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Abstract
The radiation characteristics of microalgae are of great significance for the design of photobioreactors and ocean optical remote sensing. Yet the complex structure of microalgae makes it difficult to theoretically predict its radiation characteristics based on traditional Mie theory. In this work, taking Chlamydomonas reinhardtii as an example, a multi-component cell model with a complex structure is proposed, which considers the organelles and shape of microalgae, and the volume change during the production of Chlamydomonas reinhardtii lipids. The theoretical calculation is carried out using the discrete dipole approximation method, and an improved transmission method is used for experimental measurement. The experimental data are compared and analyzed with the multi-component complex structure model, the homogeneous sphere model and the coated sphere model. The results show that the calculation accuracy of the multi-component complex structure model is higher, the error of the scattering cross-section is reduced by more than 8.6% compared with the homogeneous sphere model and coated sphere model, and the absorption cross-section and the scattering phase function are in good agreement with the experimental results. With the increase of lipids, the absorption cross-section and the scattering phase function vary slightly. However, the scattering cross-section has an observed change with increasing wavelength. In addition, the theoretical calculation error can be reduced when the influence of the culture medium is taken into account.
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1. Introduction
Microalgae is a promising raw material for biomass energy, which is widely used in the fields of biosequestration and biodiesel [1,2]. The large-scale cultivation of microalgae requires a photobioreactor, which is an important equipment for the industrial production of microalgae. The radiation properties of microalgae mainly include absorption cross-section, scattering cross-section, and scattering phase function. Studying the radiation characteristics of microalgae cells will provide basic data and theoretical support for the quantitative analysis and optimization of the transport process in the photobioreactor. Besides, it can help improve the signal recognition accuracy of real-time monitoring of the marine surface environment by satellite remote sensing, and reduce the interference of the signals produced by marine microorganisms.
Chlamydomonas reinhardtii is a kind of microalgae with a wide range of uses and a typical structure, commonly used in biological carbon sequestration and the processing and production of nutrient by-products. It possesses the advantages of strong adaptability, fast growth speed, and strong reproduction ability, which is capable of accumulating a large amount of lipids in a short period. It is likewise one of the feedstocks for biohydrogen production and biodiesel [3,4]. Through photosynthesis, Chlamydomonas reinhardtii can accumulate large amounts of lipids. Moreover, Chlamydomonas reinhardtii has high nutritional and commercial value due to its high lipid content and good quality. To realize the lipid production of Chlamydomonas reinhardtii, it is necessary to carry out reasonable cultivation and regulation, so it is important to study the radiation characteristics of Chlamydomonas reinhardtii with different lipid contents for its cultivation and growth monitoring.
In the theoretical calculation of radiation properties of microalgae or marine unicellular organisms, they are simplified to a single sphere or nucleus-shell sphere without considering the influence of the cell microstructure on the overall radiation properties. However, the error caused by this is not negligible. Zhai and others [5] studied the radiation properties of Emiliania huxleyi, modeled its radiation properties based on the symmetric and asymmetric morphology of microalgal cells, and performed a comparative analysis based on the DDA (discrete dipole approximation) method. Dong et al. [6] investigated the effects of the density and length of external spines of the spiny spherical alga Emiliania huxleyi and compared the spiny model, the mean model, and the shell sphere model horizontally, and the results showed that the external structure had a significant effect on the radiative properties of Emiliania huxleyi. Heng et al. [7] simplified the ring-distributed microalgae of Collinia into equivalent coated shell balls by projection. The internal model of microalgae was usually constructed with the assumption that the cell structure was a fixed optical constant, and its radiation characteristics were calculated according to the equivalent medium theory. It was found that with the increase of monomer number and size parameters, the deviation of calculation results will be larger. Hoeniges et al. [8] established volvox as a multi-sphere model with large balls wrapped in small balls and set the optical constant of microalgae cells as 1.355 + 0.004i. The model was predicted using the superimposed T-matrix method and Monte Carlo ray tracing (MCRT) method. The results showed that both the number and volume fraction of microalgae agglomeration affected the overall radiation characteristics. Bhowmik et al. [9] studied the model optimization during the theoretical calculation of spherical microalgae cells and obtained the optical constants of the internal components of microalgae cells (such as cytoplasm, chloroplasts, nuclei, mitochondria, and metabolites, etc.) through equivalence. Because the extraction of the internal tissue of a single cell is extremely complicated, and the optical constant is difficult to obtain accurately, there will still be some deviation between the experimental value and the construction of microalgae cells by this method. Because of the difficulty in obtaining optical constants of internal components, the input parameters of physical properties of existing cell models are generally set according to empirical values, and most microalgae models are simplified into sphericity for calculation, ignoring the influence of internal and external structures, resulting in significant deviations between theoretical calculation results and real values of radiation properties. Therefore, it is very important to construct a precise model to consider the internal and external microstructures of algae cells to improve the prediction accuracy of their radiation properties.
