Localization analysis of intercellular materials of living diatom cells studied by tomographic phase microscopy

Observation of living cells using tomographic phase microscopy (TPM) provides unique information on optical properties of cell components, although the interpretation of living cell TPM data requires further research.¹ Information on the refractive index (RI) of the observed objects can be obtained as three-dimensional (3D) data.² Rapid progress in computer technology has enabled the generation of large datasets using holotomography, and its various successful applications have been reported in the literature.³ In fact, while one pixel of a TPM image is 100–200 nm in size, more than several millions of pixels are contained in several tens of μm³ of space, which is a typical observation area in TPM.

Among the biological applications of TPM, imaging of red blood cells (RBCs) has been most popular.⁴ For example, O'Connor et al. applied TPM techniques to distinguish healthy RBCs from diseased RBCs.⁵ Kucharski and Bartczak studied the effects of low-level red light on RBC dynamics.⁶ Cardenas and Mohanty studied the thickness of RBCs using a combination of quantitative phase imaging (QPI) and optical tweezers.⁷ Furthermore, the flat shape and size of RBCs make them ideal samples for TPM.⁸ Other animal cells, including cancer cells, have also been studied using TPM.⁹ In a recent example, Karako et al. used TPM supported by deep learning to identify apoptosis and necroptosis in murine cancer cells,¹⁰ while Verduijn et al. performed quantitative imaging of cancer and sperm cells using a simultaneous dual-wavelength holographic module.¹¹ 

Diatoms, which are one of the major photosynthetic planktons, are attractive targets for TPM observation, because the diatom cells have various unique shapes based on their nanoporous silica shells known as frustules.¹² Diatoms range from several micrometers to several hundred micrometers in size, and TPM techniques can be applied in various ways to analyze the numerous shapes and sizes of diatom cells. For example, Isil et al. performed phenotypic analysis of diatoms using TPM combined with flow cytometry.¹³ Fan et al. succeeded in visualizing subcellular structures of diatoms by establishing an efficient algorithm.¹⁴ Soto et al. compared diatom cells and other objects using 3D quantitative imaging.¹⁵ Ma et al. reconstructed 3D skeleton structures of diatoms using sectioning image sequences,¹⁶ while Merola et al. compared the 3D structures of RBCs and diatoms in detail.¹⁷ 

In this work, we quantitatively investigated localization of cell components by analyzing TPM 3D images of living diatom cells.¹⁸ As an example of diatoms, which had disk like symmetric shapes, isolated Thalassiosira sp. was employed. One of the aims of this work was to visualize the distribution of intercellular components of these symmetric shape cells. We propose vertical cross sections of the observed cells were obtained using the 3D TPM images. In a pilot study by Xiu et al., a TPM technique was used to visualize distribution of intercellular components of RBCs via X–Y RI slice analysis although numerical analysis of the slices was not demonstrated.¹⁹ In our work, numerical analysis of the RI distribution was carried out using root mean square (RMS) and Moran's I analysis.^20–22 This is the report to quantitatively/statistically analyze insider structures of living cells based on physical information of cross sections of TPM data. Although we employed diatom cells, this approach can be applied to various biomaterials including animal cells.

The other purpose of this work was to evaluate cell volume based on TPM images. Although the volume of living cells could be estimated based on TPM images, there are unknown factors to consider the results. For example, the bottoms of cells that are in contact with the glass chamber are typically obscured, which may affect the estimation of cell volume. To evaluate the cell volumes obtained by TPM, similar cells were observed by scanning electron microscopy (SEM) after glutaraldehyde (GA) fixation. Because our diatom cells had disk-like shapes, it is easy to manually estimate their volume from SEM images. Our approach provides fundamental knowledge to establish biological applications of TPM, particularly for the study of living diatom cells.

