Optimization Analysis to Evaluate the Relationships between Different Ion Concentrations and Prymnesium parvum Growth Rate

Abstract

The purpose of this study was to evaluate the optimum environmental condition required for reaching the maximum growth rate of P. parvum. Eight ions (Na⁺, K⁺, CO₃²⁻, HCO₃⁻, Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻) were divided into two groups with a uniform design of 4 factors and 10 levels. The results showed a rising trend in growth rate with increasing ion concentrations. However, concentrations that exceeded the threshold led to a slowdown in the growth rate. Therefore, adequate supply of ion concentrations promoted growth of P. parvum, whereas excessively abundant or deficient ion concentrations inhibited its growth rate. Specifically, the order of impact of the first four ion factors on the growth rate was Na⁺ > HCO₃⁻ > K⁺ > CO₃²⁻. The growth rate of P. parvum reached the maximum theoretical 0.999 when the concentrations of Na⁺, K⁺, CO₃²⁻, and HCO³⁻ ions were 397.98, 11.60, 3.37, and 33.31 mg/L, respectively. This theoretical growth maximum was inferred from the experimental results obtained in this study. For other ion factors, SO₄²⁻ had the most influence on the growth rate of P. parvum, followed by Mg²⁺, Ca²⁺, and Cl⁻ ions. The growth rate of P. parvum reached the maximum theoretical value of 0.945 when the concentrations of Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻ ions were 11.52, 32.95, 326.29, and 377.31 mg/L, respectively. The findings presented in this study add to our understanding of the growth conditions of P. parvum and provide a theoretical basis for dealing with the water bloom it produces in order to control and utilize it.

1. Introduction

P. parvum is a single-celled microalgae that has the potential to cause massive fish kills [1,2]. This microalgae is suitable for growth in water with a salinity of 0.6–70.0‰, with the optimum salinity being 3.0–5.0‰. Water temperature of about 20 °C is the most suitable condition for its growth. Under some situations, the concentration of ichthyotoxins secreted by P. parvum can kill fish, causing ecological damage [3,4,5]. These toxins have been shown to have potent protease and hemolytic properties [5]. At certain concentrations, the toxin, which is dominated by chemicals known as “prymnesins”, can be fatal to gill-breathing species, such as fish [6]. In high-salinity water bodies, P. parvum can easily reproduce. In ponds and ditches in saline areas of northern China, such algae can easily reach optimum growth conditions, and the toxins they secrete cause mass mortality of cultured fish in this area [7].

The microalgae growth rate is closely related to ion concentrations in the solution environment. The relationship between algal growth and ion concentration has been studied in Chlorella, Tetrahymena, and Microcystis aeruginosa [8,9]. However, no research has been conducted on P. parvum, which is a common species in saline areas in northern China, particularly in Ningxia, and the goal of this paper is to do so. Different ions have distinct effects on microalgae. Metal ions, particularly Al³⁺, Ca²⁺, Fe²⁺, and Mg²⁺ ions, can promote the growth rate of microalgae. Hence, microalgae are cultivated using industrial wastewater to purify water [10]. The concentrations of carbon, nitrate, and magnesium are 10.000, 15.000, and 150 mg/L, respectively, showing the maximum biomass growth rate of microalgae [11]. The optimal concentrations of KNO₃, CO(NH₂)₂, and NaHCO₃ for microalgae growth rate are 500, 360, and 1500 mg/L, respectively [12]. In reality, ions have more than just facilitative impacts on microalgae. SO₄²⁻ ions can cause toxins to accumulate in microalgae cells [13], while Cl⁻ ions can effectively reduce the cell density and chlorophyll-a of microalgae [14]. Pb²⁺ ions have been shown to have toxic effects on two microalgae [15], and Cd²⁺ ions at a concentration of 7 mg/L was found to inhibit microalgae growth rate [16]. Furthermore, the ion concentration influences the growth of microalgae, either inhibiting or promoting it [17,18,19,20]. It is clear that ion concentration and microalgae growth rate have a complicated relationship. To a certain extent, the interaction between various ions will affect the growth rate of microalgae. As a result, an optimal ion concentration will boost microalgae biomass.

