# Calibration of a productivity model for the microalgae Dunaliella salina accounting for light and temperature

Quentin Béchet, Philippe Moussion, Olivier A. Bernard

► To cite this version:

Quentin Béchet, Philippe Moussion, Olivier A. Bernard. Calibration of a productivity model for the microalgae Dunaliella salina accounting for light and temperature. Algal Research - Biomass, Biofuels and Bioproducts, 2017, 21, pp.156 - 160. 10.1016/j.algal.2016.11.001. hal-01410980

HAL Id: hal-01410980

https://inria.hal.science/hal-01410980

Submitted on 27 Jan 2017

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
1 Calibration of a productivity model for the microalgae

2 Dunaliella salina accounting for light and temperature

3

4 Quentin Béchet<sup>a,b*</sup>, Philippe Moussion<sup>a,b</sup>, Olivier Bernard<sup>a,b</sup>

5

6 <sup>a</sup> Université Côte d'Azur, Inria, BIOCORE, BP 93 06902 Sophia Antipolis Cedex, France

7 <sup>b</sup> Sorbonne Universités, UPMC Université Paris 06, CNRS, UMR 7093, LOV, Observatoire

8 océanologique, F-06230, Villefranche/mer, France

9

10 * Corresponding author

11 Telephone: +33 4 92 38 71 74

12 Fax: + 33 4 92 38 78 58

13 Email: quentin.bechet@inria.fr
15

16 This study aimed to calibrate a productivity model for the algal species *Dunaliella salina*

17 accounting for the impacts of light intensity and temperature. The calibration was performed

18 by using a dedicated experimental set-up measuring short-term oxygen production rates at

19 different light intensities. The rate of photosynthesis was shown to follow a typical Monod

20 function of light intensity. The slope of Photosynthesis-light curves at low light intensity was

21 also shown to be independent on temperature and the evolution of model parameters with

22 temperature obeyed relationships consistent with previous observations in the literature.

23 Finally, the rate of respiration was shown to follow an Arrhenius function of temperature.

24 This good level of agreement with prior observations in the literature indirectly validates the

25 experimental technique used for model calibration. The resulting model should therefore yield

26 accurate productivity predictions in outdoor cultivation systems.

27

28 Keywords: Algae; *D. salina*; growth kinetics; productivity model; photosynthesis; respiration
29

1. Introduction

30

With the objective to accurately assess the economical and environmental feasibility of full-scale algal cultivation for biofuel production, a large number of studies developed mathematical models predicting algal productivity in outdoor cultivation systems [1–3].

31

32

33

These models can be used to improve process design or develop optimization strategies maximizing algal productivity. For instance, Slegers et al. [4] used a mathematical model predicting growth rates of *Phaeodactylum tricornutum* and *Thalassiosira pseudonana* to optimize the design of closed photobioreactors. Similarly, Béchet et al.[5] proposed an optimization strategy based on the dynamic control of pond depth and hydraulic retention time to increase productivity while reducing water demand, using a productivity model for *Chlorella vulgaris*. Alternatively, adapting the algal species to climatic conditions could

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

potentially boost yearly algal productivity, similarly to crop rotation used in traditional agriculture. For example, algal species having low optimal temperatures could be cultivated in colder climates or simply during winter while heat-resistant algal species could be grown in summer when pond temperature reaches higher levels. With the objective to assess the benefits of these 'algal culture rotation' strategies, it is necessary to calibrate algal productivity models for a large number of species. However, while many studies in the literature developed productivity models, these models have been calibrated on a limited number of algal species. In particular, the impact of temperature was often neglected in past studies, which limits models application to outdoor systems where temperature significantly varies [1].

50

51

Within this context, our research group has been developing mathematical models to predict algal productivity in various outdoor cultivation systems from meteorological hourly data, system design and operation. This modeling framework combined models predicting system

52

53
temperature with a biological model predicting algal productivity as a function of light and temperature. So far, the biological model has only been calibrated for a single algal species, *Chlorella vulgaris* (see Béchet et al. [6]). The objective of this study was therefore to calibrate a productivity model for another algal species, *Dunaliella salina*, this species being the third most cultivated microalgae [7]. *Chlorella vulgaris* and *Dunaliella salina* are both Chlorophyceae and share the same tolerance to high temperatures. The methodology followed in this study was therefore similar to the calibration technique followed by Béchet et al. [6], and also because the model for *C. vulgaris* accurately predicted productivities in indoor (accuracy of +/- 15% over 163 days; Béchet et al. [6]) and outdoor (accuracy of +/- 8.4% over 148 days, Béchet et al. [8]) reactors.

