Statistical approaches in modeling of the interaction between bacteria and diatom under a dual-species co-cultivation system

2.1 Microalgae culture

N. palea FACHB-2263 strains were obtained from the Freshwater Algae Culture Collection at the Institute of Hydrobiology in China. The diatom was maintained as a unialgal axenic culture at 28 °C and pH 7 under 100 μmol photons m^-2s⁻¹ with a 12light:12dark cycle. The algae were cultured in a 250 ml Erlenmeyer flask with a CSI medium. The stock culture was kept in the illumination incubator at 28 °C. The N. palea culture was maintained in our lab by transferring 1% of the culture volume to a fresh medium every two weeks. The lack of contaminating bacteria was checked by streaking aliquots on nutrient agar plates.

2.2 Bacteria culture

P. chlororaphis ACCC-19853 bacteria co-culture with the microalgae were purchased from the China Center of Industrial Culture Collection. The bacterium was axenic maintained on nutrient agar plates containing 1%–5% agar at 30 °C and pH 7. Initially, the ACCC-19853 bacteria were cultured in the nutrient broth at 30 °C. The stock solution (1 ml) was inoculated in 10 ml of the nutrient medium incubated for about five days to the exponential phase at 30 °C with shaking at 120 rpm, and growth was monitored by determining the optical density of the culture broth at 600 nm using a UV–visible spectrophotometer (Liu et al., 2018). The bacterial culture was inoculated in 500 ml of the nutrient medium incubated for ten days under the same conditions and used for extract preparation.

3.1 First-stage experiment: bacteria concentration and time interactions

The first-stage experiment has two input factors, the time with five levels (i.e., different values) (0, 12, 24, 48, 96 h) and the bacteria concentration with four levels (control, 10⁴, 10⁶, 10⁸ CFU/ml⁻¹), and three output factors, the cell density (CD x10⁶ cells/ml), dry cell weight (DCW g/l) and the total chlorophyll (TC mg/l). The full factorial design for this experiment with three replicates for each experimental run is used. The experiment is performed 60 times, three times for each experimental run (i.e., condition or level-combination) of all the possible 20 level-combinations among the five levels of the time and the four levels of the bacteria concentration. In this experiment, we cultured different bacterial cell densities with selected diatoms. The pre-culture of ACCC-19853 is used for co-cultivation experiments. The stationary phase bacteria culture was washed twice by centrifugation at 5000 rpm for 5 min and re-suspended in the medium. The co-culture was obtained by adding bacterial cells up to a final density of 1 × 10⁸ CFU/ml⁻¹, 1 × 10⁶ CFU/ml⁻¹, and 1 × 10⁴ CFU/ml⁻¹ to the culture of FACHB-2263 strains immediately after sub-culturing it in a fresh medium with an initial density of approximately 1 × 10⁶ cells/ml.

Meanwhile, the control group set up an algal culture with blank sterile NB or CSI medium. The co-culture systems were kept in a 30 °C constant temperature incubator shaker controller. The flask was incubated in algae culturing conditions for 96 h. Every day, we measured the chlorophyll and cell concentration of treated and control groups using a UV–visible spectrophotometer to represent the symbiotic relationship between algae and bacteria. The optical density (OD) ratio between the experimental and control groups is used to evaluate the OD ratio between the experimental and control groups is used to evaluate the relationship between the algae and bacteria. The treated samples were kept in an ice bath, and vital algae cells were measured immediately by counting the active cells under an inverted microscope (Olympus).

3.2 Second-stage experiment: bacteria concentration and growth phase interactions

The second-stage experiment has two inputs, the growth phase with four levels (control, stationary, exponential, lag) and bacteria concentration with five levels (0, 12.5, 25, 50, 100 ml), and three outputs, CD (x10⁶ cells/ml), DCW (g/l) and TC (mg/l). The full factorial design for this experiment with three replicates for each condition (experimental run) is used. The experiment is performed 60 times, three times for each level-combination of all the possible 20 level-combinations among the five levels of the bacteria concentration and the four levels of the growth phase. In this experiment, ACCC-19853, the crude extract is collected from the bacterial culture described by Jin et al. (2014). After we added these extracts to exudates at three different growth phases (lag, exponential and stationary) of algae cultures, studied in 500 l conical flasks. Each flask contained 250 ml of freshly inoculated N. palea, with a CD of 1.85 × 10⁶ cells/ml, 13 × 10⁶ cells/ml and 14.57 × 10⁶ cells/ml, respectively in the sterilized CSI medium. Bacterial supernatant crude extract dissolved in DMSO is added to a final concentration of 75 μg/ml⁻¹ at a DMSO content of 0.5% (v/v) and the final crude extract is divided into five values (0, 12.5, 25, 50 and 100 ml) that are used for the treatment. The control included 0.5% (v/v) DMSO only. The triplicated flasks for both treatment and control were incubated for 48 h at 28 °C with 100 μmol photons m^-2s⁻¹ and a 12 h light: 12 h dark cycle. Sampling for cell counting by a spectrophotometer is performed every day until the end of the experiment.