Waters in the Ningxia region of China, particularly in Yinchuan and North of Yinchuan areas, have a high salt alkalinity (pH ranges from 7.8 to 9.2). As a result, during the cooler seasons, when the temperature suitable for P. parvum growth can reach around 18 °C, P. parvum can multiply in large outbreaks, releasing more toxins and affecting fish growth. This can result in a sharp decline in the ecological environment and have a negative impact on the economic development of fisheries. There is currently very little published information on the growth characteristics of P. parvum and how the ionic factor impacts its growth rate. In the present study, a uniform design (UD) method [21,22,23] was used to quantify the effects of ion concentration (Na⁺, K⁺, CO₃²⁻, HCO₃⁻, Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻) on the growth rate of P. parvum. By constructing growth curves with each ion factor, we were able to estimate the optimum growth conditions for P. parvum. By studying the physiological characteristics of the growth rate of this environmentally harmful microalgae, we discuss the optimal growth rate as influenced by ionic factor conditions.

2. Materials and Methods

2.1. Purification and Culture of P. parvum

In October 2019, the experimental microalgae P. parvum was collected from fish ponds in Dawukou, Ningxia, China. After sampling, we brought them back to the laboratory for isolation, culture, and expansion in preparation for the ion concentration test. After centrifugation, microalgal water samples were incubated in F/2 medium (the composition of which is shown in

Table 1. F/2 medium composition.

Raw Material	Content (mg/L)	Component	Content (mg/L)
NaCl	363.84	Ca	17.05
Na2S04	382.66	Mg	35.47
MgS04	177.35	Na	434.46
K2S04	34.49	K	15.46
CaCl2	47.31	C032−	3.31
Na2CO3	5.85	HC03−	36.4
NaHC03	50.12	Cl_	251.05
NaN03	20.7	S042−	419.61
NaH2PO4	4.06	N	3.41
Na2SiO3	3.01	P	1.05
FeC6H5O7	2.32	Si	0.69

) for five days, with the light intensity set to 5000 lux, light/dark ratio set to 12 h:12 h, the temperature set to 18.5 ± 0.5 °C, the pH set to 8.5 ± 0.1, and the salinity set to 1.2 ± 0.1 mg/L. Water samples were filtered using filter paper. In this case, centrifugation was carried out at 2600 rpm for one minute while the temperature was kept at 20.5 ± 0.5 °C. The solution was concentrated, and the supernatant was discarded before incubating. This light time was used in this study for all cultures.

P. parvum was isolated using the plate method. A suitable amount of microalgal seeds was inoculated on a solid medium and cultured in the aforementioned environmental conditions, with the growth rate condition checked by microscopic examination once per day. The composition and content of the solid medium were as follows [24]: CO(NH₂)₂ (42.4 mg), KH₂PO₃ (8 mg), FeC₆H₅O₇ (1 mg), Na₂SiO₃ (10 mg), VB₁ (200 mg), VB₁₂ (1 mg), NaHCO₃ (500 mg), agar (6 g), potassium sorbate (25 mg), and EDTA-Na (2 mg). After 10 days, the colony of pure microalgal cells was transferred to 50 mL triangular flasks containing a sterilization medium to expand the culture. These microalgal strains were inoculated in 250 mL triangular glass bottles with F/2 medium in the above environmental conditions. When the microalgal cells had reached the logarithmic growth period (approximately 10 days), they were inoculated in a 10 L triangular glass bottle containing expansion culture. During the culture test, cell counts were obtained every 24 h. Continuous observation was carried out until the cell count stopped increasing. The logarithmic growth period of this algal cell was about 10 days. Solid medium was utilized to extract and purify the small trichogramma golden algae without counting CFU. The liquid medium was used for expansion and counting analysis using the ion impact test. These proliferated microalgae were used as test materials for the study.

2.2. Experimental Design

We used a uniform design, a new experimental design method based on the quasi-Monte Carlo method proposed by the mathematician Fang Kaitai [25]. This method can effectively reduce the number of experimental tests and is more suitable for use in multidimensional space- and data-limited situations [26]. Satisfactory results can be obtained with a smaller number of trials. Uniform design can not only overcome the disadvantage of a single-factor test, which does not consider the interaction between factors, but also solves the problem of fewer factors in orthogonal tests. A consistent design enables selection of the most representative test sites within the test range [21]. When the number of trials is the same, a multilevel setting can be performed so that the range of trials for each factor can be further investigated and the test factors can be automatically categorized. Because uniform design is currently effectively used in the optimization of microalgal culture conditions, it was chosen as the experimental theoretical basis for this study [27]. In this study, the test sites were the various ions chosen, and the test range for each factor was the ion concentration range.

