Basal body organization and cell geometry during the cell cycle in Tetrahymena thermophila

Abstract

Tetrahymena thermophila possesses arrays of motile cilia that promote fluid flow for cell motility. These consist of intricately organized basal bodies (BBs) that nucleate and position cilia at the cell cortex. Tetrahymena cell geometry and spatial organization of BBs play important roles in cell size, swimming, feeding, and division. How cell geometry and BB organization are established and maintained remains poorly understood, and prior studies have been limited due to difficulties in accurate BB identification and small sample size. We therefore developed an automated image processing pipeline that segments single cells, distinguishes unique BB populations, assigns BBs into distinct ciliary rows, and distinguishes new from mature BBs. We identified unique features to describe the variation of cell shape and BB spatial organization in unsynchronized single-cell images. The results reveal asymmetries in BB distribution and ingression of the cytokinetic furrow within the cell. Moreover, we establish novel spatial and temporal waves in new BB assembly through the cell cycle. Finally, we used measurements from single cells across the cell cycle to construct a generative model that allows synthesis of movies depicting single cells progressing through the cell cycle. Our approach is expected to be of particular value for characterizing Tetrahymena mutants.

INTRODUCTION

The construction of generative models of cell organization is a valuable approach that can provide insight into complex cellular processes, especially those with many components and/or that show significant cell-to-cell variation (Murphy, 2012, 2016). Generative models have been created to capture the spatial relationships between different cell components (Peng and Murphy, 2011; Johnson et al., 2015a) and to distinguish between different organelles based on their relationships to other organelles (Johnson et al., 2015b). In addition to studies using traditional machine learning methods, deep learning methods can produce generative models that can construct multiple organelle synthetic cell images from only single organelle images (Ounkomol et al., 2018; Donovan-Maiye et al., 2022). A particularly valuable use of generative models is to infer and visualize the dynamics of a process from static images (Johnson et al., 2015a; Ruan et al., 2020).

Motile cilia are microtubule-based organelles that undulate to produce fluid flow. In the case of multiciliated cells, tens to hundreds of motile cilia are organized into arrays that beat in a coordinated manner (Soh and Pearson, 2022). This supports fluid movement along epithelia and cell mobility. The organization of motile ciliary arrays is established by basal bodies (BBs) that support cilia formation and positioning at the cell cortex. Unique patterns of BB and cilia organization exist in multiciliated cells from different tissues and organisms (Allen, 1967; Spassky and Meunier, 2017; Soh and Pearson, 2022). Moreover, the establishment of these patterns is unique such that some patterns are maintained epigenetically within an existing pattern while others are built de novo (Sonneborn, 1964; Beisson and Sonneborn, 1965; Mitchell et al., 2007). The establishment and maintenance of BB organization are fundamental for promoting fluid flow in multiciliated organisms.

The ciliate Tetrahymena thermophila is a single-celled, multiciliated model system that utilizes epigenetic propagation of BB and ciliary patterns through the cell cycle (Sonneborn, 1964; Beisson and Sonneborn, 1965; Nanney, 1971b; Ng and Frankel, 1977; Cole and Gaertig, 2022). Tetrahymena cells possess a feeding structure or oral apparatus (OA) with ∼150 BBs and 350–700 cortical BBs aligned into 18–21 ciliary rows (Nanney, 1971a). The cortical BBs nucleate and organize motile cilia that promote cell motility (Pearson et al., 2009b; Galati et al., 2014; Junker et al., 2019; Soh and Pearson, 2022). Moreover, these BBs organize the Tetrahymena cell cortical geometry by serving as a foundation upon which the cell cortex and the cortical cytoskeleton are organized (Nanney, 1971a; Frankel, 2008). Tetrahymena BBs are longitudinally and laterally coupled to each another and the cell cortex via BB-associated appendage structures (Pitelka, 1961; Allen, 1969; Junker et al., 2019; Soh et al., 2020). In addition, cortical BBs are embedded in an actin and intermediate filament–like meshwork (Williams, 2004; Williams et al., 2006). Together, Tetrahymena BBs form an intricate network that interacts with the cortical cytoskeleton and the cell cortex. Defects in BBs, their associated appendage structures, or cortical cytoskeletons are associated with abnormal cellular cortical morphology. For example, Tetrahymena cells with disorganized BBs are often smaller, supporting the hypothesis that the number and spatial organization of BBs define cell size and geometry (Frankel, 2008; Bayless et al., 2012; Galati et al., 2014; Ruehle et al., 2020; Soh et al., 2020). For daughter cells to adopt the optimal cell geometry, parental cells need to assemble and insert new BBs into the preexisting cortical BB network before cell division (Nanney, 1971a, 1975; Frankel, 2008). How cells define the placement of new BBs during the cell cycle remains unclear.

Cells roughly double their BB number via assembly of new BBs (Nanney, 1971a; Galati et al., 2015). Tetrahymena cells display two gradients of new BB assembly across the cell surface (Kaczanowski, 1978). Similarly, the ciliate Paramecium exhibits complex morphogenetic gradients along the cell cortex, including BB assembly (Iftode et al., 1989; Sperling et al., 1991). Along the longitudinal axis of Tetrahymena cells, new BB assembly occurs at higher frequency in the medial region of the cell than at the anterior or posterior cell poles. In addition, a gradient of new BB assembly is observed along the circumferential axis of the cell, focusing new BB assembly on specific ciliary rows. By convention, the ciliary row that is positioned below the OA and is shortest in length is designated row 1. When viewed from the anterior pole of the cell, rows are then numerically labeled increasing in the counterclockwise direction with increments of one. Previous work has demonstrated that Tetrahymena cells have a unique spatial distribution of new BB assembly during the cell cycle (Nanney, 1975; Kaczanowski, 1978; Galati et al., 2015). How Tetrahymena cells control this massive and asynchronous assembly of BBs across their cell surface before cell division remains poorly understood. The unique spatial distribution of new BB assembly rules out the model that each existing BB would provide a nucleation site for one new BB assembly. Indeed, new BB assembly is not directed to a single assembly event for each parent BB, but rather new BB assembly occurs with multiple BBs assembling from a subset of mature BBs in the medial half of the Tetrahymena cell (Nanney, 1971b; Kaczanowski, 1978; Pearson et al., 2009a; Bayless et al., 2012). Whether differences in the proliferative capacity of mature BBs in assembling new BBs alone could account for the observed gradients of new BB assembly has not been established. Moreover, how Tetrahymena cells eventually double the number of BBs in all BB rows before cell division remains unclear. Past studies were limited due to low sample size and poor image resolution that hindered accurate assessment of BB maturity, and most studies extrapolated their observations on BB organization on the full-cell level based on subcellular domains (Nanney, 1971a; Kaczanowski, 1978; Iftode et al., 1989). Thus, detailed analysis of how BB number is regulated during the cell cycle requires further quantitative assessment of large cell numbers combined with computational modeling of the new BB assembly process.

