2116171626
- 32. Allahverdiyeva Y, Ermakova M, Eisenhut M, Zhang P, Richaud P, et al. (2011) Interplay between flavodiiron proteins and photorespiration in Synechocystis sp. PCC 6803. J Biol Chem 286: 24007–24014.Y. AllahverdiyevaM. ErmakovaM. EisenhutP. ZhangP. Richaud2011Interplay between flavodiiron proteins and photorespiration in Synechocystis sp. PCC 6803.J Biol Chem2862400724014
- 33. Bailey S, Melis A, Mackey KR, Cardol P, Finazzi G, et al. (2008) Alternative photosynthetic electron flow to oxygen in marine Synechococcus. Biochim Biophys Acta 1777: 269–276.S. BaileyA. MelisKR MackeyP. CardolG. Finazzi2008Alternative photosynthetic electron flow to oxygen in marine Synechococcus.Biochim Biophys Acta1777269276
- 34. Bernat G, Appel J, Ogawa T, Rogner M (2011) Distinct roles of multiple NDH-1 complexes in the cyanobacterial electron transport network as revealed by kinetic analysis of P700+ reduction in various ndh-deficient mutants of Synechocystis sp. strain PCC6803. J Bacteriol 193: 292–295.G. BernatJ. AppelT. OgawaM. Rogner2011Distinct roles of multiple NDH-1 complexes in the cyanobacterial electron transport network as revealed by kinetic analysis of P700+ reduction in various ndh-deficient mutants of Synechocystis sp. strain PCC6803.J Bacteriol193292295
- 35. Shikanai T (2007) Cyclic electron transport around photosystem I: genetic approaches. Annu Rev Plant Biol 58: 199–217.T. Shikanai2007Cyclic electron transport around photosystem I: genetic approaches.Annu Rev Plant Biol58199217
- 36. Munekage Y, Hashimoto M, Miyake C, Tomizawa K, Endo T, et al. (2004) Cyclic electron flow around photosystem I is essential for photosynthesis. Nature 429: 579–582.Y. MunekageM. HashimotoC. MiyakeK. TomizawaT. Endo2004Cyclic electron flow around photosystem I is essential for photosynthesis.Nature429579582
- 37. Battchikova N, Aro EM (2007) Cyanobacterial NDH-1 complexes: multiplicity in function and subunit composition. Physiol Plant 131: 22–32.N. BattchikovaEM Aro2007Cyanobacterial NDH-1 complexes: multiplicity in function and subunit composition.Physiol Plant1312232
- 38. Iwai M, Takizawa K, Tokutsu R, Okamuro A, Takahashi Y, et al. (2010) Isolation of the elusive supercomplex that drives cyclic electron flow in photosynthesis. Nature 464: 1210–1213.M. IwaiK. TakizawaR. TokutsuA. OkamuroY. Takahashi2010Isolation of the elusive supercomplex that drives cyclic electron flow in photosynthesis.Nature46412101213
- 39. Battchikova N, Eisenhut M, Aro EM (2011) Cyanobacterial NDH-1 complexes: novel insights and remaining puzzles. Biochim Biophys Acta 1807: 935–944.N. BattchikovaM. EisenhutEM Aro2011Cyanobacterial NDH-1 complexes: novel insights and remaining puzzles.Biochim Biophys Acta1807935944
- 40. Reed JL, Patel TR, Chen KH, Joyce AR, Applebee MK, et al. (2006) Systems approach to refining genome annotation. Proc Natl Acad Sci U S A 103: 17480–17484.JL ReedTR PatelKH ChenAR JoyceMK Applebee2006Systems approach to refining genome annotation.Proc Natl Acad Sci U S A1031748017484
- 41. Kumar VS, Maranas CD (2009) GrowMatch: an automated method for reconciling in silico/in vivo growth predictions. PLoS Comput Biol 5: e1000308.VS KumarCD Maranas2009GrowMatch: an automated method for reconciling in silico/in vivo growth predictions.PLoS Comput Biol5e1000308
- 42. Raghunathan A, Reed J, Shin S, Palsson B, Daefler S (2009) Constraint-based analysis of metabolic capacity of Salmonella typhimurium during host-pathogen interaction. BMC Syst Biol 3: 38.A. RaghunathanJ. ReedS. ShinB. PalssonS. Daefler2009Constraint-based analysis of metabolic capacity of Salmonella typhimurium during host-pathogen interaction.BMC Syst Biol338