3.3 Third-stage experiment: bacteria-alga ratio concentration and time interactions

The third-stage experiment has two inputs, the bacteria-alga ratio concentration with nine levels (10–90, 20–80, 30–70, 40–60, 50–50, 60–40, 70–30, 20–80, 10–90 ml) and the time with five levels (0, 24, 48, 72, 96 h), and three outputs, CD (×10⁶ cells/ml), DCW (g/l) and TC (mg/l). The full factorial design for this experiment with three replicates for each experimental run is used. That is, the experiment is performed 135 times, three times for each level-combination of all the possible 45 level-combinations among the five levels of the time and the nine levels of the bacteria-alga ratio concentration. In this experiment, a cell suspension of ACCC-19853 in the growth phase is diluted in nutrient broth medium of the bacterial culture, at final concentrations of 1 × 10⁸ CFU/ml ^–1are prepared. Meanwhile, we cultured and inoculated exponentially growing cultures of FACHB-2263 into these bacterial cultures at a final concentration of 1 × 10⁶ cells ml. In different ratio of co-culture species were cultured 90:10, 80:20, 70:30, 60:40, 50:50, 40:60, 30:70, 20:80 and 10:90, respectively. The total volume is 100 ml for each experiment. The mixed cultures are incubated under the same conditions described above.

3.4 Further preparation for the experiments

The biomass concentration of microalgal strain was determined by measuring the optical density at a wavelength of 680 nm with a UV–visible spectrophotometer. The calibration curve demonstrated that: (i) there is a strong linear relationship between the concentration of the DCW of the algae and its corresponding OD-680 that can be expressed as follows DCW = 0.3292 (OD-680) + 0.0192 with accuracy measured by R² = 0.9827. (ii) there is a strong linear relationship between the concentration of the CD of the algae and its corresponding OD-680 that can be expressed as follows CD = 19.527(OD-680) −1.1981 with accuracy measured by R² = 0.9912.

In order to determine the algicidal activity of strain ACCC-19853 against FACHB-2263 in all experimental groups, the following formula was used (Sankar et al., 2014). $$\mathrm{I}\mathrm{n}\mathrm{h}\mathrm{i}\mathrm{b}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}(\%)=\frac{(FI-control)-(FI-experiment)}{\mathit{FI}-control}\times 100\%,$$ where FI-experimental is the fluorescence intensity of the treated algal culture and FI-control is the fluorescence intensity of the control algal culture. The CD and TC of all experimental conditions are measured as indicators for algal growth.

The TC is calculated according to Porra (2005). Briefly, 2 ml of the N. palea algae sample is centrifuged at 4000×g for five minutes in a pellet, after that supernatant is discarded, 3 ml of methanol is added to the pellet, and the tube is boiled for 5 min under dark conditions. Then, the sample is transferred into a new centrifuge tube, which covers with aluminum foil and kept on an ice bath, and the lysate is removed by centrifuging the sample at over 5000×g for six minutes. Chlorophyll absorbance’s at 665.2 nm and 652 nm are measured by a UV–Visible spectrophotometer for chlorophyll quantification. Methanol is used as a blank solution. Chlorophyll concentrations are calculated by the following equations (Porra, 2005)

Chlorophyll-a = 16.29 (E-665.2) – 8.54 (E-652).

Chlorophyll-b = 30.66 (E-652) – 13.58 (E-665.2).

TC = 22.12(E-652) + 2.71(E-652).