To establish a deeper understanding of cell geometry and BB organization, tools for both mapping and geometrically modeling cell morphology and BB patterns are important. The motile nature of Tetrahymena cells impedes our ability to track BB organization and cell geometry changes in the same cell during the cell cycle (Soh et al., 2022). This has limited our interpretations of how these cellular features change relative to one another. We previously developed a semiautomated image analysis pipeline to characterize BB organization and cell geometry of T. thermophila cells during the cell cycle (Galati et al., 2015). However, use of this ImageJ-based approach required user verification of each BB detection and successful detection required high signal-to-noise images. These limitations led to small sample size, and thus it remains unclear how BB organization is established in relation to new BB assembly during the cell cycle. Therefore, we here describe a fully automated new image analysis processing pipeline that provides in-depth quantification of cell geometry and BB organization, allows high-throughput processing of large data sets with varying signal to noise, and allows the creation of a generative model of the dynamics of the Tetrahymena cell cycle from static images. This provides new insights into how Tetrahymena cells regulate their cell geometry in relation to BB organization.

RESULTS

Image processing pipeline to quantify cell geometry and BB organization

To analyze and model the organization of T. thermophila BBs, a large data set of individual three-dimensional (3D) images of 338 cells was created. BBs were visualized by tagging the BB component Poc1p with an mCherry (mCh) fluorophore (Pearson et al., 2009b). To ensure unbiased sampling of cells during the cell cycle, cells were not synchronized.

Building on the approach of Galati et al. (2015), we designed a dramatically improved and fully automated image analysis pipeline (TetAlyze) that processes images at high throughput (Figure 1). Briefly, the pipeline first detects and distinguishes the OA and cortical BBs (this step in the new pipeline is more sensitive than the previous approach and results in correctly detecting 5–10% more BBs; see Supplemental Table 1). Next, BBs are assigned to rows via an iterative refinement routine. BBs are then divided into immature and mature based on their total fluorescence intensity of Poc1-mCh. A BB is considered immature if the Poc1-mCh fluorescence is 50% or less than the intensity of its nearest neighbor. Finally, the cell surface area and volume are approximated using a shell connecting all BBs of the cell. Validation of the image processing pipeline was performed by comparison with manual analysis. TetAlyze correctly identified more than 99% of the cortical BBs (proportion of misidentified BBs: 0.6 ± 0.4%) and produced BB row assignments comparable to those of manual measurements (BB row quantification; manual: 19 ± 1; pipeline: 19 ± 2; Supplemental Figure 1).

FIGURE 1:

Automated microscopy image processing pipeline. (A) Raw image containing a single Tetrahymena cell. (B) I_SE, tabular structure-enhanced image. (C) Detected cell region. (D) I_B, the binary mask for potential BBs. (E) Detected potential OA region. (F) Ciliary row alignment steps illustrated from left to right. The cell’s polarity is established by estimating the anterior and posterior poles, and the cell is rotated to make its antero–posterior axis vertical. Ciliary arrays are aligned iteratively. BBs are initially connected if they are the closest anterior or posterior neighbors to each other. Short ciliary rows are extended by including more unassigned BBs. The ciliary rows are then connected and refined. With the updated aligned ciliary rows, the anterior and posterior pole positions are reestimated. This procedure is iteratively performed with the new corrected poles for 50 iterations to yield the final alignment. Red boxes highlight examples of alignment errors that are fixed in the next step. (G) Processed cell geometry and BB organization data allow us to model the relationships between cell shape, length, widths, and BB distribution by nonparametric regression. Given input numbers of ciliary rows and BBs, the fitted model can synthesize a predicted cell geometry with statistically correct cortical BB spatial organization.

Tetrahymena morphology during cell growth

Using the output from the automated segmentation and alignment, 22 features that describe BB organization and cell geometry in each cell were defined. k-means clustering revealed that these cellular features fall into four groups (Table 1). These four groups correlated well with each other across the data set.

TABLE 1:

Features used to describe BB organization and cell morphology and identification of major modes of feature variation from cell to cell.