- 43. Becker SA, Palsson BO (2005) Genome-scale reconstruction of the metabolic network in Staphylococcus aureus N315: an initial draft to the two-dimensional annotation. BMC Microbiol 5: 8.SA BeckerBO Palsson2005Genome-scale reconstruction of the metabolic network in Staphylococcus aureus N315: an initial draft to the two-dimensional annotation.BMC Microbiol58
- 44. Jensen PA, Papin JA (2011) Functional integration of a metabolic network model and expression data without arbitrary thresholding. Bioinformatics 27: 541–547.PA JensenJA Papin2011Functional integration of a metabolic network model and expression data without arbitrary thresholding.Bioinformatics27541547
- 45. Min H, Sherman LA (2010) Genetic transformation and mutagenesis via single-stranded DNA in the unicellular, diazotrophic cyanobacteria of the genus Cyanothece. Appl Environ Microbiol 76: 7641–7645.H. MinLA Sherman2010Genetic transformation and mutagenesis via single-stranded DNA in the unicellular, diazotrophic cyanobacteria of the genus Cyanothece.Appl Environ Microbiol7676417645
- 46. Van Baalen C (1962) Studies on marine blue-green algae. Bot Mar 4: 129–139.C. Van Baalen1962Studies on marine blue-green algae.Bot Mar4129139
- 47. Daniels L, Hanson RS, Phillips JA (1994) Chemical analyses. In: Gerhardt P, editor. Methods for General and Molecular Bacteriology. Washington, DC: American Society for Microbiology. pp. 512–554.L. DanielsRS HansonJA Phillips1994Chemical analyses.P. GerhardtMethods for General and Molecular BacteriologyWashington, DCAmerican Society for Microbiology512554
- 48. Endo Y (1970) A simultaneous estimation method of DNA and RNA by the orcinol reaction and a study on the reaction mechanism. J Biochem 67: 629–633.Y. Endo1970A simultaneous estimation method of DNA and RNA by the orcinol reaction and a study on the reaction mechanism.J Biochem67629633
- 49. Smith PK, Krohn RI, Hermanson GT, Mallia AK, Gartner FH, et al. (1985) Measurement of protein using bicinchoninic acid. Anal Biochem 150: 76–85.PK SmithRI KrohnGT HermansonAK MalliaFH Gartner1985Measurement of protein using bicinchoninic acid.Anal Biochem1507685
- 50. Bligh EG, Dyer WJ (1959) A rapid method of total lipid extraction and purification. Can J Biochem Physiol 37: 911–917.EG BlighWJ Dyer1959A rapid method of total lipid extraction and purification.Can J Biochem Physiol37911917
- 51. Ludwig TG, Goldberg JV (1956) The anthrone method for the determination of carbohydrates in foods and in oral rinsing. J Dent Res 35: 90–94.TG LudwigJV Goldberg1956The anthrone method for the determination of carbohydrates in foods and in oral rinsing.J Dent Res359094
- 52. Meeks JC, Castenholz RW (1971) Growth and photosynthesis in an extreme thermophile, Synechococcus lividus (Cyanophyta). Arch Mikrobiol 78: 25–41.JC MeeksRW Castenholz1971Growth and photosynthesis in an extreme thermophile, Synechococcus lividus (Cyanophyta).Arch Mikrobiol782541
- 53. Lindberg P, Schutz K, Happe T, Lindblad P (2002) A hydrogen-producing, hydrogenase-free mutant strain of Nostoc punctiforme ATCC 29133. Int J Hydrogen Energ 27: 1291–1296.P. LindbergK. SchutzT. HappeP. Lindblad2002A hydrogen-producing, hydrogenase-free mutant strain of Nostoc punctiforme ATCC 29133.Int J Hydrogen Energ2712911296
- 54. Adkins JN, Mottaz HM, Norbeck AD, Gustin JK, Rue J, et al. (2006) Analysis of the Salmonella typhimurium proteome through environmental response toward infectious conditions. Mol Cell Proteomics 5: 1450–1461.JN AdkinsHM MottazAD NorbeckJK GustinJ. Rue2006Analysis of the Salmonella typhimurium proteome through environmental response toward infectious conditions.Mol Cell Proteomics514501461
