Temporal changes in surface tension guide microtubule organization and accurate asymmetric division of Arabidopsis zygotes

Abstract

In most plants, the zygote divides asymmetrically to define the body axis. In Arabidopsis thaliana, the zygote undergoes polar cell elongation with maintaining a transverse band of cortical microtubules (MTs) at the growing cell tip. How the MT band is maintained at the actively renewing tip and whether it contributes to the asymmetric zygote division remain elusive. By combining live-cell imaging, mechanical simulation, and various perturbation analyses, we demonstrate a bidirectionally interactive feedback in which the MT band forms a mechanical frame to support polar zygote elongation, and this growth increases the calculated surface tension at the zygote tip to induce MT band formation. Furthermore, after zygote elongation is complete, the MT band guides another MT band, preprophase band, to determine the accurate cell division site. Therefore, the MT band is maintained via mechanical feedback with polar cell growth, ensuring the proper asymmetric cell division of the zygote.

Kang et al. demonstrate that mechanical feedback between surface tension and microtubules underlies polar growth of Arabidopsis zygotes. This feedback also ensures asymmetric cell division that establishes the plant body axis.

Introduction

Initiation of the main body axis is one of the first steps in developing an organism from a unicellular zygote. In most plants, ontogeny begins with the zygotic asymmetric cell division that prefigures the apical–basal axis. In Arabidopsis (Arabidopsis thaliana), the zygote undergoes polar elongation before dividing asymmetrically; thus, the apical–basal direction is already evident during zygote growth¹. Based on live-cell imaging of the zygote, we recently showed that the zygote tip, where the sperm cell fused to the egg cell, grows in the apical direction². In plant cells that undergo polar elongation, such as root hairs and pollen tubes, actin filaments (F-actin) and microtubules (MTs) align longitudinally along the direction of cell growth^3,4. Zygotes have longitudinally aligned F-actin but form a transverse band of cortical MTs at the subapical region of the growing cell tip⁵. The subapical MT band is not typical in polarly growing cells of angiosperms, but a similar structure is found in the elongating tip of protonema of southern maidenhair fern (Adiantum capillus-veneris)⁶. Both in Arabidopsis zygote and fern protonema, MT disruption caused tip swelling, implying an important role of the MT band in supporting cell elongation of a particular type of polarly elongating cells^5,7. But the mechanism of the subapical MT band formation and its role in the zygote polarization are both unclear.

Another well-known type of MT band is the preprophase band (PPB), which is formed at the future cell division site in plant cells. The PPB is generally formed at the cortical region surrounding nucleus⁸. Indeed, the division plane is formed where the migrating nucleus arrives in asymmetrically dividing cells of Arabidopsis, such as initial cells of stomata and lateral root^9,10. In the zygote, the nucleus migrates apically along F-actin, and the PPB and cell division plane form at the apical region⁵, but the relationship between these structures and the subapical MT band is unknown.

In this study, we found that the subapical MT band is retained at a constant position relative to the growing tip, and the MT band forms a mechanical frame to restrict the zygote growth direction. By combining quantitative live-cell imaging, computer simulation, and mutant analyses, we demonstrated that the polar zygote elongation induces a temporal change in calculated surface tension at the subapical region, which works as the driving force to maintain the MT band. Furthermore, after zygote growth is complete, PPB is formed near the MT band site, prior to the zygote division. These findings suggest a mechanical feedback between cell growth and MT organization underlies not only zygote polarization, but also the asymmetric division of the zygote.

Results

The MT band is maintained at a constant distance from the apical cell pole during zygote elongation

We analyzed the dynamics of zygote growth and MT structure in Arabidopsis based on time-lapse observations using MT/nucleus markers and two-photon excitation microscopy (2PEM) (Fig. 1a, Supplementary Movie 1). The MT/nucleus marker contains an MT marker (EC1p::Clover-TUA6, expressing a green fluorescent protein Clover fused with TUBULIN ALPHA6 under the control of EGG CELL1 promoter) and a nucleus marker (ABI4p::H2B-tdTomato, expressing HISTONE H2B fused with a red fluorescent protein tdTomato under the control of ABA INSENSITIVE4 promoter). As shown previously, we detected the subapical MT band during zygote elongation⁵. The MTs then form the mitotic apparatus, including the PPB, spindle, and phragmoplast, leading to asymmetric cell division (see below). We performed quantitative analysis of the images to capture the spatiotemporal dynamics of cell growth, such as cell contour, cell length (L), and tip radius (r_e), as well as detecting the MT band based on truncated Gaussian fitting of MT signal distribution along the cell centerline (Fig. 1b, Supplementary Fig. 1 and Supplementary Movie 1, see Methods). As previously observed, the zygote growth rate (dL/dt) first increased and then decreased, while cell tip radius decreased and then increased, resulting in a slightly constricted cell shape (Fig. 1c, d)². The subapical MT band remained at a constant position relative to the cell tip during zygote elongation, and gradually shifted toward the basal region where the PPB formed prior to the zygote division (Fig. 1e).

