Flux maps for three growth conditions (auto-, hetero-, and mixotrophic) were calculated using the reconstructed network and FBA. During autotrophic growth, the cell fixes carbon dioxide by converting light into cellular energy (reducing equivalents and ATP). In this study we defined heterotrophic growth as aerobic growth on acetate in the dark; the cell using acetate for both carbon and energy sources. Another metabolic mode, mixotrophic growth, is the link between the two extremes. In our model, mixotrophic growth has three inputs: light, acetate and carbon dioxide.

Autotrophic growth was simulated using a two-step optimization with a basis of 100 moles CO₂. Interestingly, the fluxes for both optimization steps were identical (as reported previously by 9), which implies the cell is optimally utilizing energy to produce biomass without needing the second constraint of minimum light energy. As expected, the majority of the carbon flux is directed through the Calvin Cycle (Figure 3). The energy required for the regeneration of GAP from 3PG to run the Calvin Cycle is supplied by photophosphorylation. Due to compartmentation and no known direct NADPH or NADH transporters, the flux through the non-cyclic ETC is almost wholly constrained by the flux from 3PG to GAP, which is the main consumption of NADH in the chloroplast. The rest of the NADPH produced by the non-cyclic ETC must be transported out of the chloroplast via an indirect shuttle. In the autotrophic case, the cell produces most of its energy from the conversion of light energy, which occurs in the chloroplast. However, there is demand for both ATP and NAD(P)H outside the chloroplast for other biosynthetic reactions. Indirect transport of this energy is accomplished by transporting GAP from the chloroplast to the mitochondria and subsequently degrading it to 3PG, releasing both ATP and NADH into the mitochondria. The calculated photosynthetic quotient (moles of oxygen released per mole carbon dioxide fixed) for the optimal flux distribution is 1.27 which agrees with the typical range of 1.0 – 1.8 for algae 24.

The basis of the heterotrophic simulation was 100 moles acetate because C. reinhardtii is only capable of growing heterotrophically on acetate and other similar 2-carbon molecules. Most of the carbon flux for heterotrophic growth is directed through the TCA cycle, as would be expected (Figure 4). Since the cell is not capable of metabolizing external sugars in the dark, almost all the energy is produced by respiration in the TCA cycle. The oxidative pentose phosphate pathway is also active, providing reducing power for use in the cytosol. Synthesis of G6P occurs via gluconeogenesis; a lack of ATP and NADH in the cytosol causes the regeneration of GAP from 3PG to take place in the mitochondria. The glyoxylate shunt is also active, which is known to be needed to metabolize acetate in E. coli 25, Neurospora crassa 26,Scenedesmus obliquus 27, A. thaliana 28 and several other organisms.

C. reinhardtii is also capable of mixotrophic growth, utilizing acetate, light and carbon dioxide for growth. Mixotrophic growth was simulated by using heterotrophic growth as the base case and allowing the uptake of carbon dioxide and light for energy. The free uptake of carbon dioxide was allowed, however to limit the biomass formed, an additional constraint on the absorbed light was added. The total absorbed light flux was fixed over a range of 0 to 2 μE/m²/s in a step-wise fashion and at each light flux, the optimal flux distribution was calculated. Fluxes that changed significantly over the range of absorbed light are plotted in Figure 5. From this graph it is evident there are two distinct regions of growth. The first resembles heterotrophic growth in which carbon fixation does not occur and the cell is producing CO₂. However, unlike the heterotrophic case above, at very low light levels, the cell has a complete TCA cycle. The flux through 2-oxoglutarate decarboxylase decreases steadily to zero at which point the flux begins to be directed through Rubisco. This could be due to the need for NAD(P)H for biomass synthesis during low light conditions, but when light intensity increases enough to send flux through Rubisco, the cell is capable of producing enough NADPH through the non-cyclic ETC to supply metabolism with NADH via transhydrogenases. In the heterotrophic case, C. reinhardtii has an incomplete TCA cycle. This could also be a result of the production of NADPH within the chloroplast and the subsequent indirect transport of reducing equivalents throughout the cell. At a light flux of approximately 0.8 μE/m²/s, flux is directed through the Calvin cycle and the cell enters the second growth regime. In this growth regime, the glyoxylate shunt flux steadily decreases while the Rubisco flux increases rapidly with increasing light. As the light increases, the flux distribution becomes more similar to the autotrophic case. The increase in biomass flux with each increase in light is slightly less than that for the first growth regime. This is due to the higher energetic demand of carbon fixation.

Quantitative results for all three growth regimes as well as reaction lists can be found at http://cobweb.ecn.purdue.edu/~jamorgan.

