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Chlamydomonas reinhardtii Metabolic Pathway Analysis for Biohydrogen Production under Non-Steady-State Operation Dongda Zhang and Vassilios S. Vassiliadis*

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Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United Kingdom ABSTRACT: This paper presents a novel structured dynamic model to simulate the metabolic reaction network of green algae hydrogen production from aerobic cultivation conditions to anaerobic cultivation conditions, which has not been addressed in the open literature to this date. An efficient parameter estimation methodology is proposed to avoid the difficulty of measuring essential kinetic parameters from experiments. By applying this methodology, the current study constructed an accurate dynamic model whose simulation results are highly comparable to the published experimental results. The current model finds that the starch generation pathway mainly competes with hydrogen production pathway, as its activity is enhanced by the cyclic electron flow pathway. From the dynamic sensitivity analysis, it is concluded that the most effective solution to enhance hydrogen production is to seek the optimal sulfur concentration in the culture, rather than to modify the activity of specific enzymes.

1.1.1. PSII Dependent Pathway. Among the three metabolic pathways, the PSII dependent metabolic pathway is particularly studied since it supplies most of the electrons (around 80%) for hydrogen production in the light photosynthetic fermentation processs.7−9 Photosystem II, a large protein complex in chloroplasts and containing the reaction center of P680, can extract electrons from water molecules by utilizing solar energy.6 Once electrons are extracted from water, they are transferred through different electron carriers including plastoquinone (PQ) in the PQ pool, cytochrome protein complex (Cyt b6 f), and plastocyanin (PC) and eventually sent to Photosystem I (PSI), a large protein complex containing the reaction center of P700. To replenish the energy loss of electrons during the transfer from PSII to PSI, PSI harvests solar energy to excite the exhausted electrons. Electrons are thereby delivered to ferredoxin (Fd). Finally, the reduced Fd is oxidized by hydrogen ions for molecular hydrogen generation, and this reaction is catalyzed by an enzyme named hydrogenase (HydA).5,7 Figure 1 shows the process of the PSII dependent metabolic pathway. The PSII-dependent metabolic pathway is only active under anaerobic cultivation conditions due to the strong inhibition of oxygen on hydrogenase activity. When oxygen is present, the hydrogen generation pathway is replaced by the general photosynthetic process, named the CO2 fixation pathway (starch generation pathway, shown in Figure 1). In this pathway, the reduced Fd donates electrons to NAD(P)+ with the help of another enzyme, ferredoxin-NADP-reductase (FNR), and then NAD(P)H (reduced NAD(P)+) passes electrons to the Calvin−Benson cycle for CO2 fixation (starch generation).7 Both the starch generation pathway and the

1. INTRODUCTION The major component leading to global warming is carbon dioxide, CO2, which is mainly released by burning fossil-based fuels such as petrol, coal, and natural gas.1 To reduce the production of CO2 and fulfill the increasing demand for energy production, seeking novel sustainable and environmental friendly energy sources has become a key research target internationally. Recently, hydrogen has been considered as an outstanding energy carrier for the future due to its high combustion heat with zero environmental impact. It has been estimated that the requirement of hydrogen as a fuel for transportation will increase from 5.4 million tons in 2025 to 100 million tons in 2050 worldwide.2 However, the present industrial hydrogen generation processes mainly rely on the utilization of nonrenewable carbon-based resources. To find alternatives to conventional hydrogen sources, developments in the field of sustainable hydrogen energy have led to renewed interest in biohydrogen production. Biohydrogen is produced by microorganisms such as photosynthetic bacteria and green algae. The most attractive advantage of using microorganisms is that they can utilize solar energy and assimilate organic acids or CO2 for biohydrogen production.1,3 Because of the availability and low investment cost of energy and carbon sources, biohydrogen production is regarded as a feasible and sustainable process to replace current hydrogen production processes. 1.1. Important Metabolic Pathways. Since4 the discovery that hydrogen can be produced by Chlamydomonas reinhardtii, a type of green algae, under anaerobic cultivation conditions without the supply of sulfur nutrient, intense research5,6 has been carried out to determine the metabolic pathways of hydrogen production in this species. At present, it is widely accepted that C. reinhardtii can generate hydrogen via three different mechanisms: (a) the Photosystem II (PSII) independent pathway, (b) the PSII dependent pathway, and (c) the light independent pathway.7 © 2015 American Chemical Society

Received: Revised: Accepted: Published: 10593

June 3, 2015 September 26, 2015 October 6, 2015 October 6, 2015 DOI: 10.1021/acs.iecr.5b02034 Ind. Eng. Chem. Res. 2015, 54, 10593−10605

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Industrial & Engineering Chemistry Research

chloroplasts is another important step involved in both LEF and CEF pathways7 (Figure 2). Hydrogen ions at the stroma

Figure 1. Illustration of different electron transfer pathways. Thick lines show the PSII dependent hydrogen production pathway. Dotdashed lines show the starch generation pathway. Dashed lines show the cyclic electron flow pathway. PSII represents Photosystem II. PQ represents plastoquinone. Cyt b6 f represents cytochrome b6 f. PC represents plastocyanin. PSI represents Photosystem I. Fd represents ferredoxin. HydA represents hydrogenase. NDH represents NAD(P)H dehydrogenase, and FNR represents ferredoxin-NADP reductase.

Figure 2. Hyrodgen ions transport pathway. ATPase represents the enzyme for ATP synthesis. Stroma and lumen are the outer side and inner side of a thylakoid in algal chloroplasts.

