Chinese Journal of Oceanology and Limnology   2017, Vol. 35 issue(3): 537-545     PDF
Institute of Oceanology, Chinese Academy of Sciences

Article Information

WANG Hui(王辉), NIU Jingyan(牛景彦), LIU Jiahui(刘佳慧), YANG Hongshuai(杨洪帅), LIU Zhigang(刘志刚)
Construction of a growth model in the green alga Tetraselmis subcordiformis using a response surface approach
Chinese Journal of Oceanology and Limnology, 35(3): 537-545

Article History

Received Oct. 24, 2015
accepted in principle Apr. 12, 2016
Construction of a growth model in the green alga Tetraselmis subcordiformis using a response surface approach
WANG Hui(王辉)1, NIU Jingyan(牛景彦)2, LIU Jiahui(刘佳慧)3, YANG Hongshuai(杨洪帅)3, LIU Zhigang(刘志刚)3        
1 Life Sciences College, Huaiyin Normal University, Huai'an 223300, China;
2 Polytechnic Department, Jiaozuo Teachers College, Jiaozuo 454000, China;
3 Fisheries College, Guangdong Ocean University, Zhanjiang 524025, China
ABSTRACT: The green alga Tetraselmis subcordiformis has been widely used as a quality live food for aquaculture species, and also has been studied as a model organism for the photo-biological production of hydrogen. We attempted to quantify the relationship between T. subcordiformis specific growth rate (SGR) and three important environmental factors (temperature, salinity, and pH) using the central composite design and response surface method under laboratory conditions. The results showed that the linear effects of temperature and salinity were significant (P < 0.05), and they were equally important in impacting T. subcordiformis specific growth; the linear effect of pH was not significant (P > 0.05); the interactive effect of temperature and pH was significant (P < 0.05), whereas the temperature × salinity and salinity × pH interactions were not significant (P > 0.05); all of the quadratic effects of the three factors were significant (P < 0.05). A model equation for specific growth rate with the three factors was established, with the unadjusted and predictive R2 as high as 0.990 and 0.921, respectively, suggesting that the model was a very good fit and that it could be used to predict SGR. Through optimizing the reliable model, an optimal 3-factor combination of 25℃/35 of salinity/pH 7.9 was obtained, at which the maximum specific growth rate (0.65) was recorded, with a desirability value of 93.8%. These experimental results could serve as guidelines for increasing T. subcordiformis production efficiency.
Key words: Tetraselmis subcordiformis     specific growth     temperature     salinity     pH     growth model    

Tetraselmis subcordiformis, which belongs to the phylum Chlorophyta class Prasinophyceae, is a marine microalga that is rich in proteins, unsaturated fatty acids, vitamins, and other nutrients. It has been extensively used as a quality live food for aquaculture species (Day et al., 1991; Tang et al., 2006). Additionally, because of its high hydrogen-producing capability, it has been used as a model organism for the photo-biological production of hydrogen (Guan et al., 2004a, b). With the rapid development of the aquaculture and bioenergy industry, the demand for microalgae will no doubt continue to rise. However, because of the many limiting factors, large-scale algal culture is inefficient and has restricted larval growth performance and cultured marine animal survival. Therefore, the improvement of algal growth and stable production of high-quality microalgae, particularly in marine fish and shellfish hatcheries, is of great importance (Pang et al., 2006).

In addition to nutritive salts in the culture media components (Davis et al., 2009; Ji et al., 2011; Yao et al., 2012; Huang et al., 2013), algal growth is affected by many other environmental factors. Many studies have been carried out to investigate the effects of ambient factors, such as temperature, salinity, pH, light, and carbon dioxide on algal growth (Leland et al., 2001; Satoh et al., 2001; Taylor et al., 2001; Cho et al., 2007; Davis et al., 2009; Yan et al., 2011). However, most of these studies only examined monofactor effects, no reliable models were established, much less model-based optimal factor combinations. To date, osmoregulation (Kirst, 1977a, b), hydrogen-producing capability (Guan et al., 2004a, b; Guo et al., 2008), and biochemical substance abstraction (Yao et al., 2013) have been reported in T. subcordiformis, but little is known about the combined effects of some important environmental factors on its growth.

In light of the fact that in nature a multitude of factors conspire concurrently to impinge on algal growth, the combined effects of three important environmental factors, temperature, salinity, and pH, on T. subcordiformis growth were investigated using the central composite design and response surface approach in the present study. The aim of this study was to determine an optimal 3-factor combination based on the reliable model derived, and, in turn, provide guidelines for high-efficiency T. subcordiformis production.