Fig. 1. MT bands are kept at a constant position from the growing zygote tip.

a Time-lapse images of a zygote expressing MT (green) and nuclear (magenta) markers. Maximum-intensity projection (MIP) images of two-photon excitation microscopy (2PEM) images are shown. Numbers indicate the time (hour:min) from the first frame. White and yellow brackets show the subapical MT band and PPB, respectively. The yellow arrowhead indicates the cell division plane. b Schematic illustration of the method used for image quantification. For details, see “Methods”. c Time course of cell growth rate (dL/dt; red) and tip radius (r_e; blue) of the zygote shown in (a). d Contour dynamics of the zygote up to just after cell division (17:20), with the time indicated by color code. e Kymograph showing MT and nuclear signal intensities, which are projected onto the zygote centerline. Background areas above the zygote are shown to indicate the apical end of the cell. Dashed black lines indicate the upper and lower ends of the MT band, as determined by Gaussian fitting (as shown in (b) and Supplementary Movie 1). The yellow arrow marks the timing of cell division. Images are representative of 14 samples. Scale bars: 10 μm. Source data are provided as a Source Data file.

The subapical MT band is required for a mechanical frame to maintain the shape of the zygote tip

To investigate the role of the MT band in zygote growth, we analyzed the effects of a MT polymerization inhibitor (oryzalin) and a MT depolymerization inhibitor (taxol) (Fig. 2). In contrast to untreated zygotes (Fig. 2a–c), the oryzalin-treated zygotes swelled, with a continuous increase in cell radius and a decrease in growth rate, revealing the loss of radial growth restriction (Fig. 2e–g, Supplementary Movie 2)⁵. MT bands disappeared and were not detectable by Gaussian fitting (Fig. 2h; compare to Fig. 2d). By contrast, taxol treatment distorted the cell shape, leading to non-uniform growth (Fig. 2i–k, Supplementary Movie 3). The MT bands occasionally became wider and reached toward the cell apex (Fig. 2l). Cell division failed in oryzalin-treated zygotes (Fig. 2e), likely due to blocked formation of the mitotic apparatus. Taxol treatment led to a longer apical cell (Fig. 2i) and thus a more symmetric division compared to untreated zygotes (Fig. 2m), suggesting that the MT band contributes to the determination of asymmetric cell division. These features were observed in all samples examined (16 oryzalin-treated zygotes and 12 taxol-treated zygotes; Supplementary Figs. 2, 3). These results indicate that the MT band is maintained at the subapical region of the zygote by the proper balance of polymerization and depolymerization and is required for a mechanical frame to restrict the zygote growth direction.

Fig. 2. The subapical MT band is required for the formation of a mechanical frame to maintain the shape of the zygote tip.

(a–l) Dynamics of untreated zygote (a–d) and zygotes treated with an MT polymerization inhibitor (1 μM oryzalin) (e–h) or a depolymerization inhibitor (10 μM taxol) (i–l). a, e, i Time-lapse images. b, f, j Contour dynamics up to just after cell division (11:20; b and 15:00; j) or nuclear condensation (14:20) (f). c, g, k Time course of cell growth rate (dL/dt; red) and tip radius (r_e; blue). d, h, l Kymographs showing MT and nuclear signal intensities. No MT band was detected in oryzalin-treated zygotes due to diffused signals (Supplementary Movie 2). Dashed black lines in (d, l) indicate the upper and lower ends of the MT band; its precise area could not be extracted by Gaussian fitting in (l) due to the distorted shape of the signal peak (Supplementary Movie 3). Yellow arrows mark the timing of cell division in (d, l). m Boxplot showing the ratio of apical to basal cell length, as an indicator of zygote division asymmetry. Center line, median; box limits, upper and lower quartiles; whiskers, maximum and minimum points within 1.5 × the interquartile range from box limits. Individual data points are also shown. Significant difference was detected by two-sided Welch’s t-test (**P = 0.00631; n = 14 and 12 for untreated (none) and taxol-treated ovules, respectively). Images are representative of 14, 16, and 12 samples for untreated (none), oryzalin-treated, and taxol-treated samples, respectively. Scale bars: 10 μm. Source data are provided as a Source Data file.