Feature	PC1 loading (50.03%)	PC2 loading (13.47%)	PC3 loading (9.06%)
Group 1	0.528	1.887	–0.280
Anterior surface area	0.071	0.042	0.003
Medial surface area	0.065	0.175	0.059
Posterior surface area	0.066	0.106	0.042
Cell major axis length	0.058	0.219	–0.054
Cell minor axis length	0.040	0.235	–0.061
Cell volume	0.068	0.196	–0.016
Average neighbor anterior BB pairwise distance	0.015	0.313	0.171
Average ciliary row anterior pairwise distance	0.044	0.047	–0.138
Average ciliary row medial pairwise distance	0.047	0.365	–0.180
Average ciliary row posterior pairwise distance	0.055	0.189	–0.108
Group 2	0.465	–1.080	0.216
Number of anterior BBs	0.058	–0.254	–0.043
Number of medial BBs	0.125	–0.185	0.050
Number of posterior BBs	0.050	–0.332	–0.035
Number of BBs	0.062	–0.240	0.014
Average number of BBs per row	0.061	–0.189	–0.046
Cell length	0.051	0.046	0.183
Average ciliary row length	0.058	0.073	0.093
Group 3	–0.045	0.721	0.570
Volume deficit	0.005	0.058	0.246
Average neighbor medial BB pairwise distance	–0.036	0.300	0.146
Average neighbor posterior BB pairwise distance	–0.014	0.363	0.178
Group 4	0.052	–0.528	0.494
Number of ciliary rows	0.018	–0.261	0.279
SD among ciliary row lengths	0.034	–0.267	0.215

Features were grouped into those describing related properties, and the first three PCs were identified. The fraction of total feature variance that is captured by each PC is shown in the column headings. The factor loadings for each PC were normalized so that their sum equals 1. Note that PC1 primarily captures cell size (features such as number of BBs, cell length, and cell volume have positive loadings in the 0.2–0.3 range), while PC2 captures aspects of BB spacing (features for neighbor pairwise distances have loadings around 0.4).

Principal component (PC) analysis was performed to identify the major types (modes) of variation within the cell population, that is, which features typically are correlated or vary together. The contributions of each feature to each PC are called factor loadings. For each PC, the sum over all features of the product of each factor loading with the value of its corresponding feature for a given cell gives the value of that PC for that cell. The definitions of the features and the factor loadings for the top three PCs are shown in Table 1. The first PC accounts for approximately 50% of the total variation in the features across all cells. As can be seen in Table 1, the features that are the largest contributors to PC1 are those related to cell surface area and volume (group 1) and number of BBs (group 2). This component is thus a strong overall measure of cell growth. The feature that contributes the most to cell growth is the number of medial BBs (Table 1; PC1 score: 0.125). The medial region of the cell is where the highest frequency of new BB assembly occurs (Nanney, 1975; Kaczanowski, 1978; Galati et al., 2015), confirming its value as an indicator of cell growth. Distinct from the first PC, the second PC accounts for an additional 13% of feature variability during the cell cycle. It shows a balance between positive contributions of group 1 features, negative contributions of group 2 features, and positive contributions of group 3 features. Group 3 primarily measures the spacing between BBs but also has a modest contribution from volume deficit. Volume deficit measures the extent to which the volume of the cell is less than that of an equivalent ellipsoid; in this case it measures the extent to which the cytokinetic furrow has ingressed during cell division. PC3 captures variation in the number of ciliary rows in a given cell as well as a major component of the variation in cell shape. The relationships between the major contributing features for each PC are shown graphically in Figure 3B.

FIGURE 3:

PC analysis of BB organization and cell morphology features (n = 338). (A) Visualization of whole cell population produced by PC analysis. A compressed visualization of cell shape is placed at each cell’s PC1 and PC2 values. (B) Venn diagram shows the contribution of major cell features to each PC. Major features for each PC refer to features whose coefficient’s absolute magnitude is above the average absolute magnitude among all features contributing to that particular PC.

Our unbiased assessment of the 22 cellular features revealed that cell size and BB number are the major factors that account for cell–cell variations during the Tetrahymena cell cycle. Figure 2 shows histograms of a few of the important features, illustrating the diversity of cells captured in our image data set. It also confirms the relationships among the major features of group 1, namely that the number of cortical BBs positively correlates with cell surface area (R = 0.774) and cell volume (R = 0.688). These quantitative results agree well with previous results demonstrating that the number of BBs correlates with simple measures of cell size (Nanney, 1975; Kaczanowski, 1978; Galati et al., 2015) and extend those results to other correlated variables such BB separation. These relationships suggest that the number of BBs can be used as a proxy for cell cycle progression and as a primary independent variable to construct generative models of cell cycle progression, as we describe in later sections.

FIGURE 2:

(A–D) Histograms of Tetrahymena BB organization statistics and cell morphology metrics. (E) Schematics for cell length and circumference measurements. (F–I) Relationships between individual cell surface area, volume, length, and circumference and its number of BBs.

To illustrate the relationship between these two fundamental modes of variation in cell shape and BB organization, Figure 3A shows a 2D depiction of each cell shape plotted at positions corresponding to their PC1 and PC2 values. The plot reflects the major morphology changes occurring during the cell cycle. Cells in the early stage of the cell cycle, having fewer BBs and being relatively smaller, are low in both PC1 and PC2 (Figure 3A, left). During the cell cycle, PC1 increases due to new BB assembly (which occurs predominantly at the medial half of the cell) and concomitant cell growth. PC2 increases modestly also, driven by a balance between these features but, as we will see later, also due to an increase in BB spacing. Moreover, the cell-to-cell variance captured by PC2 (i.e., the vertical spread in the cell positions in the plot), is smaller at the early stages but becomes larger as cells increase in size (PC1) (Figure 3A). Finally, before cell division, cells decrease in PC2 and adopt an hourglass shape (Figure 3A, bottom right). Because at this late stage, PC1 has largely stopped increasing, the change in PC2 is mainly due to changes in group 3 features, decreasing BB spacing and increasing volume deficit.

Tetrahymena BB organization is asymmetric during the cell cycle

The BB organization and cell geometry data obtained from the image analysis pipeline allowed us to ask quantitative questions about the general principles of BB organization as they relate to cell size and morphology. We first considered cortical BB spatial distribution, projecting the positions of all cortical BBs of all cells onto the surface of a unit sphere and estimating BB density (number of BBs per unit surface area) as a function of location in the cell (Figure 4A). The highest cortical BB density is found at the cell anterior and just below the OA (ciliary rows 19, 20, and 1). The cell anterior is the position of BB convergence at the cell anterior tip, and BBs are more closely positioned in this region. Moreover, BBs below the OA are the site of new OA development and the position enriched for BB assembly (Nanney, 1971b; Kaczanowski, 1978; Galati et al., 2015). Because the OA occupies a large region of the cell cortex, an alternative explanation for this higher density is that the OA compresses the spacing between BBs in ciliary rows below it. Consistent with a model where BBs compress and/or plastically move, the OA can dynamically move among BBs in row 1 in mutants affecting the Hippo signaling pathway (Jiang et al., 2017).

