Experiment and Kinetic Modeling of Soil Extract Effects on Dunaliella Primolecta Growth

Recent studies have shown that extracted soil has the potential to enhance microalgae growth. An experiment was conducted, and a kinetic model was developed to understand and predict the growth rate of Dunaliella primolecta with consideration of soil extract effects. Dunaliella primolecta was cultured and mixed with extracted soil from the Raja Musa Forest Reserve, Malaysia. At present, no model of microalgal growth associated with the soil extract effect has been developed to predict cell density and growth rate. A mathematical model was derived to describe the growth rate and cell density production of microalgae with soil extract in the cultured microplate. The prediction model of microalgae concentration agrees with the experimental data, with R 2 ranging from 0.94 to 0.98. Culturing microalgae with 1% of soil extract concentration yielded a significant increment of growth rate. However, the growth rate remained constant at a higher concentration, suggesting the percentage as an optimal value. Thus, the soil extract acts as a growth enhancer that doubles the growth rate of cultured microalgae. A parametric study was conducted to characterize the light intensity and temperature effect on the growth model concerning soil extract effect.

enhance the microalgal growth rate and cell density. The addition of soil extracts to cultured media has significantly affected nutritional values and subsequently increased microalgae concentration. According to 9 , one of the tested marine sediments added into the media has resulted in rapid methane production by the brown algae. Anaerobically treated sediments from the dairy waste area were also used as a nutrient source for bioenergy production by algae 10 . Studies by 11 and 12 have shown that soil extract from aquaculture sludge and forest soil has great potential as the enrichment media for microalgae cultivation.
Therefore, soil extracts demonstrate a promising result in improving the growth rate of microalgae.
A mathematical model is relatively an inexpensive approach for the prediction of microalgal growth. For example, in an upscale microalgae production 13 , the predicted model assisted the optimization of the microalgal processes by monitoring the interaction of influential parameters with the microalgae. Furthermore, the important interaction between influential parameters and cell growth can be quantitatively studied if the mathematical model is accurately modeled 14 .The development of the microalgae growth model closely incorporates the investigation of influential factors that affect microalgal growth. A growth model by 15 was the first model used in establishing the relationship between the nutrient limitation and specific growth rate. Later, 16 modified the Monod formulation by considering internal cell quota measurements in its formulation. Since then, many models were developed based on their formulation, associating substrate concentration with microalgal growth rate in culture media [17][18][19] .
These growth models can be grouped based on the number of their dependent parameters, i.e., single parameter or multiple parameters. The former models have been developed to predict the effect of nutrients with a process that depends on a single parameter, such as temperature 20,21 , light intensity [22][23][24] , pH 25,26 , and CO2 27,28 . Later, in the quest to predict microalgae growth by optimizing operation conditions, multiple parameters were integrated into a kinetic term of the model growth equations [29][30][31][32][33] . The growth models become more complex when the effect of fluid dynamics on microalgal growth is considered. The model required the Navier-Stoke equations and solved using the simulation software 34,35 . Despite its complex solution, the simulation model is favored for its capability to optimize the design of either raceway or other open pond systems [36][37][38] . These models consider fluid velocity, water depth, and atmospheric conditions, composed with kinetic growth parameters in its formulation.
Light intensity and temperature are two parameters generally expressed as a function of temperature in kinetic model expressions 39,40 . However, under the controlled condition in which nutrient composition is constant, the interaction of influential parameters like light intensity and temperature can be studied 41-43 . Alternatively, 44 had reviewed several microalgae simulation models for modeling algal productivity concerning light intensity and temperature effect. They categorized the light intensity simulation models into three types; average light, light gradient, and light gradients and short cycles. Furthermore, the categorized models were defined as a coupled model if the effect of temperature is considered in the model and known as an uncoupled model if contrary.
In the present study, the growth model was developed, focusing on the simulation of microalgal growth affected by the soil extract enhancer. The model was validated and compared with the experimental data.
The experimental data is the first published data of the microalgae growth with soil extract effect, collected at Raja Musa Forest Reserve, Malaysia. Furthermore, a parametric study was performed for light intensity and temperature effect on the growth model. These parameters were considered in the modeling due to their importance in assessing outdoor algae cultivation optimization. An open-source tool package environment, Python, was used to model and simulate the growth model. The growth model results were obtained on an Intel Core i5, 8 GB RAM, laptop computer.

