Available online at www.sciencedirect.com

ScienceDirect Mathematical modeling of unicellular microalgae and cyanobacteria metabolism for biofuel production Caroline Baroukh1,2, Rafael Mun˜oz-Tamayo2, Olivier Bernard2,3 and Jean-Philippe Steyer1 The conversion of microalgae lipids and cyanobacteria carbohydrates into biofuels appears to be a promising source of renewable energy. This requires a thorough understanding of their carbon metabolism, supported by mathematical models, in order to optimize biofuel production. However, unlike heterotrophic microorganisms that utilize the same substrate as sources of energy and carbon, photoautotrophic microorganisms require light for energy and CO2 as carbon source. Furthermore, they are submitted to permanent fluctuating light environments due to outdoor cultivation or mixing inducing a flashing effect. Although, modeling these nonstandard organisms is a major challenge for which classical tools are often inadequate, this step remains a prerequisite towards efficient optimization of outdoor biofuel production at an industrial scale. Addresses 1 INRA UR0050, Laboratoire de Biotechnologie de l’Environnement, avenue des e´tangs, 11100 Narbonne, France 2 INRIA, BIOCORE, 2004 route des lucioles, 06902 Sophia-Antipolis, France 3 LOV UPMC CNRS, UMR 7093, Station Zoologique, B.P. 28, 06234 Villefranche-sur-mer, France Corresponding author: Baroukh, Caroline ([email protected])

Current Opinion in Biotechnology 2015, 33:198–205 This review comes from a themed issue on Environmental biotechnology Edited by Spiros N Agathos and Nico Boon

http://dx.doi.org/10.1016/j.copbio.2015.03.002 0958-1669/# 2015 Elsevier Ltd. All rights reserved.

Introduction Certain species of microalgae or cyanobacteria can accumulate high amounts of carbon, in the form of lipids or carbohydrates. Because of their fast growth rate, they are a new and promising source of renewable biodiesel or bioethanol with production yields of an order of magnitude higher than terrestrial plants [1]. There are still several challenges for achieving a profit earning and ecofriendly production (strain selection and improvement, culturing process, harvesting, downstream processing, Current Opinion in Biotechnology 2015, 33:198–205

among others). One of the key aspects consists in optimizing the production of reserve carbon through a qualitative and quantitative understanding of their carbon metabolism [2,3]. Mathematical modeling of the metabolism has already proven to be a very efficient tool for other microorganisms for which in silico study has helped to quantify the intracellular mechanisms and has paved the way for optimizing the production of molecules of interest [4]. To date, the metabolic networks of eight microalgae and cyanobacteria species have been reconstructed (Table 1). More are expected soon since potential biofuel species such as Chlorella vulgaris or Botryoccoccus braunii have recently been sequenced [5,6]. Although they were not set up for the same species, these networks exhibit the same core network (Calvin cycle, Pentose Phosphate Pathway (PPP), TCA cycle, glycolysis, synthesis of nucleic acids and amino acids), but with different levels of detail (Table 1). In this work, we review 23 simulation studies supported by these various networks and we discuss the predicted metabolic fluxes under different light intensities. Firstly, the general behavior of photoautotrophic microorganisms submitted to different metabolic states is assessed with respect to light and organic carbon. Secondly, perspectives for dynamic simulations under permanent light variations are proposed.

Lessons from the static regime Most of the studies have focused on the quasi-steady state (QSS) under constant light regimes, using the full spectrum of metabolic analysis tools (Table 1). Flux Balance Analysis (FBA) [7], a modeling framework which predicts metabolic distribution of fluxes under constant environmental conditions (Box 1) is, however, the most widely used. It is usually performed by imposing the energy or carbon input. Fluxes are either determined experimentally or set at several values to study their influence on the metabolism. In the FBA approach, the objective function to be maximized is generally the biomass growth, even though a two-step optimization can sometimes be carried out (biomass growth and then light utilization) [8–10]. In the following, the fluxes derived under static conditions are discussed for each trophic regime.

