Georges Arroyo

Johan Carlier

Philippe Georgeault

Anthony Guibert

Dominique Heitz

Laurence Wallian

FROILOC® a novel food safety technology through localised cold and clean airflow

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

FROILOC R a novel food safety technology through localised cold and clean airflow G. Arroyo, J. Carlier, P. Georgeault, A. Guibert, D. Heitz, L. Wallian Irstea, UR OPAALE, 17 avenue de Cucillé -CS64427, 35044 Rennes, France Some industries (food, pharmaceutical) require cold and ultraclean atmospheres. FROILOC R (Patent number: PCT/FR2012/050582) blows clean and cold air over the work space while improving thermal comfort for operators thanks to warmer temperatures in the ambient air of the workshop (Standard ISO7730, Criteria PMV). The installation includes a work space with two edges facing each other, the means for distributing airflow in a localised space (work surface) and a set of transparent guide walls located in the extension of the air distribution device. The arrangement of stable aeraulic barriers is achieved due to the specific layout of aspiration methods as well as the interior and exterior walls. The airflow temperature is between -2 o C and 4 o C whilst ambient air in the facility is at least 13 o C. A two-way access to the work zone allows two operators to work simultaneously and face-to-face.

  FROILOC R : Technical description (a) Principle Improves the quality and channelling of airflow distribution Reduces the risks of mixing blown air with ambient air. The clean and cold airflow is channelled over the work station receiving the products. The difference between the temperature of the diffused air and the ambient air is at least 10 o C and the cold air is between -2 o C and 4 o C. Improves sanitary performance Satisfies the ISO 14644-1 Standard (Clean Rooms and Related Controlled Environments): Level ISO5 for clean air in contact with sensitive products. Improves work conditions (particularly in the agri-food industry) Lowers the risks associated with musculoskeletal disorders: the thermal comfort of the operators is improved (meets ISO7730 standard "Ergonomics in Thermal Atmospheres" and the PMV Index). Reduces energy consumption Two-way access to the work area Two operators working across from each other can handle products whilst keeping their partner within their field of vision. FROILOC R : Results on temperature distribution (b) Temperature map from simulation (FLUENT) (c) Temperature over the table from experiments FROILOC R : Results on cleanness (d) Particle trajectory from simulation (FLUENT) (e) Particle concentration map over the table from experiments (f) FROILOC R in food industry Focus on fluid mechanics Horizontally stratified Wall jet Mean vertical velocity maps (g) Hot jet (h) Cold jet (i) Balance between Momentum and buoyancy fluxes ⇒ Modelisation of the effects of initial momentum and buoyancy on the behavior of wall jet Vertically stratified mixing layer (j) Flow visualizations of the mixing layer in stably and unstably stratified configurations at low flux Richardson number ⇒ Study of the effects of buoyancy on entrainment and mixing in mixing layer Contact: dominique.heitz@irstea.fr


domain: info.info-au math sdv spi

text:
Quentin Béchet
email: quentin.bechet@inria.fr

Philippe Moussion

Olivier A Bernard

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

Keywords: Algae, D. salina, growth kinetics, productivity model, photosynthesis, respiration

Introduction

With the objective to accurately assess the economical and environmental feasibility of fullscale algal cultivation for biofuel production, a large number of studies developed mathematical models predicting algal productivity in outdoor cultivation systems [START_REF] Béchet | Modeling the effects of light and temperature on algae growth: State of the art and critical assessment for productivity prediction during outdoor cultivation[END_REF][START_REF] Lee | Growth kinetic models for microalgae cultivation: A review[END_REF][START_REF] Bernard | Modelling of Microalgae Culture Systems with Applications to Control and Optimization[END_REF].

These models can be used to improve process design or develop optimization strategies maximizing algal productivity. For instance, Slegers et al. [START_REF] Slegers | Scenario analysis of large scale algae production in tubular photobioreactors[END_REF] used a mathematical model predicting growth rates of Phaeodactylum tricornutum and Thalassiosira pseudonana to optimize the design of closed photobioreactors. Similarly, Béchet et al. [START_REF] Béchet | Maximizing Productivity and Reducing Environmental Impacts of Full-Scale Algal Production through Optimization of Open Pond Depth and Hydraulic Retention Time[END_REF] 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 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 [START_REF] Béchet | Modeling the effects of light and temperature on algae growth: State of the art and critical assessment for productivity prediction during outdoor cultivation[END_REF].