FIGURE 4:

Tetrahymena cell cortical BB spatial organization analysis. (A) Spatial density map of cortical BBs from the cell population at different cell stages. (B) Example of the ciliary row organization of a cell with 19 ciliary rows and 527 total BBs. We projected the 3D position of its cortical BBs onto a unit circle along the anterior–posterior axis. We notice that the row on the left side has a larger range (green area) than the right side (blue area). (C) Visualization of individual ciliary row shapes from top-down and side views of four representative 19-row cells at different cell cycle stages, respectively.

The cortical BB density is not uniform in the medial region of the cell where most new BB assembly occurs. The medial BBs on the right side of the cell (rows 12–18) are more densely packed compared with those on the left side of the cell (rows 3–8). To determine a potential explanation for this difference in BB density between the cell sides, we examined the typical path followed by each ciliary row. The cortical BBs of a representative cell with 19 ciliary rows was visualized by looking down from cell’s anterior pole along the anterior–posterior axis (Figure 4B). When viewed this way, the rows on the left side of the cell take a wider path (varying more in azimuthal angle, the angle around the anterior–posterior axis) than the rows on the right side of the cell. This can also be seen when BB positions are viewed by the side (Figure 4C). To quantify this difference for the entire cell population, we calculated the average variation (as measured by the SD) in azimuthal angle of cortical BBs in each row (Figure 5A) and the pairwise adjacent ciliary row spacing (Figure 5C). Rows on the left side have a larger azimuthal angle and spacing than those on the right. This difference is larger for cells with 19 ciliary rows than for those with 20 ciliary rows. Thus, our analysis reveals that BBs and ciliary rows are asymmetrically organized around the anterior–posterior axis. Spacing between BBs is increased on the left side of the cell in the medial region and on the right side the cell posterior (Figure 5D). This suggests that spacing in unique domains of the cell may equilibrate to uniform ciliary row lengths. Finally, spacing between BBs adjusts through the cell cycle such that the medial and posterior regions reduce spacing late in the cell cycle (Figure 5E). This is likely to accommodate the increased BB assembly and division furrow ingression (see below).

FIGURE 5:

(A) SD of the azimuthal angle of cortical BBs is shown for each row for the cell population with 19 and 20 ciliary rows, respectively. (C) Average row spacing between two adjacent ciliary rows. The distance is measured in the medial region of the cell (as illustrated in B). (D) Average BB spacing measured at three cell regions for cells with 19 and 20 ciliary rows, respectively. The curves with circular markers refer to cells with 19 ciliary rows, and the curves with asterisk markers refer to cells with 20 ciliary rows. (E) Changes in BB spacing in the three cell regions through the cell cycle.

Immature BB spatial organization changes during cell cycle

We next asked whether the above patterns in asymmetric ciliary row organization reflect the appearance of newly assembled, immature cortical BBs. Previous work identified gradients of proliferation of BBs where ciliary rows 1, 2, and 3 had the maximum number of new BBs and ciliary rows 7, 8, and 9 had the smallest number of new BBs (Kaczanowski, 1978), although it was unclear how this difference would not lead to an imbalance in BBs in each row over multiple rounds of cell division. As can be seen in Figure 6A, the region below the OA has the highest immature cortical BB density, matching the higher overall density in this region (Figure 4A) and the work of Kaczanowski (1978). There are also clear differences in immature BB density between the left and right sides, in part to be expected because the overall densities also differ (Figure 5A).

FIGURE 6:

Immature BB spatial organization. (A) Spatial density map of immature cortical BBs from the entire cell population. (B) To the changes of immature BB number at different stages in the cell cycle, we plotted the fitted regression curves of immature BB number based on the total BB number for each ciliary row. Left is rows 3–8, and right is rows 12–18. The dashed line indicates the number of BBs at which each ciliary row finishes half of its new BB assembly. (C) The relationship between this quantity and individual ciliary rows. (D) Estimation of BB replication rates during the cell cycle. The number of BBs at each time is estimated by making a cumulative histogram from the data of Figure 1A. The derivative of this curve is also shown, converted to BBs per hour assuming a cell cycle time of approximately 3 h. (E) Location of furrow ingression. Traces of cross-sections are shown for late-stage cells. The position of the OA is shown for each cell. Cells appear oval because there is some flattening (in an arbitrary direction) during preparation for imaging.

To examine whether the distribution of new BBs changes during the cell cycle, we fitted regression curves describing the number of immature BBs in each ciliary row as a function of the total number of mature cortical BBs in a given cell (Figure 6B). Newly assembled cortical BBs preferentially appear on the left side of the cell (rows 6–8 in 19 row cells, 6–9 in 20 row cells) early in the cell cycle (350–400 BBs per cell). This was verified by measuring the total number of BBs at which a given row reached 50% replication of the total number of BBs for that row (Figure 6C). To allow comparison of 19 and 20 row cells in this figure, we converted row number to the fraction of the total number of rows in a cell. The lowest number of BBs required to reach 50% occurred at fractional row 0.4, corresponding to rows 7–8, and these represent the rows assembling new BBs earliest in the cell cycle. As cells progress through the cell cycle and increase in BB number, waves of new BB assembly proceed in both directions from these initiating rows. Thus, gradients of new BB assembly enrich at unique positions on the cell cortex (Kaczanowski, 1978), shifting in position as cells progress through the cell cycle.