hydrogen production pathway are entitled linear electron flows (LEFs). To create anaerobic cultivation conditions for C. reinhardtii hydrogen production, one feasible method adopted recently is to use a sulfur deprived culture.10 As sulfur is essential for PSII repair, the lack of intracellular sulfur can lead to a dramatic decrease on photosynthetic activity since PSII contains the reaction center for water decomposition and its activity is markedly depressed. Melis and Zhang11 claim that the residual photosynthetic activity of algae in a sulfur-free culture significantly drops to less than 20% of its original activity within the first 40 h of cultivation. Oxygen produced by photosynthesis thereby is totally consumed by algae due to their high respiration rate. Furthermore, a sulfur-free culture can aggravate the degradation of ribulose 1,5-bisphosphate carboxylase (Rubisco), an essential enzyme for CO2 fixation.10 Hence, the activity of the starch generation pathway is significantly suppressed by the lack of sulfur.8 As a result, hydrogen ions become the major electron sink consuming the electrons generated through the LEF pathway under anaerobic conditions. 1.1.2. Cyclic Electron Flow Pathway. Cyclic electron flow (CEF; Figure 1) is another photosynthesis pathway simultaneous with LEF pathways. In the CEF pathway, electrons in PSI are activated by light and transferred to the PQ pool via ferredoxin and NAD(P)+. To accomplish the cycle, electrons at the PQ pool are sent back to PSI through the same chain in the LEF pathway. The distinctive characteristic of the CEF pathway is that this pathway only generates ATP but not electrons. There is no net generation of electrons since they are trapped in the cyclic electron transfer chain. A previous study12 declares that the LEF pathway is the major photosynthesis pathway for green algae in aerobic cultivation conditions, while the CEF pathway becomes the major photosynthetic pathway under anaerobic cultivation conditions. In addition to the CEF pathway shown in Figure 1, another hypothetical mechanism of the CEF pathway is that ferredoxin immediately transfers electrons to the PQ pool via ferredoxin-quinone-reductase (FQR), without the attendance of FNR and NAD(P)+.7 However, so far there is no research available that is able to identify or isolate FQR, and a recent study has demonstrated that there is no unidentified protein involved in the CEF pathway.13 Therefore, this unproven mechanism is not included in the current research. 1.1.3. Hydrogen Ions Transport Pathway. The transport of hydrogen ions between the lumen side and the stroma side of

side participate in the electron transfer step from the PQ pool to Cyt b6 f and are pumped to the lumen side in the meanwhile. Hydrogen ions at the lumen side come back to the stroma side with the formation of ATP by ATPase. At the stroma side, hydrogen ions are consumed for the generation of either starch or hydrogen depending on the culture conditions (aerobic cultivation conditions and anaerobic cultivation conditions, respectively); at the lumen side, protons are generated by water photolysis. Because of the important role of hydrogen ions during the electron transfer process, the hydrogen production rate can be suppressed if hydrogen ions at the stroma side are not sufficient.14,15 1.2. Simulation of Metabolic Reaction Network. A number of research articles have been published investigating the metabolic constraints of green algal hydrogen production by designing different experiments.16−20 However, as the activity of most metabolic pathways continuously changes during the hydrogen production period, the effect of each metabolic pathway on hydrogen production is different at each time. It is therefore time-consuming to determine all of the potential metabolic constraints for algal hydrogen production purely by experiments. As a result, simulation becomes a valuable tool to identify the change of activity of metabolic pathways and explore the interactions of different reactions in the metabolic network of algal hydrogen production. Although at this moment flux balance analysis (FBA) is the predominant method applied for microorganism metabolic mechanisms simulation,21−23 it is not valid for a dynamic reaction network due to its steady-state assumption. Furthermore, as FBA does not contain reaction kinetics, it cannot be utilized to seek the limiting reaction steps in a metabolic network. Therefore, dynamic simulation has to be implemented in the current study to accomplish the modeling of green algal biohydrogen production metabolic pathways and to identify the limiting and competing reaction steps for hydrogen production. Dynamic simulation consists of both reaction kinetics and mass balances of metabolites. Reaction kinetics can be expressed by different functional forms. For example, eq 1a shows the generalized Michaelis−Menten kinetics, which are used to depict the reaction kinetics catalyzed by enzymes with multiple substrates, and eq 1b shows the metabolic reaction induced by electrostatic force. The mass balance of metabolites is shown as eq 1c. 10594

DOI: 10.1021/acs.iecr.5b02034 Ind. Eng. Chem. Res. 2015, 54, 10593−10605

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Industrial & Engineering Chemistry Research Nij

ri = Vmax ·∏ j=1

[fb·PQH]+ + PQH 2 + H+S → fb· PQH2 + PQ + 2H+L

cj K ij + cj

f b·PQH2 decomposition reaction, r7,L

(1a)

fb·PQH 2 → fb + PQH 2

Nij

ri = ki·∏ cj

dcj dt

PSI+ reduction reaction, r8,L

(1b)

j=1

2PSI+ + 2PC → 2PC+ + 2PSI

n

=

Fd+ reduction reaction, r9,L

∑ ri·xij

(1c)

i=1

2Fd+ + 2PSI → 2PSI+ + 2Fd

where ri represents the reaction rate of reaction i, Nij represents the number of metabolites involved in reaction i, cj represents the concentration of metabolite j in reaction i, Kij represents the half-velocity coefficient of reactant j in the generalized Michaelis−Menten equation, Vmax represents the maximum reaction rate of reaction i, ki represents the reaction rate constant of reaction i, xij represents stoichiometry of metabolite j in reaction i, and n represents the number of reactions.

NAD(P)+ reduction reaction, r10,L NAD(P)+ + 2Fd + H+S → 2Fd+ + NAD(P)H

Starch reduction reaction, r11,L 1 CO2 + H+S 2 1 1 → [CH 2O] + H 2O + NAD(P)+ 2 2

NAD(P)H +

2. METHODOLOGY OF MODEL CONSTRUCTION A dynamic model consists of reaction kinetics and mass balance; the indispensable information for model construction includes the kinetic parameters of each reaction and the initial concentration of each metabolite. However, these data are always difficult to know due to the difficulty of in vivo intracellular metabolite concentration measurement. Even though some reaction kinetics have been measured by in vitro experiments, the significant different biological circumstances between in vitro and in vivo tests may lead to large errors. To solve the problem of kinetic data shortage, the current research proposes a novel method to estimate kinetic parameters. To illustrate the proposed methodology, the dynamic model for the algal hydrogen production metabolic network is shown in section 2.1.1 to section 2.1.4 as an example. 2.1. Dynamic Simulation of Algae Metabolic Network. 2.1.1. Metabolic Pathways. The metabolic pathways included in the current model are (1) the PSII dependent hydrogen generation pathway, (2) the cyclic electron flow pathway (CEF), (3) the starch generation pathway, and (4) the transport of hydrogen ions between the lumen side and the stroma side of chloroplasts. Both pathway 1 and pathway 3 can be named the LEF pathway, since they share the same electron transfer chain from PSII to Fd as shown in Figure 1. The detailed reaction steps in the four pathways are listed below. Metabolic Reaction Networks. Linear Electron Flow Pathway. Water splitting reaction, r1,L 1 PQ + H 2O → PQH 2 + O2 2 f b·PQ generation reaction, r2,L PQ + fb → fb·PQ

H2 generation reaction, r12,L 2Fd + 2H+S → 2Fd+ + H 2

HL+ transport reaction, r13,L ADP3 − + Pi 2 − + 3H+L + H+S → ATP4 − + H 2O + 3H+S