2 MATERIAL AND METHOD 2.1 Algal cultivation

The green alga, Tetraselmis subcordiformis, used for the experiment was provided by the Algae Lab of Guangdong Ocean University. Because algal activity decreases after long-term preservation, it should be activated and purified prior to experiments. The algae were inoculated into an f/2 culture solution for 4 d to activate. Algal beaker flasks were shaken 8–10 times each day to prevent algal cells from sinking and/or attaching to the beaker wall. The culture temperature was 25℃, illumination 63 μmol photons/(m2∙s) by a digital lux meter (TASI-8721, TASI, Suzhou, China), and photoperiod 14 L:10 D (light-dark). After being centrifuged and washed, the algal cells in the logarithmic growth phase were inoculated into 100-mL flasks with 50 mL f/2 culture solution containing chelated trace metals and a vitamin mix (Guillard and Ryther, 1962); the initial inoculating algal density was ~3.14×104 cells/mL. In accordance with the experimental design in Table 1, all flasks were sealed with sterilized filter paper and placed in the digital illumination incubator (GZX-150C, Nanbei, Zhengzhou, China) for culturing.

Table 1 Central composite experimental design (face-centered)
2.2 Factor regime

Because some environmental factors, such as temperature, salinity, and pH, act on algal growth concurrently, the central composite design (facecentered) was used to investigate the combined effects of these three factors on T. subcordiformis growth in the present study. Based on the outcomes of several preliminary trials, the temperature (T), salinity (S), and pH ranges were determined to be 16–34℃, 20– 46 (practical salinity units), and pH 6.0–9.0, respectively. pH and salinity were measured with a pH meter (PHS-3D, Rex, Shanghai, China) and a salinometer (S-10E, ATAGO, Fukaya-shi, Saitama, Japan), respectively.

2.3 Experimental management

Sodium hydroxide (1 mol/L NaOH) and hydrochloric acid (1 mol/L HCl) were used to adjust the pH of the algal suspension, and salinity was adjusted using sodium chloride (NaCl). Tris-HCl buffer solution was used to correct the pH of the algal suspension every 4 h to ensure that it stayed within the acceptable range (±0.2) during the experiment. The flask positions were changed every day to ensure that they were illuminated evenly.

2.4 Experimental design

When the abovementioned composite design was adopted, each factor had three levels, encoded as-1, 0, and +1, and the star arm takes ±1. In this case, the number of factorial points was eight, number of axial points six, and the number of center points was set at five to estimate and reduce pure error. Thus, there were a total of 19 experimental runs, which are listed in Table 1. To preclude systematic errors, the order of all runs was random.

2.5 Growth measurement

An algal suspension was taken at the same time each day to monitor algal growth according to the most commonly used cell count method (Andersen, 2005; Cho et al., 2007; Becker, 2008; Cai et al., 2012). In the present study, specific growth rate (SGR) was used to evaluate T. subcordiformis growth (Pang et al., 2006; Cho et al., 2007):

where, CD0 is initial cell desity (CD) and CDt is the cell density at the end of the experiment, t is the duration of algal cultivation, which was 6 d in this study; ln, natural logarithm. The cell density was calculated according to the real area of the microscopic field by averaging five samples (0.1 mL) of green algae from each of the flasks for axial and factorial runs and one sample for each center experimental run. The cell numbers were counted with a hemocytometer (0.002 5 mm2, Superior Marienfeld, BadenWürttemberg, Germany) under a microscope (BX43, Olympus, Japan).

2.6 Data analysis

The following SGR model was assumed to delineate the relationship between T. subcordiformis growth and temperature, salinity, and pH:

where, β0 is constant; β1, β2, β3 are the linear effects of temperature, salinity, and pH, respectively; β4, β5, β6 are the interactions between temperature and salinity, temperature and pH, and salinity and pH, respectively; β7, β8, β9 are the quadratic effects of temperature, salinity, and pH, respectively; ε, residual, assuming that it conforms to a normal distribution with a mean of zero. Data processing was performed in SAS software (V 9.13, SAS Institute, NC, USA), and error normality and homogeneity were checked prior to data analysis to determine if the Box-Cox transformation was necessary. All of the effects in the above model were estimated by the least squares method, and were tested using the F statistic. Model significance and adequacy were determined by ANOVA and lack-of-fit tests, respectively. After model establishment, coefficients of determination were given to examine the goodness of fit and predictive capability of the model. The combined effects of the three factors were visualized using contour and surface plots. The method suggested by Montgomery (2005) was performed to optimize the derived SGR model, the reliability of which is gauged by the desirability function whose value ranges between 0 and 1. All statistical conclusions were abstracted at the 5% significance level.