## 2. Materials and methods

### 2.1. Algae cultivation conditions and biomass characterization

The Chlorophyceae *Dunaliella salina* (CCAP 19/18) was cultivated in a cylindrical photobioreactor (diameter: 0.19 m; height: 0.41 m; culture volume: 10 L; gas phase volume: 1.6 L). The reactor was illuminated by two metal halide lamps (Osram Powerstar HQI-TS, 150W NDL, Neutralweiss de Luxe) providing a light intensity of 1440 µmol/m²-s (measured when the reactor was filled with water with a QSL-2100 PAR scalar irradiance sensor, Biospherical Instruments). Temperature was maintained at 30°C by re-circulating temperature-controlled water in a jacket around the reactor. The reactor was inoculated with a culture of *D. salina* (inoculum volume of approximately 500 mL) grown in axenic conditions (light intensity: 300 µmol/m²-s, light-dark cycle: 12:12, temperature: 27°C) and was then operated as a fed-batch system: 9L of solution was replaced every week with fresh f/2 medium [9] enriched in phosphorus and nitrogen to ensure that algal growth was not limited by nutrients (Total N and P concentrations in enriched medium: 0.22 g N-NO₃⁻/L; 0.020 g P⁻).
78 PO₃/L). Air enriched in CO₂ (2% CO₂) was continuously bubbled in the photobioreactor to ensure that CO₂ supply did not limit algal growth and also to control pH between 7 and 7.5.
79
80 Algae used for model calibration were extracted from the photobioreactor 2-3 days after medium change during the light-limited growth phase. The biomass concentration in the solution used during model calibration was measured by dry weight [10]. Glass-fiber filters (GF/C, Whatman, diameter: 25mm, No 1822-025) were first dried for several days at 60°C before being weighed. A known volume of the algal solution was then filtered; filters were then rinsed with Ammonium formate (30 g/L) to remove salt. Filters were then dried for 24 hours at 60°C before being weighed again. Dry weight concentration was measured in duplicates.
81
82
83
84
85
86
87
88

## 2.2. Productivity model description

90 Algal productivity (Pₙet, in kg O₂/s) was expressed as the difference between the gross rate of photosynthesis (P, in kg O₂/s) and the rate of endogenous respiration (ER, in kg O₂/s) [6]:

$$P_{net} = P - ER \quad (1)$$

92
93
94
95
96
97
98
99
100
101 The gross rate of photosynthesis was expressed as a function of light intensity and temperature by using a 'type-II model' as recommended by Béchet et al. [1]. This type of models is based on the assumption that the local rate of photosynthesis of single algal cells can be expressed as a direct function of the local light intensity cells are exposed to. Béchet et al. [6] used different formulas to express local rates of photosynthesis as a function of local light intensity and showed that the three formulas most commonly used in the literature all satisfyingly fit experimental data. The authors finally selected the Monod formula, as this expression was the most commonly found in literature. The gross rate of photosynthesis was therefore expressed as [6]:
102 $$P_{net} = \int_{V} P_{m}(T) \frac{\sigma_{X} I_{loc}}{K(T) + \sigma_{X} I_{loc}} X \cdot dV \quad (2)$$

where $P_m$ is the maximum specific rate of photosynthesis (kg O₂/kg-s), $T$ is the culture temperature (°C), $K$ is the half-saturation constant (W/kg), $\sigma_X$ is the extinction coefficient (m²/kg), $I_{loc}$ is the local light intensity (W/m², as photosynthetically active radiation or PAR), $X$ is the algal concentration (kg/m³) and $V$ is the culture volume (m³). The local light intensity $I_{loc}$ was expressed by using a Beer-Lambert law:

108 $$I_{loc}(l) = I_0 \exp(-\sigma_X X l) \quad (3)$$

where $l$ is the light path between the considered location and the reactor external surface (m) and $I_0$ is the incident light intensity (W/m²). The evolution of $P_m$ and $K$ with temperature was fitted to the theoretical model of Bernard and Rémond [11] as this model was shown to satisfyly fit the evolution of the specific growth rate of 15 algal species. $P_m$ and $K$ were therefore expressed as follows:

114 $$p = \begin{cases} \frac{(T-T_{max})(T-T_{min})^2}{(T_{opt}-T_{min})((T_{opt}-T_{min})(T-T_{opt})-(T_{opt}-T_{max})(T_{opt}+T_{min}-2T))} & \text{if } T_{min} \le T \le T_{max} \\ 0 & \text{otherwise} \end{cases} \quad (4)$$

where $p$ represents either $P_m$ or $K$, $\alpha$ is the maximum value of $P_m$ or $K$, and $T_{min}$, $T_{max}$ and $T_{opt}$ are the minimum, maximum, and optimum temperatures for photosynthesis (°C), respectively.

117 The rate of endogenous respiration was expressed using a first-order law:

118 $$ER = \lambda(T) XV \quad (5)$$

where $\lambda$ is the specific respiration rate (kg O₂/kg-s). Several studies showed that the rate of respiration was an exponential function of temperature [12–14]. The parameter $\lambda$ was therefore expressed as follows:

122 $$\lambda(T) = \lambda_0 \exp(\beta T) \quad (6)$$

where $\lambda_0$ (kg O₂/kg-s⁻¹) and $\beta$ (°C⁻¹) are determined experimentally.

124
125

## 2.3. Device used for model calibration

126

The device used for calibration was composed of six cylindrical glass reactors (diameter: 3.48 cm; height: 5.82 cm; volume: 55.2 mL) all equipped with an oxygen electrode (Model DO50-GS, Hach) measuring both dissolved oxygen and medium temperature. Each reactor was positioned over a LED lamp (12V PHILIPS EnduraLED 10W MR16 Dimmable 4000 K)

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

which light intensity was independently controlled. A typical experiment consisted on measuring first oxygen production rates when algae were exposed to light (light-phase) and then respiration rates when algae were in the dark (dark phase). These measurements were performed for six different light intensities (range: 0-460 W/m², as PAR) and under constant temperature (see [6] for a complete description of the oxygen measurements). These experiments were then repeated for 6 different temperatures (3.73°C; 10.2°C; 19.7°C, 27.7°C, 34.7°C; 40.9°C). Temperature was maintained constant (within approximately +/- 1°C) during the entire duration of the experiment by circulating temperature-controlled air around the reactors. The light intensity reaching the external surface of each reactor was measured by actinometry (see S1 for details). The parameters $P_m$ and $K$ for each temperature were determined by least-square fitting using the `lsqcurvefit` Matlab function. Respiration rates during the dark periods were found to be independent on the light intensity cells where exposed to during the light phase and the parameter $\lambda$ was determined from the average respiration rate in the six reactors. The parameters $T_{min}$, $T_{max}$, $T_{opt}$, were obtained by least-square fitting (using the `lsqcurvefit` Matlab function) and the parameters $\lambda_0$ and $\beta$ were estimated by log-linear regression. Algae were found to be photosynthetically inactive after exposure to 43°C for 30 min (unpublished data). $P_m$ was therefore considered null at 43°C when determining $T_{min}$, $T_{max}$, and $T_{opt}$. Based on the linear relationship between $P_m$ and $K$ (see section 3.1 for details), $K$ was also assumed null at this temperature.
## 2.4. Measurement of extinction coefficient