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 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 [START_REF] Benemann | Microalgae for biofuels and animal feeds[END_REF]. 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. [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF],

and also because the model for C. vulgaris accurately predicted productivities in indoor (accuracy of +/-15% over 163 days; Béchet et al. [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF]) and outdoor (accuracy of +/-8.4% over 148 days, Béchet et al. [START_REF] Béchet | Full-scale validation of a model of algal productivity[END_REF]) reactors.

Materials and methods

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/m 2 -s (measured when the reactor was filled with water with a QSL-2100 PAR scalar irradiance sensor, Biospherical Instruments). Temperature was maintained at 30 o 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/m 2 -s, light-dark cycle: 12:12, temperature: 27 o C) and was then operated as a fed-batch system: 9L of solution was replaced every week with fresh f/2 medium [START_REF] Guillard | Studies of marine planktonic diatoms: I. Cyclotella Nana Hustedt and Denotula Confervacea (CLEVE) Gran[END_REF] 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-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.

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 [START_REF] Zhu | Determination of biomass dry weight of marine microalgae[END_REF]. Glass-fiber filters (GF/C, Whatman, diameter: 25mm, No 1822-025) were first dried for several days at 60 o 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 o C before being weighed again. Dry weight concentration was measured in duplicates.

Productivity model description

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) [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF]:

𝑃 𝑛𝑒𝑡 = 𝑃 -𝐸𝑅 (1)
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. [START_REF] Béchet | Modeling the effects of light and temperature on algae growth: State of the art and critical assessment for productivity prediction during outdoor cultivation[END_REF]. 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. [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF] 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 [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF]:

𝑃 𝑛𝑒𝑡 = ∫ 𝑃 𝑚 (𝑇) 𝜎 𝑋 𝐼 𝑙𝑜𝑐 𝐾(𝑇)+𝜎 𝑋 𝐼 𝑙𝑜𝑐 𝑋 ⋅ 𝑑𝑉 𝑉 (2)
where Pm is the maximum specific rate of photosynthesis (kg O2/kg-s), T is the culture temperature ( o C), K is the half-saturation constant (W/kg), σX is the extinction coefficient (m 2 /kg), Iloc is the local light intensity (W/m 2 , as photosynthetically active radiation or PAR), X is the algal concentration (kg/m 3 ) and V is the culture volume (m 3 ). The local light intensity Iloc was expressed by using a Beer-Lambert law:

𝐼 𝑙𝑜𝑐 (𝑙) = 𝐼 0 𝑒𝑥𝑝(-𝜎 𝑋 𝑋𝑙) (3)
where l is the light path between the considered location and the reactor external surface (m) and I0 is the incident light intensity (W/m 2 ). The evolution of Pm and K with temperature was fitted to the theoretical model of Bernard and Rémond [START_REF] Bernard | Bioresource Technology Validation of a simple model accounting for light and temperature effect on microalgal growth[END_REF] as this model was shown to satisfyingly fit the evolution of the specific growth rate of 15 algal species. Pm and K were therefore expressed as follows:

𝑝 = { 𝛼 (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)) if 𝑇 𝑚𝑖𝑛 ≤ 𝑇 ≤ 𝑇 𝑚𝑎𝑥 0 otherwise (4)
where p represents either Pm or K, α is the maximum value of Pm or K, and Tmin, Tmax and Topt are the minimum, maximum, and optimum temperatures for photosynthesis ( o C), respectively.

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

𝐸𝑅 = 𝜆(𝑇)𝑋𝑉 (5)
where λ is the specific respiration rate (kg O2/kg-s). Several studies showed that the rate of respiration was an exponential function of temperature [START_REF] Collins | Physiological responses of Anabaena variabilis (Cyanophyceae) to intantaneous exposure to various combinations of light intensity and temperature[END_REF][START_REF] Grobbelaar | Respiration losses in planktonic green algae cultivated in raceway ponds[END_REF][START_REF] Le Borgne | Investigation and modeling of biomass decay rate in the dark and its potential influence on net productivity of solar photobioreactors for microalga Chlamydomonas reinhardtii and cyanobacterium Arthrospira platensis[END_REF]. The parameter λ was therefore expressed as follows:

𝜆(𝑇) = 𝜆 0 𝑒𝑥𝑝(𝛽𝑇) (6)
where λ0 (kg O2/kg-s -1 ) and β ( o C -1 ) are determined experimentally.

Device used for model calibration

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) 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/m 2 , as PAR) and under constant temperature (see [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF] for a complete description of the oxygen measurements). These when determining Tmin, Tmax, and Topt. Based on the linear relationship between Pm and K (see section 3.1 for details), K was also assumed null at this temperature.