Materials and methods
Experimental data. Two kg of soil was collected from the Raja Musa Forest Reserve, Malaysia (3°26ʹ45.2″N101°19ʹ20.9″E) at three (triangle) 1-m distance points. Sampling was permitted by the Hulu Selangor Forest Department of Malaysia. The soil was oven-dried at 60°C, and subsequently grind, sieved, and homogenized. The extraction process known as aqueous extraction treatment was used on the dried soil samples 45 . Milli-Q (MQ) water was used as a solvent to prepare the soil extract (SE). The soil samples were autoclaved at 105°C for 1 hour. The temperature-treated samples were then centrifuged at 700 × g for 15 minutes, filtered through a 0.7 μm glass fiber filter and stored at 4°C.
Dunaliella primolecta used in this study was isolated from Kapas Island, Terengganu, Malaysia. Conway media was prepared from five basic solutions as described by 46  The microplate-incubation technique 11 was conducted for the microalgae at 5 different SE volumes and concentration; 1, 2, 3, 6, and 10 mL, with the percentage (%) of 0%, 0.5%, 1%, 1.5%, 3%, and 5%, respectively. Media without SE was used as the control media in another microplate. The microplates were incubated for nine days, and the cell concentration was determined by cell counting via optical density (OD) at 680 nm for every 24 h using the microplate reader Infinite M200 PRO, representing cell density (cells•mL -1 ). The results of the microalgae density in different SE concentrations are tabulated in Table 1. Each sample was measured in triplicate, and the average value was acquired. plotted in the graph to show the differences between with and without soil extract effects regarding cell density. The soil extract interaction significantly affected D. primolecta growth with the highest density (7.41 10 6 cells•mL -1 ) on day 8 from the 1% SE concentration, i.e., twice the growth of the control media density result. The highest cell density for control media is 3.74  10 6 cells•mL -1 . It is noticed that the microalgae density is decreased after day 8 for all soil concentration variations, including from the control media.
Microalgae kinetic model. Having a simulation model for algae growth is advantageous, as it is more economical to study, compare, and upscale the production based on the effect of algal growth parameters.
The present work is concerned with the kinetic model of microalgae growth under SE influences, where light intensity and temperature are constant. The growth of D. primolecta is described by the growth model (simple rate laws) as in Equation (1) and revised using the Monod equation to include other parameters considered in the present work. This is done by considering the specific growth rate constant, μ, in Equation (1) as a function of a new SE parameter, with the inclusion of light intensity (LI) and temperature (T) effects, shown in Equation (2).
where is the microalgal growth rate, X (mL -1 ) is cell concentration, t (days) is time, and  (day -1 ) is a specific growth rate constant. The specific growth rate constant was calculated from the observed data in Table 1, using Equation (3) as follows, and the result is given in Table 2.
where 1 and 2 are the cell density on days t1 and t2, respectively. The t1 is taken at day 1, while t2 is at Here, is the maximum specific growth rate under optimal condition, ( ) is the effect of suboptimal for soil extract, ( ) is the effect of suboptimal for light intensity, and ( ) is the effect of suboptimal for temperature.

Simulation of soil extract influences. Equation that reflects the SE effect on the microalgal growth is
based on the Monod equation and given below.
where (mL) is the soil extract concentration and (mL) is the soil extract half-saturation constant.
The is determined from the specific growth rate versus the SE concentration graph, where the data are taken from Table 2 and plotted in Figure 2.
Referring to Figure 2, the maximum specific growth rate is 0.487 day -1 at 2 mL (1%) SE concentration.
The half-saturation dashed line at 0.5 is where the SE concentration equals the half-saturation constant growth by 50%. The 0.5 is equal to 0.393 day -1 and yields equal to 0.5 mL. Figure   2 shows that any value higher than 1% soil concentration will result in the decline of growth rate, suggesting that the 2 mL (1%) SE concentration as the optimal value. In evaluating the optimal soil extract concentration value, the fixed value of 25°C temperature is under a fixed light intensity of 33.75 μmol•m -2 s -1 . and applied to bacterial growth by 49 and applied to microalgal growth by 41 . Thus, the model has a great potential to be coupled with a physical model in predicting the temperature in a raceway or a photobioreactor to upscale.
Light is regarded as the primary factor that significantly affects microalgal growth. The light intensity effect of the average light intensity is expressed and shown in Equation (6). Even though the light intensity is dependent on the depth, it is tolerable to assume that the depth effect is negligible because a microplate was used in the experiment.
The equation is used to simulate the effect of light intensity on the growth of D. primolecta assumed in a well-mixed system, where (μmol•m -2 s -1 ) is light intensity, (day -1 ) is the initial slope of the light response curve, (μmol•m -2 s -1 ) is light intensity for which growth is maximal (with respect to light), (day -1 ) is the maximum growth rate for the optimal light intensity and temperature (°C).
Simulation of temperature influences. In a well-mixed system, the temperature is uniformly distributed in the culture media. Thus, the temperature effect on microalgal growth rate is defined by the optimal temperature for growth and the minimum and maximum water temperature, as described in Equation (7). with where (°C) is water temperature, (°C) is the temperature below which the growth is assumed to be zero, (°C) is the temperature above which there is no growth, (°C) is the optimal temperature at the maximal growth rate. The equation could simulate at any temperature range, i.e., above and below the optimum temperature (Mayo 1997).
Referring to Equation (4) and substituting it with all terms in Equation (5), (6), and (7), a complete kinetic model is yielded, representing the SE, light intensity, and temperature influences on microalgal growth, Equation (10).
The governing equation is established by substituting Equation (10) into Equation (2), as shown in Equation (11).
Equation (11) Table 3. Parameters Values of the growth model Figure 3 shows light intensity limitation, part of the terms in Equation (11). The SE and temperature are fixed at 2 mL and 25°C, respectively. The light intensity is bound between 5 to 1700 μmol•m -2 s -1 . A high increase in the growth rate can be observed between 5 and 75 μmol•m -2 s -1 . At these lower intensities of light, where the growth rate is usually proportional to light intensity, photosynthesis activity is limited by the rate of photons captured. Light intensity reaches a saturation condition, and the growth rate is maximal when algae become lightly saturated 44 . This condition is reflected in the graph, where the light intensity term gives constant (between 0.691 to 0.702 day-1 ) growth rate at 450 μmol•m -2 s -1 and higher. This indicates an optimum light intensity point regarding the maximum growth rate, suggesting that the optimum light intensity value is not greater than 450 μmol•m -2 s -1 . Nevertheless, the light intensity term in Equation (10) could not simulate the decrease rate of microalgae due to the deactivation of protein in photosynthesis 50 .   and media with SE concentration. Figure 5 shows the growth of D. primolecta at different soil extract concentrations, 0%, 0.5%, 1%, 1.5%, 3%, and 5%.