In addition, using the histogram of the number of BBs per cell in the real cell population (Figure 1A), we can convert our cell cycle proxy of number of BBs into a measure of the fraction of the cell cycle each cell has completed. This also gives the rate at which BBs are being replicated at each point in time (Figure 6D).

Given the asymmetry of BB replication, it was also of interest to determine whether there is asymmetry of ingression of the cytokinetic furrow. Figure 6E shows cross-sections, through both the cytokinetic furrow and the wider regions above it, for example cells late in the cell cycle. The results suggest that ingression begins nearly opposite to the OA.

Generative model of Tetrahymena BB organization in a single cell

As discussed in the Introduction, generative models are powerful tools that can integrate information from individual cells to produce a model that proposes how different aspects of cell organization can be predicted from a small number of primary variables. We therefore sought to learn a generative model that can synthesize a predicted cell geometry with statistically correct cortical BB spatial organization conditional on two input parameters, the number of BBs and the number of ciliary rows. To do this, we fitted models for cell shape, length, widths, and cortical BB distribution (see Materials and Methods). We then tested how similar synthetic cells generated from only those two input parameters were to real cells that had those parameters. We generated a synthetic cell to match each of the 338 real cells, calculated its 22 features, and calculated PCs using the factor loadings found from the real cells (Figure 7A).

FIGURE 7:

Synthetic cells and cell cycle trajectories. (A). For each real cell, we synthesized a synthetic cell with the same number of ciliary rows and BBs and calculated its 22 features. These were transformed using the PC analysis transformation from the real cells, and the PC values for each real (blue) and synthetic (red) cell are shown. The univariate distributions of the two PC are also shown above and to the right of the scatterplot (after slight smoothing with Gaussian kernels). (B) Synthetic cell cycle trajectories. Starting from small synthetic cells with either 19 (pink) or 20 (orange) ciliary rows and 370 BBs on average, new BBs were added as predicted by the generative model, and an appropriate new cell shape was inferred. The features and PCs were calculated for all synthetic cells, and lines show the simulated trajectory followed by each original cell. The PC values for all (individual) real cells are also shown (green). (C) Example cell cycle progression trajectory synthesized from the generative model along with representative microscopy images of real cells at the corresponding cell stages. BBs with lighter color in synthetic cell models refer to newly assembled BBs. A movie is provided as Supplemental Movie 1.

Movie S1.

Download video file ^{(1.4MB, mp4)}

figure7d

The difference between the synthetic and real distributions in PC1 (which, as described above, is an overall measure of cell growth) is small, indicating that all of the features contributing to PC1 are reconstructed well by the generative model. This is consistent with the high degree of correlation among the group 1 and group 2 features (and the large PC1 factor loading for the number of BBs). The difference is somewhat larger for PC2 (which captures BB separation and cell shape). This may come from the fact that our fitted model does not capture all of the variation in the group 3 features and thus the variation among synthetic cells is smaller than that of real cells. To quantitatively assess the difference between the distributions of each PC, we did a statistical comparison of the feature distributions of the real and synthetic cell populations (see Materials and Methods). The weighted KL divergence between the two distributions was 0.0778 (0 indicates no divergence, and 1 indicates complete divergence). This confirms the visual conclusion that the synthetic cells are representative of real BB organization and cell morphology. Once again, this highlights our finding of coordination between different aspects of these cell characteristics.

Generative model of Tetrahymena BB organization through the cell cycle

The cells in our image data set were collected at random and thus cover the entire T. thermophila cell cycle. This allows us to generate synthetic cell cycle trajectories by predicting changes in cell shape and BB organization as we simulate cell growth by gradually increasing the number of BBs. The trajectories start with a synthetic cell with roughly 360 BBs and either 19 or 20 ciliary rows, and new BBs are iteratively added as described in Materials and Methods. At each growth iteration, the BB organization and cell morphology were also adjusted according to our generative model. The trajectories stop when the cell contains more than 730 BBs, a time point when the cell undergoes division. To validate that these simulated cell cycle progressions match the characteristics of individual real cells, each cell trajectory was described by the 22 features and plotted in the PC2/PC1 space. Figure 7B shows two sets of example synthetic cell cycle trajectories, one with 19- and one with 20-ciliary rows. The trajectories match the real cell populations and coincide with the cell cycle progression described in Figure 7A. Figure 7C shows examples of cells from a typical trajectory matched with real cells with the same number of BBs. The cell shape in each trajectory starts as approximately ellipsoidal and then gradually transforms to a pyriformis shape and becomes larger in size. Then the cell waist shrinks as a cytokinetic furrow ingresses before cell division/cytokinesis. Using the relationships between number of BBs and relative cell cycle time provided by Figure 6D, we generated simulated movies of a single cell progressing through the entire cell cycle as a function of elapsed time (Supplemental Movie 1).

DISCUSSION

Automated analysis and modeling of cellular morphology and BBs during the cell cycle

Here, we develop a significantly improved image processing and analysis pipeline for T. thermophila cell microscopy images that automatically detects and segments the BBs and cells, establishes cell polarity, and aligns the detected BBs into ciliary arrays with high accuracy. Using this pipeline, we analyzed 338 unsynchronized cell images by measuring their cell sizes and geometries, OA and cortical BB spatial organizations, and ciliary row organizations from the processed images.

Visualization of cellular asymmetries

We then measured 22 features that describe BB organization and cell geometry during the Tetrahymena cell cycle. By performing PC analysis, we were able to illustrate cell cycle progression in a dimensionality-reduced, 2D plot. Consistent with past studies, our unbiased assessment of the 22 cellular features identified the spatial organization of BBs as a key contributor to the variation of cell morphology through the cell cycle (Nanney, 1971a, 1975; Iftode et al., 1989; Galati et al., 2015). In addition, we demonstrated that BBs are asymmetrically distributed to different sides of the Tetrahymena cell, with BBs being denser on the cell’s right side. Consistent with unique patterns in BB density, the ciliary paths are longer on the cell’s left side and spacing between BBs is also larger compared with the arrays on the cell’s right side (Figure 5D). We predict that such asymmetries impact cell swimming behavior.