Measurement of extinction coefficient

The extinction coefficient σX 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 [START_REF] Morel | Optical modeling of the upper ocean in relation to its beiogenous matter content (case I waters)[END_REF], the extinction coefficient was expressed as follows:

𝜎 𝑋 = 𝐴𝑋 𝐵 (7)
where ) -𝜆(𝑇)𝑋𝑆𝐿 (8

A
)
where T is the culture temperature ( o C), I0 is the incident light intensity at the reactor bottom (W m -2 ), Pm, K and λ are the temperature-dependent model parameters (see Equations 4 and 6), σX 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 (m 2 ), respectively.

Monte-Carlo simulations

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

-The extinction coefficient σX: coefficients A and B in Equation 7were 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 [START_REF] Hatchard | A New Sensitive Chemical Actinometer. II. Potassium Ferrioxalate as a Standard Chemical Actinometer[END_REF] (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. [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF].

In practice, the uncertainties on the parameters Pm, K and λ 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 (σX). A total of 2000 artificial data sets were thus generated and the parameters Pm, K and λ were determined with a minimization algorithm for each data set. This approach yielded a normal distribution for Pm, K and λ, which allowed determining confidence intervals for each of these parameters. These resulting confidence intervals were then used to determine levels of uncertainty on the parameters Tmin, Tmax, Topt, λ0 and β through another set of Monte-Carlo simulations (see [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF] for further details on Monte-Carlo simulations).

Conversion coefficients from oxygen to biomass productivity

The productivity model developed in this study predicts algal productivity in terms of oxygen (see Equations 1-6). For engineering purposes, it is however necessary to express productivities in terms of biomass. The conversion from oxygen to biomass productivities was performed by following the approach of Béchet et al. [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF]. This conversion was based on the assumption of a photosynthetic quotient of 1 mole of CO2 consumed for the production of . 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 photoinhibition was minimal, as suggested by Bernard [START_REF] Bernard | Hurdles and challenges for modelling and control of microalgae for CO 2 mitigation and biofuel production[END_REF]. Experimental errors caused relatively high uncertainty on fitted values of Pm and K as shown in Table 1 and especially at the temperature of 40.9 o 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 Pm and K separately. In other words, various combinations of Pm and K could yield equally satisfying fits in Figure 1.

In spite of these levels of inaccuracy, Figure 2 shows that Pm and K were correlated (R 2 = 0.87558), which was previously observed by Béchet et al. [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF]. The ratio Pm/K indeed represents the maximum 'yield' of photosynthesis (in kg O2/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 [START_REF] Davison | Environmental effects on algal photosynthesis: temperature[END_REF], which explains the linearity observed in Figure 2.

Figure 3 shows that experimental values of Pm 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 [START_REF] Bernard | Bioresource Technology Validation of a simple model accounting for light and temperature effect on microalgal growth[END_REF] 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 Tmin, Tmax, and Topt as shown in Table 2. This similarity is explained by the linearity between Pm and K shown in Figure 2. The values of Tmin, Topt and Tmax are within the range of values obtained by Bernard and Rémond [START_REF] Bernard | Bioresource Technology Validation of a simple model accounting for light and temperature effect on microalgal growth[END_REF] for 15 other algal species. The value of the maximum temperature Tmax is in the upper range of reported values for other algal species, which may be explained by two reasons. Firstly, D. salina is known to resist to high temperatures as this species is naturally found in shallow water bodies in which temperature can reach relatively high values [START_REF] Borowitzka | Commercial Production of β-carotene by Dunaliella salina in open ponds[END_REF][START_REF] Gómez | The effect of temparature and irradiance on the growth and carotenogenic capacity of seven strains of Dunaliella salina (Chlorophyta) cultivated under laboratory conditions[END_REF]. In addition, this model calibration is based on shortterm measurements of photosynthesis (approximately 30 min) while Bernard and Rémond [START_REF] Bernard | Bioresource Technology Validation of a simple model accounting for light and temperature effect on microalgal growth[END_REF] fitted their model on growth rate measurements obtained over several days of cultivation.