The scheme was optimized using distributed parameter systems (DPS) homogeneous design software as well as multifactor and square term regression analysis. The eight ions were divided into two groups, and the effect of different ion concentrations on the optimal growth rate of P. parvum was determined using a uniform design with 4 factors and 10 levels with a $U_{10}^{*}$(10⁴) homogeneous design table.

Table 2. Experimental factors (Na⁺, K⁺, CO₃²⁻, and HCO₃⁻ ions) and established levels.

Experiment Number	Levels of Experimental Factors
	Na+	K+	CO32−	HCO3−
	X1 (mg/L)	X2 (mg/L)	X3 (mg/L)	X4 (mg/L)
1	250	9	9	20
2	550	6	2	55
3	650	12	5	25
4	400	3	7	35
5	350	27	1	30
6	300	24	6	60
7	200	15	3	45
8	500	21	4	15
9	450	18	10	50
10	600	30	8	40

shows the established levels of the experimental factors for group 1, namely sodium ion (Na⁺), potassium ion (K⁺), carbonate ion (CO₃²⁻), and bicarbonate ion (HCO₃⁻). The experimental treatment was divided into 10 groups, with each group receiving three parallel samples (30 bottles in total). The specific ion content measured in the field environment of the water for microalgae growth was as follows: Na⁺ 397.9 mg/L, K⁺ 14.11 mg/L, C0₃²⁻ 5.6 mg/L, HC0₃⁻ 37.0 mg/L, Ca²⁺ 14.46 mg/L, Mg⁺ 45.85 mg/L, Cl⁻ 300.0 mg/L, and S0₄²⁻ 460 mg/L. The ion concentration range influencing the growth of P. parvum was finally determined by referring to related research results of other scholars [28,29,30,31].

Similarly,

Table 3. Experimental factors (Ca²⁺, Mg⁺, Cl⁻, and S0₄²⁻ ions) and established levels.

Experiment Number	Levels of Experimental Factors
	Ca2+	Mg+	Cl−	S042−
	X5 (mg/L)	X6 (mg/L)	X7 (mg/L)	X8 (mg/L)
1	6	25	550	250
2	24	20	200	600
3	30	30	350	300
4	15	15	450	400
5	12	55	150	350
6	9	50	400	650
7	3	35	250	500
8	21	45	300	200
9	18	40	600	550
10	9	60	500	450

shows the established levels of the experimental factors for group 2, namely calcium ion (Ca²⁺), magnesium ion (Mg²⁺), chloride ion (Cl⁻), and sulfate ion (SO₄²⁻). The experimental design was identical to that of group 1.

2.3. Culture Methods and Conditions

A 250 mL triangular glass bottle was used for the experiment (60 bottles in total). The basic nutrient solution was F/2 medium, and the volume of the nutrient solution was 100 mL with an inoculation ratio of 1:10 (%, v/v). The light incubation conditions of the medium were light intensity of 5000 lux and light/dark ratio of 12 h:12 h. Eight samples were treated in the manner shown in Table 1 and Table 2, with three replicates for each treatment. The average value of repeated treatments was used as a parameter. The samples were cultured in a constant temperature and light culture shaker for 10 days (oscillation frequency 100 rpm and temperature range 18.0 ± 0.5), with counting proceeding after the exponential growth rate period.

2.4. Determination of Microalgal Growth Rate

The cell density of the samples was calculated under a light microscope using a hemocytometer plate made of 0.1 mL high-quality thick glass (0.10 mm, 1/400 mm², Changde Bkmam Biotechnology Co., Ltd., Changde, China). After incubation for 10 days, the growth rate of the microalgal reached the exponential growth period. From the 10th day onwards, sample counts were started so that the growth rate of P. parvum could be determined. The growth rate of microalgae cells can be calculated according to the following equation [32]:

$$\mathrm{Growth}\mathrm{rate}\left(\mathrm{K}\right)=3.322\times \left(\log (N_t\right)-\log \left(N_0\right))/\left(t-t_0\right)$$

(1)

where t is the duration of the experiment, $N_0$ is the initial cell density before the experiment, and $N_t$ is the cell density at day t of the experiment. This is the growth rate as a function of polymeric ion concentration (i.e., salinity) [33].