The extinction coefficient $\sigma_X$ was experimentally determined by measuring the light intensities entering and exiting the reactors for different algal concentrations (see S2 for details). Similarly to the formula proposed by [15], the extinction coefficient was expressed as follows:

$$ \sigma_X = AX^B \quad (7) $$

where A and B are empirical coefficients ($A = 79.1$; $B = -0.37$, see S2 for details). The dependence of the extinction coefficient on algal concentration was mostly due to light scattering by algal cells. Scattered photons indeed exited the reactors through the lateral side of the reactors. This effect was reinforced by the fact that LEDs lamps did not emit light in a vertical direction but in a cone of an angle 30°, which increases the fraction of light lost through the reactors lateral sides. When the algal concentration increased, most of photons were absorbed by algal cells and the fraction of light exiting the reactors through the lateral sides decreased. This explains why the extinction coefficient is less sensitive to X for high algal concentrations (Equation 7; see S2 for further detail). Calibration experiments were therefore performed at relatively high algal concentrations to ensure that most of incoming light was absorbed by algae.

## 2.5. Application to the calibration device

Based on Equations 1-7, the algal productivity in each reactor used for model calibration was expressed as follows:

$$ P_{net}(T, I_0) = \frac{P_m(T)S}{\sigma_X} \ln \left( \frac{K(T)+\sigma_X I_0}{K(T)+\sigma_X I_0 \cdot \exp(-\sigma_X X_L)} \right) - \lambda(T) X_{SL} \quad (8) $$

where T is the culture temperature (°C), $I_0$ is the incident light intensity at the reactor bottom (W m⁻²), $P_m$, K and $\lambda$ are the temperature-dependent model parameters (see Equations 4 and
6), $\sigma_X$ is the extinction coefficient (see Equation 7), X is the algal concentration (kg m⁻³), and L and S are the reactor height (m) and section surface area (m²), respectively.

## 2.6. Monte-Carlo simulations

Monte-Carlo simulations were performed to quantify the impact of experimental error on the fitted values of model parameters P_m, K and $\lambda$. Namely, four key measurements were found to have a significant impact on model parameters:

- The extinction coefficient $\sigma_X$: coefficients A and B in Equation 7 were found to vary in the ranges 74.50-82.78 and -0.20--0.48, respectively (see S2 for details);

- The dissolved oxygen concentration: oxygen probes were found to be accurate at +/- 4.7% (see S3 for details);

- The incident light intensity I₀: Measurements by actinometry were assumed to be accurate at +/-10% based on the study of Hatchard and Parker [16] (See S1 for details).

- The algal concentration X: an accuracy of +/-7% on dry weight measurements was assumed by analogy with the study of Béchet et al. [6].

In practice, the uncertainties on the parameters P_m, K and $\lambda$ were obtained from the following Monte-Carlo approach. Assuming that errors were normally distributed, a large artificial data set was generated by adding a normally distributed error to the measurements (algal concentration X, light intensity I₀ and oxygen concentration) and the extinction coefficient ($\sigma_X$). A total of 2000 artificial data sets were thus generated and the parameters P_m, K and $\lambda$ were determined with a minimization algorithm for each data set. This approach yielded a normal distribution for P_m, K and $\lambda$, which allowed determining confidence intervals for each of these parameters. These resulting confidence intervals were then used to determine levels
199 of uncertainty on the parameters $T_{min}$, $T_{max}$, $T_{opt}$, $\lambda_0$ and $\beta$ through another set of Monte-Carlo
200 simulations (see [6] for further details on Monte-Carlo simulations).

201

202 2.7. Conversion coefficients from oxygen to biomass productivity
203 The productivity model developed in this study predicts algal productivity in terms of oxygen
204 (see Equations 1-6). For engineering purposes, it is however necessary to express
205 productivities in terms of biomass. The conversion from oxygen to biomass productivities
206 was performed by following the approach of Béchet et al. [6]. This conversion was based on
207 the assumption of a photosynthetic quotient of 1 mole of CO₂ consumed for the production of
208 1 mole of O₂ during the light reactions of photosynthesis, which was supported by the
209 experimental measurement of the photosynthetic quotient of a close algal species (*Dunaliella
tertiolecta*) by Wegmann and Metzner [17]. This photosynthetic quotient of 1 does not
210 include respiratory mechanisms and only reflects photosynthesis. From the knowledge of
211 algal composition and by considering that nitrate was used as a nitrogen source, the following
212 conversion coefficients were obtained (see S4 for details):
213

$$
214 \quad - P_m' [\text{kg/kg-s}] = 0.75 (\pm 0.10) P_m [\text{kg O}_2/\text{kg-s}]
$$

$$
215 \quad - \lambda' [\text{kg/kg-s}] = 0.75 (\pm 0.10) \lambda [\text{kg O}_2/\text{kg-s}] \text{ at daytime}
$$

$$
216 \quad - \lambda' [\text{kg/kg-s}] = 0.9375 (\pm 0.10) \lambda [\text{kg O}_2/\text{kg-s}] \text{ at nighttime}
$$

