S-systems sensitivity analysis of the factors that may influence hydrogen production by sulfur-deprived Chlamydomonas reinhardtii

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Available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/he

S-systems sensitivity analysis of the factors that may influence hydrogen production by sulfur-deprived Chlamydomonas reinhardtii Orlando Jorqueraa, Asher Kiperstoka, Emerson A. Salesb, Marcelo Embiruc- uc, Maria L. Ghirardid, a

Department of Environmental Engineering, Bahia Center for Clean Technologies (TECLIM), Federal University of Bahia, Rua Aristides Novis no. 2, 41 andar, Escola Politecnica, Salvador 40.210-630, BA, Brazil b Department of Physical Chemistry, Chemistry Institute, Federal University of Bahia, Brazil c Polytechnique Institute, Federal University of Bahia, Salvador 40.210-630, BA, Brazil d National Renewable Energy Laboratory (NREL), 1617 Cole Blvd., Golden, CO 80401, USA

art i cle info

ab st rac t

Article history:

We built a metabolic map of the hydrogen production process by the microalga

Received 19 November 2007

Chlamydomonas reinhardtii, mathematically modeled this map in the S-systems formalism,

Received in revised form

then analyzed the effect of variations in the value of different model parameters on the

29 January 2008

overall response of the system. The mathematical model exhibited behavior similar to that

Accepted 29 January 2008

described in literature for photosynthetic algal hydrogen production by sulfur-deprived

Available online 18 April 2008

algal cultures. This behavior consists of an initial phase during which oxygen is transiently

Keywords: Metabolic map Hydrogen Microalgae Mathematical model S-systems

generated and then consumed, followed by an anaerobic phase that is characterized by generation of hydrogen. Our analysis of the effect of independent variables on the hydrogen production process mostly agrees with previous work [Horner J, Wolinsky M. A power-law sensitivity analysis of the hydrogen-producing metabolic pathway in Chlamydomonas reinhardtii. Int J Hydrogen Energy 2002;27: 1251–1255]. Moreover, a more detailed study of the effects of parameter modification (rate constants and kinetic order) indicated that genetic engineering of the hydrogenase expression, activity and stability may lead to increased performance of the process. Published by Elsevier Ltd. on behalf of International Association for Hydrogen Energy.

1.

Introduction

Atmospheric CO2 accumulation due to fossil fuel burning contributes to global warming. Non-fossil energy sources that generate electricity and hydrogen, such as biomass, wind and solar energy have been proposed as alternatives to fossil fuels. Hydrogen is a plausible energy carrier because it can be produced renewably, it can be utilized cleanly (its combustion generates water as a product), it has a favorable energy/

weight ratio, and it can be converted into electricity in fuel cells for a variety of applications. Amongst the different technologies available for hydrogen production, the bio-photolytic pathway is considered a promising alternative since it is accompanied by CO2 consumption (although the overall process is carbon neutral) and it involves a direct conversion of solar energy into hydrogen, without the need to accumulate any chemical intermediates [1,2].

Corresponding author. Tel.: +1 303 384 6312; fax: +1 303 384 6150.

E-mail addresses: [email protected] (O. Jorquera), [email protected] (A. Kiperstok), [email protected] (E.A. Sales), [email protected] (M. Embiruc-u), [email protected] (M.L. Ghirardi). 0360-3199/$ - see front matter Published by Elsevier Ltd. on behalf of International Association for Hydrogen Energy. doi:10.1016/j.ijhydene.2008.01.054

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Nomenclature PSII PSI PQ PC Cytb6f NADPH

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Fd FNR H2ase Mito Fer a; b g; h m,n

Photosystem II Photosystem I plastoquinone plastocyanin cytochrome b6f (NADP) nicotinamide adenine dinucleotide phosphate

ferredoxin ferredoxin NADP reductase hydrogenase mitochondria fermentation rate constants kinetic orders independent and dependent variables

functions is not significant during the first couple of days, but becomes more widespread as a function of time. This observation has led to a renewed interest in microalgae hydrogen production as a possible process to produce gas hydrogen in commercial form [12,13]. The sulfate-deprivation method for hydrogen production consists of two phases: an initial phase that involves a gradual decline in the water oxidation activity (which is responsible for O2 evolution) and over-accumulation of carbohydrate (in the form of starch), followed by a H2-production phase that is driven by residual photosynthetic water oxidation and anaerobic degradation of starch (see

One of the major barriers preventing the utilization of biological systems for commercial hydrogen production at present is the sensitivity of the biological catalyst to oxygen [3,4]. A few years ago, Melis et al. [5] discovered a physiological way to manipulate cultures of microalgae to induce hydrogen production without the need to continuously remove oxygen from the medium. Under sulfur deprivation, some microalgae such as Chlamydomonas reinhardtii can become anaerobic and produce hydrogen continuously for a few days [6–11]. The procedure is based on the selective effect of sulfate deprivation on the O2 evolution properties of the algae. The effect of sulfate deprivation on other cellular

CHLOROPLAST O2

(-)

(-)

DNA (X34)

mRNA H2 ase (X17)

O2

(-)

(-)

Fer

Pyruvate (X7) (X18)

(X16)

SO4 (X22)

STROMA

H+ out (X19)

H+ in PSII (X1)

H2O (X21)

THYLAKOID MEMBRANES

LUMEN

Mito (X29)

ATPase (X25)

O2(X2)

PSII

Precursor PSII (X33)