Results and discussion
The relationship between D. primolecta growth and SE concentration can be described by the present growth model. The model output agrees well with the experimental data over a wide range of soil concentration percentages, where the lowest R 2 equals 0.94, and the highest R 2 equals 0.98. Furthermore, from Figure 5, the model accurately predicts the cell density value at the initial stage and the maximum density value. Meanwhile, Table 4 shows that the deviation between the growth model and experimental result at maximum density is too small. However, a slight discrepancy is noticeable at the internal stage In all soil extract concentrations, the growth curve exhibits the well-known exponential curve growth. As expected, the organic matter in SE contributes to the higher growth rate of the microalgae. It is observed that the SE has a significant effect on the cell density of D. primolecta. From the growth curve in Figure   5(a)-(d), a lag phase is observed on days 1-4, and the algae started their log phase after day 4 until day 8.
During the lag phase, the cell densities in the SE and control media exhibit are almost similar, revealing that the nutrient concentration from both cultured media could promote the growth of D. primolecta at almost similar rates. However, when the log phase started after day 4, the higher nutrient content in the SE media supported the higher rate of cell multiplication demand. This pattern can be observed from the graphs by comparing the control media curve with the SE growth curve, with a significantly higher rate in terms of cell density observed from day 4 until day 8, during the log phase. After day 8, D. primolecta growth entered the stationary phase and achieved its maximum nutrient intake.  Effect of light intensity on a microalgae growth model. The parametric study shows that the growth model in Figure 6(c) obtained comparable results with the experimental data at 33.7 μmol•m -2 s -1 . For light intensity that is lower than 33.7 μmol•m -2 s -1 , the model shows a lower growth rate with cell density that did not exceed the maximum cell density (7.41  10 6 cell/mL), as shown in Figures 6(a)   temperatures was studied on microalgae growth using Equation (11) to analyze its effect with constant soil extract concentration (1%) and light intensity (33.7μmol•m -2 s -1 ) values. The growth pattern of D.
primolecta is observed at 5 different temperatures: 10°C, 17°C, 25°C, 31°C, and 33°C, as shown in Figure   7 (a-e). The equation can describe the temperature effect either below or above the optimal temperature. Figure 7 shows that at 25°C, i.e., a similar environment temperature, a good correlation between the growth model and experimental data is noted, acquired by Equation (11). Meanwhile, lower growth rates and cell densities are observed in low temperatures, as illustrated in Figures 7(a) and (b). Subsequently, at temperatures exceeding optimal value, the microalgal growth rate decreased, as depicted in Figures 7(d) and (e). This is generally due to the effect of enzyme or modified proteins involved in the photosynthetic process affected by heat stress 52 .

Conclusion
In this study, a growth model of D. primolecta with soil extract (SE) effects was developed. The Monod model was integrated to consider the soil extract, light intensity, and temperature effects in the growth model. The developed model has permitted the obtention of the cell density and growth rate at any soil extract concentration. The model growth rate compared well with the experimental data, with R 2 ranging from 0.94 to 0.98. The maximum growth rate for microalgae with soil extract is 0.487 day -1 , i.e., double growth compared to the growth rate without SE (0.299 day -1 ). The optimum light intensity and temperature of 33.75 μmol•m -2 s -1 and 25°C have been verified in the parametric study.