The SGR measurements (means±SD) corresponding to each factorial and axial run are presented in the rightmost column in Table 1. Because there were five samples for each factorial and axial point, standard deviations are provided. The factor regimes were strictly manipulated over the course of experiment so their standard deviations were smaller, indicating that the SGR measurements were precise. To check model adequacy using the lack-of-fit test, five center points are listed separately, standard errors are not provided.

3.1 Model adequacy

ANOVA was performed to analyze the T. subcordiformis growth data, the results of which are given in Table 2. The model was highly significant (P < 0.01); and the lack-of-fit P-value was 0.163 8, showing that the model was adequate.

Table 2 Model analysis of variance and lack-of-fit test
3.2 Model development

The following model equations in terms of coded and actual factors were obtained, respectively:

unadjusted R2 was 0.990, and predictive R2 was 0.921 for the models. Visual inspection of internally studentized residuals plotted against experimental growth revealed no clear pattern. Because the type of design used in this experiment was orthogonal, those nonsignificant terms can be directly removed from the above models without re-estimating all of other effects or coefficients.

To directly comparing the effects of varying factors on the response, we had all three factors coded in this study to eliminate the influence of factor unit. From the above coded SGR model equation, we could clearly see that temperature and salinity were almost equally important in influencing T. subcordiformis growth.

3.3 Visualization of the combined effects of the three factors on T. subcordiformis growth

The linear effects of temperature and salinity on T. subcordiformis specific growth were highly significant (P < 0.01) (Table 2), that of pH was not significant (P>0.05); the quadratic effects of the three factors were all highly significant (P < 0.01); the interaction of temperature and pH was significant (P < 0.05), whereas the temperature×salinity and pH×salinity interactions were nonsignificant (P>0.05).

Visualizations of the combined effects of the three factors on T. subcordiformis specific growth are presented in Figs. 13. The response surface plots revealed that the specific growth varied with each factor in a curvilinear fashion because all three quadratic effects were highly significant (Table 2). When one factor was held at an intermediate level, T. subcordiformis specific growth increased gradually to a peak and then declined as the other two factors increased. The maximal specific growth was ~0.64, to which the 3-factor combination, 25℃/35 of salinity/ pH 8.0 corresponded. The model-predicted SGR values at varying 3-factor combinations are presented in Fig. 4.

Figure 1 Response surface for the combined effects of temperature and salinity on T. subcordiformis growth rate (pH=7.5)
Figure 2 Response surface for the combined effects of temperature and pH on T. subcordiformis growth rate (S=35)
Figure 3 Response surface for the combined effects of salinity and pH on T. subcordiformis growth rate (T=25℃)
Figure 4 Cube plot displaying the combined effects of temperature, sainity, and pH on T. subcordiformis specific growth rate (SGR) Numbers on axes outside the cube indicate the minimum and maximum values of the factors used in the experiment; the numbers at corners inside the cube show the predicted SGR of this algal species at specific combinations of the three factors.
3.4 Model optimization

The prerequisite for model optimization is that the model must be reliable. As mentioned above, the SGR model was very reliable. The procedure proposed by Montgomery (2005) was used to optimize the SGR model derived, then the optimum 3-factor combination of 25℃\35 of salinity\pH 7.9 was obtained, at which the greatest SGR of 0.65 (95% C.I. 0.63–0.68) was observed, with a desirability function value as high as 0.938.

4 DISCUSSION 4.1 Effects of temperature, salinity, and pH on T.subcordiformis growth

Temperature is one of the most important environmental factors impacting microalgal growth, enzyme activity, metabolism, reproduction, and survival (Davison, 1991; Raven and Geider, 1988). In the present study, we first examined the linear effects of three environmental factors. The linear effect of temperature on SGR was highly significant (Table 2); the variation of SGR with temperature ranging from 16℃ to 34℃ was highly nonlinear, indicating the existence of a quadratic temperature effect (Figs. 1 and 2). SGR peaked at ~25℃ with the other two factors held unchanged. Temperature affects algal growth mainly through modulating photosynthesis and respiration (Raven and Geider, 1988; Davison, 1991). As temperature increases, algal photosynthesis and respiration are enhanced, and growth accelerates accordingly; when temperature goes outside of the suitable range, algal photosynthesis and respiration are inhibited, and growth is retarded (Davison, 1991). Huang et al. (2011) reported results analogous to ours in terms of the effect of temperature on microalgal growth.