Formate (X14)

NADP+ (X24)

e starch+ ePSII (X3) (X6)

(X31)

Acetate (X13)

Acetate (X13)

PSI (X23)

Starch (X5) H+ in PQ (X4) PQ e starch (X6) e PSII (X3)

hv

Pyruvate (X7)

NADPH (X9) FNR (X32)

H+out

CO2 (X30)

H+out (X19)

Fdox (X20)

hv

ATP (X12)

H2 (X11)

H2 ase (X10)

e PSI (X8)

NADPH (X9)

O2

H+out

NUCLEUS

ATP (X12)

MITOCHONDRIA CO2 celular (X15)

ADP Pi (X26) (X27) Other ATP consumers (X28)

STROMA

Fig. 1 – Schematic of the metabolic map representing the process of hydrogen production by sulfur-deprived Chlamydomonas reinhardtii (see Nomenclature in the text).

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Fig. 1). The observed decrease in the water oxidation activity of PSII is caused by the decrease in the turnover of the D1 protein, an essential component of PSII that is inactivated in the light and re-synthesize at very fast rates subsequently. In the absence of sulfate, D1 turnover is impaired due to the lack of sulfurylated residues [14] and PSII activity is gradually lost. Light is essential for the generation of hydrogen in the second phase through two different pathways [15,16]: (a) water oxidation, catalyzed by the photosynthetic activity of PSII, followed by delivery of electrons to the PQ pool and to PSI, from PSI, electrons are transferred to Fd; (b) delivery of electrons liberated from the initial steps of starch degradation in the chloroplast to the PQ pool and subsequently transferred from the PQ pool to Fd through the photosynthetic activity of PSI. Ferredoxin (Fd) serves as physiological electron donor to the [FeFe]-hydrogenase and is responsible for the electronic connection between [FeFe]-hydrogenase and the photosynthetic electron transport chain in the chloroplasts of green microalgae [17]. In order to mathematically model the above-described process, the following sequence of steps was considered (see also Fig. 1): incident light hn is absorbed by the pigments associated with PSII and PSI (chlorophylls and carotenoids) and transferred to their respective reaction centers. At PSII, light energy drives a charge separation reaction that originates an electron at the reducing side and a positive charge at the donor side of PSII. A manganese-containing co-factor, present at the donor side of PSII, extracts electrons from water in a four-step reaction, releasing O2 and protons to the lumenal side of the thylakoid membrane. The electron in the reducing side is transferred to the acceptor plastoquinone (PQ). The full reduction of PQ to PQH2 requires two electrons and is accompanied by the uptake of two protons from the chloroplast stroma. PQH2 diffuses along the thylakoid membrane and transfers electrons to the cytochrome b6f and, concomitantly, protons to the luminal side. The resulting proton gradient is one of the major contributors to the building of a proton motive force across the thylakoid. Cyclic transfer of electrons through the complex b6f, the Q-cycle, contributes to additional proton translocation across the membrane and thus increases the proton motive force. Concomitantly, light absorption by PSI results in a second charge separation reaction that also releases an electron at its reducing side and an oxidant at PSI’s oxidizing side. Electron flow from the cytb6f complex reduces the charge separated oxidizing side of PSI, while the electrons released at PSI’s reducing side are transferred to the soluble carrier ferredoxin (Fd). Under aerobic photosynthetic conditions, reduced Fd is responsible for the conversion of NADP+ to NADPH in the chloroplast stroma, a reaction catalyzed by the ferredoxinNADP-oxidoreductase enzyme (FNR). NADPH is used as a reductant in the dark reactions that fix CO2 and store sunlight energy in the form of carbohydrates and starch. Simultaneously, the proton motive force generated by proton translocation coupled to photosynthetic electron transfer is converted into ATP by the enzyme ATPase, thus providing the energy required for CO2 fixation as well as to other ATPconsuming reactions in the alga. Under anaerobic conditions, the CO2 fixation pathway is turned off (as observed by the lack

33 (2008) 2167 – 2177

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of immunological detection of Rubisco after 48 h of sulfur deprivation [18]), the [FeFe]-hydrogenase is expressed, and reduced Fd can catalyze H2 production instead of NADP+ reduction, as described by the following equation: 2Hþ þ 2Fdred

hydrogenase

!

H2 þ 2Fdox .

(1)

It is important to notice that anaerobic conditions induce starch degradation as well [8,18]. The initial steps of starch degradation to pyruvate occur in the chloroplast and release NADH. This reductant can provide electrons to the photosynthetic electron transfer chain at the level of PQ, in a reaction catalyzed by the PQ-oxidoreductase enzyme. The later steps of pyruvate oxidation take place either in the chloroplast (through fermentative pathways that originate acetate, ethanol or formate) or in the mitochondria, where pyruvate is decarboxylated to acetate which then enters the TCA cycle. As a result of mitochondrial respiration, O2 is consumed and CO2 is produced. As expected, this complex biological process is characterized by the occurrence of many integrated metabolic pathways whose activities are not always linear, that is, where quantitative variations in the parameters that describe them cause nonlinear quantitative variations in the system’s response. It is possible, however, to mathematically formulate such complex biochemical system by, for instance, an S-systems approach [19]. In an S-system formulation, the rate of change for each canonical observable state (Xi) of the system as a function of time is described by a differential equation (see Eq. (2)). The left-hand side of an S-system equation is the first time-derivative of Xi. The right-hand side of an S-system equation is the difference between two power-law terms. Each term represents, respectively, the processes that contribute to the accumulation of state Xi and to its consumption. As such, each is the product of a constant (ai or bi), called a generalized rate constant, and the concentrations of the canonical observable states (Xi), raised to a power (gi,j or hi,j), called the generalized kinetic order for each specific state [20]. The subscripts i,j corresponds to the effect of the jth observable state on Xi. The independent and dependent variables are represented by m and n. nþm nþm Y gij Y hij dwi ¼ ai  wj  bi  wj : dt j¼1 j¼1

(2)

Mathematical models based on the S-systems have been used to describe the hydrogen production process by microalgae [21,22]. Our current work complements previous models and explores in more detail the effect of variations of the kinetic parameters on a larger number of state variables.