The autotrophic biomass yield is 28.9 g biomass for every mole of carbon taken up (Table 5), based on the elemental analysis of C. reinhardtii, this is 100% of the carbon taken into the cell. This is of course due to the production of energy from light during photosynthesis, so no net carbon is lost during respiration. In contrast, the heterotrophic biomass yield is 15 g per mole carbon, which implies that almost half of the carbon taken in by the cell is used for energy production instead of biomass formation. The fraction of carbon used for energy production is quite high compared to another photosynthetic organism, Synechocystis 9, which only utilized 37% of the carbon for energy. This is due to the difference in energy content of the substrate. Synechocystis utilizes glucose, which has significantly higher energy content per mole than acetate; glucose has a standard heat of combustion of -2.8 kJ/mole compared to -0.8 kJ/mole for acetate. During mixotrophic growth, the biomass yield of C. reinhardtii increases from 13.5 to 22.9 g per mole carbon. With increasing light flux, the cell can direct more carbon towards biomass and less towards energy production, however, the amount of carbon fixed per photon is constant. Therefore, the maximum yield is lower than the autotrophic yield because it is limited by the energy in the cell. During mixotrophic growth, the cell must utilize acetate and it has to divert some carbon away from biomass and towards energy production.

Flux estimates for autotrophic growth were compared to estimated fluxes for the cyanobacteria, Synechocystis sp PCC 6803 9. One major difference is the flux through the cyclic and non-cyclic ETCs (Table 6). Although both organisms utilize approximately the same amount of energy to produce each kilogram of biomass, the flux through the ETCs are split quite differently. Synechocystis has a much higher flux through the non-cyclic ETC than C. reinhardtii which is due mainly to the compartmentation in the model; due to a lack of a direct NAD(P)H transporter in C. reinhardtii, the flux through the non-cyclic ETC is constrained to match the need for NADPH in the chloroplast. Any additional NAD(P)H is indirectly transported via shuttles, but these shuttles are also constrained by mass balances and steady state assumptions. In contrast, since Synechocystis is prokaryotic and unicellular, it can use the non-cyclic ETC to produce all the NADPH needed in the cell. Therefore, to make up for the energetic difference of having a lower flux through the non-cyclic ETC, C. reinhardtii must have a larger flux through the cyclic ETC. Cellular compartmentation also comes into play in the total moles of oxygen produced. The only reaction the cell can use to produce oxygen in both organisms is the non-cyclic ETC, which is why the production of oxygen from C. reinhardtii is lower than that of Synechocystis. Comparison of the biomass yields per 100 moles carbon dioxide from both organisms shows yet another difference; Synechocystis has a lower yield than C. reinhardtii, 2.43 kg and 2.89 kg respectively. Part of this difference can be explained by the use of a lumped biomass equation for Synechocystis which specifies the loss of approximately one mole of carbon dioxide per kilogram biomass formed in order to have a balanced reaction. In contrast, the C. reinhardtii model is much more detailed and the carbon dioxide lost during biosynthesis can be fixed because it is not required to be present on the right hand side of the biomass formation equation to balance the reaction. This results in 2.47 moles of carbon dioxide loss for the production of 2.43 kilograms of Synechocystis, which translates to a loss of 0.11 kg of biomass. Another element that contributes to the difference in yield is the carbon content of the 2 organisms; Synechocystis is reported to be 51% carbon 9 while C. reinhardtii was measured to be 48% carbon, which explains at least 0.15 kilograms difference in biomass yield. Due to the nature of the optimization technique employed, which allows the cell to use unlimited energy in the first step, the difference in yields can be attributed to these two factors and it is not due to a lack of energy.

The reconstructed metabolic network provided the information necessary to develop a stoichiometric model 42. A stoichiometric model takes the form S·v = 0, where S is the stoichiometric matrix and v is a vector of fluxes. The stoichiometric matrix and flux vector is constructed by writing a steady-state mass balance on each intracellular metabolite in each compartment, this set of mass balances is then converted to matrix form. Reversible reactions are separated into one forward and one reverse reaction in order to constrain all fluxes to be positive, therefore minimizing solution time. An additional constraint was added to only allow one direction of a reversible reaction to be active by introducing a binary variable 9. Since the resulting model was underdetermined, linear programming was used to solve for optimal fluxes.

Maximize biomass subject to: ∑ j s ij υ j = 0  for every i ∈ M i ∑ j s ij υ j ≤ 0  for every i ∈ M r ∑ j s ij υ j ≥ 0  for every i ∈ M p υ j ≥ 0 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@B814@

where s_ij is the stoichiometric coefficient of the i^th metabolite in the j^th reaction, v_j is the flux of the j^th reaction, M_i is the set of intracellular metabolites, M_r is the set of reactants other than substrate, and M_p is the set of products excreted.

A mixed integer linear program was formulated in the GAMS environment (GAMS Development Corporation, Washington, DC) and the optimum solution was found using the ILOG CPLEX 8.100 solver (ILOG, Inc. Mountain View, CA).