2.5. Data Analysis

The multifactor test method and multiple regression analysis were used to reduce the number of tests using a homogeneous design. Using the optimized scheme, regression equations were established for the growth rate of P. parvum with Na⁺, K⁺, CO₃²⁻, HCO₃⁻ Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻ ion factors. Excel 2013 and DPS v17.10 statistical analysis software were used to conduct multiple regression analysis of data, and OriginPro 2019a software was used to draw a graph of the obtained model.

3. Results and Analysis

3.1. Establishment of the Regression Model of Na⁺, K⁺, CO₃²⁻, HCO₃⁻, and Growth Rate

The results of the relationship between P. parvum growth rate and Na⁺, K⁺, CO₃²⁻, and HCO₃⁻ concentrations are shown in

Table 4. Results of the growth rate of P. parvum under different concentrations of Na⁺, K⁺, CO₃²⁻, and HCO₃⁻.

Experiment Number	Experimental Factors				Experimental Parameters
	Na+	K+	CO32−	HCO3−	Growth Rate
	X1	X2	X3	X4	Y1 (Cell/d)
1	250	9	9	20	0.417
2	550	6	2	55	0.591
3	650	12	5	25	0.669
4	400	3	7	35	0.644
5	350	27	1	30	0.638
6	300	24	6	60	0.515
7	200	15	3	45	0.447
8	500	21	4	15	0.391
9	450	18	10	50	0.644
10	600	30	8	40	0.555

.

A quadratic polynomial regression equation was generated using Na⁺ (X₁), K⁺ (X₂), CO₃²⁻ (X₃), and HCO₃⁻ (X₄) as independent variables and growth rate (Y₁) as the dependent variable using multiple quadratic stepwise regression analyses:

Y₁ = −45.4705 + 27.4436logX₁ + 1.6676logX₂ + 0.8747logX₃ + 12.7100logX₄ − 5.2779(logX₁)² − 0.7832(logX₂)² − 0.8289(logX₃)² − 4.1737(logX₄)²

By partial correlation analysis, the partial correlation coefficients of P. parvum growth rate and variables X₁, X₂, X_3, and X₄ were 0.9992, 0.9990, 0.9981, and 0.9995, respectively, with p-values of 0.03, 0.03, 0.04, and 0.02, respectively, indicating that the P. parvum growth rate was significantly correlated with variables X₁, X₂, X_3, and X₄. The r-value of the regression equation was 0.9997, and the p-value of the F-test was 0.036 (<0.05), indicating that the regression relationship between Na⁺, K⁺, CO₃²⁻, HCO₃⁻, and P. parvum growth rate was significant. The model was consistent with the experimental data (Table 4), thereby strongly reflecting the relationship between Na⁺, K⁺, CO₃²⁻, HCO₃⁻, and the growth rate of P. parvum.

The standardized regression coefficients of the factors in the regression equation and the optimal combination of the experimental factors are shown in

Table 5. The standardized regression coefficients of the model and optimal combination.

Factors	Na+	K+	CO32−	HCO3−
	X1	X2	X3	X4
Standardized regression coefficients	44.9493	5.1378	2.6947	24.3353
Growth rate (Y1 = 0.999)	398.02	11.60	3.37	33.3

. The experimental conditions that would promote the growth rate of P. parvum were determined by optimizing the regression equation Y₁.

The growth rate reached the maximum theoretical value of 0.999 when the Na⁺, K⁺, CO₃²⁻, and HCO₃⁻ concentrations were 398.02, 11.60, 3.37, and 33.31 mg/L, respectively.

3.2. Mathematical Models of the Relationships between P. parvum Growth Rate and Individual Factors (Na⁺, K⁺, CO₃²⁻, and HCO₃⁻)

A multifactor and square stepwise regression model was used to analyze the influence of a single factor after dimensionality reduction. To easily analyze the influence of a single factor on the growth rate, a submodel of the relationship between every single factor and the growth rate was obtained by fixing other factors at the optimal level.