2.

Materials and methods

2.1.

Metabolic map

A metabolic map of hydrogen production by sulfur-deprived C. reinhardtii was designed, based on the known physiological

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Table 1 – List of dependent and independent values and their respective nominal values

2.3. Analysis of the effect of variations in the independent variables and parameters on the system

Initial values of dependent variables (n)

The effect of varying the value of the independent variables or parameters on the stationary state of the model (in terms of the H2-production rate) was obtained by: (a) changing the value of the independent variables by 50% and (b) varying the value of the parameters (rate constants and kinetic order) by 10%, respectively. In the S-system formalism, dependent variables are a system component or pool of components whose value is affected by changes in the system during an experiment. The independent variable represents a system component or pool of component that itself is unaffected by changes in the system. The latter are thus kept constant during the experiment [20].

Protons from PSII (X1) Oxygen (X2)

1 0.1 1  108

Electrons from PSII (X3) Protons from PQ (X4) Starch (X5) Electrons from starch oxidation (X6) Pyruvate (X7) Electrons from PSI (X8) NADPH (X9) Hydrogenase (X10) Hydrogen (X11) ATP (X12)

1  107

Acetate (X13)

5

Formate (X14) Intracellular CO2 (X15) PSII (X16) H2ase expression (X17)

1  106 1  103

1

Initial values of independent variables (m) Light (X18) Protons in the stroma (X19) Ferredoxin oxidized (X20) Water (X21)

1  104 1  103

Sulfate (X22)

1  106 1  106

NADP+ (X24)

1  106 1  109

ADP (X26)

1  108

Other ATP consumers (X28) Mitochondrial respiration (X29) Extracellular CO2 (X30) Fermentation (X31)

10 1  105

PSI (X23)

ATPase (X25)

Phosphate (X27)

FNR (X32) Precursor to PSII (X33) DNA (X34)

2.363 10 1  105 0.8 0.1 1

100 1 100 100 0.01 100 3  103 1  104 1 1 1

processes of normal oxygenic photosynthesis and of sulfurdeprived H2-production [5,6,11,23,24].

2.2.

Mathematical model of the process

An S-system model of the metabolic map, consisting of 17 differential equations, 17 state variables, 34 rate constants and 77 kinetic orders was built, using the known fluxes described in literature for normal oxygenic photosynthesis in normal oxygenic conditions (http://www.genome.jp/kegg/ pathway.html), and adapted to anaerobic, sulfur-deprived, H2-producing conditions as described above. The S-system translation of the metabolic map was implemented in PLASs (http://www.dqb.fc.ul.pt/docentes/aferreira/ plas.html). The generalized rate constants were set to a value of 0.1 (except in the case of b9, b13 and b17, which were set to 1, and of a3, which was set to 0.01). The generalized kinetic orders were originally assigned a value of 1 for the production reactions and to 1 for the consumption or inhibition reactions (except in the case of h5,30 and h8,32 which were set to 2). As experimental data are not available for all the dependent variables, it is difficult to make reliable estimates of their actual values. Nominal initial values of the dependent and independent variables are shown in Table 1.

3.

Results

3.1. Metabolic map of hydrogen production by sulfurdeprived C. reinhardtii The metabolic map of the hydrogen production process by sulfur-deprived C. reinhardtii is represented in Fig. 1. As described in Section 1, the process includes photosynthetic components (PSII, PQ, cytb6f (not shown), PSI, Fd, FNR, NADP(H), CO2, starch, H2ase, ATPase), fermentation-related species (starch, pyruvate, Fer, acetate, formate, ethanol), mitochondrial reactions (Mito) and generalized cellular functions (other ATP consumers). The expression of the H2ase is controlled at the transcriptional and translational level by oxygen, although only the latter is shown in Fig. 1. Hydrogen production is competitive with NADPH generation, and the flux of electrons to either pathway is expected to depend strongly on the oxygen concentration. The activity of PSII is considered a variable, since it will change according to the concentration of sulfate in the medium; the activity of PSI, on the other hand, was kept constant, given that it has been reported not to vary much by changes in the sulfate levels [5,24]. We have included a PSII precursor in the model to represent the transcriptional and translational processes that lead to an active D1 protein-containing PSII. The accumulation and degradation of this ‘‘precursor’’ is also regulated by the levels of sulfate in the medium in the model.

3.2.