Consistent with the distribution patterns of BB density, newly assembled BBs asymmetrically localize in gradients on different sides of the cell. Interestingly, we found that the distribution of new BB assembly dynamically changes through the cell cycle. Early in the cell cycle (fewer than 400 total BBs per cell), new BB assembly is enriched on the cell’s left side (rows 7–9) (Figure 6). As cells advance in the cell cycle, new assembly gradually shifts outward in both directions from this initiation point. This result revises the previous conclusion that BB assembly was low in this region (Kaczanowski, 1978), which was presumably because few cells early in the cell cycle were sampled in that prior study. This suggests a spatial and temporal distribution of new BB assembly that changes as the cell cycle progresses. Spatial distributions of new BB assembly have also been described in Paramecium (Iftode et al., 1989; Sperling et al., 1991). Understanding how the regulatory factors responsible for new BB assembly differentially localize to and promote BB assembly will establish a new mechanism for the spatial control of new BB assembly (Iftode et al., 1989).

To study the cell morphology changes throughout the cell cycle, a synthetic generative model of average cell geometry based on the number of BBs and ciliary arrays was created using nonparametric regression and spline fitting approaches. Our generative model is statistically accurate to reflect the cell geometry at different cell cycle stages and allows us to create synthetic cell model trajectories that reflect the cell geometry changes throughout the cell cycle. Because we cannot yet visualize BB assembly by live cell imaging throughout the cell cycle, these predictive models allow us to systematically and quantitatively organize the aspects of the spatial and temporal control of Tetrahymena BB assembly.

Method to study mutants with abnormal BB organization and cell morphology

In the future, we anticipate that our image analysis and modeling approach will prove to be useful in the study of Tetrahymena genetic mutants. First, the high accuracy measurement of BB numbers and cell morphology will provide a quantitative output for genetic mutants and the potential variable outputs. Such analyses can then be studied in the context of the 22 parameters measured here and can be further expanded to understand additional cellular parameters contributing to the mutant phenotype. Finally, generative models will next test how BB assembly and distribution promote the unique features that are specific to such mutants. For example, we predict that quantitative analyses of mutants like the disA-1 mutant could predict whether the distributions of both BB assembly and loss are spatially and temporally dysregulated through the cell cycle (Jerka-Dziadosz et al., 1995; Galati et al., 2014; Soh et al., 2020). Such quantitative tools may inform novel BB and cortical morphogenetic regulators.

MATERIALS AND METHODS

Tetrahymena thermophila culture

A wild-type T. thermophila strain (B1868) that endogenously expresses the mCh-tagged BB component Poc1 protein was grown in 2% SPP media (2% proteose peptone, 0.2% glucose, 0.1% yeast extract, and 0.0003% Fe-EDTA) (Pearson et al., 2009a). Cells were grown to mid–log phase (2–4 × 10⁵ cells/ml) as determined using a Coulter Counter Z1. Cells were not cell cycle synchronized.

Light microscopy

Imaging experiments were performed using an inverted microscope (Nikon Ti Eclipse) with a 60× Plan-Apo (NA 1.40) objective lens (Nikon) and a spinning-disk module (CSU-X1; Yokogawa). Images were acquired at room temperature. They were captured with a charge-coupled-device camera (iXon X3; Andor Technology) and Slidebook imaging software (3i—Intelligent Imaging Innovations). Image voxel size was 180 nm × 180 nm × 200 nm. To ensure accurate representation of BB organization and cell volume, care was taken to ensure that the entire cell volume was captured. Image acquisition conditions were kept constant across each of three biological replicates.

Preservation of cell morphology

To retain cell morphology, Tetrahymena cells were fixed using 1 ml of 3.2% paraformaldehyde/PHEM (PHEM, 60 mM PIPES, 25 mM HEPES, 10 mM EGTA, and 2 mM MgCl₂, pH 6.9) + 0.24% Triton X-100 for 5 min at 25°C. Next, cells were washed three times with PHEM buffer. Finally, cells were mixed with 80 µl of mounting media (Citifluor AF1) and introduced into 50 × 50 µm microfluidics chambers to prevent cell compression (Soh et al., 2022).

Tetrahymena cell, oral apparatus, basal body, and cell pole detection

Pipeline processing began by normalizing the voxel values into a range of 0–1. To initially separate the foreground and background signals, the normalized image was blurred with Gaussian filters with a bandwidth of 20 voxels in each of the three dimensions. This blurred image was subtracted from the normalized image to yield image I. The identification of BBs in this image is complicated by the fact that the fluorescence signal is not evenly distributed among the z-slices. It is typically stronger on the side of the cell where the coverslip/objective is positioned—this facilitates light collection and detection. Conversely, light is scattered more on the opposite side of the coverslip and this leads to less light collection and weaker fluorescence signal. Therefore, a Hessian-based multiscale filter (the MATLAB “fibermetric” function with a thickness of five voxels) was used to enhance the tubular and blob structures to yield a signal-enhanced image I_SE.

The image typically has a large proportion of background pixels. Each cell was segmented from other cells and extraneous objects by 1) making a 2D maximum-intensity projection (MIP); 2) setting a threshold of 0.1 times the mean value of the MIP, subtracting this threshold value from the MIP, and blurring the subtracted MIP using a Gaussian filter with a bandwidth of 1; 3) sequentially applying a Laplacian of Gaussian filter and another Gaussian filter with a bandwidth of 2.5; 4) separating the foreground region (cell region) by applying Otsu thresholding; 5) applying image opening on the detected cell to fill holes, and 6) removing objects smaller than 5000 pixels (162 μm²) (to remove other incomplete cells from the image). I and I_SE were then cropped to the cell region plus a margin of two pixels.