217

218 3. Results and discussion

219 3.1. Rate of photosynthesis

220 Figure 1 shows that the Type-II model coupling a Monod formula with the modified Beer-
221 Lambert law was able to describe the evolution of the rate of photosynthesis with light
222 intensity. These PI-curves do not exhibit the typical decrease at high light intensities due to
photo-inhibition observed for *D. salina* in dilute cultures through chlorophyll fluorescence measurements by Combe et al. [18]. This is explained by the high algal concentration that ensured that only a small fraction of cells were photo-inhibited, so that the impact of photo-inhibition was minimal, as suggested by Bernard [19]. Experimental errors caused relatively high uncertainty on fitted values of *P*<sub>m</sub> and *K* as shown in Table 1 and especially at the temperature of 40.9°C as the gross productivity was only measured at two light intensities (the oxygen net productivity was negative at low light intensities due to high respiration rates at this temperature, and oxygen concentration remained null during all experiment). Because of these experimental uncertainties, it was difficult to accurately identify *P*<sub>m</sub> and *K* separately. In other words, various combinations of *P*<sub>m</sub> and *K* could yield equally satisfying fits in Figure 1. In spite of these levels of inaccuracy, Figure 2 shows that *P*<sub>m</sub> and *K* were correlated (R<sup>2</sup> = 0.87558), which was previously observed by Béchet et al. [6]. The ratio *P*<sub>m</sub>/*K* indeed represents the maximum 'yield' of photosynthesis (in kg O<sub>2</sub>/W-s), i.e. the amount of oxygen produced through photosynthesis per unit light energy captured by cells. For low light intensities, this maximum yield is theoretically independent of temperature [20], which explains the linearity observed in Figure 2.

Figure 3 shows that experimental values of *P*<sub>m</sub> followed a typical response to temperature characterized by a slow increase from cold to optimal temperatures before a fast drop for higher temperatures. The model of Bernard and Rémond [11] especially developed for this type of temperature response thus provides a good fit to experimental data (Figure 3).

Interestingly, the model of Bernard and Rémond successfully described the evolution of *K*, with similar values for *T*<sub>min</sub>, *T*<sub>max</sub>, and *T*<sub>opt</sub> as shown in Table 2. This similarity is explained by the linearity between *P*<sub>m</sub> and *K* shown in Figure 2. The values of *T*<sub>min</sub>, *T*<sub>opt</sub> and *T*<sub>max</sub> are within the range of values obtained by Bernard and Rémond [11] for 15 other algal species. The
248 value of the maximum temperature $T_{max}$ is in the upper range of reported values for other algal
249 species, which may be explained by two reasons. Firstly, *D. salina* is known to resist to high
250 temperatures as this species is naturally found in shallow water bodies in which temperature
251 can reach relatively high values [21,22]. In addition, this model calibration is based on short-
252 term measurements of photosynthesis (approximately 30 min) while Bernard and Rémond
253 [11] fitted their model on growth rate measurements obtained over several days of cultivation.

254 Even if Bernard and Rémond [11] did not calibrate their model on *D. salina* data, this
255 difference in time scales may explain the relatively high $T_{max}$ value (43°C) as short-term and
256 long-term algal responses are not controlled by the same biological processes. Oxygen
257 production indeed reflects the rate of initial non-enzymatic steps of photosynthesis (usually
258 referred to as "light reactions"), while carbon fixation through Calvin cycle and more
259 generally growth involve enzymatic processes that are more impacted by temperatures. For
260 example, Béchet et al. [6] showed that *Chlorella vulgaris* was unable to sustain growth at a
261 constant temperature of 35°C for more than 1-2 hours while the oxygen productivity peaked at
262 38°C. The uncertainty on $P_m$ and $K$ showed in Table 1 caused levels of uncertainty on $T_{max}$,
263 $T_{min}$ and $T_{opt}$ similar to the confidence intervals presented by Bernard and Rémond [11], even
264 if methods for uncertainty estimations were based on different approaches (Table 2).