Mathematical model of the metabolic map

As mentioned in Materials and methods, the process of hydrogen generation was modeled by 17 differential equations. All the rate constants were constrained to have a positive value (by definition). Kinetic orders were set to +1, except for g7,2, g10,2, g11,2, g13,2, g14,2, g6,2 and g5,2, which were given negative values (since they represent inhibitory responses, see Table 1). The overall process is likely to be first order kinetic or higher. Several of the steps taken individually, in fact, represent reactions that occur in membranes and as a result may have a kinetic order higher than 1 [25]. A measure of the stability of a system of differential equations is given by its eigenvalues, which can be estimated

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by the PLASs program. A negative value for an eigenvalue’s real part and a zero for its imaginary part represent high system stability. Different values denote less stability. In our model, X5 (concentrations of starch) and X6 (electrons from starch oxidation) were assigned negative values very close to zero, suggesting variability, particularly when the amount of sulfate in the medium is zero. The stability of the system increases as the amount of sulfate increases. The dependent and independent variables are described in Table 1, while the differential equations representing the model are listed below: g

g

g

h

h

g

g

g

h

h

g

X3 ¼ a3 

g X213;21



g X163;16



g X183;18

h X33;3

 b3 



X4 ¼ a4 

g X34;3



g X64;6



g X194;19

þ þ Vþ 1 ¼ V2 ¼ V 3 ,

where V1, V2 and V3 are the production rates of X1, X2 and X3, which can also be written as g

g

g X56;5

g X26;2

g

g

g

g

g

g

g

g

a1  X221;22  X161;16  X181;18 ¼ a2  X222;22  X162;16  X182;18 ¼ a3  X223;22  X163;16  X183;18 .

(21)

g1;22 ¼ ¼

h X233;23

h

qV X22 X22 g 1 g g ¼ ða2  g2;22  X221;22  X161;16  X181;18 Þ  þ  qX22 V V2 g2;22  Vþ 2 Vþ 2

¼ g2;22 .

(22)

By analogy, the following applies: g1;22 ¼ g2;22 ¼ g3;22 ,

 b4  X44;4  X254;25

ðprotons from PQÞ; g

(20)

(4)

(5) h

(19)

(3)

h

ðelectrons from PSIIÞ;

ðH2ase expressionÞ:

Restrictions for flow aggregation are represented by

X2 ¼ a2  X212;21  X162;16  X182;18  b2  X22;22  X292;29  X182;18 ðoxygenÞ;

h

X17 ¼ a17 X3417;34  b17  X1717;17

Since these three rates are only dependent on photosynthetic water oxidation, they should be the same. Using the definition by Voit [20], the kinetic order for the first of the above reactions can be calculated as

h

X1 ¼ a1  X211;21  X161;16  X181;18  b1  X11;1  X251;25  X181;18 ðprotons from PSIIÞ;

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(23)

(6)

g

h

h

X5 ¼ a5  X95;9  X125;12  X305;30  b5  X55;5  X25;2

(7)

ðstarchÞ;

X6 ¼ a6 



 b6 



h X236;23

ðelectrons from starchÞ; g

g

(8) h

h

h

h

X7 ¼ a7  X57;5  X27;2  b7  X77;7  X317;31  X297;29  X27;2 (9)

ðpyruvateÞ; g

g

g

g

h

h

h

h

X8 ¼ a8  X188;18  X238;23  X38;3  X68;6  b8  X88;8  X208;20  X108;10  X328;32 ðelectrons from PSIÞ;

(10)

O2 concentration (relative units)

6 h X66;6

5 4 3 2 1 0 0

X10 ¼ a10 



g X249;24

g X1710;17





g X89;8

g X210;2

g



g X329;32

 b10 

g

 b9 

h X1010;10

g

h X99;9

ðNADPHÞ;

ðhydrogenaseÞ;

h

g

g

g

(13)

g

g

X12 ¼ a12  X412;4  X112;1  X2612;26  X2712;27  X2512;25 h

h

 b12  X1212;12  X2812;28 g

(14)

ðATPÞ;

g

h

h

X13 ¼ a13  X3113;31  X213;2  b13  X1313;13  X2913;29

ðacetateÞ;

X14 ¼ a14 



X15 ¼ a15 

g X715;7

g X215;2

g



g X214;2

g

 b14   b15 

h X1414;14

h X1515;15

h

X16 ¼ a16  X2216;22  X3316;33  b16  X1616;16

ðformateÞ;

ðintracellular CO2 Þ, ðactive PSIIÞ;

200

250

300

0.03 hv

0.3 hv

2.3 hv

0.06 hv

1.3 hv

5.3 hv

10.3 hv

(15)

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0

g X3114;31

150

(12)

g

ðhydrogenÞ;

100

(11)

X11 ¼ a11  X1011;10  X1911;19  X811;8  X211;2  b11  X1111;11

50

Time ,h

Oxygen evoluiton (relative units)

X9 ¼ a9 

g X199;19

(16)

(17)

(18)

2

4

6

8

10

12

Light intensity (relative units)

Fig. 2 – Modeled graphs of: (A) Light saturation curves of photosynthesis, i.e., O2 concentration as a function of time under different relative and arbitrary levels of illumination (represented by different symbols). (B) Maximum rates of O2 evolution as a function of the relative light intensity.

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Oxygen production (relative units)

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0.35

140

0.30

120

0.25

100

0.20

80

0.15

60

0.10

X2 X11

0.05 0.00 1

40

Hydrogen production (relative units)

2172

20

0 11 21 31 41 51 61 71 81 91 101 111 121 131 141 Time,h

Fig. 3 – Modeled graph of the variations in O2 (open circles) and H2 (closed circles) concentrations as a function of time under sulfur-deprived conditions.

g1;16 ¼ g2;16 ¼ g3;16 ,

(24)

g1;18 ¼ g2;18 ¼ g3;18 ,

(25)

a1 ¼ a2 ¼ a3 .