In general, cortical MTs are known to support rigid cell wall formation by guiding cellulose synthase complexes¹¹. Therefore, to investigate whether the subapical MT band functions as a mechanical frame through cell wall formation, we performed dual observation of the MT/nucleus marker and cellulose-specific dye Calcofluor White (CFW) (Supplementary Fig. 4a–e). Ovules expressing the MT/nucleus marker were fixed, cleared using ClearSeeAlpha, and stained with the CFW¹². Although fixation-induced damage slightly distorted the zygotes and attenuated MT signals, clear CFW staining was observed in the basal and lateral regions of elongating zygotes, whereas little or no signal was detected in the apical region above the MT band (Supplementary Fig. 4a, b, Supplementary Movie 4). In dividing zygotes after the MT band had disappeared, CFW signals were observed across the entire cell surface, including the apical region and newly forming cell plate (Supplementary Fig. 4c, d), and this uniform signal persisted after division (Supplementary Fig. 4e). Since transmission electron microscopy (TEM) revealed a continuous outer layer covering the entire cell surface at all stages examined before and after fertilization (Supplementary Fig. 4f), other cell wall materials, such as pectin and callose, might also contribute to maintaining the zygote tip structure, as in other polar growing cell¹³.

The MT band is located at the subapical region where the time changes of estimated surface tension reach a maximum

Next, we explored how the MT band is maintained at a constant position in the actively renewing zygote tip. MTs are proposed to act as tension sensors; thus, cortical MT alignment can change in response to cell surface tension^14,15. Therefore, we estimated the mechanical properties of growing zygotes by combining computer modeling with time-lapse imaging. We recently found that zygote growth can be reconstructed using the viscoelasto-plastic deformation model¹⁶, which simulates cell morphogenesis (deformation from the initial to next shape) based on two mechanical parameters: the expansion force from inside the cell (turgor pressure: P) and the deformability of the cell surface (surface extensibility: Φ) (Fig. 3a, Supplementary Fig. 5a, b, see “Methods”)¹⁷. Although surface extensibility is a complex variable with spatial distribution, we determined that a single parameter defining the range of extensible area (extensibility range: l_g), combined with turgor pressure, is sufficient to describe hemispherical tip deformation of the zygote (Supplementary Fig. 5c, d)¹⁶. Therefore, we searched for a suitable combination of P and l_g at each time point that explains the actual dynamics of zygote deformation, i.e., changes in the growth rate and tip radius obtained from the wild type time-lapse data shown in Fig. 1 (Fig. 3b, c, Supplementary Fig. 5e), and reconstructed the model zygote (compare ‘Data’ and ‘Model’ in Fig. 3d). Based on the model zygote, we calculated the spatial distribution of circumferential surface tension (one of the surface mechanical stresses in the circumferential direction: σ_θ) with respect to the surface distance from the zygote apex. The value below the subapical region was clearly larger than that at the tip at all time points examined (Fig. 3e, Supplementary Movie 5). To precisely estimate the temporal change of σ_θ, we calculated the time derivative of the surface tension (Dσ_θ/Dt), considering the zygote tip as a moving coordinate system of surface points (see “Methods”). This time change markedly increased at the subapical region, which corresponds to the MT band position (Fig. 3f, g, Supplementary Movie 5), leading to the hypothesis that the MT band is maintained at the subapical region by the temporal change (i.e., the constant increase) of surface tension. Moreover, the temporal average of MT band width (6.6 µm, Fig. 3g) was wider than the region of maximum time change (2.2 µm, Fig. 3f). This observation is consistent with our agent-based model simulations of cortical MT organization (“Methods”) where MT bands can form that are wider than the external cue zone mimicking the large time change region (Supplementary Fig. 6).

Fig. 3. MT bands are present at the subapical region where the time change of surface tension reach a maximum.

a Schematic illustration of the viscoelasto-plastic deformation model. For details, see “Methods”. b–d Results of parameter estimation for the untreated wild-type (WT) zygote are shown in Fig. 1a. b Comparisons of cell growth rate (dL/dt) and cell tip radius (r_e) between time-lapse observation data (Data; magenta) and reconstructed model zygote (Model; green). c Estimated turgor pressure (P) and extensibility range (l_g). d Comparisons of the contour dynamics of Data and Model. Only the right half of the zygote tip is shown. e–g Calculated circumferential surface tension (σ_θ) (e), its time change (Dσ_θ/Dt) (f), and observed MT signal intensity (g) (Supplementary Movie 5). Values at each distance from the zygote tip (S) are plotted with color codes, as shown to the right of each graph. Magenta lines and crosses in (g) indicate the MT bands and their centers, respectively. Source data are provided as a Source Data file.

Tension-induced MT band formation requires balanced MT polymerization and depolymerization

To evaluate the usefulness of the viscoelasto-plastic deformation model and to further examine the relationship between cell growth, tension dynamics, and MT organization, we searched for a suitable combination of P and l_g that reproduces the actual deformation of oryzalin- and taxol-treated zygotes shown in Fig. 2 (Fig. 4a–c, g–i). In oryzalin-treated zygotes, the estimated l_g, the range of tip extensible area, ranged from 7.6 to 9.6 µm (Fig. 4b), which was larger than that in untreated zygotes (from 5.9 to 8.6 µm; Fig. 3c). In contrast, taxol-treated zygotes showed a smaller l_g ranging from 5.4 to 6.5 µm (Fig. 4h). Consistent with the findings described above, this difference in l_g values likely reflects changes in mechanical constraint for the tip expansion: oryzalin-induced loss of the MT band and taxol-induced widening of the band represent weakening and strengthening of the mechanical frame, respectively.