In this study, both the linear and quadratic effects of salinity were highly significant (Table 2). As with temperature, SGR varied with salinity in a nonlinear manner because of the presence of a significant salinity quadratic effect (Figs. 1 and 3). Su et al. (2003) reported the same variation in red-tide algal growth with salinity, although they did not examine the quadratic effect of salinity. The green alga T. subcordiformis is highly salinity-tolerant or euryhaline, and in our study it still grew outside the salinity range of 20–46, but its growth was seriously suppressed. When the other factors were kept stable, the optimal salinity level was ~34, deviation from which resulted in a marked decline in SGR. Although marine microalgae are to a large extent tolerant to salinity variations, when it is either too high or too low, algal metabolism and growth are suppressed because osmoregulation is adversely effected (Kirst, 1977a; Sudhir and Murthy, 2004; Yao et al., 2012).

Although the effect of pH on algal growth is viewed as an important factor, there have been very few reports to date (Moss, 1973; Kosourov et al., 2003; Su et al., 2003). Yao et al. (2013) reported that the pH of an algal solution can be altered by the metabolic activities of microalgae per se; this would cause the pH to deviate from pre-specified regimes, and therefore, affect algal growth. We also observed this phenomenon during our investigation. Therefore, based on the study by Liu et al. (2014), we investigated the combined effects of three factors. In the present study, the linear effect of pH on T. subcordiformis growth was nonsignificant (Table 2). This result is reasonable considering that this algal species can normally grow and reproduce within pH 6–9. This result was not in accordance with Xu et al. (2009). Different algal species, pH range, ability to adjust acid-base equilibrium, and other conditions may have resulted in the differences between our results and theirs. In our study the quadratic effect of pH was highly significant (Table 2), indicating a curvilinear variation in SGR with pH (Figs. 2 and 3). pH mainly affects algal growth by modulating microalgal carbonate balance (Moss, 1973; Su et al., 2003; Xu et al., 2009). Figures 2 and 3 show that a pH of ~8 is suitable for faster growth. Additionally, the buffer agent was added to the algal solution to maintain pH at fixed levels in our experiment.

4.2 Combined effects of temperature, salinity, and pH on T. subcordiformis growth

It can be seen very clearly in Fig. 4 that at the combination of low temperature and low pH, SGR varied from 0.09 at 20 to 0.18 at 46, a 2-fold increase. Under low salinity and low pH conditions, SGR changed very little from 16℃ to 34℃. When algal cells were exposed to low temperature and low salinity conditions, SGR increased almost 1.6 times when pH increased from 6 to 9. SGR increased 1.75 times from 20 to 46 under high temperature and high pH conditions. Under high salinity and low pH, SGR decreased by 22.22% from 16℃ to 34℃. Compared with the highest SGR value at the optimal 3-factor combination obtained through optimizing the SGR model, we can see that all of the SGR values obtained at suboptimal factorial combinations were smaller. This implies that SGR and biomass is potentially greater when the optimal factorial combination is applied.

When examining the combined influence of multiple factors on a certain response, interactions often occur between factors (including higher-order ones). Montgomery (2005) has suggested that the interaction is more important than the main effects of the factors. For instance, the effect of the same factor on microalgae growth even varies with environment (Moss, 1973). The presence of interactions can have important implications for the interpretation of statistical models. In practice, this makes it more difficult to predict the consequences of changing the value of one factor, particularly if the factors it interacts with are either hard to measure or difficult to control. In the present study, a significant temperature × pH interaction was detected (Table 2), and this interaction was antagonistic to T. subcordiformis growth. Liu et al. (2014) reported a significant interaction between temperature and salinity, but in our study this interaction was nonsignificant. This means that the simultaneous influence of temperature and pH on T. subcordiformis SGR is not additive, and a suitable temperature-pH combination should be kept to induce higher enzymatic activity for faster growth (Kosourov, 2003; Yao et al., 2013). The interactions between factors of interest vary from case to case, and should be analyzed separately. For example, Cho et al. (2007) reported an interaction when examining the effects of temperature and salinity conditions for growth in the green algae Chlorella ellipsoidea and Nannochloris oculata.