Thalassiosira sp. was isolated from seawater collected in Shimoda, Japan. The isolated specimens were amplified by subculture with Guillard f/2 culture medium in 30 ml of Daigo artificial seawater.²³ 

For TPM observation, 3 ml of the cell suspension was transferred onto a Tomodish (Tomocube, Inc., Daejeon, South Korea). Tomocube (HT-2, Tomocube, Inc.), a commercially available TPM instrument, was operated at room temperature. The laser wavelength was 532 at 0.05 mW. The field of view (FOV) and exposure period were 40.816 μm and 0.971 ms, respectively. The objective lens (×60, N.A. 1.2) was inserted into the culture medium during the observation.

The observation was carried out using the following procedure. First, a still picture was taken. Then, 30-s movies (frame rate: 0.06 s; 50 still pictures) of the same cell were captured. Maximum intensity projection (MIP) and 3D figures were prepared using the initial still image data. Cell volume analysis and other analyses were also performed using the still image data. Time-lapse analysis was carried out using movie data.

For SEM observation, the cell suspension was fixed with 1% glutaraldehyde (GA) at room temperature for 1 h. Excess GA was removed by centrifugation (10 min at 3000 rpm; five times). The cell suspension (100 μl) was transferred to a coverslip and air-dried. The coverslip was sputter-coated for 2 min using a MSP-1S coating device (VACUUM DEVICE, Inc., Ibaraki, Japan) with an Au–Pd (4:6) target. The samples were observed using a JSM-6510 microscope (JEOL, Ltd., Tokyo, Japan) at an acceleration voltage of 20 kV.

TPM data were analyzed using TomoStudio software (Version 2.7.40; Tomocube, Inc.) to obtain maps of the RI values of each cell. From the 3D array RI data of 184 $×$ 184 $×$ 212 pixels read by MATLAB (9.11.0.1809720 (R2021b) Update 1, The MathWorks, Inc., USA), the cross section was acquired as the 2D array RI data of 65 $×$ 65–100 $×$ 100 depending on the size of each cell. The RMS (root mean square) of the acquired 2D array RI data was calculated by the following equation:¹⁹ 

Here, $xi$ are the RI values for each pixel. For the same array for which RMS was calculated, Moran's I statistic was calculated by the following equation:^{20,21,23–25}

Here, $xi$ and $xj$ are the RI values for each pixel, n is the total number of data in the array, $X¯$ is the average value of $xi$⁠, and $wij$ is the spatial weight matrix. The spatial weight matrix was defined based on the following equation:

Here, $dij$ is the geometric distance value of i and j whose adjacency is defined by the rook type in the 2D square grid model.²¹ The matrix was normalized by rows. RMS and Moran's I statistics were calculated using R (4.1.2).

The diatom cell has a disk-like shape. We used TPM to observe living cells and localize the intracellular components using RI distribution data. Figure 1(a) shows a schematic view of the cross-sectional analysis of the TPM images. A TPM image includes 3D information because of the use of the holotomographic technique. Thus, cross sections of the disk-shaped diatom cells could be determined using the 3D data from a single image. In Figs. 1(b)–1(h), lateral-cross sections were visualized at various depths (0–3.5 μm). The cell surface was assumed to be the origin of the vertical axis (0 μm).

Figure 1(b) shows the cross section of the cell surface. As defined in the color bar, the yellow areas indicate high RI values (∼1.43), whereas the light blue areas indicate lower RI values (∼1.41). Although the diatom cell had a symmetrical disk shape, the RI distribution was not uniform. Figure 1(c) shows a cross section of the same cell at 0.5-μm depth. Interestingly, the locations of the yellow and light blue parts were not the same, as shown in Figs. 1(b) and 1(c). Because the image was obtained at almost the same time, cell deformation over time is negligible. Thus, the observed localization was probably statically present in the cell body.

When we continued to visualize deeper planes of the same cell, the RI image became obscure at 2.5-μm depth. In general, TPM images are obscure at the bottom of the diatom cells. Thus, the height of the cell was approximately 2.5 μm. As shown in Figs. 1(b)–1(f), materials with higher RI values were located at the rim areas. Diatom cells have silica shells known as frustules, and high-RI values are likely attributed to the silica-containing components.