Fig. 4. Disruption of MT turnover affects the tension-induced MT band formation.

a–l Results of parameter estimation (a–c, g–i) and comparisons of tension and MT band pattern (d–f, j–l) for the oryzalin-treated zygote shown in Fig. 2e (a–f) and the taxol-treated zygote shown in Fig. 2i (g–l). a, g Comparisons of cell growth rate (dL/dt) and cell tip radius (r_e) between time-lapse observation data (Data; magenta) and reconstructed model zygote (Model; green). b, h Estimated turgor pressure (P) and extensibility range (l_g). c, i Comparisons of the contour dynamics of Data and Model. d–f, j–l Calculated circumferential surface tension (σ_θ) (d, j), its time change (Dσ_θ/Dt) (e, k), and observed MT signal intensity (f, l) (Supplementary Movies 6, 7). Magenta lines and crosses in (l) indicate the MT bands and their centers. No MT band was detected in oryzalin-treated zygotes (Supplementary Movie 2). Source data are provided as a Source Data file.

We further calculated the spatial distribution of estimated surface tension (σ_θ) and its time change (Dσ_θ/Dt) with respect to the zygote apex. Similar to untreated zygotes, both oryzalin- and taxol-treated samples exhibited an increase in Dσ_θ/Dt in the subapical region (Fig. 4d, e, j, k, Supplementary Movies 6, 7). However, as noted above, an MT band was not detected in this region in oryzalin-treated zygotes (Fig. 4f), whereas taxol-treated zygotes displayed a broader MT band (8.1 µm, Fig. 4l) than in untreated samples (6.6 µm, Fig. 3g). These results suggest that while growth-dependent changes in tension still occur under both drug treatments, abnormal MT stability disrupts the proper organization of MT bands in response to the mechanical cues.

Taken together, these findings lead us to propose bidirectional mechanical feedback between MT organization and cell growth: the subapical MT band forms a mechanical frame that restricts radial expansion at the zygote apex, while the growth-dependent increase in surface tension promotes MT band formation through the regulation of MT turnover.

Continuous zygote elongation is required to maintain the subapical MT band

To test this mechanical feedback hypothesis, we examined the importance of growth-dependent changes in tension for MT band maintenance (Fig. 5). For this purpose, we introduced the MT/nucleus marker described above into an Arabidopsis mutant in the mitogen-activated protein kinase kinase kinase YODA (YDA), yda-2991, in which zygote growth arrests prematurely^18,19. Live-cell imaging of yda showed that the subapical MT band was initially present in young zygotes (before 05:20 in Fig. 5d; compare to Fig. 5a, Supplementary Movie 8). However, as cell elongation slowed (Fig. 5e), MT signals dispersed and the MT band was no longer detectable by Gaussian fitting (after 05:40 in Fig. 5d, f; compare to Fig. 5a–f).

Fig. 5. The MT band disappears after zygote elongation ceases.

a–f Dynamics of wild-type (WT, a–c) and yda (d–f) zygotes expressing MT (green)/nuclear (magenta) markers. a, d Time-lapse images. White and yellow brackets show the MT band and PPB, respectively. Yellow arrowheads indicate the cell division plane. b, e Time course of cell growth rate (dL/dt; red) and tip radius (r_e; blue). c, f Kymographs showing MT and nuclear signal intensities. Dashed black lines indicate the MT band based on Gaussian fitting. The fitting of yda shows the disappearance of the subapical MT band after 05:20 and the appearance of the PPB at 10:40 (Supplementary Movie 8). Note that the nuclear signal was faint and barely detectable. Yellow arrows mark the timing of cell division. g–l Results of parameter estimation (g–i) and comparisons of tension and MT band pattern (j–l) for the yda zygote shown in (d). g Comparisons of cell growth rate (dL/dt) and cell tip radius (r_e) between time-lapse observation data (Data; magenta) and reconstructed model zygote (Model; green). h Estimated turgor pressure (P) and extensibility range (l_g). i Comparisons of the contour dynamics of Data and Model. j–l Calculated circumferential surface tension (σ_θ) (j), its time change (Dσ_θ/Dt) (k), and MT signal intensity (l) (Supplementary Movie 9). Magenta lines and crosses in (l) indicate the MT bands and their centers, respectively. Magenta and orange arrowheads indicate when the large time change of surface tension is lost (03:20) and when the MT bands are no longer detectable (05:40), respectively. Images are representative of 14 and 12 samples for WT and yda, respectively. m Boxplot showing the ratio of apical to basal cell length. Center line, median; box limits, upper and lower quartiles; whiskers, maximum and minimum points within 1.5 × the interquartile range from box limits. Individual data points are also shown. Significant difference was detected by two-sided Student’s t-test (**P = 2.17 × 10⁻⁹; n = 14 and 12 for WT and yda, respectively). WT zygotes correspond to “none” in Fig. 2m. Scale bars: 10 μm. Source data are provided as a Source Data file.