4.1 Results and discussions for the first-stage experiment

The interactions between co-cultures are used to examine the formation of the growth activities of the diatom under different bacterial cell concentrations at different time intervals that were grew well in laboratory culture. The results in Figs. 1A-1C and Table 1 for this stage demonstrate that:

• The FACHB-2263 grows when increasing the concentration of the ACCC-19853 (10⁴, 10⁶ and 10⁸ CFU/ml⁻¹). The agreements to significant (p < 0.05) decreased on the CD, DCW and TC concerning time (12, 24, 48 and 96 h). The lowest means of the CD and DCW are 0.6889 × 10⁶ cells/ml and 0.0126 g/l, respectively at time 96 h and concentration 10⁸ CFU/ml⁻¹. The TC production generally decreases with increasing the concentrations of the ACCC-19853 strains from 48 h after exposure to the highest concentrations of bacterial strain, resulted in complete growth inhibition.

• The CD, DCW and TC are correlated with the bacterial concentration (treatment) and the time during the co-cultivation condition. The CD and the DCW have the same behavior with the time and the concentration of the bacteria. There is a positive weak linear relationship $(\mathrm{r}=0.39$ ) between the CD (DCW) and the time. There is a negative linear relationship ( $\mathrm{r}=-0.63$ ) between the CD (DCW) and the concentrations of the bacteria. There is a negative linear relationship ( $\mathrm{r}=-0.63$ ) between the TC and the concentrations of the bacteria. There is a positive linear relationship ( $\mathrm{r}=0.77$ ) between the TC and the CD that can be given as follows TC = 3.93 + 3.21CD. The accuracy of this equation is measured by R² = 0.6. There is a positive linear relationship ( $\mathrm{r}=0.77$ ) between the TC and the DCW that can be given as follows TC = 3.77 + 192.27 DCW. The accuracy of this equation is measured by R² = 0.6.

• There is a very low algicidal activity in the concentrations of 10⁴ CFU/ml⁻¹ at 96 h. When the amount-exceeded concentration of 10⁶ CFU/ml⁻¹, the CD intensity in the treatment groups significantly decreases compared to the control group, and the algicidal rates in 12, 24, 48, and 96 h are 9.03, 25.4, 31.5 and 44.3%, respectively for 10⁶ CFU/ml⁻¹, while for 10⁸ CFU/ml⁻¹ are 18.6, 30, 50.3 and 62.8%, respectively. In this co-culture, the bacterial number increases over a period of 96 h, but the efficiency of the FACHB-2263 growth decreases based on the analysis of the concentration of the CD, DCW and TC. The inhabitation efficiency increases dramatically with increasing the concentrations of the ACCC-19853 strains, and it reaches the maximum value at 96 h. The ACCC-19853 strain has algicidal activity when the time increases, the percentage of the CD decreases dramatically. Therefore, we chose an experimental concentration of 10⁸ CFU/ml⁻¹ as the ACCC-19853 strain for the follow-up experiments. Follow-up experiments are needed in many cases to get more information about the behavior of the studied phenomenon and break the confounding among the input factors to effectively estimate their effects (Elsawah, 2016; Elsawah and Qin, 2017).

4.2 Results and discussions for the second-stage experiment

The CD, DCW, and TC content in the FACHB-2263 concerning the ACCC-19853 extract treatment are investigated. In addition, all the phases of the FACHB-2263 cell cycle (lag, exponential and stationary) are treated with the ACCC-19853 strain crude extracted with different concentrations observed in the control cultures. The results in Figs. 2A-2C and Table 1 for this stage demonstrate that:

• When compared with the control, the dose-dependent treated group showed a significant decrease at 24 h after adding the crude extract under which the CD, DCW, and TC continually declined for the duration of the experiment. A prompt CD reduction is observed with the ACCC-19853 extract when higher concentration (100 ml), at lag, exponential and stationary phase the CD contents recorded 0.27, 2.06, and 1.05 × 10⁶ cells/ml, respectively, when compared with the control. For the DCW and TC, the same effect when higher concentrations (100 m1) at 24 h exposure of crude extract are recorded 0.01, 0.04, and 0.02 g/l and 7.08, 13.48 and 11.06 mg/l, respectively when compared with the control.

• There is a strong positive linear relationship ( $\mathrm{r}=0.96$ ) between the TC and the CD that can be given as follows TC = 8.53 + 1.77CD. The accuracy of this equation is measured by R² = 0.92. There is a strong positive linear relationship ( $\mathrm{r}=0.96$ ) between the TC and the DCW that can be given as follows TC = 8.4 + 105.02 DCW. The accuracy of this equation is measured by R² = 0.92. The TC has a positive weak linear relation ( $\mathrm{r}=0.41$ ) with the growth phase and a negative, weak linear relation ( $\mathrm{r}=-0.38$ ) with the time.