Figure 2 shows a similar analysis of three different cells. Figures 2(a), 2(d), and 2(g) show MIP images of the three cells. The MIP image shows the highest RI values for each lateral position. The image is a combination of the slices to make a 3D image appear as a 2D image. Thus, localization of cell components could be simply visualized in a MIP image at the first glance. One of the advantages of MIP images is intuitive understanding of the localization only with one image. The MIP images suggested that the cell components were not uniform, although the cells had symmetrical disk shapes. Figures 2(b), 2(e), and 2(h) show X–Y cross sections of RI images at 1.0-μm depth. Although every cell showed different features, in general, the boundary areas had higher RI values. Figures 2(c), 2(f), and 2(i) show the same cells at 2.0-μm depth. Compared with the cross sections at 1.0 and 2.0 μm, some parts revealed different RI distributions (indicated by the arrows).

Statistical analysis of the RI distributions of 25 individual cells was carried out using the RMS and Moran's I values. The RMS is the square root of the value obtained by squaring the variable and calculating the mean value.¹⁹ The RMS is used in analysis such as atomic force microscopy as an index to quantify the degree of surface unevenness. Here, the RMS was used to quantify the high and low RI values in the observation area. Moran's I statistic is one way to quantify a measure of spatial autocorrelation.^21,22,24 Spatial autocorrelation is an indicator of how similar the variables at a point and its neighbors are. Moran's I indicates a value between −1 and 1. If I is close to −1, the data are uniformly distributed. If I is close to 0, the data are randomly distributed. If I is close to 1, the data are a cluster distribution.^21,22,24 Here, Moran's I statistic was used to quantify the spatial localization of specific RI values due to the influence of intracellular and extracellular tissues in the observation region as a spatial autocorrelation. Figure 3(a) shows the RMS values at each depth (from the cell surface 0 μm to a depth of 3.5 μm). Data for 25 cells were drawn using 25 polygonal lines. From the cell surface to a depth of 2 μm, the RMS values of most of the cells ranged from 1.340 to 1.370. Because the RMS value of a flat surface is defined as 1, it is clear that the obtained RI values reflect the localization of cell components. The RMS with a height of 0.5–2.0 μm in which the observed region was close to the center of the cell was larger than the RMS value of 1.338 in the solvent-only region. This indicates the presence of cellular tissue with a higher index of refraction than the solvent. Furthermore, the higher the RMS value, the larger the region of high RI values. There were no significant differences in RMS values at different depths. At depths of 2.5, 3, and 3.5 μm, RMS values were slightly decreased. It is possible that TPM data are less accurate at such depths.

Figure 3(b) shows Moran's I values at different depths (cell surface 0 to 3.5 μm). In general, Moran's I values ranged between 0.955 and 1.004; the values did not fluctuate beyond this range even at depths of 2.5, 3 , and 3.5 μm. Moran's I values were as close to 1 as possible at almost all heights, indicating that the index of refraction was highly clustered in all observation regions. This is because the number of data used in the calculation was enormous, 65 $×$ 65–100 $×$ 100, so there were large regions where different RI values were localized such as cell tissues and solvents.