Cyclic Electron Flow. PQH2 generation reaction, r1,C PQ + NAD(P)H + H+S → PQH 2 + NAD(P)+

f b·PQ generation reaction, r2,C PQ + fb → fb·PQ

PC+ reduction reaction I, r3,C fb·PQ + PC+ → [fb·PQ]+ + PC

PQH2 oxidation reaction, r4,C [fb·PQ]+ + PQH 2 + H+S → fb·PQH + PQ + 2H+L

PC+ reduction reaction II, r5,C fb·PQH + PC+ → [fb· PQH]+ + PC

PQH2 oxidation reaction, r6,C [fb·PQH]+ + PQH 2 + H+S → fb· PQH2 + PQ + 2H+L

f b·PQH2 decomposition reaction, r7,C fb·PQH 2 → fb + PQH 2

PSI+ reduction reaction, r8,C 2PSI+ + 2PC → 2PC+ + 2PSI

Fd+ reduction reaction, r9,C

PC+ reduction reaction I, r3,L +

2Fd+ + 2PSI → 2PSI+ + 2Fd

+

fb·PQ + PC → [fb·PQ] + PC

NAD(P)+ reduction reaction, r10,C

PQH2 oxidation reaction, r4,L

NAD(P)+ + 2Fd + H+S → 2Fd+ + NAD(P)H

[fb·PQ]+ + PQH 2 + H+S → fb·PQH + PQ + 2H+L

HL+ transport reaction, r11,C

+

PC reduction reaction II, r5,L +

ADP3 − + Pi 2 − + 3H+L + H+S → ATP4 − + H 2O + 3H+S

+

fb·PQH + PC → [fb· PQH] + PC

Reactions in the hydrogen ion transport pathway are included in the LEFs and CEF pathways for convenience. Pi

PQH2 oxidation reaction, r6,L 10595


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Industrial & Engineering Chemistry Research represents the phosphate for ATP synthesis. f b·PQ, [f b·PQ]+, f b·PQH, [f b·PQH]+, and f b·PQH2 are complex intermediate compounds composed by plastoquinone and cytochrome b6 f. H+L and H+S are hydrogen ions at the lumen side and stroma side, respectively. 2.1.2. Initial Concentrations of Proteins. The initial concentration of photosynthetic proteins including PSI, PQ, PC, Cyt b6 f, and Fd has to be determined. Although there are only five types of proteins, each protein includes at least two states, which are the oxidation state and the reduction state. Some proteins such as PQ and Cyt b6 f even have up to six or seven different states due to the complicated reaction mechanisms in the electron transfer chain.18 Since previous research11,24−30 only measured the total concentration of each type of protein, the current research assumes that the different states of each protein have the same initial intracellular concentration. This assumption is partially supported by previous research which measured the concentration of some photosynthetic proteins at different states and found that they are very similar.31 The initial concentration of each protein in the current model is shown in Table 1. The

2. Calculate the number of independent reactions in the metabolic network (number of reactions − rank of stoichiometric coefficient matrix). 3. Choose the reactions which can be easily measured as the independent reactions, and then measure the reaction rate of these reactions. 4. Calculate the reaction rate of other reactions. 5. Find the concentration of each protein under the same steady-state from published literature. 6. Calculate the kinetic constant of each reaction by eq 1b. 7. Use switch functions to simulate the change of reaction rates when the culture condition is changed. In the current research, the metabolic network can be assumed as steady-state when the culture is aerobic and nutrient-sufficient, as cells can grow healthily in these conditions. In addition, when the dynamic process operating conditions such as light intensity, temperature, aeration, and mixing are considered to be optimum, the metabolic network can also be assumed as steady-state. As the number of independent reactions is equal to 2, the water-splitting reaction in the LEF pathways and the PSI reduction reaction in the CEF pathway are chosen as the independent reactions since their reaction rates have been accurately measured by previous studies.11,12,14 The initial concentration of each protein in the sulfur-sufficient culture has also been measured and shown in Table 1. The kinetic constants in the current research thereby can be estimated by processing the estimation method outlined above. The detailed kinetic equation of each reaction step and the mass balances of metabolites are shown below: Kinetic Equations. Linear Electron Flow. Water splitting reaction, r1,L

Table 1. Initial Concentrations (amol cell−1) of Proteins and Metabolites in the Current Modela material

initial value

material

initial value

PSI PSI+ fb f b·PQ [f b·PQ]+ f b·PQH f b·PQH2 [f b·PQH]+ PQ PQH2

2.3 2.3 0.75 0.75 0.75 0.75 0.75 0.75 2.63 2.63

PC PC+ Fd+ Fd H2 [CH2O] NAD(P)+ NAD(P)H HL+ HS+

4.5 4.5 0.6 0.6 0 0.3 × 106 12 12 0.05 0.05

r1,L = k1,L·f (Q)1.5

f b·PQ generation reaction, r2,L −18

r2,L = k 2,L·fb·PQ

These values are obtained from refs 11, 24−30. 1 amol = 1 × 10 mol. f b represents the cytochrome b6 f, and [CH2O] represents intracellular starch. HL+ denotes the hydrogen ions at the lumen side, and HS+ denotes the hydrogen ions the stroma side. a

PC+ reduction reaction I, r3,L r3,L = k 3,L·(fb·PQ) ·PC+

PQH2 oxidation reaction, r4,L r4,L = k4,L·[fb·PQ]+ ·PQH 2 ·H+S

impact of the initial concentration of the proteins involved can be estimated by initial condition dynamic sensitivity analysis treating them as parameters, and this is shown in section 3.5. 2.1.3. Estimation of Kinetic Constants in the Metabolic Network. Most reactions in the present metabolic network are induced by electrostatic force, and their kinetics can be expressed in eq 1b. Other reactions which involve the participation of enzymes can be described by eq 1a. In the current model, only reactions catalyzed by NDH, FNR, and HydA are expressed by eq 1a. Because the value of Kij in these specific reactions is much higher than the concentration of the corresponding substrate,32,33 eq 1a can be approximately simplified to eq 1b. As a result, in the current model, all of the reaction kinetics are expressed by eq 1b. To solve the challenge that little work has been contributed to measure the in vivo biochemical kinetics in the current metabolic network, a novel method is proposed in the present research to estimate the kinetic constant of each reaction. The procedure is explained below: 1. Find a condition where the current metabolic network is under steady-state.