(26)

Initially, the mathematical model was used to test the changes in O2 evolution activity of a sulfur-replete, aerobic, photosynthetic process. As shown in Fig. 2A, the model correctly represented the temporal changes in O2 concentration expected upon illumination of the algae under different light intensity levels, up to a stationary state. Indeed, by plotting the initial slope of each curve as a function of light intensity (Fig. 2B), we obtained typical light saturation curves of photosynthesis [25,26]. The time courses for oxygen and hydrogen production under sulfur deprivation are shown in Fig. 3. The results indicate the same trend described in the literature [7], that is, a transient increase in the oxygen levels at the start of the process, followed by O2 consumption to levels low enough to generate anaerobiosis in the culture medium. This allows the cells to start producing hydrogen. The results shown in Fig. 3, thus, validate the model in correctly predicting the temporal changes in extracellular levels O2 and H2 evolution during the sulfur deprivation process.

3.3. Analysis of the effect of variations in the independent variables and parameters Two major types of factors are expected to affect H2 levels and H2-production rates upon sulfur deprivation: (a) persistent changes in the value of the independent variables and (b) permanent changes in the parameters of the system, that is, rate constants and kinetic orders [20]. A change in the value of independent variables could result from environmental factors (such as light intensity or temperature) that cause the system to achieve a new stationary-state level of H2 concentration. In contrast, changes in parameters may represent biochemical changes within the organism, independent of ambient conditions, which affect the rates of H2

production. Such changes could be caused, for instance by a mutation that results in the alteration of the activity of a specific enzyme.

3.3.1. Variations in independent variable vs. stationary levels of H2 production The effect of variations in the value of the independent variables on the stationary-state level of H2 produced (X11) is shown in Figs. 4A and B. It is clear that X18 (light intensity) and X19 (proton concentration in the stroma) greatly affect the maximum hydrogen levels observed at the stationary state (X11). The effect of variations in the level of stromal protons (X19), which represent a decrease in stromal pH, agrees with the experimental results of Kousorov et al. [16]. An increase in X23 (PSI), as expected, causes an increase in the maximum hydrogen level. An increase in X29 (other consumers of ATP) causes only a slight increase in the maximum level of X11 (Fig. 4A). On the other hand, an increase in the sulfate concentration (X22) during H2 production significantly decreases the maximum level of H2 produced, which also agrees with reported experimental results. Kousorov et al. [27] showed that readdition of sulfate during the H2-production phase of sulfur deprivation resulted in the transient inhibition of H2 production, decrease in the total output of H2 and restoration of the maximum specific rate of H2 production by the cultures. Fig. 5 represents the estimated effect of sulfate re-addition (at t ¼ 58 h) to concentrations of, respectively, 2, 5 and 10 times over that of the control sample. Our system thus correctly modeled the results of Kousorov et al. [27], showing that hydrogen accumulation decreased with the addition of sulfate and, following consumption of the added sulfate, increased again to arrive at a new stationary-state level, lower than that of the control samples. Finally, variations in the amount of the PSII precursor (X33) also decrease the total amount of H2 produced. In this work, the X33 variable (PSII precursor) represents mathematically the overall transcriptional/translational process previous to the accumulation of a mature, active PSII (see Section 3.1). If

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33 (2008) 2167 – 2177

150 X11

50 Dep var

% Effect

100

0 -50

X33

X32

X31

X11 X30

X29

X28

X27

X25

X26

X24

X22

X23

X20

X18

X19

-100

Independent variable 0 -2

-6

Dep var

% Effect

-4

-8 -10

X33

V(X11) X31

X29

X27

X25

X23

V(X11) X20

X18

-12

Independent variable Fig. 4 – Relative effect of variations in the value of different independent variables (shown in the X-axis) on (A) the stationarystate amount of H2 produced and (B) the rate of H2 produced. Note that the variables are defined in Table 1.

Hydrogen produced (relative units)

140

the amount of X33 increases, the amount of active PSII will also increase, leading to a higher rate of O2 evolution and thus decreasing the amount of hydrogen produced.

120 100 80 60

3.3.2. Variations in independent variable vs. maximum rates of H2 production

X11 (0.1)control X11(2) X11 (5) X11 (10)

40 20 0 0

50

100

150

200

250

Time after sulfur deprivation,h

Fig. 5 – Effect of re-addition of sulfate to the amount of H2 produced by sulfur-deprived C. reinhardtii cultures. Different amounts of sulfate (see different symbols) were added at the time-point indicated by the arrow.

Fig. 4B shows that, in contrast to their effect on total accumulation of H2, variations in X18 (light intensity), X19 (proton concentration in the stroma), X22 (sulfate concentration), X23 (PSI) and X33 (the precursor to PSII) cause the most significant decrease in the rates of H2 production. These effects can be explained by a concomitant increase in O2 evolution expected to occur as the values of X18, X22 and X33 increase. However, the effect of changes in these variables is fairly small compared to their effect in the total amount of

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accumulated H2, and it is not clear whether the observed effects are statistically significant. Additionally, even smaller effects were observed upon variations in X20 (Fdox), X29 (mitochondrial respiration) and X32 (FNR activity). In its current format, the model does not include the inhibition of CO2 fixation that occurs under sulfate deprivation due to inactivation of Rubisco [18]. However, if we apply the necessary constraints to the model in order to account for this inactivation, we observe no effect of different levels of extracellular CO2 on hydrogen production (results not shown). Moreover, when we model an inhibitor of CO2 fixation (between X30 and X5), we then clearly observe that hydrogen production depends on the amount of starch accumulated before hydrogen production commences (data not shown).