In this work, the effects of cell microstructure on radiation characteristics of Chlamydomonas reinhardtii cells were analyzed from both internal and external aspects. Based on the microstructure of microalgae, a multi-component cell model with complex structure was proposed, which considered the internal organelles and external morphology of microalgae. Three different models of the lipid-free state, lipid state, and lipid-rich state of Chlamydomonas reinhardtii were established by using this modeling method. The absorption cross-section, scattering cross-section, and scattering phase function of the cell model were calculated theoretically by the DDA method. The theoretical results were compared with the experimental data, the transverse analysis was carried out with a variety of simplified models, and the influence of the culture medium on the theoretical results of the proposed model was considered.
2. Structural morphology and modeling
Chlamydomonas reinhardtii has a complex structure, with external structures such as flagella and internal components such as chloroplasts, nuclei, mitochondria, lipid aggregates, and vacuoles [10]. Naturally cultured Chlamydomonas reinhardtii are often egg-shaped or ellipsoidal, with a fixed shape due to the support of the cell wall, thus facilitating swimming (e.g., Figs. 1(a)-(g)).
Fig. 1. Segmentation model of wild-type Chlamydomonas reinhardtii cell tomogram and illustration of Chlamydomonas reinhardtii movement analysis [10,11]. (a) 3D tomography reconstruction of Chlamydomonas reinhardtii, (b-g) schematic diagram of organelles distribution in Chlamydomonas reinhardtii, (h) schematic diagram of flagellate movement analysis, and (i) electron microscopic picture of cell wall.
In this modeling process, the shape of Chlamydomonas reinhardtii was created as egg-shaped to approximate the external morphology of the actual microalgae. In the internal structure, chloroplasts are cup-shaped and roughly positioned concentrically with the lower part of the Chlamydomonas reinhardtii cell (e.g., Fig. 1(b)). The mitochondria are distributed discretely and adhesions occur between different mitochondria (e.g., Fig. 1(c)). The flagella of Chlamydomonas reinhardtii are mainly used for cell motility. The flagellum tends to be morphologically variable and the flagellum plucks water to generate thrust, which drives the cell movement. The analysis revealed that, on average, the flagellar motility was mostly flat on both sides (e.g., Fig. 1(h)). The nucleus is a large agglomerate, located at the top side of the cell (Fig. 1(e)). The vacuoles are multiple agglomerates, similar to the nucleus, also located on the apical side of the cell (Fig. 1(f)). The intracellular lipid of Chlamydomonas reinhardtii was distributed discretely, parallel to the cell wall (Fig. 1(g)).
As mentioned above, the surface morphology of Chlamydomonas reinhardtii chloroplasts in their natural state is uneven, and more complex models are needed to describe their shape to represent the morphology of chloroplasts. Therefore, the standard deviation of 0.05 Gaussian stochastic sphere method was used to model its overall morphology (Gaussian stochastic sphere is a stochastic statistical model often applied to model irregular particle shapes [12,13]). For the nucleus, a Gaussian stochastic sphere with a standard deviation of 0.1 was used. The vesicles are more discrete and suitable for completion using multiple Gaussian combinations. The distribution of lipids and mitochondria is discrete and can be approximated by using randomly distributed agglomerates to mimic their distribution state; agglomerate adhesion occurs during modeling, but this is also more consistent with the factual distribution. The final model morphology is shown in Fig. 2, where (a) and (b) the cell wall and cytoplasm are omitted for the convenience of showing the internal organelles. The overall morphological features are shown in Fig. 2(c).
Fig. 2. Schematic diagram of the theoretical calculation model of Chlamydomonas reinhardtii. (a),(b) Lipid state Chlamydomonas reinhardtii model, (c) the overall appearance of Chlamydomonas reinhardtii, (d) the lipid-rich state model, (e) the lipid-free state model, (f) the homogeneous sphere model, and (g) the coated sphere model of Chlamydomonas reinhardtii.