Autotrophy Autotrophy is characterized by high fluxes in the photosynthetic pathways (Figures 1a and S1). Beyond these pathways, fluxes drop considerably in terms of absolute www.sciencedirect.com

Modeling of photoautotrophic metabolism for biofuels Baroukh et al. 199

Table 1 Metabolic modeling frameworks applied to microalgae and cyanobacteria Specie Procaryotes Arthrospira platensis Synechocystis sp. PCC 6803

Cyanothece sp. ATCC 51142 Eucaryotes Chlorella pyrenoidosa Chlamydomonas reinhardtii

Ostreococcus tauri Ostreococcus lucimarinus Tisochrysis lutea

GDS

6¼ Ia,

–

–

–

–

– – H H – H H H H H

– – – – – – – – – –

Ha,lh,hy

H

61

Ha,m,hg

484

458

[31] [13] [29] [16] [42] [43]

160 280 280 2190 1725 871

[43] [21]

Ref

#Rea

#Met

[12]

121

134

[8]

70

46

[38] [39] [10] [20] [19] [40] [15] [41] [11] [41]

56 831 882 380 956 493 863 1156 759 946

[17]

FBA

FVA

EFM

Ha

–

–

Ha,m,hg

–

48 704 790 291 911 465 795 996 601 811

Ha,m,hg Ha,m,hg Ha,m,lh,hg Ha,m,hy – Ha,m,hg Ha,m,lh,hg Ha,hy Ha,m,hy Ha,hy

719

587

[14]

67

[9]

FCA

m

D/N cyc

Simu

#Param

Comp q data

H

–

S

1

H

8

8

–

H

–

S

1

–

–

–

– – – – Ha,m,hg – – – – –

H – H H – – H H H –

– H – H – H H – H –

– – – P – – – – H –

S S S S S S S S S&D S

1 1 1 1 1 1 1 1 45 1

– H – – – H – H – –

– 5 – – – 20 – 31 – –

– 102 – – – 36 – 31 – –

–

–

–

H

–

S

1

H

1

20

–

–

–

–

–

–

S

1

–

–

–

Ha,m,ha

–

–

–

–

H

–

S

2

–

–

–

164 278 278 1068 1862 1014

Ha Ha Ha Ha,m,ha,hs Hm,ha H

– H – H – –

– – H – – –

– – – – – –

– – – H – –

H H H – – –

– – – – – –

S S S S S S

3 22 22 3 1 0

– H – H – –

– 10 – 6 – –

– 75 – 7 – –

964

1100

H

–

–

–

–

–

–

S

0

–

–

–

132

157

–

–

–

–

–

H

H

D

10

H

7

50

#variables

#data points

Ref: reference, #Rea: number of reactions, #Met: number of metabolites, FBA: Flux Balance Analysis, EFM: Elementary Flux Mode analysis, FCA: Flux Coupling Analysis, GDS: Gene Deletion Studies, 6¼Ia,m: different light intensities studied in the autotrophic and mixotrophic states, D/N cyc: day/ night cycle simulation, P: partial day/night cycle simulated, Simu: mode of simulation (S: static, D: dynamic), #Param: number of parameters to estimate, Comp q data: comparison with quantitative experimental data, #variables: number of model’s variables compared to experimental data, #data points: total number of experimental data points used for comparison with model’s simulation results. FBA and FCA simulations were performed in aautrotrophy, mmixotrophy, lhlight heterotrophy, hgglucose hetetrotrophy, hyglycogen heterotrophy, ha acetate heterotrophy, hsstarch heterotrophy. To compare the models, our definition of ‘number of parameters to estimate’ stands for the number of information needed to simulate the FBA or DFBA models. Light, CO2 or organic carbon fluxes were not counted as parameters, nor was biomass composition. Maintenance terms were counted as parameters to estimate, as they are usually determined so that biomass growth predictions match experimentally measured biomass growth. However, it was not counted as experimental data validation. When several metabolic states were simulated, the parameters were counted for only one state since the same parameter was estimated several times. For [38–40], the parameters to estimate were inherited by the use of Shastri et al. [8] biomass equation, which includes a maintenance term. For [29], the parameters to estimate were inherited by the use of the model of Cogne et al. [13]. For [11], seven biomass compositions were necessary to perform DFBA. We counted six of them as degrees of freedom.

