Modeling Growth of Microalgae Dunaliella Salina under Different Nutritional Conditions

Problem statement: The aim of this study was to find the empirical model that describes the growth kinetics of Dunaliella salina, with low production cost and to estimate parameters of this model. Approach: In this study the strain of D. salina UTEX 200 was cultivated in seawater (0.5 M NaCl) at room temperature with agitation of 150 rpm and luminous intensity of 60 mmols.m-2.s-1. The synthetic medium AS100 (0.2 M NaCl) was used in this study for comparison purposes and in order to determine the optimal growth of the microalgae. Kinetics of growth and β-carotene production was determined in a period of 15 days. Results: After the analysis of the behavior graphic, an unstructured model was used for describing the cell growth (logistic model). It was observed that the model was well adjusted to experimental data for the two conditions of analysis. It was observed that alga produces carotenoids under conditions of stress, in which the cell division are retarded. In the case of cells grown in seawater (higher salt concentration), the cell growth was lower but the concentration of β-carotene was higher. Conclusion: In general, these results suggest that D. salina presents higher potential for β-carotene accumulation and that high salinity decreases cellular concentration (measured by the parameter Xm of the kinetic model proposed); however there is an increase in β-carotene production.


INTRODUCTION
Carotenoids are natural pigments with much diversified structure-yet similar in their general chemical structure-and widely spread in nature, where they fulfill their essential biological functions. Carotenoids, some of which are provitamin A, have a range of diverse biological functions and actions, especially regarding human health. The carotene's pigment is of international importance because of its dual function as vitamin and colorant in the food industry to pigment salmon, trout and poultry meat, or to intensify the color of egg yolk (Martelli et al., 1992;Johnson and Schroeder, 1995). The β-carotene also present other physiological effects as inhibitor of cancer and some diseases concerning photosensible skin. It also increases immunological response to certain types of infection (Mayne, 1996).
Dunaliella salina, unicellular green microalgae, halophylic with free wall, is scientifically interesting for its capacity of producing β-carotene and glycerol. D. salina can accumulate a very high concentration, (up to 14% ) of cell dry weight of β-carotene under conditions of high light, high salinity and nutrient deprivation and it is recognized as the best biological source of this carotenoid Markovits et al., 1993;Lee, 2001). Severe conditions such as high salinity, low nutrient levels, high irradiance and high temperature have been claimed to induce β-carotene production in the cell but, at the same time, decrease the number of cells per culture volume by affecting cell division (Tafreshi and Shariati, 2006). Ben-Amotz and Avron (1983) showed that the salinity and irradiance have an additive or synergistic effect on carotenogensis in D. salina.
Among the factors that influence the productivity of biomass and β-carotene content in D. salina, salinity is a very important of them. Some studies have shown a direct relationship between β-carotene production and growth-limiting conditions such as increasing salinity. Therefore, several strategies have been used for introducing β-carotene in Dunaliella mass cultures by changing salt concentration Tafreshi and Shariati, 2006). Other authors commented that the salinity does not have a clear effect on β-carotene accumulation per cell (Gomez et al., 2003). It seems that the effect of salinity, like other inducing actors on β-carotene production in D. salina, is strain-dependent and that only a few strains of Dunaliella have the potential to produce up to 10% β-carotene (Ben-Amotz and Avron, 1983).
The world market for carotenoids was estimated at $887 million in 2004 and $1 billion in 2009 and 80% of this market is attributed to carotenoids that can be produced by using the invention process (Vermeglio, 2010). Today, D. salina is one of the most used microalgal species for mass culture due to its ability to accumulate b-carotene, a molecule which in this alga can represent up to 95% of total carotenoids (Jimenez and Pick, 1994). The global yield of Dunaliella is estimated at about 1,200 ton per year (Pulz and Gross, 2004). It was relevant to establish a mathematical model capable of describing D. salina growth and to study the maximum production of b-carotene. Mathematical models have an important role in the optimization of the fermentation process. The most widely used unstructured models for describing cell growth are the Monod kinetic model, the logistic equation and the Haldane model. The logistic equation is a substrate independent model. It can finely describe the inhibition of biomass on growth, which exists in many batch fermentations (Mitchell et al., 2004;Younesi et al., 2006).
The aim of this study was to find this empirical model that describes the growth kinetics of D. salina, consideres the effect of increasing the salinity in the two different culture mediums and estimates this model's parameters. Moreover, this study aims to assess the production of β-carotene using these two mediums.

MATERIALS AND METHODS
Algal material and growth condition: Dunaliella salina UTEX 200 was cultivated in seawater (Copacabana beach, Rio de Janeiro, Brazil) (Table 1) at room temperature (25 ± 2°C) with agitation of 150 rpm and continuously illuminated by fluorescent lamps providing 60 mmols.m-2.s-1 at the surface of the flasks. The pH was controlled to stay at pH 7.6 by injecting carbon dioxide. For comparison, synthetic medium AS100 (Vonshak, 1986) modified with the addition of 0.2 M NaCl was also used to determine the microalgae optimal growth. The initial concentration of seawater was determined by Mohr method (Sheen and Kahler, 1938), which uses chromate ions as an indicator in the titration of chloride ions with silver nitrate standard solution.
Biomass concentration: Cell counts were carried out using a 0.1 mm deep Neubauer haemocytomer.
Determination of β-carotene content: An aliquot (5.0 mL) of D. salina cell suspension was centrifuged at 3000xg for 15 min. The pellet obtained was washed with distilled water and, after water removal by centrifugation, suspended in acetone. The cell membrane is ruptured because of water (osmotic shock), thus extracting β-carotene along with chlorophyll. The extracting separates from cell debris by centrifuging it at 3000 xg for 10 min. β-Carotene was assessed according to Ben-Amotz and Avron (1983). The β-carotene content of Dunaliella cells was given by pigment content per cell (pg.cell −1 ).