3. Chlamydomonas reinhardtii cell model and theoretical model
3.1 Organelle and cell component parameters
As shown in Table 1, statistics on the volume ratio and optical parameters of the cell fractions of Chlamydomonas reinhardtii are presented. The parameters related to the cell wall are not provided in the table, mainly due to the limitations of the TEM technique, where the cell wall cannot be represented, but its thickness can be obtained by measuring electron microscopic sections [14]. The average thickness of the cell wall of 0.115 µm was obtained by averaging multiple measurements as shown in Fig. 1(i) for the electron microscopy images and scale of Chlamydomonas reinhardtii [11]. The radiative properties of microalgae are closely linked to the particle size of microalgae, as shown in Fig. 4 in the experiments. The average particle size of Chlamydomonas reinhardtii in the nitrogen-free phase was 3.097 µm with a volume of 124.43 µm3, and the absolute size was then inferred using the proportional relationship between the volumes of the components.
Table 1. Parameters and volume ratios of each fraction of Chlamydomonas reinhardtii
The refraction index and absorption index are important basic parameters for studying radiation properties. It is necessary to consider both environmental factors and microalgae factors when calculating the radiation characteristics of Chlamydomonas reinhardtii. Microalgae live in water (culture medium), and the refractive index of water is generally considered to be constant, but in practice, the refractive index of water will change with the increasing wavelength [15,16], so the refractive index of water with continuous wavelength is used to calculate. The refraction index is mainly related to each organelle component. Although it is very difficult to extract and measure the refraction index of a single organelle at continuous wavelength through experiments, the relative value changing with wavelength can still be used to calculate [17], to get closer to the real situation. The absorption of microalgae is mainly dominated by pigments, and once determining the pigment type, pigment mass fraction, and water volume fraction, the absorption can be calculated from the pigment content in dried microalgae. The absolute absorption coefficient k of chloroplasts, on the other hand, can be calculated by [9]:
In the above formula, ρdm is the density of the main pigment contained in the chloroplast. The dry matter density is 1400 kg/m3 [18], and the dry mass fraction of chlorophyll a, chlorophyll b, and carotene is 55.8 g/kg, 27.9 g/kg, and 17.9 g/kg, respectively [9]. In the formula, x is the volume fraction occupied by water in microalgae under normal conditions, which is usually 0.78, and E is the specific spectral absorption coefficient of each pigment. The data used in this study come from [19]; Wi is the dry weight ratio of various pigments in microalgae cells. Wt is the volume ratio of chlorophyll-containing pigment in microalgae cells.
Proteins, lipids, and carbohydrates in microalgae have the same light absorption. Although the ratio of the material content of various organelles is difficult to obtain, it can be calculated from the organic matter content of microalgae as a whole, using Maxwell-Garnett mixing theory. The absorption index parameters for proteins, lipids, and carbohydrates used therein were derived from measurements by the double optical pathlength transmission method and the ellipsometry method (DOPTM-EM) [16]. The method can also be used for the analytical calculation of the equivalent refractive indices of homogeneous spheres and coated spheres as well as absorption indices. The Maxwell-Garnett mixture theory calculation equation [20] is as follows:
In the above equation, εb = mλ2 denotes the dielectric constant corresponding to the component with the highest volume ratio in each mixed component of the model, and Fi denotes the volume fraction occupied by the component of microalgae in each part of the model structure.
It can be observed from Fig. 3(a) that the refraction index of each part of the model decreases with wavelength, which is similar to the changing trend of the refraction index of the main components of microalgae. The range of values for the refractive indices of the cell wall, cytoplasm, mitochondrion, and chloroplast are 1.36-1.53 [18], 1.36-1.49 [18], 1.36-1.40 [18], and 1.36-1.40 [18], respectively. Refractive index values for the nucleus range from 1.36 to 1.40. The refractive index of the flagella changes from 1.39 to 1.44, while the refractive index of the lipid varies from 1.47 to 1.50 [17]. The vacuole has refractive indices that range from 1.34 to 1.37. The refractive index of the homogeneous sphere and coated sphere varies in the range of 1.38-1.42 and 1.37-1.41, respectively. In Fig. 3(b), the homogeneous single-sphere model and the coated sphere model have the same absorption peak position as the photosynthetic pigment, and the absorption of the two models is also relatively close in numerical value, mainly because the model considers the same pigment type and content in the equivalent calculation.
3.2 Theoretical model
DDA is an excellent method for the theoretical calculation of discrete radiation properties, which can flexibly deal with scattering particles of arbitrary geometry and composition. The basic principle of DDA is to use a large number of tiny dipole stacks to show the structure and shape of the calculated particles and use the polarization effect of the dipole interaction to obtain the dipole moment of the cubic lattice by solving the linear equations, to calculate the numerical method of electromagnetic scattering and absorption. The ADDA v.1.5.0, developed by Maxim A. Yurkin and Alfons G. Hoekstra [21], was used in this case.