PC+ reduction reaction II, r5,L r5,L = k5,L·(fb·PQH) ·PC+

PQH2 oxidation reaction, r6,L r6,L = k6,L·[fb·PQH]+ ·PQH 2 ·H+S

f b·PQH2 decomposition reaction, r7,L r7,L = k 7,L·(fb·PQH 2)

PSI+ reduction reaction, r8,L r8,L = k 8,L·PSI+·PC

Fd+ reduction reaction, r9,L

r9,L = k 9,L·Fd+· PSI NAD(P)+ reduction reaction, r10,L r10,L = k10,L·NAD(P)+ ·2Fd · H+S 10596


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Industrial & Engineering Chemistry Research Starch reduction reaction, r11,L r11,L =

d(fb·PQ) = r2,L − r3,L − r3,C + r2,C dt

k11,L·NAD(P)H ·H+S

d([fb·PQ]+ ) = r3,L − r4,L − r4,C + r3,C dt

H2 generation reaction, r12,L r12,L = k12,L·Fd ·H+S

d(fb·PQH) = r4,L − r5,L − r5,C + r4,C dt

HL+ transport reaction, r13,L r13,L = k13,L·H+L ·f (Q)1.5

d([fb·PQH]+ ) = r5,L − r6,L − r6,C + r5,C dt

Cyclic Electron Flow. PQH2 generation reaction, r1,C r1,C = k1,C·PQ·NAD(P)H

d(PC+) = 2r8,L − r3,L − r5,L + 2r8,C − r3,C − r5,C dt

f b·PQ generation reaction, r2,C r2,C = k 2,C·fb·PQ

d(PC) = r3,L − 2r8,L + r5,L + r3,C − 2r8,C + r5,C dt

PC+ reduction reaction I, r3,C

d(PSI+) = 2r9,L − 2r8,L − 2r8,C + 2r9,C dt

r3,C = k 3,C·(fb·PQ) ·PC+

PQH2 oxidation reaction, r4,C

d(PSI) = 2r8,L − 2r9,L + 2r8,C − 2r9,C dt

r4,C = k4,C·[fb·PQ]+ ·PQH 2 ·H+S

PC+ reduction reaction II, r5,C

d(Fd+) = 2r10,L − 2r9,L + 2r11,L + 2r10,C − 2r9,C dt

+

r5,C = k5,C·(fb·PQH) ·PC

d(Fd) = 2r9,L − 2r10,L − 2r11,L − 2r10,C + 2r9,C dt

PQH2 oxidation reaction, r6,C +

r6,C = k6,C·[fb·PQH]

·PQH 2 ·H+S

d(H 2) = r10,L dt

f b·PQH2 decomposition reaction, r7,C r7,C = k 7,C·(fb·PQH 2)

d([CH 2O]) = 0.5r11,L − rR dt

PSI+ reduction reaction, r8,C r8,C = k 8,C·PSI+·PC

d(H+S ) = 2r13,L − r4,L − r6,L − r4,C − r6,C + 2r11,C dt

+

Fd reduction reaction, r9,C r9,C = k 9,C·Fd+· PSI

d(H+L ) = r4,L = r6,L − 2 + r4,C + r6,C − 2r11,C dt

NAD(P)+ reduction reaction, r10,C

where f(Q) and rR are introduced in section 2.2. The detailed explanation of the water splitting reaction kinetics is also introduced in section 2.2. 2.1.4. Discrete Event Modeling. The kinetics of metabolic pathways in micro-organic cells change rapidly due to the sudden change of culture conditions. For example, when sulfur is depleted, the starch generation pathway is suppressed, and the hydrogen production pathway is stimulated. The activity of the CEF pathway is also enhanced as it can generate a significant amount of photosynthetic ATP for cell maintenance. However, the regulation of these reaction rates is accomplished by a complicated biological control system and is quite difficult to represent by mathematical equations. A discrete model thus is constructed to simplify the complex cellular regulation system. Switch functions, which are similar to the Heaviside step function but differentiable, are utilized to mediate the rapid switch of reaction kinetics34,35 because they are capable of providing smooth changes when reactions are terminated or started due to a sudden change of the environment. In general, the switch function is expressed by eq 2, and the shift response of the equation is determined by the sharpness factor, r.

r10,C = k10,C·NAD(P)+ ·2Fd · H+S

HL+ transport reaction, r11,C r11,C = k11,C·H+L ·f (Q)1.5

Mass Balance Equations. d(PQ) = −r1,L − r2,L + r4,L + r6,L − r1,C − r2,C + r4,C dt + r6,C

d(PQH 2) = −r4,L − r6,L + r1,L + r7,L + r1,C − r4,C − r6,C dt + r7,C

d(fb) = −r2,L + r7,L − r2,C + r7,C dt

d(fb·PQH 2) = −r6,L − r7,L − r7,C + r6,C dt 10597


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Figure 3. Simulated oxygen concentration at different time. (a) Oxygen concentration when the switch function is excluded. (b) Oxygen concentration when the switch function is added.

⎛ f (x) = 0.5⎜⎜1 + ⎝

⎞ ⎟⎟ x + r2 ⎠

dS = −rS·X dt

x

(2)

rX = rmax ·

Switch functions can also help to avoid a negative concentration when the consumption rate of a substrate does not depend on its concentration. For example, although the consumption rate of oxygen due to algal respiration is a function of oxygen concentration in the culture, the expression of cell respiration rate does not include oxygen concentration in general. Therefore, a negative oxygen concentration may be induced numerically after the time when oxygen concentration drops to zero (Figure 3a). To avoid negative oxygen concentrations, a switch function is applied to block the oxygen consumption rate (set it to zero) once oxygen is totally consumed (Figure 3b). This switch function is formulated as eq 3. The sharpness factor in the current study is selected as 0.1 so that the transition from aerobic conditions to anaerobic conditions is prompt. f (O2 ) =

+ r2

(4c) (4d)

where rX is the cell growth rate, X is the cell density, S is the substrate concentration in the culture, rS is the consumption rate of the substrate, rmax is the maximum specific growth rate, KS is the substrate half velocity coefficient, YS/X is the substrate yield coefficient. Model 2.