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(expression of H2ase activity), b2 (O2 consumption) and b16 (PSII inactivation). On the other hand, decreased hydrogen accumulation is observed upon variations in the following rate constants: a3 (PSII activity), a16 (accumulation of active PSII), b3 (consumption of electrons produced by PSII), b6 (utilization of electrons from starch degradation by non-photosynthetic pathways), b10 (inactivation of the H2ase), b11 (consumption of hydrogen) and b17 (down-regulation of H2ase expression). As mentioned in Section 3.3, alterations in rate constants imply permanent changes in the biochemistry of the system. As such, one may preliminarily conclude from Fig. 6A that genetic engineering attempts for increased electron transfer from PSI (a8), overexpression of the H2ase (a11 and a17), increased H2ase activity (a10), increase in the availability of processes that consume intracellular oxygen (b2), a more stable H2ase (b10), stabilization of hydrogenase gene transcription and translation (b17) and reduction in the consumption of electrons from starch degradation by fermentative pathways (b6) may result in higher H2 accumulation. Fig. 6B shows the influence of variations in the rate constants on the rate of hydrogen production. Interestingly,

3.3.3. Variations in dependent variable vs. parameter changes 3.3.3.1. Rate constants. The effect of variations in the rate constants (see Eqs. (3)–(19)) on the maximum H2 accumulation level is shown in Fig. 6A. Variations in the following rate constants increase hydrogen accumulation, as expected: a8 (PSI activity), a10 (hydrogenase activity), a11 (H2 production), a17

25 X11

15 10 5 0 -5 -10 -15 -20

Dep var

% Effect

20

α3

α6

α9 α12 α15

β1

β4

β7

β10

β13

X11

β16

Rate Constants 3 2 V(X11)

1

Dep var

% Effect

0 -1 -2 -3 -4 -5 -6

α3

α6

α9

α12 α15

β1

β4

β7

β10

β13

V(X11)

β16

Rate Constants Fig. 6 – (A) Relative effect of variations in the value of different rate constants (shown in the X-axis) on total H2 accumulation. (B) Relative effect of variations in the value of different kinetic rate constants (shown in the X-axis) on the rate of H2 production. The rate constants are defined in Eqs. (3)–(19).

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that the effects on rates of hydrogen production by varying any of the above rate constants are much smaller than the effects on overall hydrogen accumulation.

some of the rate constants whose variations resulted in increased hydrogen accumulation (Fig. 6A) display opposite behavior with respect to the rates of H2 production, such as a8 (PSI activity), a11 (H2 production) and b2 (O2 consumption). These observations indicate that, although more hydrogen accumulates upon increases in a8, a11 and b2, it takes longer under these conditions to achieve stationary state. Under the same token, as less hydrogen accumulates upon increases in a3 (generation of reductants by PSII), a16 (PSII activity) and b6 (consumption of reductants generated by starch oxidation), the stationary state is reached earlier. Additionally, variations in the following rate constants affect H2-production rates but not H2 accumulation: a9 (NADPH production by FNR, the competitive pathway for photosynthetic electrons) and b8 (utilization of electrons generated at PSI). Finally, variations in the following variables elicit a qualitatively similar response with respect to total H2 accumulated and rates of H2 production: b16 (PSII inactivation) and b17 (down-regulation of the H2ase expression). We do caution the reader, though,

3.3.3.2. Kinetic order. The kinetic order of a reaction reflects the interactions between the chemical species that participate in the reaction. In order to increase the total accumulation of H2 (Fig. 7A), the order of the following reactions must be increased from 1 in the model (we list only the ones that have major effects): g3,16 in Eq. (5) (electron-generating activity of PSII), h6,6 in Eq. (8) (consumption of electrons generated from starch oxidation), g10,2 in Eq. (12) (inhibitory effect of O2 on H2ase), g11,2 in Eq. (13) (inhibitory effect of O2 on hydrogen generation) and g16,22 in Eq. (18) (activation of PSII synthesis by sulfate). Similarly, major decreases in the total amount of H2 accumulated were observed when the kinetic orders of the following reactions were decreased: h2,2 in Eq. (4) (consumption of oxygen as function of O2 concentration), g8,6 in Eq. (10)

100 80

X11

60 20 0

Dep var

% Effect

40

-20 -40 -60

h16,16

g16,22

X11 g11,2

g11,8

g10,2

g8,6

h6,6

g3,16

h2,2

-80

Kinetic order

0 -2 -6 Dep Var

% Effect

-4 -8 -10 -12 -14 -16

V(X11)

-18 h2,2

g8,6

h10,10

V(X11) g11,8

h12,28

h16,16

Kinetic order

Fig. 7 – (A) Relative effect of variations in different kinetic orders (shown in the X-axis) on total H2 accumulation. (B) Relative effect of variations in different kinetic orders (shown in the X-axis) on the rate of H2 production. The kinetic orders are defined in Eqs. (3)–(19) and the relevant ones are discussed in the text.