Interestingly, several cells among the total of 25 showed slightly different values. The results for cell Nos. 4 and 9 were rather different from those of the other 23 cells in terms of RMS values. Furthermore, Moran's I values of cell Nos. 10, 17, 21, and 25 were highly deviated compared with those of other cells. One of these causes is probably the percentage of high RI values in the observation area. As clear from the equation, the RMS value increases as the percentage of higher RI increases. Numbers 4 and 9 show that the percentage of high RI values was higher than that of other individuals in the depth to which the numerical value was added to the graph [see Fig. 3(a)]. However, the difference in low RMS values between these four cells was not as pronounced as the difference in Moran's I values. In addition, Moran's I values of Nos. 4 and 9, which had a large RMS value, were not significantly different from those of other individuals. On the other hand, Nos. 10, 17, and 25, in which Moran's I value was significantly lower than other cells at a depth of 2.0–3.5 μm, are thought to have a lower percentage of high RI values at that depth [see Fig. 3(b)]. Indeed, the RMS values of these four individuals tended to be lower than those of the other individuals but not as significantly as Moran's I values [see Fig. 3(a)]. In other words, it is considered that the RI values of no. 10, 17, 21, and 25 tended to have a slightly random spatial distribution of RI values than other individuals. In the TPM analysis, it was found that different information can be obtained by calculating the RMS and Moran's I values for the same individual data.

Although there have been many papers of living cells by TPM, the cross-sectional analysis was not a popular approach. Furthermore, numerical and statistical analysis of cell components based on physical information involved in TPM data has not been reported. We think one of the reasons to hesitate the numerical analysis might be due to huge amounts of RI data. We proposed a simple and effective approach to quantitatively and statistically analyze distribution of cell components by combining cross sections of TPM images and RMS/Moran's I methods.

Time-lapse images of the X–Y cross sections of a diatom at the cell surface [Fig. S1(a)– S1(c)] and at depths of 1.0 μm [Figs. S1(d)–S1(f)] and 2.0 μm [Figs. S1(g)–S1(i)] indicated that there were no significant changes in the RI distributions over time. Thus, we believe that the differences in RI distributions among different X-Y cross sections at different depths originate from actual cell structures and not from artifacts.

The cell volumes and surface areas of the diatom cells were estimated using TPM images. Numerical results of the analysis for the 25 individual cells were indicated in Table S1. The average cell volume and surface area of the 25 cells estimated from the TPM data were 96.9 ± 26.2 μm³ and 129.0 ± 26.7 μm², respectively. In fact, in the TPM data, the bottoms of the cells were obscure, because the images were based on holograms [Figs. 1(h) and 1(i)]. In addition, mean RI, dry mass, and sphericity were estimated as 1.4 ± 0.0, 27.8 ± 7.0, and 0.8 ± 0.1, respectively, although further approaches are necessary to verify the results.

To evaluate the TPM-based cell volume estimation, we observed diatom cells using SEM. Living diatom cells were fixed with GA on a glass surface, rinsed with water, and dried (Fig. S2). Using the diameters and lengths of 13 individual cells, the cell volumes and surface areas were estimated to be 105 ± 18 and 127 ± 13 μm², respectively. We believe that TPM images provide reliable estimations of cell volumes and surface areas if we assume that SEM provides reliable values.

In addition, several other parameters can be obtained from TPM data. The average projected cell areas were 25.9 ± 5.1 μm². The value suggests the diameters of the disk-shaped diatom cells. The mean RI values of the cells were 1.4 ± 0.0, although the RI values were localized in the cells. Averaged concentrations and dry masses of the cells were 0.3 ± 0.0 pg/μm³ and 27.8 ± 7.0 pg, respectively. The sphericity of the cells was 0.8 ± 0.1. This suggests that the disk-type diatoms had nearly symmetrical shapes.

In summary, we demonstrated analyzing localization of cell components of living diatom cells based on optical information of TPM data. Cross-sectional analysis of TPM images well visualized the localization of the observed cells. Statistical analysis of RI values of each cross section image by RMS and Moran's I methods provided the localization of cell components as numerical values. Cell volumes estimated from TPM data were similar to those obtained using SEM. Our work provided a hint to quantitatively analyze biomaterials using physical information of TPM data.

See the supplementary material for the following figures and table: Fig. 1: Time lapse X–Y cross sections from DHM; Fig. 2: SEM images of fixed diatom cells; Table S1: Numerical analysis of 25 individual diatom cells.

This study was financially supported by JST SICORP Japan (Grant No. JPMJSC19E1).