In the DDA calculation, the number of dipoles per wavelength is required to be greater than 10, and the minimum dipole in the model parameters used in this theoretical calculation is 25 nm. Where |m|kd is an important parameter in the calculation process, ADDA requires that the parameter |m|kd should be less than 0.5 [6], m is the optical constant of the particle, k = 2π/λ, and d is the size of the cubic lattice. The maximum value of |m|kd in this theoretical calculation is 0.459. Since the scatter is not symmetrical, the result of the average orientation was calculated with the parameters of 16 × 8 × 16 after many validations for convergence.
The calculation formula for radiation characteristics is as follows [21]:
The absorption cross section is Cabs, the attenuation cross section is Cext, and the scattering cross section is Csca. In the above equation, Einc(r) is the incident electric field, E(r) is the total electric field, and χ(r) is the magnetic susceptibility of the medium at r. Usually, the result calculated by ADDA is not renormalized. It is necessary to normalize the phase function to satisfy the following formula:
4. Experimental measurement
To verify the accuracy of theoretical calculations and to further explore the influencing factors of the radiation characteristics of microalgae, experimental measurements are necessary. In the present experiments with Chlamydomonas reinhardtii, the number density of Chlamydomonas reinhardtii was obtained by counting with a CCD camera optical biomicroscope (model UB203i) using a counting frame (frame size 20 × 20 mm, sample volume 100 ul). Figure 4 shows the micrographs and cell size distribution of Chlamydomonas reinhardtii, resulting in an average diameter of 4.046 µm. The particle size distribution of microalgae is an extremely important parameter for the comparison and validation of experimental theoretical calculations. The size of Chlamydomonas reinhardtii was analyzed by fitting the diameter to a circle or by fitting the distribution of the short and long axes to an ellipse using Image View software.
There are various methods for measuring the radiation properties of microalgae, and to fully eliminate the effect of reflection errors between media and obtain more accurate results, the attenuation and absorption cross sections and the scattering phase function of microalgae suspensions were measured in this work using an improved transmission method [22].
Among them, the normal-hemispherical transmittance experimental measurements were made using an integrating sphere (RTC-060-IG, Labsphere, USA) and a lock-in amplifier and monochromator-based measurement system (Omni-DR830-SDU, Beijing Jolyhan Light Instruments Co., Ltd.). The normal-normal transmittance was measured by a spectroscopic ellipsometer with a resolution of 0.1 nm (RC2-DI, J. A. Woollam, USA). The thickness of the microalgae diluent vessel glass was 1630 µm and the optical range was 9800 µm. The scattering phase function was taken at a wavelength of 515 nm and the angular range was 0.1-150°, which was measured by a multi-angle polarized light scatter (LISST-VSF, Sequoia Scientific, USA).
5. Results and discussion
Figure 5 compares the calculation results of the radiation characteristics using the multi-component complex structure model of Chlamydomonas reinhardtii, the homogeneous sphere model, and the coated sphere model at 400-900 nm wavelength, respectively, and verifies with the experimental results. Figure 5(a) shows the change of absorption cross-section varying with the wavelength. The results of the multi-component complex structure model are in better agreement with the experimental results, and the peak and valley values of the curve are consistent. The absorption peaks calculated by the multi-component complex structure model, homogeneous sphere model, and coated sphere model are all concentrated around 450 nm and 670 nm. The first absorption peak is wide and mainly caused by the joint action of chlorophyll a, chlorophyll b, and carotene, while the second absorption peak is mainly determined by chlorophyll a [19,23]. After 700 nm, the pigment effect disappears and is replaced by the absorption of lipids, proteins, and carbohydrates. The average relative error of the multi-component complex structure model is 11.02%, the error of the coated sphere is 19.53% and the error of the homogeneous sphere is 21.63%. The first absorption peak of the homogeneous sphere and coated sphere is different from the experimental value, but the multi-component complex structure model is in good agreement. This is mainly because the multi-component complex structure model considers the specific location and morphology of the chloroplast and concentrates the main chlorophyll in the chloroplasts in the model, and its structure is closer to the actual distribution of cell structure.
Fig. 5. Theoretical and experimental results of radiation characteristics of Chlamydomonas reinhardtii. (a) Theoretical calculation and experimental results of absorption cross-sections, (b) scattering cross-sections, and (c) scattering phase function for different models.