Na⁺: Y(X₁) = −34.6758 + 27.4436logX₁ − 5.2779(logX₁)²

(2)

K⁺: Y(X₂) = 0.1113 + 1.6676logX₂ − 0.7832(logX₂)²

(3)

CO₃²⁻: Y(X₃) = 0.7682 + 0.8747logX₃ − 0.8289 (logX₃)²

(4)

HCO₃⁻: Y(X₄) = −8.6773 + 12.7100logX₄ − 4.1737(logX₄)²

(5)

The influence curves of every single factor on the growth rate are shown in Figure 1. The effect of various factors on growth rate was similar to what is shown in Figure 1.

When the concentration was low, each factor had a positive effect on the growth rate, which was under the effect of the main model. The contribution of the quadratic term became more and more important with the increase in the independent variable. When the independent variable exceeded a certain value, the single factor changed the growth rate to a negative effect. The growth rate of P. parvum first increased and then decreased with increasing ion concentrations. The growth rate reached the theoretically highest point of 0.999 with Na⁺, K⁺, CO₃²⁻, and HCO₃⁻ concentrations of 397.98, 11.60, 3.37, and 33.31 mg/L, respectively.

3.3. Establishment of the Regression Model of Ca²⁺, Mg²⁺, Cl⁻, SO₄²⁻, and Growth Rate

The results of the relationship between P. parvum growth and Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻ concentrations are shown in

Table 6. Results of the growth rate of P. parvum under different concentrations of Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻.

Experiment Number	Experimental Factors				Experimental Parameters
	Ca2+	Mg+	Cl−	S042−	Growth Rate
	X5	X6	X7	X8	Y2 (Cell/d)
1	6	25	550	250	0.605
2	24	20	200	600	0.419
3	30	30	350	300	0.691
4	15	15	450	400	0.470
5	12	55	150	350	0.675
6	9	50	400	650	0.520
7	3	35	250	500	0.468
8	21	45	300	200	0.413
9	18	40	600	550	0.692
10	9	60	500	450	0.626

.

The quadratic polynomial regression equation generated using Ca²⁺ (X₅), Mg²⁺ (X₆), Cl⁻ (X₇), and SO₄²⁻ (X₈) concentrations as independent variables and growth rate (Y₂) as the dependent variable is as follows:

Y₂ = −46.7636 + 2.4173logX₅ + 11.4688logX₆ + 3.3727logX₇ + 25.9886logX₈ − 1.1389(logX₅)² − 3.7780(logX₆)² − 0.6709(logX₇)² − 5.0430(logX₈)²

(6)

By partial correlation analysis, the partial correlation coefficients of P. parvum growth rate and variables X₅, X₆, X_7, and X₈ were 0.9987, 0.9994, 0.9878, and 0.9997, respectively, with p-values of 0.03, 0.02, 0.04, and 0.07, respectively, indicating that the P. parvum growth rate was significantly correlated with variables X₅, X₆, X_7, and X_8. The r-value of the regression equation was 0.9997, and the p-value of the F-test was 0.036 (<0.05), indicating that the regression relationship between Ca²⁺, Mg²⁺, Cl⁻, SO₄²⁻, and P. parvum growth rate was significant. The model fit the data well (Table 6), and the regression model reflected the relationship between Ca²⁺, Mg²⁺, Cl⁻, SO₄²⁻, and P. parvum growth rate. The standardized regression coefficients for each factor in the regression equation were as follows: Ca²⁺ 6.5372, Mg²⁺ 20.1762, Cl⁻ 5.9333, and SO₄²⁻ 39.1108.

By optimizing the regression equation Y₂, the optimal growth rate condition of P. parvum was derived. The optimal combination of each experimental factor is given in

Table 7. The standardized regression coefficients of the model and optimal combination.

Factors	Ca2+	Mg2+	Cl−	SO42−
	X5	X6	X7	X8
Standardized regression coefficients	6.5372	20.1762	5.9333	39.1108
Growth rate (Y2 = 0.945)	11.52	32.95	326.29	377.31

.

The growth rate of P. parvum reached the maximum theoretical value of 0.945 when the Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻ concentrations were 11.52, 32.95, 326.29, and 377.31 mg/L, respectively.