To evaluate this further, we used the viscoelasto-plastic deformation model to identify parameter combinations of P and l_g that reproduce the observed deformation of the yda zygote (Fig. 5g–i), and calculated the circumferential surface tension to compare with the MT band pattern (Fig. 5g–l, Supplementary Movie 9). We found that MT bands were maintained at the subapical region as long as cell elongation caused a large time change of estimated tension (Fig. 5k, l). Once this time change diminished (at 03:20), the MT band also disappeared within a few hours (by 05:40; Fig. 5k, l). These results support the notion that growth–driven changes in tension are critical for the maintenance of the subapical MT band.

Although it has been proposed that MTs can autonomously sense tension via tubulin itself, some regulatory factors are also known to rearrange MT patterns in response to tension; a well-known factor is the MT-severing enzyme KATANIN1 (KTN1)^20,21. Therefore, we examined the behavior of zygotes of the KTN1 mutant ktn1-2, which shows abnormal cell division patterns during embryogenesis²². Since ktn1 homozygous plants produce very few seeds, we used self-fertilized ktn1 heterozygous mother plants, in which approximately one-quarter of the embryos exhibited cell division defects (25.0%, n = 64; Supplementary Fig. 7a). Similarly, approximately one-quarter of the zygotes derived from ktn1 heterozygous mothers expressing the MT/nucleus marker showed delayed phragmoplast expansion (28.6%, n = 14), consistent with the ktn1 phenotype reported in other tissues²³, but none of these zygotes showed detectable abnormalities in MT band maintenance, cell elongation, or subsequent PPB formation (Supplementary Fig. 7b, Supplementary Movie 10). These results suggest that KTN1 may not be a crucial factor in the mechanical feedback between cell growth and MT organization.

MT bands guide PPB formation prior to asymmetric division of the zygote

In yda mutant zygotes, the PPB appeared, while after the disappearance of the subapical MT band (at 10:40; Fig. 5d, f, Supplementary Movie 8). The PPB formed away from the subapical region, resulting in a more symmetric than wild type (Fig. 5m). Since MT stabilization due to taxol treatment also affected asymmetric cell division (Fig. 2m), we tested whether the MT band is involved in determining the position of the PPB by examining the positional relationships among the MT band, PPB, nucleus, and cell division plane in wild-type zygotes (Fig. 6a, b). Before cell division, the PPB appeared slightly below the region containing the subapical MT band, above the nucleus (Figs. 1e, 6a and Supplementary Movie 1). The gap was subtle but consistent, as shown by significant differences of the center positions of the MT band, PPB, and nucleus (Fig. 6b). The spindle formed between the PPB and nucleus, establishing the cell division plane (Fig. 6a). Indeed, the cell division site was significantly different from the sites of all these structures, except for the spindle (Fig. 6b), showing that the division plane is formed between the nucleus and PPB.

Fig. 6. The division plane forms between the MT band and nucleus.

a Time-lapse images of wild-type (WT) zygote expressing MT (green)/nuclear (magenta) markers. Enlarged images from Fig. 1a are shown. PPB (yellow rectangle) forms below the MT band (white rectangle) and above the nucleus (cyan arrowhead). Cell division plane (yellow arrowhead) forms between the PPB and nucleus as shown by the dashed lines. b Boxplot showing center positions of the indicated structures. MT band and PPB are shown with the nucleus at the same time points. Significant differences for each structure relative to the cell division plane, and for the MT band and nucleus relative to PPB, were determined by Wilcoxon’s signed rank test (n = 13). n.s., not significant; *P < 0.05 and **P < 0.01. “Division plane” samples correspond to “none” in Fig. 2m. c Time-lapse images of Sgr2 zygote. Upper and lower panels show MIP and midplane images, respectively. A spherical vacuole (Vac) occupying the zygote tip prevents the nucleus from reaching the tip. Cell division plane forms at the nuclear position (Supplementary Movie 11). d Boxplot showing the ratio of apical to basal cell length. Significant difference was detected by two-sided Student’s t-test (**P = 0.00166; n = 14 and 18 for WT and sgr2, respectively). WT zygotes correspond to “none” in Fig. 2m. e, f Time-lapse images of WT (e) and trm678 (f) zygotes, expressing MT(SG)/nucleus markers. WT shows dynamics similar to (a). trm678 lacks a PPB, and cell division plane forms at the nuclear position (Supplementary Movie 12). Images are representative of 18, 21, and 24 samples for sgr2, WT, and trm678, respectively. g Boxplot showing the ratio of apical to basal cell length. Significant difference was detected by a two-sided Brunner-Munzel test (**P = 2.21 × 10⁻⁹; n = 21 and 24 for WT and trm678, respectively). For all boxplots, the center line, median, box limits, upper and lower quartiles, whiskers, maximum and minimum points within 1.5 × the interquartile range from the box limits. Individual data points are also shown. Scale bars: 10 μm. Source data are provided as a Source Data file.