magnitude [11]. Upper glycolysis is in the glyconeogenic direction to produce carbohydrates and sugar precursor metabolites (PEP, G6P, R5P) necessary for growth (Figures 1a and S1). For cyanobacteria, since Calvin cycle and PPP are merged, autotrophy can be characterized by a PPP in the reductive mode [8]. The TCA cycle is non-cyclic and acts as a hinge to produce www.sciencedirect.com

metabolite precursors for biomass growth [11,12,13] (Figure 1a). This is not as obvious for microalgae, for which lower glycolysis, TCA cycle and PPP coupled to oxidative phosphorylation can be used to meet energy demands in compartments of the cell other than the chloroplast (Figure S1). Hence TCA can be cyclic and respiration can have a non-negligible flux [14] compared Current Opinion in Biotechnology 2015, 33:198–205

200 Environmental biotechnology

Box 1 Metabolic modeling tools Static modeling tools A metabolic network can be mathematically represented by its stoichiometric matrix (K) of size m  r. Each row of this matrix corresponds to a metabolite, each column to a reaction and the entries are the stoichiometric coefficients. A mass-balance on the metabolism implies that:

1 S BC C C dB @ P A 0 KS 1 B KC C B dM C ¼B ¼ @ K P A:v:B dt dt KB 0

(1)

where M is the metabolite concentration vector composed of substrate S, intracellular metabolites C, excreted products P and biomass B, and v is the vector of the kinetic rates of reactions. Because of a lack of experimental data, v is difficult to estimate [32]. To overcome this issue, a common hypothesis, called the balanced-growth hypothesis or the quasi-steady state assumption (QSSA), assumes that the system is in a steady-state, that is there is no accumulation of internal metabolites:

K C  v ¼ 0; and v i  0

if v i is irreversible;

i 2 f1; . . . ; rg

(2)

In any realistic large-scale metabolic model, there are more reactions than there are compounds (r > m). In other words, there are more unknown variables than equations, so there is no unique solution to (2). Nevertheless, the set of solution is a cone, which can be described by a set of generating vectors called Elementary Flux Modes (EFMs) [33]. Any solution of (2) is a positive linear combination of the EFMs:

K C :v ¼ 0 , v ¼ E:a;

a0

(3)

with E the matrix of the EFMs and a a vector of positive coefficients. One analysis tool is thus to study the matrix E. Indeed, EFMs correspond to the minimal building blocks of the metabolic network [34]. Another analysis tool is to study the coupled reactions in the set of solutions of (2). For example, coupling reactions to the reaction R are null when R is null. This is Flux Coupling Analysis (FCA) [35]. Although there are several solutions of (2), it is possible to reduce the set of solutions using optimization. For example, it can be assumed that the microorganisms optimize their biomass growth. This approach is called Flux Balance Analysis (FBA) [7]. Sometimes several solutions still exist after performing FBA. Flux Variability Analysis (FVA) allows to find the minimal and maximal flux that can carry each reaction while satisfying the optimal objective value found in FBA [21]. Finally, Gene Deletion Studies (GDS) examine the effect of a reaction deletion on the results obtained with any of the previous tools (mostly FBA) so as to find ideal metabolic engineering targets [36]. Dynamic modeling tools a

Thanks to EFM analysis ðv ¼ E:aÞ; the biological system can be viewed as a set of macroscopic reactions [37]: ðK S :EÞ:S!ðK P :EÞ:P þ ðK B :EÞ:B, with 0 1 K S :E a the kinetic rates of the macroscopic reactions described by the stoichiometric matrix K 0 ¼ @ K P :E A. System (1) can thus be transformed into: K B :E

0

1 S d@ P A B ¼ K 0 :a:B; dt

a0

(4)