(3)

2.2. Dynamic Model for Algae Growth. The watersplitting reaction in both starch and hydrogen generation pathways is catalyzed by PSII whose activity is determined by the intracellular sulfur concentration. As the culture for algal hydrogen production is sulfur-free, the consumption rate of intracellular sulfur concentration is totally determined by cell growth rate. The time to switch the culture from aerobic condition to anaerobic condition is also dependent on cell growth rate, as the oxygen consumption rate is affected by biomass concentration. Therefore, it is important to include algal growth kinetics in the dynamic model. 2.2.1. Comparison of Different Dynamic Models. Two types of dynamic models derived from the Monod equation are mainly used for microorganism growth simulation. Detailed equations of both models are shown below. The difference between the two models is that the first model does not include the accumulation of intracellular nutrient concentration, as it assumes all the intracellular nutrients absorbed by cells are immediately consumed for cell division and maintenance. Hence, the first model is not valid in this research because the change of intracellular sulfur concentration needs to be included. Model 1.

dX = rX ·X dt

S S + KS

rS = YS/ X ·rX

O2 O22

(4b)

dX = rX ·X dt

(5a)

dQ = rS − rX ·Q dt

(5b)

dS = −rS·X dt

(5c)

rX = rmax ·f (Q )

(5d)

rS = YS/ X ·rmax ·

S S + KS

(5e)

where Q is the nutrient quota (ratio between intracellular nutrient mass and biomass) and f(Q) is the influence of nutrient quota on the microorganism growth rate. A recent study36 has applied the second model, also named the Droop model, to simulate C. reinhardtii cell growth in a sulfur-deprived culture. Consequently, the values of kinetic parameters presented in the previous work are selected in the current research.36 Also added is a cell respiration term in the Droop model, as the algal respiration rate in this case is quite significant. The modified algal growth equation is shown in eq 6a. The detailed modified Droop model for algal hydrogen production in the current study is presented in eqs 6a−6f.

(4a) 10598

dX = μmax ·f (Q ) ·X − rR ·X dt

(6a)

dQ S = YS/ X ·μmax · − μmax ·f (Q ) ·Q dt S + KS

(6b)

dS S = −YS/ X ·μmax · ·X dt S + KS

(6c) DOI: 10.1021/acs.iecr.5b02034 Ind. Eng. Chem. Res. 2015, 54, 10593−10605

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Industrial & Engineering Chemistry Research dO2 = 0.5·r1,L·X − YO/ X ·rR ·X ·f (O2) dt

f (Q ) − fmin 1 − fmin

⎛ Q ⎞k Q ⎟⎟ = ⎜⎜ ⎝ Q max ⎠

r1,L = k1,L·f (Q )K

Table 2. Parameter Values in eqs 6a−6f and Initial Operating Conditions of the Batch Operationa

(6d)

parameter

value

unit

parameter

value

unit

μmax rR YO/X f min K kQ

0.15 1.08 × 105 1.42 0.056 1.50 0.596

h−1 amol L−1 h−1 mg g−1

Qmax X0 S0 O2,0 Q0

9.44 0.10 0.0 0.009 7.0

mg g−1 g L−1 mg L−1 g L−1 mg g−1

(6e) (6f)

where Q is intracellular sulfur concentration (sulfur quota), S is culture sulfur concentration, O2 is oxygen concentration in the culture, f(Q) is the impact of sulfur quota on cell growth rate, μmax is maximum biomass specific growth rate, YS/X and YO/X are sulfur and oxygen yield coefficients, respectively. rR is the specific cell respiration rate, KS is the sulfur half-velocity coefficient, r1,L is the reaction rate of the water splitting reaction, Qmax is maximum sulfur quota in cells, f min is the minimum f(Q) when the sulfur quota drops to its minimum value, k1,L is a fitting parameter. f(O2) is the switch function introduced in section 2.1.4. kQ and K are fitting parameters. 2.2.2. Expression of f(Q) and Oxygen Net Consumption Rate. In the Droop model, an accurate expression of f(Q) is essential because it represents the impact of intracellular nutrient concentration on cells’ growth rate. Specific to the current research, f(Q) represents the influence of intracellular sulfur concentration on photosynthesis activity. Despite its importance, there is no theoretical expression of f(Q) since the influence of intracellular nutrient concentration on cells’ growth is very complicated. By modifying the expression presented in ref 36, eq 6e is derived in the current research. Parameters in eq 6e are fitted using the published experimental data from ref 4. The oxygen consumption rate is also important since hydrogenase is activated after the depletion of oxygen. During the batch operation, oxygen is continuously generated by algal photosynthesis; meanwhile it is consumed by cell respiration. Because of the remarkable damage on PSII, the oxygen production rate drops lower than the oxygen consumption rate, and the culture eventually switches to anaerobic conditions. Equation 6d is used to calculate oxygen concentration as a function of time. The first term on the right-hand side of the equation represents the oxygen production rate as it is a function of water splitting reaction rate (r1,L), and the second term represents the oxygen consumption rate which is assumed dependent on cell respiration rate. In addition, the current study assumes that the reaction rate of the water splitting step is exponentially dependent on f(Q), as this reaction is catalyzed by PSII, whose activity is dependent on sulfur quota. Thus, the reaction rate of the water splitting reaction is shown in eq 6f. Finally, by estimating the model parameters based on previous published data,11 the parameter values in eqs 6a−6f and the initial operating conditions in the batch process are listed in Table 2. 2.3. Sensitivity Analysis. Sensitivity analysis is commonly applied to dynamic models to measure the effect of model parameters to model state variables.38,39 A normalized sensitivity has been defined by previous research38 and is shown by eq 7. This normalized sensitivity (εij(t)) reflects the proportional change of model output (zi(t)) due to the proportional change of a model parameter (pj) and in effect comprises an elasticity measure. A positive sensitivity means increasing the parameter can increase the associated state variable value, while a negative sensitivity suggests that increasing the parameter will reduce the associated state

μmax is obtained from ref 37. rR is obtained from ref 11. YO/X is obtained from ref 36. f min, kQ, K, and Qmax are estimated by fitting the published data in ref 11. Light intensity in these experiments was kept around 200 μmol m−2 s−1. Temperature was fixed around 25° C, and cells are wild type C. reinhardtii strain. The initial biomass concentration, oxygen concentration, culture sulphur concentration, and sulphur quota are obtained from ref 36. a

variable value. Furthermore, a larger sensitivity also indicates that the effect of the parameter on the model output is greater (more significant). pj dz (t ) εij(t ) = · i zi(t ) dpj (7) In the current study, the state variable studied as model output is hydrogen production, and the model parameters are the kinetic constants of the reactions in the metabolic network. As the current work selects eq 1b to represent the kinetics of the metabolic network, the reaction rates are proportional to their kinetic constants. The sensitivity thereby reflects the change of hydrogen production with respect to the change of reaction rate. By conducting extensive sensitivity analysis studies, both the limiting reaction steps and the competing pathways for hydrogen production in the metabolic network can be identified. Finally, the parameter estimation in the present research is implemented in Wolfram Mathematica 10. Once the current model is constructed, it is implemented in Wolfram Mathematica 10 in the current work to estimate the dynamic performance of green algal biohydrogen production process. Sensitivity analysis in the present study is also conducted in Wolfram Mathematica 10.40