4.3 Model building and optimization

Most studies on the effects of environmental factors on algal growth have used single-factor designs (Moss, 1973; Naoki et al., 1979; Davison, 1991; Taylor et al., 2001; Zhou et al., 2001; Su et al., 2003; Kosourov et al., 2003; Sudhir and Murthy, 2004; Li et al., 2007; Davis et al., 2009; Xu et al., 2009; Huang et al., 2011, 2013; Yao et al., 2013), and few have used the two-factor crossover design (Moss, 1973; Cho et al., 2007). The central composite design we used in this study has advantages over the above ones (Montgomery, 2005). In our study we found that factor linear effects alone were not sufficient to delineate the growth of this alga (R2 too low). After the quadratic effects were added to the SGR model, they were highly significant (Table 2). Cho et al. (2007) also reported highly significant quadratic effects of salinity on specific growth rate in C. ellipsoidea and N. oculata at a constant temperature of 25℃. The presence of the factor quadratic effect and interaction showed that SGR varied with all three factors in a curvilinear fashion. An extreme value was only observed under these circumstances, which in our case was the maximum SGR value (Figs. 13). We obtained a nonlinear SGR model with three environmentally important factors for the first time using the central composite design in the present study. The coefficient of determination of the model equation was as high as 99%, indicating that this SGR model fitted the experimental data perfectly; and the nonsignificant P-value (0.163 8) for the lack-of-fit test demonstrated the greater adequacy of the model (Table 2). Additionally, the very high predictive R2 (0.921) of the model also exhibited its excellent capability for projection, as is very important in application. Although Cho et al. (2007) reported the relationships between semilogarithmic growth in C. ellipsoidea and N. oculata and day of culture, they were all linear and only suitable for specific temperature-salinity combinations. They did not give a unified SGR model, and these linear relationships in principle could not be used to predict multifactorial effects on SGR. Furthermore, in contrast to the 2-factor model for T. subcordiformis growth by Liu et al. (2014), our model is obviously more general because it contains three factors.

The green alga T. subcordiformis can be tolerant of a wide range of temperatures and salinities. For example, they can grow and reproduce in seawater with temperatures varying 7–30℃ and salinity 8–80 (Zhou et al., 2001; Yao et al., 2013; Liu et al., 2014). But environmental tolerance does not necessarily reflect suitable conditions for maximum production. Because we developed a reliable SGR model in this study, we optimized the nonlinear model using the procedure in Montgomery (2005). We found that the optimal 3-factor combination was 25℃\35 of salinity\pH 7.9, at which the greatest T.subcordiformis SGR (0.65) was recorded, with the reliability as high as 93.8%. This optimal factor combination was derived by optimizing the reliable SGR model built, as is different from the method for obtaining the optimal factor combination by Cho et al. (2007). It can be seen clearly from Figs. 13 that departure from the optimal 3-factor combination would result in a rapid decrease in T. subcordiformis growth; furthermore, the composition of lipids and fatty acids (Naoki et al., 1979; Zhou et al., 2001), absorption of nutritive salts (Ji et al., 2011; Huang et al. 2013), and hydrogen-producing capability (Guan et al., 2004a, b; Ji et al., 2011) would suffer. Therefore, the acquisition of an optimal factor combination is of great importance.

4.4 Methods for measuring algal growth

Two methods, optical density and cell count (biomass), are typically used to gauge microalgal growth. Andersen (2005), Pang et al. (2006), Cho et al. (2007), and Becker (2008) have suggested the latter method. Cai et al. (2012) and Liu et al. (2014) bore out the wide applicability of the former, pointing out that this approach was expedient and highly efficient for measuring algal cell growth. In view of the flaws with the optical density method, such as the occurrence of backscattering when optical density is >1, we used the latter to investigate the combined impacts of three environmental factors. Additionally, levels of some nutritive salts, such as nitrogen and phosphorus elements, in the culture medium (Liu et al., 2007; Huang et al., 2013), initial algal density (Li et al., 2007), photoperiod, and irradiance (Zhou et al., 2001) also significantly influence algal growth. Therefore, we maintained these factors at the same levels throughout the study to account for this.

In practice, environmental factors might vary outside the factor ranges set up in the present study as a result of photosynthesis and/or seasonal changes, thus, further study to examine changes in algal growth within wider factor ranges is necessary. However, based on our findings, the algal growth patterns are not likely to differ in wider factor ranges. Considering that during production relevant measures are taken to monitor and keep environmental factors at the most suitable combinations, such as the optimum factor combination obtained in this study, our factor regimes seem acceptable.


We examined variations in T. subcordiformis SGR in response to changes in three environmental factors under laboratory conditions. A very regular pattern in SGR changes was observed. The pattern was highly nonlinear because of the quadratic and interactive effects of the factors of interest; therefore, predicting SGR without detailed experimental data is not possible. Within the ranges setup in the experiment, temperature and salinity were equally important, pH had no significant effect. Incorporating three environmental factors into the SGR model produced reasonable, reliable SGR predictions. The optimal 3-factor combination was obtained by optimizing the reliable SGR model constructed. Productivity of this microalga would likely improve with the application of our optimum factorial combination. More reliable models examining the combined effects of additional factors would also be helpful in the future.

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