265
266 3.2. Respiration rate
267 Figure 4 shows that the specific respiration rate increased exponentially with temperature over
268 the range of temperatures tested. Similar observations were reported for a large number of
269 algal species as reviewed by Robarts and Zohary [23]. Based on the values reported in Table
270 1, the coefficients $\lambda_0$ and $\beta$ (with corresponding confidence intervals at 95%) were 6.45 $10^{-7}$
271 (+/- 0.34 $10^{-7}$) $s^{-1}$ and 0.0715 (+/- 0.0002) $^\circ C^{-1}$, respectively.

272
273 4. Conclusions
274 The results obtained during the model calibration performed on *D. salina* are consistent with
275 prior observations in the literature, namely:

276 - The rate of gross oxygen productivity followed a typical Monod-like response to light
277 intensity;

278 - The maximum specific rate of oxygen production was linearly correlated to the half-
279 saturation constant of the Monod model, indicating that oxygen production efficiency
280 is as expected independent of temperature at low light intensities;

281 - The evolutions of the maximum specific rate of photosynthesis and half-saturation
282 constant with temperature satisfyingly fitted Bernard and Rémond's model.

283 - Respiration rates were shown to increase exponentially with temperature, which is
284 consistent with prior observations in the literature.

285 - These results also confirm that *Dunaliella salina* can grow in a relatively wide
286 temperature range and resist to relatively high temperatures.

287 These results indicate that the experimental technique used for model calibration is valid
288 and that the productivity model should yield accurate predictions in outdoor cultivation
289 systems.

290

291

292

293 Acknowledgments:

294 The authors are grateful for the support of the ANR-13-BIME-004 Purple Sun and the
295 Inria Project Lab *Algae in silico*. Margaux Caïa (Inria BIOCORE/LOV) is acknowledged
296 for early work on the device used for model calibration.

297
299 [1] Q. Béchet, A. Shilton, B. Guieysse, Modeling the effects of light and temperature on
300 algae growth: State of the art and critical assessment for productivity prediction during
301 outdoor cultivation, Biotechnol. Adv. 31 (2013) 1648–1663.

302 [2] E. Lee, M. Jalalizadeh, Q. Zhang, Growth kinetic models for microalgae cultivation: A
303 review, Algal Res. 12 (2015) 497–512. doi:10.1016/j.algal.2015.10.004.

304 [3] O. Bernard, F. Mairet, B. Chachuat, Modelling of Microalgae Culture Systems with
305 Applications to Control and Optimization, in: C. Posten, S. Feng Chen (Eds.),
306 Microalgae Biotechnol., Springer International Publishing, Cham, 2016: pp. 59–87.
307 doi:10.1007/10_2014_287.

308 [4] P.M. Slegers, P.J.M. van Beveren, R.H. Wijffels, G. Van Straten, A.J.B. van Boxtel,
309 Scenario analysis of large scale algae production in tubular photobioreactors, Appl.
310 Energy. 105 (2013) 395–406. doi:10.1016/j.apenergy.2012.12.068.

311 [5] Q. Béchet, A. Shilton, B. Guieysse, Maximizing Productivity and Reducing
312 Environmental Impacts of Full-Scale Algal Production through Optimization of Open
313 Pond Depth and Hydraulic Retention Time, Environ. Sci. Technol. (2016)
314 acs.est.5b05412. doi:10.1021/acs.est.5b05412.

315 [6] Q. Béchet, P. Chambonnière, A. Shilton, G. Guizard, B. Guieysse, Algal productivity
316 modeling: A step toward accurate assessments of full-scale algal cultivation,
317 Biotechnol. Bioeng. 112 (2015) 987–996. doi:10.1002/bit.25517.