3. RESULTS AND DISCUSSION 3.1. Kinetic Constants in the Model. By using the parameter estimation method proposed in the current research, the kinetic constants in the metabolic reaction network and algae growth model are shown in Table 3. 3.2. Influence of Different Metabolic Pathways on Hydrogen Production. The present study compares the model prediction and experimental results of hydrogen production when different metabolic pathways are activated. Figure 4 shows the simulated hydrogen production when specific pathways are inactivated. From Figure 4b, it is found that when all of the pathways in the current model are activated, the model prediction result of hydrogen production matches the experimental results fairly well. Table 4 shows the model prediction result of total hydrogen production in the first 120 h of the photofermentation process, when different pathways are activated. It is found that when only the LEF pathway for hydrogen production is activated, the simulated hydrogen production is approximately twice that of the experimental result. This is quite similar to previous work,15 10599


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Industrial & Engineering Chemistry Research Table 3. Kinetic Parameters in Current Modela parameter

value

unit

parameter

value

k1,L

1.08 × 106

K12,L *

3.03 × 106

h−1

k2,L

5.48 × 105

amol L−1 h−1 L amol−1 h−1 L amol−1 h−1 L2 amol−2 h−1 L amol−1 h−1 2 L amol−2 h−1 h−1

k13,L

2.16 × 107

h−1

k3,L

3.20 × 105

k4,L

1.10 × 10

k5,L

3.20 × 105

k6,L

1.10 × 107

k7,L

1.44 × 106

k8,L

1.04 × 105

k9,L

7.83 × 105

k10,L

1.50 × 105

K*10,L

1.50 × 104

k11,L k12,L

unit

k1,C

6.85 × 103

k2,C

1.17 × 10

k3,C

6.40 × 104

k4,C

2.19 × 106

k5,C

6.40 × 104

L amol−1 h−1

k6,C

2.19 × 106

k7,C

2.88 × 105

k8,C

2.08 × 104

k9,C

4.32 × 106

9.00 × 105

L amol−1 h−1 L amol−1 h−1 L amol−1 h−1 h−1

k10,C

1.57 × 105

0.0

h−1

k11,C

3.00 × 104

7

Table 4. Comparison of Total Hydrogen Production (mol g−1 biomass) and Hydrogen Productivity (mmol g−1 biomass h−1) at the 120th Hour of the Photo-fermentation Process When Different Metabolic Pathways Are Activated

5

activated metabolic pathways

L amol−1 h−1 L amol−1 h−1

LEF pathway for hydrogen production LEF pathways for hydrogen and starch generation LEF pathways and CEF pathway all metabolic pathways (including H+ transport) previous experimental result

L amol−1 h−1 2 L amol−2 h−1 L amol−1 h−1 L2 amol−2 h−1 −1 h

H2 production

H2 productivity

0.0536 0.0479

0.447 0.399

0.0376 0.0301

3.133 2.508

0.0267

2.225

that a very high proton gradient from the lumen side to the stroma side of chloroplasts is induced by the enhancement of CEF pathway activity, as the CEF pathway becomes the predominant photosynthetic pathway in anaerobic conditions. The high proton gradient thereby leads to a lack of hydrogen ions at the stroma side. Because the electron transfer chain needs the participation of hydrogen ions at the stroma side, the electron transport rate is sequentially suppressed. Hence, hydrogen production rate is inhibited. The present model also verifies the above conclusion. From the model, it is found that the concentration of hydrogen ions at the lumen side increases from 3-fold to 10-fold compared to that at the stroma side when the CEF pathway is included under the anaerobic conditions. Nevertheless, previous work cannot explain why only a 30% improvement of hydrogen production is observed instead of a 128% improvement when only offsetting the proton gradient rather than inhibiting the activity of the CEF pathway.15 If the CEF pathway suppresses the hydrogen production pathway solely by inducing a high proton gradient, the increase of hydrogen production by inhibiting the CEF pathway and by offsetting the proton gradient should be the same. Although15 it is hypothesized that the CEF pathway might also consume the electrons generated through the water-splitting reaction, which should be used for hydrogen production, this hypothesis is highly doubtful as has been demonstrated by recent research that electrons presented in the CEF pathway are purely provided by PSI, while those for hydrogen and starch generation are provided by PSII.12 As a result, there must be other metabolic pathways consuming the electrons obtained from PSII and suppressing hydrogen production pathway, and the CEF pathway should also lower hydrogen production by other mechanisms. This indicates clearly that the pathway is not fully understood and that further research should be conducted to elucidate the

L amol−1 h−1 L amol−1 h−1 L amol−1 h−1 −1 h

k*i denotes the kinetic constant of reaction i in the anaerobic condition. Since r12,L, the hydrogen reduction reaction, does not exist in the aerobic condition, it assumes that HydA has a similar reaction activity compared to FNR.41 From previous research,31,42 it is found that in anaerobic conditions the activity of CEF pathway enhances 3* is assumed fold compared to that in aerobic conditions; therefore, ki,C to be 3-fold of ki,C and not listed in the table. a

which found a 128% increase in hydrogen production by inhibiting the activity of other pathways. By blocking the hydrogen ions’ transport pathway, the current hydrogen production simulation result is significantly enhanced by 25%, which is similar to the 30% increase measured by previous experimental work.15 A remarkable increase in hydrogen production is also found in the current work by completely inhibiting the activity of the CEF pathway. However, hydrogen production does not change much when the starch generation pathway is inhibited (listed in Table 4), suggesting that this pathway is not competitive to the hydrogen generation pathway when the other metabolic pathways are not activated. Previous research partially explained the reason why the CEF pathway can suppress hydrogen production.14,15 It was claimed

Figure 4. Comparison of simulation and experimental results of hydrogen production under different conditions. (a) Only the LEF pathway for hydrogen production is activated. (b) All of the metabolic pathways are activated. Crossed circle points are measured in ref 37, filled circle points are measured in ref 10, and triangular points are measured in ref 43. 10600


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Figure 5. Comparison of net accumulation of intracellular starch when the starch generation pathway is active or inactive in anaerobic conditions. (a) Starch generation pathway is not included in the anaerobic condition. (b) Starch generation pathway is included in the anaerobic condition. Crossed circle points are reported in ref 24, and filled circle points are reported in ref 14.