Unlike heterotrophic organisms that utilize the same substrate as the source of both carbon and energy, photoautotrophic organisms require two substrates, one for energy (light) and one for carbon (carbon dioxide). Due to the input of two substrates, FBA simulations can be run in either light or carbon limitation conditions. To simulate carbon limitation, the model is allowed unlimited light, which calculates an optimal biomass flux. No fermentation products were detected in the media during growth (see maximum uptake rates discussion) therefore, in the absence of carbon overflow products, the yield of biomass is fixed because the only outlet for carbon is biomass. For photoautotrophic metabolism, a more meaningful result is to find the flux distribution that maximizes biomass while minimizing energy usage. Therefore the optimization is done in two steps. The first step is to maximize biomass with no constraint on light and the second is to fix the biomass and minimize light. Flux distributions for the heterotrophic case are the result of a one-step optimization to maximize biomass.

Chlamydomonas reinhardtii strain CC-400 cw15 mt+ was acquired from the Chlamydomonas Genetics Center. Cells were cultivated at 25°C in 250 ml flasks with a working volume of 50 ml and an agitation rate of 200 RPM. Heterotrophic and mixotrophic cells were grown in TAP media 43 and autotrophic cells were grown in similar media without addition of acetic acid. Mixotrophic and autotrophic cultures were grown under constant illumination at an average fluence rate of 65 μE/m²/s. All cells were grown in the presence of atmospheric carbon dioxide levels. Growth was monitored spectrophotometrically by measuring absorbance at 750 nm.

In order to add constraints on nutrient and light uptake to the model, additional experimental measurements were taken. Maximum growth rates were measured for all three growth conditions from three separate experiments. The results are shown in Table 7. For autotrophic growth, the maximum carbon dioxide uptake rate was calculated to be 2.04 mmol/g biomass/hr. The maximum solar light flux was set to be 2100 μE/m²/s 44. For heterotrophic growth, the maximum acetate uptake rate was measured using high performance liquid chromatography (HPLC) coupled to an refractive index detector (RID) detector and was found to be 12.06 mmol/g biomass/hr. The same HPLC method was used to look for fermentation products, but none were detected and therefore they were not included in the model. The biomass growth yield on acetate was measured in exponentially growing cells to be 3.12 ± 0.23 kg biomass/100 moles acetate from three independent experiments.

In order to convert the calculated total photons from the model to a flux (μE/m²/s), the surface area per kilogram biomass must be calculated. Based on experimental measurements, the dry weight of a typical C. reinhardtii was determined to be 0.2 pg. The length and width of cell were assumed to be 10 μm and 3 μm respectively 43 based on literature values. The geometry of the cell was assumed to be a prolate spheroid. The surface area per kilogram biomass was then calculated to be 389 m²kg^-1.

Growth associated and non-growth associated maintenance requirements were also included in the model. Growth associated energy is included to account for partially unknown energy requirements for transport, biosynthesis and polymerization 42 while non-growth associated accounts for cellular maintenance operations such as DNA repair, cell wall maintenance, and pH control. Growth associated maintenance was found to be 29.89 mmol ATP/g biomass by fitting the model to the experimentally determined biomass yield by changing the ATP requirement. This value falls into the range of published values for growth associated maintenance values 234567. Autotrophic and mixotrophic maintenance requirements were assumed to be the same. Non-growth associated maintenance requirements range from 0.36 mmol ATP/g DW hr for Lactobacillus plantarum to 7.60 mmol ATP/g DW for E. coli. For C. reinhardtii, non-growth associated maintenance was assumed to be 1.50 mmol ATP/g DW 357.

The biomass composition was determined separately for each of the three growth regimes: autotrophic, mixotrophic and heterotrophic growth. Lipids were measured using the chloroform-methanol extraction method of Ishida et al. 45. The resulting water layer and pellet were then dried and resuspended in 0.2 N NaOH and diluted by a factor of 5. This solution was then assayed for protein content with the Pierce BCA protein assay kit (Pierce Biotechnology, Inc. Rockford, IL). The amino acid composition (Additional file 3) was estimated from Gas chromatography-mass spectrometry (GC-MS) analysis of hydrolyzed protein (data not shown). Chlorophyll a and b were measured 43 and subtracted from the total lipid measurement. DNA and RNA were assumed to be constant for all growth conditions; the DNA content was determined by Chiang et al46 to be 1.23 × 10^-7 μg per cell and the RNA content was assumed to be 28-fold higher than the DNA content 47. The GC content of DNA was measured to be 62.1% 43 and the same GC content was assumed for RNA. Carbohydrate composition was calculated as the balance of the fraction dry weight. The elemental composition of lyophilized cells was also determined. In all cases except elemental composition, experiments were done in triplicate.