Only kinetic rates a need to be postulated. However, in any realistic large-scale metabolic model, the number of EFMs is very large, which results in a high number of kinetic laws a to postulate. Each dynamic metabolic modeling framework brings a different solution to this problem:  Dynamic Flux Balance Analysis (DFBA) reduces the number of EFMs using optimization [23].  Macroscopic Bioreaction Models (MBM) reduces the number of EFMs using experimental data [24].  Hybrid Cybernetic Modeling (HCM) reduces the number of EFMs by projecting the solution space into the yield space of much lower dimension [25].  Lumped Hybrid Cybernetic Modeling (LHCM) reduces the number of EFMs by clustering them into families and representing each cluster with an average EFM [26].

to photophosphorylation (Figure S1), while this is not the case for cyanobacteria [12]. Light influence has a low impact on qualitative flux distribution as long as light remains the limiting factor Current Opinion in Biotechnology 2015, 33:198–205

[11]. However, in the case of excessive light and limiting carbon, photophosphorylation pathways have a totally different behavior [15]. To meet energy and carbon demands of the rest of the metabolism and provide a constant ATP/NADPH ratio of 1.5 necessary for www.sciencedirect.com

Modeling of photoautotrophic metabolism for biofuels Baroukh et al. 201

Figure 1

(a) G6P

Ru5P

S7P

R5P

F6P GAP

GAP X5P

CO2 RuBP

3PG PEP PYR

F6P

E4P

GAP

ICIT AcCoA

OA

AKG

MAL

SUC FUM

(b)

GLU G6P

6PG

Ru5P

R5P

S7P

F6P

F6P

GAP

E4P

X5P GAP 3PG

F6P

PYR

GAP

ICIT

PEP AcCoA

OA

AKG

MAL

SUC

(c) GLU Ru5P

S7P

R5P

F6P

GAP X5P

E4P

GAP RuBP

3PG PEP PYR

CO2 AcCoA

OA

F6P

GAP

ICIT AKG Current Opinion in Biotechnology

Autotrophic, heterotrophic and mixotrophic central metabolism flux map of a cyanobacterium. Flux maps were obtained using a modified model of Synechocystis sp. PCC 6803 developed by Shastri and Morgan [8], where the glyoxylate shunt was replaced by a bypass through succinate semialdehyde in accordance with the recent result of Knoop et al. [11]. Details about how the results are obtained are described in File S1. The dashed arrows indicate the flux related to biomass formation. (a) Autrophy flux map. Net assimilation of 100 mol of CO2. (b) Heterotrophy flux map. Net assimilation of 100 mol of glucose. (c) Mixotrophy flux map. Net assimilation of 100 mol of glucose and 44 mol of CO2.

photosynthesis [15], alternative electron flows (AEF) and photorespiration play a major role in dissipating the excessive energy entering the metabolism [15]. Excessive light energy is thus dissipated at the level of www.sciencedirect.com

Another interesting question is the influence of the quality of light on photoautotrophic metabolism. Indeed, the absorption of a photon depends on its wavelength. This influences energy availability and impacts growth. Chang et al. [16] studied the influence of eleven light sources on the metabolism and showed that the 674 nm red LED with a minimum incident photon flux of 360 mE m2 s1 was the optimal light source for growth; this has been confirmed experimentally. Vu et al. [17] studied the effect of the light source in a more fundamental way, by simulating the effect of a photon imbalance between photosystem I and photosystem II. They quantified the importance of the presence of the AEF to rebalance the energy imbalance created (excess of ATP or excess of NADPH), in accordance with the results of Nogales et al. [15].

Heterotrophy

FUM G6P

photophosphorylation and the rest of the metabolism stays fairly unchanged in terms of relative fluxes. The presence of AEF and photorespiration thus confers a great robustness of the photosynthesis pathways to light changes, bringing a homeostatic incoming energy to the metabolism.