Figure 6. Sensitivity of hydrogen production with respect to the reaction rate of different reactions. (a) Positive sensitivity. The solid line represents reaction 1 (r1,L), the water-splitting. The dashed line denotes reaction 12 (r12,L), the hydrogen ions reduction reaction catalyzed by hydrogenase. The dot-dashed line represents reaction 13 (r13,L), the transport of hydrogen ions from the lumen side to the stroma side. (b) Negative sensitivity. The solid line represents the FNR catalyzed reaction (electrons transfer between Fd and NAD(P)+) in both starch generation and CEF pathways (r10,L + r10,C). The dashed line denotes the starch generation reaction (r11,L, a simplified reaction to represent the Calvin−Benson cycle). The dot-dashed line represents the FNR catalyzed reaction only in the starch generation pathway (r10,L). The dotted line denotes the FNR catalyzed reaction only in the CEF pathway (r10,C).

matter and complete the existing knowledge about these organisms. 3.3. Influence of Different Metabolic Pathways on Starch Production. Although the LEF pathway for starch generation is the major algal photosynthetic pathway in aerobic conditions, few researchers have focused on the study of this pathway during the hydrogen production period. Previous research44 mentions that this pathway may exist in anaerobic conditions, but its activity is supposed to be severely inhibited and not competitive to the hydrogen production pathway. To verify that if starch is generated during the hydrogen production period, the current work simulates the consumption rate of starch under different conditions. Figure 5 compares the net accumulation of intracellular starch concentration in a sulfur-deprived culture with the absence or presence of starch generation pathway. The initial increasing period happens when the culture is still aerobic, and it is followed by the consumption period after the culture switches to anaerobic. Since the current work assumes that all the electrons from photosynthesis during aerobic conditions are used for starch generation, the initial accumulation of starch is decidedly overestimated. However, this overestimation does not have much effect on the current work, as the present study mainly focuses on the simulation of starch consumption in the anaerobic period. From Figure 5a, it is found that the starch consumption rate which excludes the starch generation pathway in the anaerobic condition is much sharper than the previous experimental results, while that including the starch generation pathway (Figure 5b) shows a very similar tendency compared to the experimental results as the deviation between the simulation and experimental results is almost constant. Therefore, the

current simulation results conclusively indicate that the starch generation pathway still exists under the anaerobic conditions. Previous research45 also found that when the Calvin−Benson cycle (the important pathway for starch generation) is destroyed in an algal mutant, whose photosynthetic activity is much lower than the wild type, more hydrogen can be generated than before. For the wild type algae, a slight increase in hydrogen production is also observed even if the experiment is stopped in the initial hydrogen production period.45 Despite the current work having demonstrated that the starch generation pathway is not competitive with the hydrogen generation pathway if other pathways included in the current study (CEF pathway, hydrogen ion transport pathway, etc.) are inactivated, attention has to be paid to the fact that these metabolic pathways are actually activated during the anaerobic conditions. In particular, it is notable that the CEF pathway and the starch generation pathway share the same metabolic reaction which is the electron transfer step catalyzed by FNR from ferredoxin (Fd) to NAD(P)+. When the CEF pathway does not exist, electrons from ferredoxin may mainly be sent to hydrogenase (HydA) for hydrogen reduction as the activity of starch generation pathway is severely damaged under the anaerobic conditions. Nevertheless, because the CEF pathway is the major photosynthetic pathway under anaerobic conditions, it is quite possible that electrons from ferredoxin are mainly sent to NAD(P)+ to cycle through the CEF pathway. Since the CEF pathway only utilizes the electrons provided by PSI, the electrons generated by PSII but accepted by NAD(P)+ through the CEF pathway will be sent to the starch generation pathway. Thus, the activity of the starch generation pathway can be partially recovered. On the basis of the current modeling results, two hypotheses are proposed in this work: (1) the starch generation pathway 10601


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the hydrogen generation pathway instead of the competing pathways. It is noted that other reactions have much less sensitivity compared to those represented in the table, which indicates their unimportant influence on hydrogen production. Therefore, they are not shown in Table 5. Compared to the considerations of adding chemicals to inhibit the activity of competing pathways, developing new mutants with a low activity of the starch generation pathway seems to be a better strategy to enhance green algal biohydrogen production. For example, at this moment, the strain which characterizes the highest biogas production rate is cyanobacterium Cyanothece sp. ATCC 51142.46 To guarantee the high biogas productivity of this strain, a photoheterotrophic growth culture is always provided so that many more electrons from the carbon source (glycerol) can be delivered for biogas production through the PSII independent pathway.47,48 Since the metabolic mechanisms of green algal and cyanobacterial hydrogen production are very similar, by providing organic carbon source such as acetate, algal mutants with a lower activity of the starch generation pathway may have the potential to improve biogas productivity via the PSII independent pathway. However, attention should also be focused on enhancing the activity of r1,L (water-splitting step), since this reaction is the primary limiting step for biogas production. Specific to this reaction, as its activity is predominately determined by the sufficiency of intracellular sulfur concentration which is accumulated from extracellular sulfur sources, by precisely controlling the culture operating conditions such as sulfur feeding rate, it is possible to maintain a relatively high activity of the water-splitting reaction with all the produced oxygen consumed by biomass respiration so that the culture is kept anaerobic. In order to balance the effects of intracellular sulfur concentration on biogas production, both the optimal process operation mode (fed-batch, batch, or continuous mode) and associated optimal operating conditions such as optimal initial sulfur concentration and optimal nutrient feeding rate have to be determined by further work. Finally, as the current parameter estimation method can only calculate the apparent kinetic constant which corresponds to the apparent reaction rate, the present model is not capable of detecting if the diffusion of small proteins such as PQ and PC limits the overall reaction rate of the electron transfer chain or if it is lowered by the diffusion of small proteins. However, the current study finds that the sensitivity of hydrogen production with respect to the reactions potentially including the diffusion of small proteins is negligible, which means hydrogen production is almost independent of the apparent activity of these reactions. Hence, even if the diffusion of small proteins does exist, it should not suppress hydrogen production. 3.5. Impact of Initial Protein Concentrations on Hydrogen Production. Finally, to check if the concentration of different types of proteins under different states (oxidation and reduction) has a significant impact on the simulated hydrogen production, sensitivity analysis is also used to measure this effect. Based on the result, it is found that hydrogen production is most sensitive to the initial concentration of NAD(P)H and NAD(P)+ (both of them have a sensitivity of −0.26), and also PQ (a sensitivity of 0.18). In terms of other proteins, it is found that hydrogen production is slightly affected by two kinds of large protein complex, [f b·PQH]+ and [f b·PQ]+, as their sensitivities are 0.019. The sensitivity of hydrogen production to the initial