- 55. Smith RD, Anderson GA, Lipton MS, Pasa-Tolic L, Shen Y, et al. (2002) An accurate mass tag strategy for quantitative and high-throughput proteome measurements. Proteomics 2: 513–523.RD SmithGA AndersonMS LiptonL. Pasa-TolicY. Shen2002An accurate mass tag strategy for quantitative and high-throughput proteome measurements.Proteomics2513523
- 56. Callister SJ, Dominguez MA, Nicora CD, Zeng X, Tavano CL, et al. (2006) Application of the accurate mass and time tag approach to the proteome analysis of sub-cellular fractions obtained from Rhodobacter sphaeroides 2.4.1. Aerobic and photosynthetic cell cultures. J Proteome Res 5: 1940–1947.SJ CallisterMA DominguezCD NicoraX. ZengCL Tavano2006Application of the accurate mass and time tag approach to the proteome analysis of sub-cellular fractions obtained from Rhodobacter sphaeroides 2.4.1. Aerobic and photosynthetic cell cultures.J Proteome Res519401947
- 57. Fang R, Elias DA, Monroe ME, Shen Y, McIntosh M, et al. (2006) Differential label-free quantitative proteomic analysis of Shewanella oneidensis cultured under aerobic and suboxic conditions by accurate mass and time tag approach. Mol Cell Proteomics 5: 714–725.R. FangDA EliasME MonroeY. ShenM. McIntosh2006Differential label-free quantitative proteomic analysis of Shewanella oneidensis cultured under aerobic and suboxic conditions by accurate mass and time tag approach.Mol Cell Proteomics5714725
- 58. Shen Y, Tolic N, Zhao R, Pasa-Tolic L, Li L, et al. (2001) High-throughput proteomics using high-efficiency multiple-capillary liquid chromatography with on-line high-performance ESI FTICR mass spectrometry. Anal Chem 73: 3011–3021.Y. ShenN. TolicR. ZhaoL. Pasa-TolicL. Li2001High-throughput proteomics using high-efficiency multiple-capillary liquid chromatography with on-line high-performance ESI FTICR mass spectrometry.Anal Chem7330113021
- 59. Kelly RT, Page JS, Zhao R, Qian WJ, Mottaz HM, et al. (2008) Capillary-based multi nanoelectrospray emitters: improvements in ion transmission efficiency and implementation with capillary reversed-phase LC-ESI-MS. Anal Chem 80: 143–149.RT KellyJS PageR. ZhaoWJ QianHM Mottaz2008Capillary-based multi nanoelectrospray emitters: improvements in ion transmission efficiency and implementation with capillary reversed-phase LC-ESI-MS.Anal Chem80143149
- 60. Zimmer JS, Monroe ME, Qian WJ, Smith RD (2006) Advances in proteomics data analysis and display using an accurate mass and time tag approach. Mass Spectrom Rev 25: 450–482.JS ZimmerME MonroeWJ QianRD Smith2006Advances in proteomics data analysis and display using an accurate mass and time tag approach.Mass Spectrom Rev25450482
- 61. Polpitiya AD, Qian WJ, Jaitly N, Petyuk VA, Adkins JN, et al. (2008) DAnTE: a statistical tool for quantitative analysis of -omics data. Bioinformatics 24: 1556–1558.AD PolpitiyaWJ QianN. JaitlyVA PetyukJN Adkins2008DAnTE: a statistical tool for quantitative analysis of -omics data.Bioinformatics2415561558
- 62. Sun J, Sayyar B, Butler JE, Pharkya P, Fahland TR, et al. (2009) Genome-scale constraint-based modeling of Geobacter metallireducens. BMC Syst Biol 3: 15.J. SunB. SayyarJE ButlerP. PharkyaTR Fahland2009Genome-scale constraint-based modeling of Geobacter metallireducens.BMC Syst Biol315
- 63. Feist AM, Herrgard MJ, Thiele I, Reed JL, Palsson BO (2009) Reconstruction of biochemical networks in microorganisms. Nat Rev Microbiol 7: 129–143.AM FeistMJ HerrgardI. ThieleJL ReedBO Palsson2009Reconstruction of biochemical networks in microorganisms.Nat Rev Microbiol7129143
- 64. Mahadevan R, Schilling CH (2003) The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metab Eng 5: 264–276.R. MahadevanCH Schilling2003The effects of alternate optimal solutions in constraint-based genome-scale metabolic models.Metab Eng5264276