Several organic carbon sources such as glucose or acetate have been represented in models. If glycogen or glucose is used, upper glycolysis is in the downward direction (Figure 1b). However if the carbon source used should be acetate, the glycolysis reactions would go forward, leading to synthesis of carbohydrates and sugar precursor metabolites (PEP, G6P, and R5P). The glyoxylate shunt is, in this case, mandatory for growth [18]. However, the presence of the glyoxylate shunt is currently under debate for certain cyanobacteria species, as for example, Synechocystis PCC 6803 [11], since the corresponding genes are not annotated within the genome. Metabolic flux predictions under heterotrophy differ greatly from the ones obtained for photoautotrophy (Figure 1a and b). The main carbon flux is the TCA cycle which produces precursor metabolites for growth and energy thanks to oxidative phosphorylation (Figure 1b). Energy demands are also met thanks to glycolysis if in a downward direction (Figure 1b). Around 40% of the carbon is lost through respiration [8,10]. Heterotrophy is characterized by an oxidative PPP to meet demands in NADPH for synthesis of macromolecules (lipids, amino acids, and nucleotides) (Figure 1b). However, the presence of NADPH dehydrogenase complex converting NADH to NADPH is usually preferred as source of NADPH implying a nearly null flux into the PPP [8,11]. Experiments tend to show that NADPH dehydrogenase complex has negligible activity and that NADPH synthesis is mainly performed through the PPP. Current Opinion in Biotechnology 2015, 33:198–205

202 Environmental biotechnology

This in silico artefact can be corrected by limiting the flux in the NADPH dehydrogenase complex [11]. Autotrophy and heterotrophy fluxes differ only by the layout of the core carbon network (Calvin cycle, glycolysis, TCA cycle, and PPP). However, the rest of the metabolic network (synthesis of amino acids, DNA, RNA and proteins) does not vary significantly in terms of relative fluxes. This suggests that the anabolic part of the metabolism is independent of growth conditions. It has been illustrated by comparing Flux Coupling Analysis results of the autotrophic and the heterotrophic states of cyanobacteria metabolism [19]. Even though there were quantitative differences between the two states, the coupling of the anabolic part of the metabolism was independent of the growth conditions. This can be explained by the classical bow tie structure of microorganisms: there is a great diversity of inputs (photosynthesis or glycolysis), while the diversity in the way the inputs are transformed to outputs remains much smaller.

Mixotrophy The distribution of fluxes in mixotrophic conditions is a weighted mix between autotrophy and heterotrophy, depending on the light/organic compound ratio used for the simulation. The available light (or CO2 in case of limiting CO2) compared to organic carbon thus defines whether glycolysis is in the gluconeogenic direction, the TCA cycle is not acting as a cycle or the PPP is in the reductive mode for cyanobacteria (Figure 1c). Whatever the case, oxidative phosphorylation is less used because energy can be generated from photophosphorylation (Figure 1c). Shastry and Morgan [8] and Boyle and Morgan [9] showed the existence of a threshold in light intensity (at constant organic carbon input and unlimited CO2). Light intensities below this threshold induce a heterotrophy-like metabolism while light intensities above this threshold induce autotrophy-like metabolism. Knoop et al. [20] studied the influence of an increase in organic carbon source and at the same time a decrease in light intensity to partially simulate a day–night cycle. They showed that a shift between a heterotrophy-like state to an autotrophylike state still occurred.

Towards a dynamic regime With the exception of the work of Knoop et al. [11] and Baroukh et al. [21], all the considered studies have been performed under constant environmental conditions (including light) (Table 1). However, for largescale cultivation, microalgae and cyanobacteria are submitted to the permanent fluctuating light combined with the flashing effect due to mixing [22]. The metabolism adaptation under these dynamic conditions is poorly known. Current Opinion in Biotechnology 2015, 33:198–205