In wild-type zygotes, the MT band and the nucleus are located close to each other, making it difficult to distinguish their individual contributions to PPB positioning. To overcome this limitation, we focused on the shoot gravitropism2-1 (sgr2-1) mutant, in which the nucleus remains distant from the apical region of the zygote¹⁹. The SGR2 gene encodes a phospholipase A1-like protein localized to the vacuolar membrane, and in sgr2, large and rigid vacuoles occupy the apical region in the zygote, preventing the nucleus from reaching the apical pole^24–26. We performed live-cell imaging of MT/nucleus marker in the sgr2 background (Fig. 6c, Supplementary Fig. 8a–c and Supplementary Movie 11). During zygote elongation, the subapical MT band was properly maintained, while the large apical vacuole blocked the nucleus from approaching the apical region (Fig. 6c). The PPB formed at the subapical MT band site, rather than around the nucleus, indicating an effect of the subapical MT band on PPB positioning.

In sgr2 zygotes, the large vacuole persistently occupied the apical region during mitosis, and unlike in wild type, the spindle did not shift toward the PPB site (Fig. 6c). Consequently, the division plane formed at the nuclear position, resulting in a more symmetric division than in wild type (Fig. 6d). This situation hindered the assessment of the direct effect of the PPB on division plane positioning. Therefore, we then focused on the core regulator of PPB formation, TON1 RECRUITING MOTIF (TRM), whose triple mutant (trm678) lacks a visible PPB²⁷. As bright transgenic plants were not obtained with the above-mentioned MT/nucleus marker in this background, we constructed a modified MT marker by replacing Clover with the brighter fluorescent protein tdStayGold (EC1p::tdStayGold-TUA6)²⁸, and combined it with the above nuclear marker (ABI4p::H2B-tdTomato), hereafter referred to as MT(SG)/nucleus.

We confirmed that wild-type zygotes carrying the MT(SG)/nucleus marker showed comparable behavior to those expressing the original MT/nucleus marker (Fig. 6e, Supplementary Fig. 8d–f; compare to Figs. 6a, 1a–e). The trm678 zygotes showed proper cell elongation and retained subapical MT band, but this MT signal dispersed without forming the PPB before cell division (at 12:00; Fig. 6f, Supplementary Fig. 8g–i, and Supplementary Movie 12). Consequently, the spindle and division plane formed at the nuclear position, resulting in a more symmetric division than wild type (Fig. 6f, g). These results indicate that in the absence of a PPB positioned apically relative to the nucleus, the spindle fails to relocate upward.

Taken together, our data indicate that the MT band contributes to PPB positioning and that the PPB, in turn, adjusts the spindle positioning to ensure precise asymmetric zygote division in wild-type Arabidopsis.

Discussion

We propose a bidirectionally interactive feedback mechanism whereby polar zygote growth produces a large time change in the estimated surface tension, which in turn restricts the zygote growth direction via MT band formation, ultimately supporting accurate asymmetric cell division (Fig. 7).

Fig. 7. Schematic representation of dynamics and the proposed mechanism.

Diagram summarizing the mechanical feedback of polar zygote elongation and MT organization, and the role of the MT band in supporting the accurate asymmetric zygote division.

In most animal and plant cells, the dynamic behavior of the cortical cytoskeleton is crucial for growth dynamics. In plants, the rigid cell wall generally covers the entire cell surface. In contrast, we found that the zygote tip lacks a clear CFW signal, suggesting that the MT band itself and/or cell wall components whose synthesis is induced by the MT band may act as a mechanical frame to restrict the direction of zygote growth. However, the precise spatiotemporal relationship between the MT band and the cell wall, and the wall materials that maintain the zygote tip structure, remains unclear. Currently, no live-imaging method has been established for simultaneously visualizing both cell wall synthesis and MT band dynamics in zygotes, as commonly used cell wall dyes for living cells, such as propidium iodide and Pontamine Fast Scarlet 4B, cannot penetrate ovules²⁹. Therefore, establishing such techniques, for example by generating fluorescent markers to visualize the region of cellulose synthesis in zygotes, and combining them with MT inhibitors, will help elucidate the role of the cell wall in mechanical feedback during zygote growth. In addition, it will be important to investigate cell wall components other than cellulose, particularly pectin, since a mutation in NIMNA, which encodes a polygalacturonase (a pectin-degrading enzyme), has been reported to impair zygote elongation³⁰. Furthermore, in the tobacco pollen tube (another type of polar growing cell), the apical wall is largely composed of viscoelastic, methyl-esterified pectins, where cellulose is not detected, and this pectin-rich wall is thought to protect the growing cell tip from rupture during rapid cell elongation^31–33.