Even if Bernard and Rémond [START_REF] Bernard | Bioresource Technology Validation of a simple model accounting for light and temperature effect on microalgal growth[END_REF] did not calibrate their model on D. salina data, this difference in time scales may explain the relatively high Tmax value (43 o C) as short-term and long-term algal responses are not controlled by the same biological processes. Oxygen production indeed reflects the rate of initial non-enzymatic steps of photosynthesis (usually referred to as "light reactions"), while carbon fixation through Calvin cycle and more generally growth involve enzymatic processes that are more impacted by temperatures. For example, Béchet et al. [START_REF] Béchet | Algal productivity modeling: A step toward accurate assessments of full-scale algal cultivation[END_REF] showed that Chlorella vulgaris was unable to sustain growth at a constant temperature of 35 o C for more than 1-2 hours while the oxygen productivity peaked at 38 o C. The uncertainty on Pm and K showed in Table 1 caused levels of uncertainty on Tmax, Tmin and Topt similar to the confidence intervals presented by Bernard and Rémond [START_REF] Bernard | Bioresource Technology Validation of a simple model accounting for light and temperature effect on microalgal growth[END_REF], even if methods for uncertainty estimations were based on different approaches (Table 2).

Respiration rate

Figure 4 shows that the specific respiration rate increased exponentially with temperature over the range of temperatures tested. Similar observations were reported for a large number of algal species as reviewed by Robarts and Zohary [23]. Based on the values reported in Table 1, the coefficients λ0 and β (with corresponding confidence intervals at 95%) were 6.45 10 -7

(+/-0.34 10 -7 ) s -1 and 0.0715 (+/-0.0002) o C -1 , respectively.

Conclusions

The results obtained during the model calibration performed on D. salina are consistent with prior observations in the literature, namely:

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

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

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

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

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

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

  experiments were then repeated for 6 different temperatures (3.73 o C; 10.2 o C; 19.7 o C, 27.7 o C, 34.7 o C; 40.9 o C). Temperature was maintained constant (within approximately +/-1 o 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 Pm 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 λ was determined from the average respiration rate in the six reactors. The parameters Tmin, Tmax, Topt, were obtained by leastsquare fitting (using the lsqcurvefit Matlab function) and the parameters λ0 and β were estimated by log-linear regression. Algae were found to be photosynthetically inactive after exposure to 43 o C for 30 min (unpublished data). Pm was therefore considered null at 43 o C

2 . 5 .

 25 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 o , 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 (Equation7; 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. Application to the calibration device Based on Equations 1-7, the algal productivity in each reactor used for model calibration was expressed as follows: )+𝜎 𝑋 𝐼 0 𝐾(𝑇)+𝜎 𝑋 𝐼 0 •𝑒𝑥𝑝(-𝜎 𝑋 𝑋𝐿)

1 3 . Results and discussion 3 . 1 .Figure 1

 3311 Figure1shows that the Type-II model coupling a Monod formula with the modified Beer-

FiguresFigure 1 :

 1 Figures

Figure 2 :

 2 Figure 2: Values of the maximum specific growth rate Pm vs. the half-constant K (dots:

Figure 3 :

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

Figure 4 :

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

Figure 1 396 Figure 2

 3962 Figure 1 396

  Figure 3 400

Figure 4

 4 Figure 4 402

Table 1 :

 1 Model parameters values at different temperatures (values in parenthesis indicateconfidence level at 95% estimated through Monte-Carlo simulations). Values of Pm and λ in kg/kg-s can be obtained by using the conversion coefficients provided in Section 2.6. Values

	of K can be obtained in μmol/kg-s by using a conversion factor of 4.79 μmol/W-s (based on
	the spectral distribution of device lamps shown in S1).
	Temperature ( o C)	3.7	10.2	19.7	27.7	34.7	40.9
		0.165	0.571	1.19	2.08	1.77	1.35
	Pm (10 -4 kg O2/kg-s)
		(0.014)	(0.096)	(0.25)	(0.43)	(0.33)	(0.88)
		0.479	2.46	2.79	4.77	3.34	3.28
	K (10 4 W/kg)
		(0.095)	(0.64)	(0.87)	(1.34)	(0.89)	(3.31)
		0.88	1.22	2.55	5.45	7.53	11.5
	λ (10 -6 kg O2/kg-s)
		(0.05)	(0.06)	(0.13)	(0.28)	(0.39)	(0.6)

Table 2 :

 2 Bernard and Rémond's model parameters for Pm and K (values in parenthesis indicate confidence interval at 95% estimated through Monte-Carlo simulations) -Symbols are defined in Equation4. Values of α for K can be obtained in μmol/kg-s by using a conversion

	factor of 4.79 μmol/W-s
	Parameter (unit) Tmin ( o C)	Topt ( o C)	Tmax ( o C)	α

Acknowledgments:

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