We then identified the potential OA region in the cropped image I by applying a threshold of 0.45 × (max(MIP)–min(MIP)). The resulting connected components with sizes larger than 75 voxels (0.486 μm³) were considered the potential OA area.

The next step was to detect the fluorescence tagged BBs in the cropped I. I_SE was binarized using a threshold of half of its Otsu threshold (the factor of a half was used to make sure immature BBs with dimmer signals are not missed). This mask was applied on cropped I by setting the pixels to 0 if they are 0 in the mask and keeping the original values if they are 1 in the mask to produce image I_B. Potential BB centers are then identified by finding local maxima in I_B. These potential BBs were divided into OA and cortical BBs. OA BBs have a stronger fluorescence signal, so they were identified using a threshold of the 95th percentile of the nonzero pixel values in I_B. OA BBs were also assumed to have relatively more even intensities than the cortical BBs and to always lie in the potential OA area described above. Because all cortical BBs should lie on the surface of the cell, an α-shape 10% thinner than the cell surface was fitted and potential BBs inside it (presumably arising from noise) were discarded. Finally, the resulting cortical BBs were divided into mature and immature BBs by defining immature BBs as those having an intensity less than or equal to 50% of their nearest neighbor.

To find the anterior pole and posterior pole, 10 farthest pairs of the potential BBs were found, and the k-means clustering algorithm was used to group those points into two clusters; the centers of two clusters were the initial estimates of the poles. The pole positions were iteratively further adjusted with the expectation-maximization algorithm, as follows. The currently estimated poles were used for ciliary row alignment (see below), and the average positions of the heads and tails of all the aligned ciliary rows were used as the new estimated poles. This process was iterated 50 times. The pole closer to the OA region was denoted the anterior pole. Using the initial poles, the cell was centered and rotated to be vertical. We defined the direction from the posterior pole to the anterior pole as the z-axis, and the (x–y) plane as perpendicular to this line.

Ciliary row alignment

A rule-based alignment pipeline was used to align identified BBs into multiple ciliary rows (using the current estimate of the pole positions). First, a pairwise distance N × N matrix, D, for all BBs was calculated, where N is the number of identified BBs, using

where B_i = (x_i, y_i, z_i), B_j = (x_j, y_j, z_j), and wEu(⋅) is a a weighted Euclidean distance function,

where w = 0.75 when both BBs lie in the anterior region, ||B_i – antPole ||₂ < 9 and ||B_j – antPole ||₂ < 9; w = 0.5 otherwise. The function Dis2Plane (p₁, p₂) was used to calculate the distance between point p₁ and the plane defined by p₂, the anterior pole and the posterior pole. Z₁ and Z₂ are two normalization factors defined as and . Because the distance metric is critical to the alignment, the weights for the two distance components were chosen by iterative visual examination to maximize the vertical appearance of the rows; the chosen values were w₁ = 0.7 and w₂ = 0.3.

With the pairwise distances for all pairs of BBs, BBs were connected to each other if each of them was the closest anterior or posterior neighbor to the other; this resulted in an initial alignment with lots of short rows. To include more unassigned BBs into the currently aligned rows, for each ciliary row, starting from the head and tail of the row, remaining neighbor unassigned BBs were found and iteratively added into the row if they did not result in sharp angles with the current ciliary rows. To further maintain the rows naturally, short rows were connected if one row’s head was close to the other row’s tail and they did not form sharp angles or crossover along the row. If a BB in the aligned ciliary row resulted in a sharp angle, that BB was removed and the two remaining parts of the row were connected. Finally, all rows shorter than 8 μm were discarded.

Once the final alignment is reached, the major and minor axes are chosen as axes of the largest horizontal cross-section ellipse of the cell body. These are found by projecting all BBs onto the x–y plane and performing PC analysis on the projected BBs; the resulting PCs are the major axis and the minor axis.

Validation of image processing pipeline

The image processing pipeline was validated by comparing three metrics that assess BB organization between manual inspection and the image processing pipeline. This was done for three replicates of 10 cells each. First, the accuracy of cortical BB identification was determined based on the number of BBs that were missed by the processing pipeline. “Missed BBs” were either attributed to dim BBs or BBs that are so closely positioned that they were not spatially resolved by our imaging system. Second, the average inter-BB distance was calculated for both manual measurement and the image processing pipeline. Third, the number of assigned ciliary rows was tabulated for both the image processing pipeline and manual determination (which was done by estimating the number of rows in half of the cell). In addition, the accuracy of the image processing pipeline in determining immature BBs was assessed by manual inspection of immature BBs (dim Poc1p-mCh fluorescence signal) that were identified by the pipeline. The fraction of immature BBs per cell that was identified by our image processing pipeline is consistent with prior literature (Galati et al., 2015).

Cell features

To group features into similar subsets, we performed k-means clustering on 22 features for different cluster numbers (2, 3, 4, and 5), and finally grouped them into four groups as this gave reasonable and interpretable groupings. The loading factors of features for each PC were normalized so that their sum for a particular PC equals 1. To identify the major features contributing to each PC, we calculated the average magnitude of loading factors for a PC among all features and chose those features whose loading factor’s magnitude was above the average magnitude.

Generative model of Tetrahymena morphology

The generative model synthesizes average cells conditional on two input parameters, the number of BBs and the number of ciliary rows. We assume that the BB positions and cell morphology will depend on only the two input parameters and that synthetic cells can be generated by averaging the properties of those measured cells with similar numbers of BBs and ciliary rows. For simplicity, we treat the cell length, widths, surface outline, and BB distribution on the cell surface as four independent components. Specifically, we fitted three first-order local polynomial regression functions with the Epanechnikov kernel using the number of BBs (m) as the independent variable and the cell length, major axis width, and minor axis width (separately) as the response (dependent) variable (y) by minimizing the following objective for each new m

where N is the total number of cells we measured, m_i and y_i are the number of BBs and the response value for the ith real cell, respectively, K(⋅) refers to the Epanechnikov kernel function, Δm is the largest difference in m among the measured samples, and β₀ and β₁ are regression coefficients that are determined for each m before making a prediction y for that m. The fitted curves are shown in Figure 8, A–C.