3.4. Mathematical Models of the Relationships between P. parvum Growth Rate and Individual Factors (Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻)

The following simple regression models revealing the relationship between an individual factor and growth rate (Y) were obtained using dimension reduction analyses in which the other factors were maintained at optimal levels:

Ca²⁺: Y (X₅) = −0.3385 + 2.4173logX₅ − 1.1389(logX₅)²

(7)

Mg²⁺: Y (X₆) = −7.7598 + 11.4688logX₆ − 3.7780(logX₆)²

(8)

Cl⁻: Y (X₇) = −3.2946 + 3.3727logX₇ − 0.6709(logX₇)²

(9)

SO₄²⁻: Y (X₈) = −32.5383 + 25.9886logX₈ − 5.0430(logX₈)²

(10)

As we can see from Figure 2 and the dimensionality reduction equation, the growth rate of P. parvum first increased and then decreased with increasing ion concentration. The growth rate reached the theoretically highest point of 0.945 with Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻ concentrations of 11.51, 32.95, 326.29, and 377.31 mg/L, respectively.

4. Discussion

By regulating the fluidity of cell membranes, Na⁺ ion can maintain the osmotic pressure of algal cells and influence lipid synthesis in the cells. This can change the dynamics of substance exchange across the plasma membranes as well as the solubility of CO₂ and O₂ in the environment, thereby affecting the metabolic rate of algal cells. Microalgae growth can be influenced by K⁺ ion. An increase in K⁺ ion concentration can cause intracellular Na⁺ ion loss, which can raise the pH of microalgae cells. This could then affect the growth and physiological state of the microalgae [34]. Na⁺ and K⁺ ions are elements necessary for microalgal growth rate. Thus, their concentrations inevitably affect the growth rate of algae. The growth rate of P. parvum increased with increasing concentrations of Na⁺ and K⁺ ions in this study but began to decrease when the respective concentration thresholds were reached. This suggests that too high concentrations of Na⁺ and K⁺ ions can inhibit the growth rate of P. parvum. Furthermore, when the standardized regression coefficients were compared, it was discovered that the effect of Na⁺ ion on the growth rate of P. parvum was greater than that of K⁺ ion.

The growth rate of microalgae depends on inorganic carbon fixation for photosynthesis. Free CO₂ and HCO₃⁻ can be absorbed and utilized by microalgae as a source of inorganic carbon, whereas CO₃²⁻ is not readily used for photosynthesis in microalgae. As a result, the CO₂ buffer system in the culture medium is essential for the microalgal growth rate. Some algal species, such as Scenedesmus sp. [35], Nannochloropsis salina [36], and Chlorella kessleri [37], can use HCO₃⁻ ion to support rapid growth. The concentration of NaHCO₃ is known to have a significant effect on the growth characteristics of Isochrysis. Microalgae might utilize the HCO₃⁻ ion in the environment via two mechanisms. The first is the transmembrane transport of external HCO₃⁻ ion into the cytosol, where HCO₃⁻ ion is decomposed into CO₂ by intracellular carbonic anhydrase enzyme for photosynthesis. The second is the secretion of extracellular carbonic anhydrase enzyme by some microalgae. Carbonic anhydrase speeds the dehydration of HCO₃⁻ into CO₂. The CO₂ is then transported through the membrane into the microalgal cells [38,39]. As different microalgal species produce carbonic anhydrases enzyme with different enzymatic activities in different locations, their ability to utilize HCO₃⁻ ion in the environment is also different. The addition of 1000 mg/L of NaHCO₃ into the culture medium was found to have the best growth-promoting effect in chlorella (Chlorella vulagris ESO-31) [40]. The addition of 0.6 g/L of NaHCO₃ to the BG-11 medium increased the biomass of the microalgae Scenedesmus [36]. Furthermore, when the NaHCO₃ concentration was 1600 mg/L, the maximum abundance of three marine microalgae were obtained. An appropriate amount of NaHCO₃ can improve the photosynthetic efficiency of Tetraselmis suecica and N. salina and promote the absorption of other nutrient salts by microalgal cells [36]. However, excessive NaHCO₃ can inhibit the microalgal growth rate [40]. As CO₃²⁻ ion cannot be directly utilized by microalgae, HCO₃⁻ ion becomes an essential ion for the microalgal growth rate, and its concentration could affect the growth rate of microalgae. Moreover, HCO₃⁻ and CO₃²⁻ ions and CO₂ together constitute a carbonic–carbonate system in the water, where they can interchange into one form or another under certain conditions. Under alkaline conditions, both carbonate and bicarbonate are readily present, and carbonate is more likely to undergo hydrolysis. In this study, the growth rate of P. parvum first increased as the HCO₃⁻ and CO₃²⁻ ion concentrations increased but then began to decrease when the respective concentration thresholds were reached. This suggests that excessively high concentrations of HCO₃⁻ and CO₃²⁻ ions could inhibit the growth rate of P. parvum. Furthermore, the effects of HCO₃⁻ ion on the growth rate of P. parvum was found to be greater than that of CO₃²⁻ ion based on the standardized regression coefficients of each factor in the growth regression equations.