318 [7] J. Benemann, Microalgae for biofuels and animal feeds, Energies. 6 (2013) 5869–5886.
319 doi:10.3390/en6115869.

320 [8] Q. Béchet, A. Shilton, B. Guieysse, Full-scale validation of a model of algal
321 productivity, Environ. Sci. Technol. 48 (2014) 13826–13833.

322 [9] R.R.L. Guillard, J.H. Ryther, Studies of marine planktonic diatoms: I. Cyclotella Nana
323 Hustedt and Denotula Confervacea (CLEVE) Gran., Can. J. Microbiol. 8 (1962) 229-
324 239. doi:10.1139/m62-029.

325 [10] C.J. Zhu, Y.K. Lee, Determination of biomass dry weight of marine microalgae, J.
326 Appl. Phycol. 9 (1997) 189-194. doi:10.1023/A:1007914806640.

327 [11] O. Bernard, B. Rémond, Bioresource Technology Validation of a simple model
328 accounting for light and temperature effect on microalgal growth, Bioresour. Technol.
329 123 (2012) 520-527. doi:10.1016/j.biortech.2012.07.022.

330 [12] C.D. Collins, C.W. Boylen, Physiological responses of Anabaena variabilis
331 (Cyanophyceae) to instantaneous exposure to various combinations of light intensity
332 and temperature, J. Phycol. 18 (1982) 206-211.

333 [13] J.U. Grobbelaar, C.J. Soeder, Respiration losses in planktonic green algae cultivated in
334 raceway ponds, J. Plankton Res. 7 (1985) 497-506. doi:10.1093/plankt/7.4.497.

335 [14] F. Le Borgne, J. Pruvost, Investigation and modeling of biomass decay rate in the dark
336 and its potential influence on net productivity of solar photobioreactors for microalga
337 Chlamydomonas reinhardtii and cyanobacterium Arthrospira platensis, Bioresour.
338 Technol. 138 (2013) 271-276. doi:10.1016/j.biortech.2013.03.056.

339 [15] A. Morel, Optical modeling of the upper ocean in relation to its biogenic matter
340 content (case I waters), J. Geophys. Res. 93 (1988) 10749-10768.
341 doi:10.1029/JC093iC09p10749.

342 [16] C.G. Hatchard, C.A. Parker, A New Sensitive Chemical Actinometer. II. Potassium
343 Ferrioxalate as a Standard Chemical Actinometer, Proc. R. Soc. London A Math. Phys.
344 Eng. Sci. 235 (1956) 518-536.
345 http://rspa.royalsocietypublishing.org/content/235/1203/518 abstract.

346 [17] K. Wegmann, H. Metzner, Synchronization of Dunaliella cultures, Arch. Mikrobiol. 78
347 (1971) 360-367. doi:10.1007/BF00412276.
348 [18] C. Combe, P. Hartmann, S. Rabouille, A. Talec, O. Bernard, A. Sciandra, Long-term adaptive response to high-frequency light signals in the unicellular photosynthetic eukaryote Dunaliella salina, Biotechnol. Bioeng. 112 (2015) 1111–1121.

349
350

351 [19] O. Bernard, Hurdles and challenges for modelling and control of microalgae for CO 2 mitigation and biofuel production, J. Process Control. 21 (2011) 1378–1389.
doi:10.1016/j.jprocont.2011.07.012.

352
353

354 [20] I.R. Davison, Environmental effects on algal photosynthesis: temperature, J. Phycol. 27 (1991) 2–8. doi:10.1111/j.0022-3646.1991.00002.x.

355
356
357

358 [22] P.I. Gómez, M.A. González, The effect of temperature and irradiance on the growth and carotenogenic capacity of seven strains of Dunaliella salina (Chlorophyta) cultivated under laboratory conditions, Biol. Res. 38 (2005) 151–162.

359
360

361 [23] R.D. Robarts, T. Zohary, Temperature effects on photosynthetic capacity, respiration, and growth rates of bloom-forming cyanobacteria, New Zeal. J. Mar. Freshw. Res. 21 (1987) 391–399. doi:10.1080/00288330.1987.9516235.