FIGURE 8:

Fitting curves in generative modeling. (A–C) Local polynomial regression on cell’s widths and length conditional on the number of BBs. Here, each data point refers to a measured real cell. (D) Example of cell outline fitting via smoothing spline. Note that the cell outline is fitted for each individual cell. Each point refers to a cortical BB in this cell.

Cell outline

To quantitatively model the morphology of each cell body, we fitted the cell surface using the outermost BB coordinates. We assume that the horizontal cross-plane (X–Y plane) of the cell body is an ellipse, which can be written in the polar coordinate system as

where w₁ and w₂ are the major and minor axis widths. To model the cell outline, we learned the relationship between z and the cross-section r² using a spline fit of r² = f(z/h). Note that the z coordinate of each BB is normalized by the cell length, h; the normalized z/h coordinates will range from 0 to 1. Fitting was done with the Smoothing Spline model in MATLAB with a smoothing parameter of 0.995. An example fitted cell outline is shown in Figure 8D.

We also adopted a local weighting strategy for generating cell outlines. After fitting the cell outline for each individual real cell, we generate the cell outline, f, for a new cell with m BBs using

where K(⋅) is the Epanechnikov kernel function with a bandwidth of 20; m_i and f_i refer to the number of BBs of the ith real cell and its corresponding cell outline.

Basal body spatial distribution

We found that the BB distribution is denser in the anterior region than in the medial region and even sparser in the posterior region. We therefore created a precise model of this behavior. For each cell, we first normalized the z-coordinates of measured BBs, z, by the cell length, . Then, the cumulative density function (CDF) of BBs along the z-axis for each cell, that is, the fraction of BBs whose z-coordinates are lower than an input length, was estimated from the histogram of all z’ values. To enable sampling of new BB lengths given a CDF, we fitted an inverse CDF using third-order polynomials with the bin height of the histogram as the independent variable and the bin center position as the dependent variable.

Similar to the cell outline, a local weighting strategy was also used to generate a new BB density function,

where K(⋅) is the Epanechnikov kernel function with a bandwidth of 20; m_i and g_i refer to the number of BBs of the ith real cell and its corresponding CDF.

To generate individual BB coordinates for a new cell with n rows and m BBs, we first sample the number of BBs in each ciliary row according to the learned number of BBs distribution (Figure 3). Then, for each ciliary row with n_i BBs, we sample n_i points ranging from 0.03 to 0.98, and with the estimated inverse CDF, we can calculate the normalized z-coordinates, z’, for n_i BBs in this row. To calculate the corresponding normalized x–y coordinates, r² for each is calculated from the spline fit described above. To locate the BB in the polar coordinate system, we sample n evenly spaced angle values over 2π; the BBs in the ith row are assigned . However, the ciliary rows are not always vertical from the anterior pole to the posterior pole; to model the variation and dependency among the ciliary rows, we sample individual θ values for each BB as follows:

where θ_ij denotes the polar angle associated with the jth BB in the ith ciliary row. That is, the polar angle, θ, of a BB is conditional on its neighbor BBs at the same ciliary row and neighbor ciliary row. The x and y coordinates for each BB are then calculated as

Feature comparison

To quantitatively assess the differences between the distributions of the PC between synthetic and real cells, we smoothed the discrete feature values for each PC into continuous distributions with Gaussian kernels, as shown at the top and right part of Figure 5, and calculated the weighted KL divergence as follows,

Here, p_k and q_k are the smoothed distributions of the kth PC of the synthetic and real cells, respectively; w_k refers to the fraction of the variance explained by the kth PC.

Cell cycle modeling

Because our unsynchronized images cover the Tetrahymena cell at different stages of its cell cycle, we can further expand our generative model to be a dynamic model that can generate a temporal sequence of synthetic cells that cover cell growth until cell division. We assume that the number of ciliary rows is static during one cell cycle. Because the model we described above depends only on the number of ciliary rows and BBs, this means that the number of BBs will be the only factor that drives the synthetic cell growth. From the BB detection results, we found that the fraction of immature BBs in the anterior (0.75 < z’ ≤ 1), anterior medial (0.5 < z’ ≤ 0.75), posterior medial (0.25 < z’ ≤ 0.5), and posterior (0 < z’ ≤ 0.25) regions were 0.0523, 0.1639, 0.1645, and 0.1361, respectively. To simulate a single cell through a full cell cycle, we start with a synthetic cell containing only mature BBs. We then iteratively choose a small proportion of mature BBs in each region to incorporate daughter BBs. To be specific, we select kp/T BBs in each cell region, and a daughter (immature) BB is added next to each selected BB. Here, k is the number of immature BBs predicted from the current cell stage, p is the fraction of immature BBs in that cell region, and T is a manually chosen parameter (set to 3 in this work) that defines how many iterations after its birth it takes for a newly created BB to be considered mature. The ciliary row in which the new BB is placed is selected according to the fraction of new BBs in each ciliary row at the current cell stage as shown in Figure 6B. The newborn BB is placed next to its mother BB and gradually moves in the anterior direction according to the BB density we estimated.

Availability

All original images are available from https://github.com/murphygroup/PearsonGroupImages. All source code and intermediate results are available as a Reproducible Research Archive at https://github.com/murphygroup/TetAlyze. The TetAlyze software accepts a wide range of image formats.

Abbreviations used:

BB

basal body

CDF

cumulative density function

mCh

mCherry

MIP

maximum-intensity projection

OA

oral apparatus

PC

principal component

3D

three dimensional.