We also showed that MT alignment depends on cell growth. The MTs were proposed to function as a tension sensor in various experiments. For example, in an in vivo experiment, forcing protoplasts to change shape led to MT rearrangement³⁴. In the protoplasts, the tension-induced MT pattern was reoriented after several hours, indicating that MTs can respond to temporal changes in tension, rather than the absolute magnitude of tension, with a time lag. Similarly, in the current study, the MT band in yda zygotes disappeared a few hours after the loss of a large time change of estimated surface tension. Our observation that the MT band was wider than the region of maximum time change of estimated tension would also show the delayed response of MTs to the changing stress pattern. In plant tissues, where neighboring cells are tightly anchored by cell walls, damage to and growth of adjacent cells cause external changes in tension and promote MT-dependent cell morphogenesis to adjust the overall tissue shape^15,35. By contrast, the zygote is surrounded by a fluidic giant cell, the endosperm, and thus would freely grow without significant external forces. Therefore, the zygote may induce internal changes in tension by regulating its own growth rate, resulting in cell polarization and, thus, asymmetric cell division. In this stand-alone situation, it seems reasonable that the zygote adopts a simple mechanical mechanism to autonomously amplify subtle polarity information, such as sperm entry from the apical end, leading to the formation of the apical–basal axis.

We also found that the MT band finally shifted toward the basal region, where the PPB formed, and that a division plane formed between the PPB and the nucleus. These events were overlooked in the previous study when the zygotic MT dynamics were first live-imaged⁵, but were discovered in this study by improved image quantification techniques, such as the MT signal tracking by Gaussian fitting and precise comparison of PPB and nucleus locations. Based on these findings, we proposed that the MT band has a dual function: supporting the polar zygote elongation via mechanical feedback and guiding PPB position for influencing cell division asymmetry (Fig. 7).

In zygotes, the nucleus migrates polarly to the apical region along longitudinally aligned F-actin, and thus disruption of F-actin leads to the nucleus being positioned at the cell center⁵. In such zygotes, cell division occurs at the nuclear position⁵, as observed in yda zygotes, indicating that nuclear position is a major determinant of the division plane. Accordingly, the MT band would act as a fine-tuning factor, guiding PPB formation slightly above the nucleus and thereby promoting an even more asymmetric division. The positional gap of PPB and the nucleus seems odd, since the PPB usually forms around the nucleus, but pre-adjusting PPB position via MT patterning should be an effective strategy to ensure asymmetric division. Indeed, in a recent study, polarly localizing proteins in the leaf epidermis depleted stable MTs from a particular cell domain and thus limited the area in which the PPB could form³⁶. Nevertheless, this epidermis cell divides at the nuclear position³⁷, highlighting the uniqueness of the zygote that forms the PPB and the division plane at a different location than the nucleus. In tobacco BY-2 cells, cytoplasmic MTs that link the PPB and the prophase nucleus promote the formation of a bipolar spindle oriented perpendicular to the PPB³⁸. In wild-type zygotes, in which the PPB and nucleus are slightly offset, MTs accumulate predominantly on the nuclear surface distal to the PPB, whereas in sgr2 and trm678 zygotes, both of which lack the perinuclear PPB, MTs cover the entire nuclear surface instead of adopting a bipolar arrangement (Fig. 6). These observations suggest that a similar PPB-dependent mechanism operates to adjust spindle positioning in the zygote.

The findings that trm678 zygotes retained the MT band but failed to form PPB, and that yda zygotes formed the PPB in a different position several hours after the disappearance of the MT band indicate that the MT band and PPB form via different molecular mechanisms (Figs. 5, 6). However, we can only speculate about the mechanisms that determine the exact position of the PPB in zygotes; therefore, it will be important to establish methods to specifically disrupt the MT band prior to PPB formation and thereby clarify the relationship between the MT band, cell shape, and PPB positioning. As mentioned above, the pre-depletion of MTs inhibits PPB formation³⁶. Therefore, it appears to make sense that the PPB forms near the MT band site, an abundant source of MTs. Since apical cell geometry is crucial for setting proper transverse division, an early event in radial axis formation³⁹, the MT band–dependent setting of the precise division site in the zygote would be important for the formation of a small spherical apical cell for subsequent embryo patterning.

Our findings demonstrated that a simple, autonomous mechanism utilizing spatiotemporal mechanical changes and a cytoskeleton that precisely senses them directly leads to the initial event of plant ontogeny. Therefore, this work will facilitate the interdisciplinary research of plant biology with mechanical engineering, physics, and data science, which will enable the manipulation of seed development to enhance agriculture.