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(generation of reductant by PSI as a function of the number of electrons originated from starch oxidation), g11,8 in Eq. (13) (H2 production as a function of the number of electrons originated from PSI), and h16,16 in Eq. (18) (inactivation of PSII as a function of PSII concentration). Although it is easy to understand the modeled effect of some of the variations described above, it is not always simple to rationalize the observed data. There are many other parameters whose variations affect the rate of H2 production, as shown in Fig. 7B. As a rule, though, their effect is much lower, below 30%, when compared to the results shown in Fig. 7A. The major decreases in the rate of H2 production were observed following variations (increases or decreases) in the kinetic order for the following rate constants: h2,2 in Eq. (4) (consumption of O2), g8,6 in Eq. (10) (contribution of starch oxidation to the generation of reductants by PSI), h10,10 in Eq. (12) (degradation of the H2ase), g11,8 in Eq. (13) (effect of light on H2 generation) and h16,16 in Eq. (18) (inactivation of PSII). Interestingly, we detected no major effect on the H2 production rates by increasing the kinetic order of h12,28 (other ATP consumers) in contrast with Horner and Wolinski [21]. The latter reported a significant decrease in the rates of H2 production by increasing the kinetic order of ‘‘other ATP consumers’’ above a value of 2.

4.

Conclusion

The elaboration of metabolic and mathematical models is of great importance since it allows one to predict the behavior or trend of a variable in response to imposed changes to a system. The observed behavior of the system can be compared to data in the literature, or can provide the basis for new experiments. In the case of hydrogen production, the main problem a modeler faces is parameter estimation. As posited by Horner and Wolinski [21], an adequate kinetic model of H2 production by sulfur-deprived C. reinhardtii must correctly predict the start and the end time-points of gas production, as well as the rates of H2 and O2 production. Our metabolic model of the algal system under normal sulfurreplete conditions follows the behavior described in the literature for the response of photosynthetic O2 evolution as a function of irradiance (Fig. 2). Under sulfur-deprived conditions, the temporal response of O2 and H2 production predicted by the model also reflects data in the literature (Fig. 3). Moreover, the modeling of sulfur re-addition to the sulfurdeprived system correctly corresponds to published information [27]. There is more uncertainty regarding different metabolic aspects of the model, such as the production of acetate and formate through fermentation, the rates of mitochondrial respiration, and the rates of anaerobic starch degradation. However, given these constraints, the model is still a reliable mathematical representation of the metabolic map shown in Fig. 1. This is demonstrated by the sensitivity analyses done here, where the influence of variations in the independent variables as well as variations in the rate constants and kinetic orders of the described reactions were studied. The current model, which is based on the analysis done by Horner and Wolinsky [21], builds upon their simple metabolic

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map and includes many other reaction steps and pathways. However, the basic predictions reached by the former are still shown to be valid in our model: (a) the model satisfies the calibration requirements; (b) normal photosynthetic mechanisms solely drive O2 production in the aerobic phase of sulfur deprivation and (c) the switch from O2 to H2 photoproduction does not require complete shut-off of O2 evolution. However, we have not tested Horner et al.’s. premise that H2 photoproduction is linear with irradiance nor we did not observe a negative effect of increasing the kinetic order of X28 (other ATP consumers, Eq. (14)) to values above 2 (see Section 3.3.3.2 above). Although the results presented here are to be understood only in a qualitative sense, due to unavoidable simplifications resultant from the lack of literature data, they constitute an initial attempt at trying to understand the complex factors involved in photohydrogen production. Within these limitations, we have been able to identify possible targets for protein engineering with the aim of increasing H2 production by sulfur-deprived algae. Among the most feasible to accomplish are: over-expression of the hydrogenase, increase in hydrogenase stability, up-regulation of hydrogenase gene transcription, increase in O2 consumption, and reduction in electron consumption from starch by fermentative pathways. We must point out, however, that there is evidence in the literature for excess hydrogenase activity in sulfur-deprived C. reinhardtii [16], which would seem to contradict the conclusions above. However, Kousorov et al. [16] measured hydrogenase activity using methyl viologen as the electron donor, not ferredoxin, its physiological electron donor. As reported by Winkler et al. [28], the specific activity of the algal hydrogenase in the presence of ferredoxin as the electron donor is about 40% of that measured with methyl viologen as the electron donor. It is clear that similar analyses could provide important information for other biological systems as well. Sensitivity analyses done through the S-systems formulation could provide much needed identification of the effect of metabolic engineering of pathways for generation of biofuels. Many research groups are working on re-routing reductants from competitive pathways (such as ethanol production) towards H2 production (e.g., [29]).

Acknowledgments The Research Support Foundation for the State of Bahia (FAPESB) (OJ and ME), the Research Support Foundation of Brazil (CNPq) (AK and ME) and the US DOE’s Hydrogen, Fuel Cell and Infrastructure Technologies Program (MG). We are thankful to Dr. Horner for his careful reading of the manuscript and for his many suggestions and comments. R E F E R E N C E S

[1] Esper B, Badura A, Rogner M. Photosynthesis as a power supply for (bio-) hydrogen production. Trends Plant Sci 2006;11:543–9.