Even if they are static, these studies provide first insights of photoautotrophic metabolism submitted to day–night cycles. Indeed, heterotrophy can be visualized as nighttime, where metabolism breaks down carbon storage molecules (carbohydrates, lipids) into precursor metabolites and energy to continue growth and maintenance [11,20]. Similarly, mixotrophy appears in early morning or late afternoon, when light is not intense enough to meet the carbon and energy growth demands which are palliated by consumption of carbon storage molecules. The rest of the day is mainly characterized by an autotrophic regime. Hence a full 24 hour day–night cycle can be viewed as a succession of these states (Figure S1) [11,20]. A dynamic framework is however necessary to represent a complete day–night cycle as well as the consequent accumulation of storage molecules during the day and their consumption at night. Dynamic metabolic frameworks exist, such as the Dynamic Flux Balance Analysis (DFBA) [23], Macroscopic Bioreaction Models (MBM) [24], Hybrid Cybernetic Models (HCM) [25] and Lumped Hybrid Cybernetic Models (L-HCM) [26] (Box 1). These approaches rely on the balanced-growth hypothesis, which assumes there is no intracellular accumulation of metabolites (Box 1), but contradicts the experimental observation of large accumulation of lipids and carbohydrates during the day and their consumption during the night [27,28]. A manner to circumvent this issue is to represent these metabolites as products of the cell during the day and substrates during the night. Knoop et al. [11], using DFBA, computed dynamic metabolic fluxes for a full day–night cycle. They observed a complex transition in the metabolic fluxes over a 24hour period, during which the metabolism shifted from a night-time heterotrophy-like metabolism, dominated by respiration, to a day-time autotrophic metabolism with inorganic carbon fixation. Yet, in their work, Knoop et al. indirectly set fluxes to carbon storage by imposing a different biomass composition at each time-shift. The result is an artificial increase of glycogen biomass quota during the day and its decrease during the night. Their method indeed predicted all metabolic fluxes dynamically but did not predict the fluxes towards carbon storage. DFBA relies on instant optimization of biomass growth. However, this classical optimization target is not adapted to microalgae or cyanobacteria in day–night cycles as it constrains all the incoming carbon to feed biomass synthesis, and none for carbon storage. Finding an objective function in order to represent both biomass growth and accumulation of carbon storage molecules is not trivial. To circumvent this issue, the solution consists in setting either the fluxes of carbon storage or the fluxes of biomass synthesis, maintenance (ATP ! ADP + Pi) and all other futile cycles (including AEF and photorespiration). Another solution could be an optimization on 24 hour, with www.sciencedirect.com

Modeling of photoautotrophic metabolism for biofuels Baroukh et al. 203

the presence of a maintenance term or minimal growth term during the night, which would require a carbon source. This approach should lead to solutions for which there is carbon storage during the day. However, if more than one type of carbon storage molecules is present (e.g., lipids and starch), one of these molecules could be favored without biological justification. The other dynamic metabolic modeling frameworks have not yet been used for day–night cycles. However given the high number of Elementary Flux Modes (EFMs) obtained from their metabolic network (around 30,000) [29], a reduction using experimental data may not be sufficient to use MBM [24]. HCM or LHCM also seems to present difficulties in obtaining a simple model with identifiable parameters. Indeed, these methods rely on families of EFMs determined from the consumed substrates. Here, with light, CO2 and carbon storage molecules as substrates, at least three different families are necessary: one for autotrophy, one for mixotrophy and one for heterotrophy. For HCM, each family will lead to at

Figure 2

(i)

(ii)

(iii) + (iv) α2

SN2

S2 → P2

α1

S1 → P1

SN1

α3

SN3

S3 → P3 α4

S4 → P4

SN4 dM dt

K = (SN1 ...SSN )

= KvB

dM ′ dt

= K ′ αB

Current Opinion in Biotechnology

Modeling approach of DRUM decomposed into four steps. (i) Find in the literature or build the metabolic network of the microorganism under study. (ii) Group metabolic reactions into sub-networks assumed to follow the QSSA. (iii) Reduce each sub-network to a set of macroscopic reactions using elementary mode analysis. (iv) Define kinetic laws for macroscopic reactions obtained and deduce an ODE system. The figure was taken from Ref. [21].