Figure 5(b) shows the variation of the scattering cross section with wavelength, and the trough values are concentrated around 450 nm and 680 nm. The results show that the error of the multi-component complex structure model is within 15% at the 400-500 nm band and 570-700 nm band, and the overall average relative error is 10.77%. The average relative error of the coated model is 20.3%, while that of the homogeneous model is 16.47%. The deviation between the multi-component complex structure model and the experimental results at the 500-600 nm band is mainly because the overall distribution of the microalgae model tends to be modular compared with the actual microalgae, resulting in a large difference in the refractive index between components, electromagnetic scattering interference between components, and higher scattering in some bands. The multi-component complex structure model reduces the deviation caused by the interference of larger components because of the comprehensive consideration of the influence of components.
Figure 5(c) shows the change of scattering phase function with the increase of scattering angle. It can be seen from the figure that the homogeneous sphere oscillates the most due to the interference of particles, followed by the coated sphere model, and the multi-component complex structure model gradually flattens out with the increase of scattering angle. Because the particle size of microalgae is much larger than the wavelength, the scattering phase function has strong forward scattering. From the perspective of a comprehensive comparison of the three models, the three models almost coincide between 0 and 10° because they use the same basic parameters, but all of them have the oscillation phenomenon that is common in theoretical calculation of small and medium particle size. With the increase of scattering angle, the resonance of the multi-component complex structure model gradually disappears after 60°. Compared with the homogeneous model and the coated model, the multi-component complex structure model considering the actual shape is closer to the scattering phase function distribution of the experiment, and the curve is smoother after 45° when it almost gets rid of the influence of resonance, which is in good agreement with the experimental results. After 70°, the multi-component complex structure model gradually approximates the experimental result curve. After 100°, it is almost consistent with the experimental value and reaches the extreme value at 180°. The experimental results disappear after 150°, which is caused by the limitation of measuring instruments, and the phase function values of all angles cannot be measured completely.
Figure 6 shows the comparison of the effects of different lipid contents on radiation characteristics of Chlamydomonas reinhardtii. They are the lipid-free state, lipid state, and lipid-rich state, respectively. As shown in Fig. 6(a), under the three conditions with different lipid content, the absorption cross sections of the three states increased slightly with the lipid content, of which the most was the lipid-rich state, followed by the lipid-free state. This is mainly because the absorption index of lipids is the largest and the absorption cross-section increases with the increase of lipids. At 400-450 nm wavelength in the figure, the absorption cross-section of the lipid-free state has a slight fluctuation, which is mainly influenced by the structure of the model. Figure 6(b) shows the scattering cross-section results of the three states. The valley value of the scattering curve is concentrated around 450 nm and 680 nm, which coincides with the peak value of the absorption cross-section. The changes in lipids are mainly reflected in the wavelength ranges of 350-400 nm and 600-750 nm. Because the pigment has little influence in this wavelength range, the overall fluctuation of the curve is reduced and the overall stability is more stable under the influence of lipids. The calculation results of the scattering phase function of the three states are shown in Fig. 6(c). When the scattering angle is 0°, the scattering image function has the largest value. The lipid-free state and the lipid state is almost the same, while the difference between the lipid-rich state is larger. It can be seen that a small amount of lipids has little effect on the scattering phase function, while a large amount of lipids will enhance the scattering phase function.
Fig. 6. Theoretical calculation results of radiation characteristics of different lipid state models of Chlamydomonas reinhardtii. (a) Absorption cross-section, (b) scattering cross-section, and (c) scattering phase function in different lipid states.
6. Conclusions
To summarize, a multi-component complex structure cell model considering microalgae organelles and shapes is proposed by taking Chlamydomonas reinhardtii as an example to more accurately calculate the radiative properties of algal cells. The results show that compared with the homogeneous sphere model and the coated sphere model, the multi-component complex structure model fully takes into account the actual microstructure distribution of microalgae components, and eliminates the scattering errors. The accuracy of the scattering cross-section of the multicomponent complex structure cell model is improved by 8.5% and 10.6% compared with that of the homogeneous sphere model and the coated sphere model, respectively. In addition, under the premise of consistent input of basic parameters, the absorption cross-section accuracy of the multi-component microstructure model is improved by 9.53% and 5.7% compared with the homogeneous sphere model and the coated sphere model, respectively. The accurate modeling makes the scattering phase function of the multi-component complex structure cell model more consistent with the experimental results. This work provides a new idea for the modeling of typical particles such as cells and data and theoretical references for their high-precision theoretical calculations.
Funding
National Natural Science Foundation of China (52106080); Fundamental Research Funds of Shaanxi Key Laboratory of Artificially-Structured Functional Materials and Devices (AFMD-KFJJ-22206).
Disclosures
The authors declare no competing interests.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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