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[2] Rupprecht J, Hankamer B, Mussgnug JH, Ananyev G, Dismukes C, Kruse O. Perspectives and advances of biological H2 production in microorganisms. Appl Microbiol Biotechnol 2006;72:442–9. [3] Prince RC, Kheshgi H. The photobiological production of hydrogen: potential efficiency and effectiveness as a renewable fuel. Crit Rev Microbiol 2005;31:19–31. [4] Ghirardi ML, Posewitz MC, Maness PC, Dubini A, Yu J, Seibert M. Hydrogenases and hydrogen photoproduction in oxygenic photosynthetic organisms. Annu Rev Plant Biol 2007;58:71–91. [5] Melis A, Zhang L, Forestier M, Ghirardi ML, Seibert M. Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green alga Chlamydomonas reinhardtii. Plant Physiol 2000;122:127–35. [6] Melis A, Happe T. Hydrogen production. Green algae as a source of energy. Plant Physiol 2001;127:740–8. [7] Kosourov S, Tsygankov A, Seibert M, Ghirardi ML. Sustained hydrogen photoproduction by Chlamydomonas reinhardtii: effects of culture parameters. Biotechnol Bioeng 2002;78:731–40. [8] Tsygankov A, Kosourov S, Seibert M, Ghirardi ML. Hydrogen photoproduction under continuous illumination by sulfurdeprived, synchronous Chlamydomonas reinhardtii cultures. Int J Hydrogen Energy 2002;27:1239–44. [9] Fouchard S, Hemschemeier A, Caruana A, Pruvost J, Legrand J, Happe T, et al. Autotrophic and mixotrophic hydrogen photoproduction in sulfur-deprived Chlamydomonas cells. Appl Environ Microbiol 2005;71:6199–205. [10] Kim JP, Kang CD, Sim SJ, Kim MS, Park TH, Lee D, et al. Cell age optimization for hydrogen production induced by sulfur deprivation using a green alga Chlamydomonas reinhardtii UTEX 90. J Microbiol Biotechnol 2005;15:131–5. [11] Kruse O, Rupprecht J, Bader KP, Thomas-Hall S, Schenk PM, Finazzi G, et al. Improved photobiological H2 production in engineered green algal cells. J Biol Chem 2005;280:34170–7. [12] Melis A. Green alga hydrogen production: progress, challenges and prospects. Int J Hydrogen Energy 2002;27:1217–28. [13] Ghirardi ML, Amos W. Hydrogen photoproduction by sulfurdeprived green algae—status of the research and potential of the system. Biocycle 2004;45:59. [14] Wykoff DD, Davies JP, Melis A, Grossman AR. The regulation of photosynthetic electron transport during nutrient deprivation in Chlamydomonas reinhardtii. Plant Physiol 1998;177:129–39. [15] Happe T, Hemschemeier A, Winkler M, Kaminski A. Hydrogenases in green algae: do they save the algae’s life and solve our energy problems? Trends Plant Sci 2002;7:246–50.

33 (2008) 2167 – 2177

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[16] Kousorov S, Seibert M, Ghirardi ML. Effect of extracellular pH on the metabolic pathway in su´lfur deprived, H2-producing Chlamydomonas reinhardtii cultures. Plant Cell Physiol 2003;44:146–55. [17] Florin L, Tsokoglou A, Happe T. A novel type of iron hydrogenase in the green alga Scenedesmus obliquus is linked to the photosynthetic electron transport chain. J Biol Chem 2001;276:6125–32. [18] Zhang L, Happe T, Melis A. Biochemical and morphological characterization of sulfur-deprived and H2-producing Chlamydomonas reinhardtii (green alga). Planta 2002;214: 552–61. [19] Savageau MA. Biochemical systems analysis: a study of function and design in molecular biology. Reading, MA: Addison-Wesley; 1976. [20] Voit E. Computational analysis of biochemical systems: a practical guide for biochemists and molecular biologists. Cambridge: Cambridge University Press; 2000. [21] Horner J, Wolinsky M. A power-law sensitivity analysis of the hydrogen-producing metabolic pathway in Chlamydomonas reinhardtii. Int J Hydrogen Energy 2002;27:1251–5. [22] Park W, Moon IL. A discrete multi state model for the biological production of hydrogen by phototrophic microalga. Biochem Eng J 2007;36:19–27. [23] Winkler M, Hemschemeier A, Gotor C, Melis A, Happe T. [Fe]hydrogenases in green algae: photo-fermentation and hydrogen evolution under sulfur deprivation. Int J Hydrogen Energy 2002;27:1431–9. [24] Ghirardi ML. Hydrogen production by photosynthetic green algae. Indian J Biochem Biophys 2006;43:201–10. [25] Savageau MA. Michaelis–Menten mechanism reconsidered: implications of fractal kinetics. J Theor Biol 1995;176:115–24. [26] Polle JEW, Kanakagiri S-D, Melis A. tla1, a DNA insertional transformant of the green alga Chlamydomonas reinhardtii with a truncated light-harvesting chlorophyll antenna size. Planta 2003;217:49–59. [27] Kosourov S, Makarova V, Fedorov A, Tsygankov A, Seibert M, Ghirardi M. The effect of sulfur re-addition on H2 photoproduction by sulfur-deprived green algae. Photosynth Res 2005;85:295–305. [28] Winkler M, Heil B, Heil B, Happe T. Isolation and molecular charcterization of the [Fe]-hydrogenase from the unicellular green alga Chlorella fusca. Biochim Biophys Acta 2002;1576:330–4. [29] Rachman MA, Furutani Y, Nakashimada Y, Kakizono T, Nishio N. Enhanced hydrogen production in altered mixed acid fermentation of glucose by Enterobacter aerogenes. J Ferment Bioeng 1997;83:358–63.