Statistical analysis:
The representation and estimation of the model's parameters were performed using Statistica 7.0 software.

Kinetics:
Dunaliella salina was cultivated at laboratory scale to increase β-carotene content of the biomass by using two different salinity conditions. It was possible to observe that cell density increased from 1.2×10-5 to 4.5×10-5 cell.mL −1 in a period of 3 days when cultivated in seawater, with an initial concentration of 0.5 M. However, when AS100 (0.2 M) culture medium was used for the same period that the previous experiment, cell concentration increased from 1.2×10-5 to 5.6×10-5 cell.mL −1 (Fig. 1). This may be because when a microalga is grown in saline environment, osmosis plays a defining role. If very high salinity is used in the medium, the external environment of the cell contains a hypertonic solution, i.e., higher concentration of solute (NaCl) and lower concentration of water, than that present inside the cell. In such conditions, there is a net flux of water molecules leaving the cell. This results in cell shrinkage and subsequent destruction of the cell and cell components (plasmolysis) (Boussiba and Vonshank, 1992).
β-carotene concentration: The β-carotene content of D. salina cells during the 15 days (AS100 medium) and 10 days (seawater medium) following salt stress were determined and expressed on β-carotene per cell (Fig. 2).

DISCUSSION
Growth kinetics was determined as a maximum period of 15 days. After behavior graphic analysis, a kinetic model was developed to fit experimental data (Fig. 1).
Empirical equations that have been proposed to describe these curves ( Fig. 1) are shown in Eq. 1. The equation does not include the effect of nutrient concentration on growth. To do so, it would require the modeling of intraparticle diffusion processes. The empirical equations are simply fitted to experimental growth profiles by non-linear regression.
The logistic equations have been used for quite a while. The causes of the growth deceleration are not specified in the simple empirical growth kinetic equations.
The kinetic model is given by the following equation: Where: X = The biomass concentration (dependent variable) T = The time (independent variable) X m [cell.mL −1 ] = The maximum possible microbial biomass X 0 [cell.mL −1 ] = The initial biomass m [t-1] = The specific growth rate constant The parameters X m and m were estimated by the least square method. The numerical method quasi-Newton was used to solve the system of nonlinear equations, obtained from the least square method. The parameters estimated for two cultures mediums are shown in Table 2.
It was verified that the proposed model fit very well the experimental data obtained for both the growth conditions analyzed, especially when the microalgae were cultivated in seawater. It was observed that high salinity decrease the growth in this alga.  The parameter X m (value of maximum biomass concentration) was higher when the microalgae was grown in AS100 (0.2 M NaCl) medium, where the highest cell concentration was experimentally observed. However, higher concentration of β-carotene was observed when seawater was used. According to , salinity is a major inducing factor of carotenogenesis in some species of halotolerant green algae Dunaliella. D. salina could survive in mediums containing a wide range of NaCl concentrations ranging from about 0.05 M to saturation (around 5.5 M) (Chen et al., 2009).
The model fit was verified by standard deviations of the parameters, normal probability plot of residuals and coefficient of determination. The model generated from the experimental data of seawater medium provided a better linear fit of the data than the model generated from AS100 (0.2 M NaCl) medium (Fig. 1). The correlation coefficient was higher for seawater medium (0.998) than for AS100 (0.2 M NaCl) (0.996), as shown in Table 2. Fig. 3 shows the normal probability plot, which presented normal distribution, as required by least square method. A residual plot allows visual assessment of the distance of each observation from the fitted line (Kasperski and Schneider, 1997). In addition, residuals from seawater and AS100 (0.2 M NaCl) were normally distributed (Fig. 3). The residuals should be randomly scattered in a constant width band about the zero line, if the prior assumption of constant variance is met. Runs of residuals above or below the zero line may indicate a non-linear relationship. In general, the results for both seawater and AS100 (0.2 M NaCl) mediums present all points close to the line and contained within the limits of 95%.
It was observed that alga produces carotenoids under conditions of stress, in which cell division are retarded. When cells were grown in seawater (higher salt concentration) cell growth was lower, but the concentration of β-carotene was higher (Fig. 2). Indeed, the higher the salinity-and, as a result, the lower the growth rate of the alga-the higher the amount of light absorbed by the cell during a division cycle. This situation can lead to higher accumulation of β-carotene per cell (Tafreshi and Shariati, 2006).
In contrast to other green algae, Dunaliella do not contain rigid cell wall . As a result, cells respond rapidly to the changes in osmotic pressure. β-carotene accumulation in D. salina at two different salinities confirmed that the stress caused by increases in salt concentration increases the concentration of β-carotene in the cell.
β-carotene is a secondary metabolite and the cells under conditions of stress as a protection mechanism produce these molecules. When salinity is increased, it behaves like stress, which enhances β-carotene production.
In general, these results suggest that D. salina presents higher potential of β-carotene accumulation and that high salinity decreases biomass concentration (measured by the parameter Xm the kinetic model proposed); however, there is an increase in b-carotene production. This model can be used to verify the maximum rate of cell growth under a constant light intensity, in order to maximize the production of bcarotene.

CONCLUSION
It was observed that the model was well adjusted to experimental data for the two conditions of analysis. Above all, it showed good result when microalgae were cultivated in seawater. The maximum value of biomass concentration, in both cases, seems conveniently described by the parameter X m .
High salinity decreases the biomass concentration (measured by parameter X m ); however, there is an increased of β-carotene production.
Therefore, it is recommended that adjusting salinity properly is one of the best strategies to achieve optimal β-carotene production in mass cultures of D. salina.