Ca²⁺ ion is essential for cell division. It plays an important role in the formation of the middle lamella and mitotic spindle during mitosis. Ca²⁺ ion also maintains stability of the cell wall, cell membrane, and membrane-bound proteins and is involved in the regulation of various biochemical processes in the cells. Ca²⁺ ion can regulate the intercellular ion environment and reduce the adverse effects caused by low pH, toxic ions, and nutritional imbalances. Ca²⁺ ion is implicated in the regulation of many physiological processes. It also serves as an important structural element. Ca²⁺ ion can promote plant growth and increase photosynthesis capacity, but a high Ca²⁺ ion concentration might inhibit the growth rate and photosynthesis of microalgae [41]. Mg²⁺ ion is an essential nutrient for plants. Its main function is to act as and participate in photosynthesis in combination with light energy and enzymatic actions. Mg²⁺ ion is also important for protein metabolism. It has a significant effect on the microalgal growth rate. The growth rate of Microcystis aeruginosa was significantly inhibited in an Mg²⁺-depleted environment, whereas a higher mass concentration of Mg²⁺ ion also inhibited its growth rate [42]. The growth rate of P. parvum increased with increasing concentrations of Ca²⁺ and Mg²⁺ ions but began to decrease when the respective concentration thresholds were reached. This indicates that too high concentrations of Ca²⁺ and Mg²⁺ ions can inhibit the growth rate of P. parvum. Furthermore, by comparing the standardized regression coefficients, it was discovered that the effect of Mg²⁺ ion on the growth rate of P. parvum was greater than that of Ca²⁺ ion.

The salinity of a microalgal culture medium is determined by Cl⁻ ion concentration. Cl⁻ is the main ion that makes up and affects the salinity of a water body. Each microalgal species has a distinct salinity value required for its optimal growth. Suitable salinity promotes cell growth. In contrast, a salinity value below or above the optimal range for microalgae might affect their osmotic pressure and reduce their solute absorption capacity, resulting in the inhibition of microalgal growth rate [43]. SO₄²⁻ is an intermediate nutrient required for the growth and development of photoautotrophs. Its significance comes right after the three primary nutrients nitrogen, phosphorus, and potassium. An appropriate amount of sulfur can promote rapid growth and reproduction of microalgal cells [44], whereas less sulfur can decrease the protein and carbohydrate contents of microalgae, leading to the accumulation of a large number of lipids [45]. The growth rate of P. parvum increased with increasing concentrations of Cl⁻ and SO₄²⁻ ions but began to decrease when the respective concentration thresholds were reached. This indicates that too high concentrations of Cl⁻ and SO₄²⁻ ions can inhibit the growth rate of P. parvum. Not only that, by comparing the standardized regression coefficients, it was found that the effect of SO₄²⁻ ion on the growth rate of P. parvum was greater than that of Cl⁻ ion.

5. Conclusions

The main goal of the current study was to determine the effect of different ions and concentrations on the growth rate of P. parvum. Too high or too low concentrations of the selected eight ions inhibited the growth rate of P. parvum. Through the optimization analysis of the growth equation, combined with the numerical simulation of the one-way regression model, we found that the growth rate of P. parvum reached the theoretical maximum of 0.999 when the concentrations of Na⁺, K⁺, CO₃²⁻, HCO₃⁻ were 398.02, 11.60, 3.37, and 33.31 mg/L, respectively. Moreover, the Na⁺ ion had a greater effect on the growth rate than the three other ions. For Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻ ions, the analysis result showed that the growth rate of P. parvum reached the maximum theoretical value of 0.945 when the Ca²⁺, Mg²⁺, Cl⁻, and SO₄²⁻ concentrations were 11.51, 32.95, 326.29, and 377.31 mg/L, respectively.