• The crude extract at higher concentration (100 ml) inhibited the growth rate of the FACHB-2263 efficiency by 91.2% at stationary phase showed highly active followed by lag phase (88.5%) and exponential phase (82.5%). Whereas the lower concentrations (12.5 ml) exhibited decreased inhibition at the lag phase (25.5%) showed a high growth inhibition rate compared with the stationary and exponential phases, respectively. Bacterial inhibition is too short, or the algae density is still too low to occur because some algae bacteria have been shown to kill senescent algae cells only in the lag phase (Lian et al., 2021).

4.3 Results and discussions for the third-stage experiment

We next examined to understand the ability of the strains ACCC-19853 and FACHB-2263 to grow successfully under controlled co-cultivation under laboratory conditions. The results of this stage in Figs. 3A-3D and Table 1 demonstrate that:

• The algicidal activity of the different ratio concentrations of the cultures is reflected in the intensity of the algal CD even lower concentration of the ACCC-19853 with a higher concentration of the FACHB-2263 showed the algicidal activity compared with the intensity in the control group.

• The CD and DCW have the same linear behavior ( $\mathrm{r}=1$ ). The CD and DCW have a negative weak linear relationship ( $\mathrm{r}=-0.32$ ) with the time. There is a strong positive linear relationship ( $\mathrm{r}=0.92$ ) between the CD and the algae that can be given as follows CD = 0.18–0.55Aalgae. The accuracy of this equation is measured by R² = 0.85 and mean square error (MSE) = 3.63. There is a strong negative linear relationship ( $\mathrm{r}=-0.92$ ) between the CD and the bacteria that can be given as follows CD = 17.1–0.18Bacteria. The accuracy of this equation is measured by R² = 0.85 and MSE = 3.63. There is a strong positive linear relationship ( $\mathrm{r}=0.92$ ) between the DCW and the algae that can be given as follows DCW = 0.003Algae-0.008. The accuracy of this equation is measured by R² = 0.85 and MSE = 0.001. There is a strong negative linear relationship ( $\mathrm{r}=-0.92$ ) between the DCW and the bacteria that can be given as follows DCW = 0.29–0.003Bacteria. The accuracy of this equation is measured by R² = 0.85 and MSE = 0.001.

• The means of the CD and DCW are decrease when the concentration of the bacteria increases, the concentration of the algae increases, and the time increases. The experimental condition (bacteria 10, algae 90 and time 0 h) has the maximum means of the CD and DCW. However, the experimental condition (bacteria 90, algae 10 and time 96 h) has the smallest means of the CD and DCW. The experimental condition (bacteria 40, algae 60 and time 0 h) has the maximum standard deviations of the triplicate of the CD and DCW, i.e., the triplicate of the CD and DCW have significant differences.

• The CD and DCW have the same normalized values. When the concentration of the bacteria is more than (less than) 50 ml, the CD will be less than (more than) 8.27. When the concentration of the algae is more than (less than) 50 ml, the CD will be more than (less than) 8.27. When the concentration of the bacteria is more than (less than) 50 ml, the DCW will be less than (more than) 0.14. When the concentration of the algae is more than (less than) 50 ml, the DCW will be more than (less than) 0.14.

• The percentage of the CD has positive relations with the concentration of the bacteria and time and negative relations with a concentration of the algae. That is, when the concentration of the bacteria increases, the percentage of the CD increases; when the concentration of the algae increases, the percentage of the CD decreases; and when the time increases, the percentage of the CD increases. Growth inhibition efficiency results revealed that when the concentration of the ACCC-19853 and time increase, the percentage of the CD decreases. The algicidal rate of the treatment groups with the concentrations of the bacteria: algae (90:10, 80:20, 70:30, 60:40, 50:50 40:60, 30:70, 20:80 and 10:90) reached 96.4, 88.7, 79.4, 76.2, 70.5, 24.6, 23.7, 21.2 and 17.3%, respectively,

• The concentration, time and the interaction between them have a significant effect (significant difference in means) on the CD and DCW. Post hoc tests show significant differences between the means of any two hours and any two concentrations.

• Moreover, the TC in the algal cells was significantly decreased under the effect at different ratio concentrations of algicidal culture (p < 0.05) from 48 h of treatment, and the maximum inhibitory effect of the bacterial culture is achieved within 96 h exposure. Most of the diatom cells lysed after adding the ACCC-19853 strain culture for 48 h and the microalgae culture faded to white color.