362
363

364
<table><caption>Table 1: Model parameters values at different temperatures (values in parenthesis indicate confidence level at 95% estimated through Monte-Carlo simulations). Values of $P_m$ and $\lambda$ in kg/kg-s can be obtained by using the conversion coefficients provided in Section 2.6. Values of $K$ can be obtained in $\mu\text{mol/kg-s}$ by using a conversion factor of 4.79 $\mu\text{mol/W-s}$ (based on the spectral distribution of device lamps shown in S1).</caption><tr><td>Temperature (°C)</td><td>3.7</td><td>10.2</td><td>19.7</td><td>27.7</td><td>34.7</td><td>40.9</td></tr><tr><td>P<sub>m</sub> (10<sup>-4</sup> kg O<sub>2</sub>/kg-s)</td><td>0.165<br>(0.014)</td><td>0.571<br>(0.096)</td><td>1.19<br>(0.25)</td><td>2.08<br>(0.43)</td><td>1.77<br>(0.33)</td><td>1.35<br>(0.88)</td></tr><tr><td>K (10<sup>4</sup> W/kg)</td><td>0.479<br>(0.095)</td><td>2.46<br>(0.64)</td><td>2.79<br>(0.87)</td><td>4.77<br>(1.34)</td><td>3.34<br>(0.89)</td><td>3.28<br>(3.31)</td></tr><tr><td>λ (10<sup>-6</sup> kg O<sub>2</sub>/kg-s)</td><td>0.88<br>(0.05)</td><td>1.22<br>(0.06)</td><td>2.55<br>(0.13)</td><td>5.45<br>(0.28)</td><td>7.53<br>(0.39)</td><td>11.5<br>(0.6)</td></tr></table>
Table 2: Bernard and Rémond's model parameters for $P_m$ and K (values in parenthesis indicate confidence interval at 95% estimated through Monte-Carlo simulations) - Symbols are defined in Equation 4. Values of $\alpha$ for K can be obtained in µmol/kg-s by using a conversion factor of 4.79 µmol/W-s

<table><thead><tr><th>Parameter (unit)</th><th><i>T</i><sub>min</sub> (°C)</th><th><i>T</i><sub>opt</sub> (°C)</th><th><i>T</i><sub>max</sub> (°C)</th><th>α</th></tr></thead><tbody><tr><td><i>P</i><sub>m</sub> (kg O<sub>2</sub>/kg-s)</td><td>-7.8 (8.4)</td><td>34.0 (3.9)</td><td>43.0 (0.1)</td><td>2.08 10<sup>-4</sup> kg<br>O<sub>2</sub>/kg-s</td></tr><tr><td>K (W/kg)</td><td>-15.4 (17.3)</td><td>33.7 (8.0)</td><td>43.0 (0.4)</td><td>4.77 10<sup>4</sup> W/kg</td></tr></tbody></table>

375
376 Figures

377

378 Figure 1: Gross rate of photosynthesis vs. incident light intensity at different temperatures

379 (dots: experimental data; plain lines: theoretical fitting) - Error bars represent standard

380 deviation of error caused by experimental error. Light intensities in W/m² can be converted

381 into µmol/m²-s by using a conversion factor of 4.79 µmol/W-s.

382

383 Figure 2: Values of the maximum specific growth rate *P*<sub>m</sub> vs. the half-constant *K* (dots:

384 experimental data; plain line: linear regression) - Error bars indicate the standard deviation

385 estimated through Monte-Carlo simulations.

386

387 Figure 3: Evolution of the maximum specific oxygen productivity and half-saturation constant

388 with temperature (dots: experimental data; plain line: fitting with Bernard and Rémond's

389 model) - Error bars represent the standard deviation estimated through Monte-Carlo

390 simulations. Values of *K* can be obtained in µmol/kg-s by using a conversion factor of 4.79

391 µmol/W-s.

392

393 Figure 4: Evolution of the respiration specific rate with temperature (dots: experimental data;

394 plain line: fitting to an exponential function as described by Equation 6) - Error bars represent

395 standard deviation estimated through Monte-Carlo simulations.
<figure><img src="image_2.png" /></figure>
<figure><img src="image_3.png" /></figure>
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /></figure>