mainly competes with the hydrogen production pathway and limits the hydrogen production rate; (2) the CEF pathway suppresses hydrogen production not only by inducing a high proton gradient but also by enhancing the activity of the starch generation pathway. 3.4. Identification of Limiting Reaction Steps and Competing Metabolic Pathways. To verify the hypotheses proposed in the current research, sensitivity analysis is conducted in the current model. The sensitivity of hydrogen production with respect to different reaction rates is shown in Figure 6. The starting time (time 0) in Figure 6 corresponds to the commencement time of hydrogen production in the photofermentation process (the 60th hour). Figure 6a shows the positive sensitivities, which implies that these reactions are the limiting reaction steps for hydrogen production in the hydrogen generation pathway. By improving the reaction rates of these reactions, hydrogen production can be enhanced. For example, it can be found that a 1% increase in the reaction rate of r12,L (the reduction of hydrogen ions catalyzed by hydrogenase) can lead to a 0.5% increase in hydrogen production independently of fermentation time. The watersplitting reaction (r1,L) is found to have the highest sensitivity, although its value slightly decreases with operating time, which means it is the major limiting reaction step for hydrogen production. Figure 6b presents the negative sensitivities and suggests that these reactions are the competing metabolic pathways for hydrogen production. By inhibiting the activity of these reactions, hydrogen production will be improved. It is easy to see that the FNR catalyzed reaction (the electron transfer step from Fd to NAD(P)+) only shows negligible influence on hydrogen production if the CEF pathway is not included. However, its effect is markedly enhanced by the presence of the CEF pathway and becomes the major competing reaction step (the same reaction step exists in both the starch generation pathway and CEF pathway, r10,L + r10,C) for hydrogen production. As a result, more electrons are transported to the starch generation pathway because of the high activity of the CEF pathway, and the current hypotheses are verified. To optimize hydrogen production, it is very important to ensure that the fermentation process is conducted under the operating conditions such that the most sensitive reaction steps do not limit hydrogen production. Since sensitivity reflects the importance of reaction steps on hydrogen production (over the course of time), by ranking sensitivities the significance of each reaction step on hydrogen production can be obtained. From Table 5, it is seen that the order of the reactions with the highest sensitivity measure does not change with time, and algal hydrogen production is primarily limited by the activity of Table 5. Rank of the Sensitivity of Hydrogen Production with Respect to Different Reaction Steps at Different Time (Hour) in the Current Metabolic Network rank

t0

t10

t50

1 2 3 4 5 6 7

r1,L (+0.711) r12,L (+0.499) r10,L + r10,C (−0.379) r10,C (−0.319) r13,L (+0.263) r11,L (−0.143) r10,L (−0.049)

r1,L (+0.683) r12,L (+0.506) r10,L + r10,C (−0.425) r10,C (−0.361) r13,L (+0.304) r11,L (−0.126) r10,L (−0.053)

r1,L (+0.659) r12,L (+0.511) r10,L + r10,C (−0.471) r10,C (−0.405) r13,L (+0.326) r11,L (−0.108) r10,L (−0.059) 10602


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Industrial & Engineering Chemistry Research concentration of other proteins is much lower than 0.019 and can be neglected. As a result, a more accurate concentration of NAD(P), NAD(P)+, and PQ should be measured in the future to improve the accuracy of the current model. It is also important to notice that the accuracy of the current model is not much influenced by the initial concentration of any proteins, since the greatest sensitivity is only −0.26. Hence, the current simplification that the different states of each protein have the same initial intracellular concentration is acceptable.

4. CONCLUSION Because of the unsteady-state (dynamic) photofermentation process, the current study proposes an advanced methodology for dynamic model construction to determine the limiting nature of key steps and competing metabolic pathways in biochemical processes. The methodology is applied to the green algal hydrogen production process. A novel parameter estimation method is proposed to facilitate the construction of the current model. By blocking the activity of specific pathways and comparing with the previous experimental results, the accuracy of the proposed model is verified. The present study concluded that due to the high activity of the cyclic electron flow pathway under anaerobic cultivation conditions, the activity of the algal starch generation pathway is significantly improved since these two pathways share the same electron transfer step from ferredoxin to NAD(P)H. Therefore, the starch generation pathway becomes the main competing metabolic pathway for hydrogen production, and its activity should be suppressed in future research. By carrying out a dynamic sensitivity analysis, the current work suggests different solutions to improve hydrogen production. As the reaction rate of water splitting is determined by the activity of Photosystem II, which is dependent on the intracellular sulfur concentration, further work should focus on identifying the optimal sulfur concentration in the culture so that the activity of Photosystem II can be kept high while the culture can also be maintained under the anaerobic conditions.

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AUTHOR INFORMATION

ATPase = enzyme for ATP synthesis Pi = phosphate f b·PQ = intermediate compound composed by PQ and Cyt b6 f [f b·PQ]+ = intermediate compound composed by PQ and Cyt b6 f f b·PQH = intermediate compound composed by PQ and Cyt b6 f [f b·PQH]+ = intermediate compound composed by PQ and Cyt b6 f f b·PQH2 = intermediate compound composed by PQ and Cyt b6 f H+L = hydrogen ions at the lumen side H+S = hydrogen ions at the stroma side [CH2O] = intracellular starch ri = reaction rate of reaction i Nij = number of metabolites involved in reaction i cj = concentration of metabolite j in reaction i Kij = half-velocity coefficient of reactant j Vmax = maximum reaction rate of reaction i ki = reaction rate constant of reaction i xij = stoichiometry of metabolite j in reaction i n = number of reactions rX = cell growth rate X = cell density S = substrate (sulfur) concentration in the culture rS = consumption rate of substrate (sulfur) KS = substrate (sulfur) half velocity coefficient YS/X = substrate (sulfur) yield coefficient Q = intracellular nutrient (sulfur) concentration O2 = oxygen concentration in the culture μmax = maximum biomass specific growth rate YO/X = oxygen yield coefficient rR = specific cell respiration rate Qmax = maximum sulfur quota f min = minimum f(Q) k1,L = Droop model fitting parameter kQ = Droop model fitting parameter K = Droop model fitting parameter

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Corresponding Author

*Tel.: 44 (0)1223 330142. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.Z. gratefully acknowledges the support from his family. The authors would also like to acknowledge Mr. Fabio Fiorelli for his meaningful suggestions. Finally, the authors wish to thank the anonymous reviewers for their insightful comments.

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NOMENCLATURE PSII = Photosystem II PQ = plastoquinone Cyt b6 f = cytochrome b6 f PSI = Photosystem I PC = plastocyanin HydA = hydrogenase NDH = NAD(P)H dehydrogenase FNR = ferredoxin-NADP reductase Fd = ferredoxin 10603


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