Box 2 Modeling framework for handling unbalanced metabolism Traditional metabolic models are based on the balanced growth hypothesis. However, balanced growth is inadequate to describe photoautotrophic metabolism under diurnal cycles. A novel modeling framework, named DRUM (Dynamic Reduction of Unbalanced Metabolism), has been proposed to handle unbalanced metabolism [21]. In the DRUM approach, the full metabolic network is split into sub-networks (SNs). Each SN is assumed to hold the quasi steady state assumption (QSSA). The metabolites interconnecting the subnetworks, which are named A, are allowed to accumulate and thus can behave dynamically. The QSSA for sub-networks relies on the presence of: firstly, metabolic pathways corresponding to metabolic functions, secondly, group of reactions regulated together, and thirdly, different compartments in a cell (e.g., mitochondria). The metabolites (A) interconnecting the sub-networks are either situated at a branching point between several pathways or are end-products of metabolic pathways (e.g., macromolecules). DRUM is briefly described in Figure 2. For a batch operation, DRUM translates mathematically into:

0

1 S BP C C dB @ A A 0 K0 1 S B K0 C B dM 0 0 AC ¼ ¼B @ K 0 A:a:B ¼ K :a:B dt dt P K 0B where M0 2 Rnm0 is the reduced vector of compounds, consisting of substrates (S), products (P), accumulating metabolites (A) and functional biomass (B). K 0 2 Rnm0 nE is the stoichiometric matrix of the macroscopic reactions and a 2 R nE its associated rates. Note that in the full model described in step i. K 2 R nmnr, v 2 Rnr , while for the 0 resulting model provided by DRUM K 2 Rnm0 nE and a 2 R nE, such that nm0  nm and nE  nr. DRUM provides a parsimonious structure model that allows to represent the evolution of the macroscopic scale of the bioprocess as well as intracellular processes and accumulation of metabolites.

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least three EFMs. This implies a high number of kinetic rates and hence a challengingly high number of parameters to be estimated (at least 50). For LHCM, computation of the average EFM representing each family is hindered by the computation of the weights, which would need adaptation to take into account the presence of carbon storage molecules. Another solution is to moderately relax the balancedgrowth hypothesis. Accumulation of some intracellular metabolites becomes possible while the model remains simple enough for parameter identification based on experimental data. This was performed by Baroukh et al. [21], who proposed to split the full network into sub-networks and to assume each sub-network at balanced-growth. In this way, the metabolites linking the sub-networks can accumulate and generate the dynamics of the whole network. This idea relies on the notion of cell functions, often associated to co-regulation. It supports a new modeling framework named DRUM and accounting for the non-balanced growth hypothesis [21]. The principles of the approach are briefly described in Box 2. The framework has been successfully implemented to represent the dynamic metabolism of a microalgal species during a 24 hour day–night cycle. It accurately predicted the experimental measurements at an intracellular scale (accumulation of lipids and carbohydrates, chlorophyll and functional biomass) and at a macroscopic scale (biomass growth, consumption of substrates).

Conclusions Static metabolic studies have given first insights into metabolic fluxes submitted to dynamic light changes. Current Opinion in Biotechnology 2015, 33:198–205

204 Environmental biotechnology

However, tailored modeling approaches need to be set up, relaxing some classical hypotheses, to represent a full day–night cycle. This is of crucial importance for predicting outdoor dynamics of lipids and carbohydrates. More comparison with experimental measurement is presently required to consolidate the predictive potential of metabolic modeling. Other highly dynamic environmental factors may affect the metabolism under outdoor industrial conditions. Among these factors, temperature has a strong influence on the cell enzymatic processes [30] and its effect on the metabolism should be further investigated.

Conflict of interest The authors declare no conflict of interest.

Acknowledgements C. Baroukh was supported by a Contrat Jeune Scientifique (CJS) INRAINRIA fellowship. R. Mun˜oz-Tamayo benefited from the support of the ANR-12-BIME-004 Facteur 4 project. This work also benefited from the support of the ANR-13-BIME-004 Purple Sun project.

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. copbio.2015.03.002.

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