Methods

Plant growth conditions and transgenic lines

All Arabidopsis lines are in the Col-0 background. The yda-2991, ktn1-2 (SAIL_343_D12), sgr2-1, and trm678 triple mutants were described previously^19,24,27,40. The MT marker (EC1p::Clover-TUA6, coded as MU2228) was previously described⁴¹. The MT(SG) marker (EC1p::tdStayGold-TUA6, coded as HM06) was generated by replacing Clover with tdStayGold²⁸. These markers were combined with a nuclear marker ABA INSENSITIVE4 (ABI4)p::H2B-tdTomato (coded as MU2463), which contains the 981-bp ABI4 promoter⁴², the full-length coding region of H2B (AT1G07790), tdTomato, and the NOS terminator in the pPZP211 binary vector. Plants were grown at 18–22 °C under continuous light or long-day conditions (16-h light/8-h dark).

Time-lapse observations and histological analysis

The zygote live-cell imaging was performed using a laser-scanning inverted microscope A1 (Nikon) equipped with a pulse laser (Mai Tai DeepSee; Spectra-Physics) and AX (Nikon) equipped with an ultrafast tunable laser (InSight X3 Dual option; Spectra-Physics) as previously described^43,44. Time-lapse images were acquired every 20 min at 25 or 31 z-stacks with 1-μm intervals and using a 40 × water-immersion objective lens (CFI Apo LWD WI; Nikon) with Immersol W 2010 (Zeiss) immersion medium. Fluorescence signals were detected by the external non-descanned GaAsP PMT detectors. In the A1 system, we used two dichroic mirrors (DM495 and DM560), a short-pass filter (492 nm/SP) for CFW stain (see below), a band-pass filter (525/50 nm) for Clover and tdStayGold, and a mirror for tdTomato. In AX system, we used three dichroic mirrors (DM488, DM560 and DM685), and three band-pass filters (457/70 nm for CFW stain, 525/50 nm for Clover and tdStayGold, and 605/70 nm for tdTomato).

For inhibitor treatment, 0.1% DMSO and individual inhibitors [0.1% DMSO containing 1 μM oryzalin (Chem Service) or 10 μM taxol (Wako, Paclitaxel)] were added to the media ∼1 h before observation, as previously described⁴⁵.

For cell wall staining, tissue clearing was performed using ClearSeeAlpha solution¹². The self-pollinated pistils were fixed with 4% (w/v) PFA for 1 h in PBS under vacuum (∼690 mmHg) at room temperature. Fixed pistils were washed in PBS and cleared with ClearSeeAlpha for 3–5 days. Then the cleared pistils were stained with 1 mg/ml CFW (Wako) in water overnight and then mounted in ClearSeeAlpha droplet. The observation was performed with the above microscope (AX). The images were acquired at 25 z-stacks of 1-μm intervals using the above objective lens.

For DIC microscopy of embryo morphology, ovules were cleared in a chloral hydrate solution and observed using a Zeiss Axio Imager A1, as previously described⁴⁶.

Maximum intensity projection (MIP) and image processing were performed using NIS-Elements software (Nikon) or Fiji (https://fiji.sc/). MIP images were generated by projecting all 25 or 31 xy-images, except for Sgr2, where 14 out of 31 images containing the zygote were used to avoid background signal from the ovule.

Transmission electron microscopy (TEM)

Unfertilized and fertilized wild-type ovules were fixed in 2% glutaraldehyde, 4% paraformaldehyde, and 50 mM sodium cacodylate, pH 7.4, overnight at 4 °C. The tissue segments were washed in buffer and post-fixed for 3 h in 2% osmium tetroxide in 50 mM sodium cacodylate buffer at 4 °C. The tissue was then dehydrated in a graded ethanol series and further incubated in ethanol, transferred into propylene oxide, infiltrated, and embedded in Quetol 651. A series of thin sections (80 nm) was stained with 2% uranyl acetate and lead stain solution at room temperature and examined using a JEM-1400Plus transmission electron microscope (JEOL) at 80 kV, and the images were acquired with a VELETA CCD camera (Olympus Soft Imaging Solutions).

Quantification of growth rate and tip shape from live-cell imaging sequence

The location of the zygote in the ovules can fluctuate due to floating and ovule growth in liquid cultivation medium. Based on the previously developed coordinate normalization (image-based and contour-based) methods to fix the zygote position², we developed an improved coordinate normalization (improved CN), using the normalized cross-correlation function^47,48 between the image at the reference time and that at time t using a parallel shift $\left(u,v\right)$ and a rotation $\theta$ as follows.

$$C\left(u,v,\theta \right)=\frac{{\sum }_{x,y}\left[I_{ref}\left(x,y\right)-\overline{I_{ref}}\right]\left[I_t\left(x\left(\theta \right)-u,y\left(\theta \right)-v\right)-\overline{I_t\left(u,v,\theta \right)}\right]}{{\left\{{\sum }_{x,y}{\left[I_{ref}\left(x,y\right)-\overline{I_{ref}}\right]}^2{\sum }_{x,y}{\left[I_t\left(x\left(\theta \right)-u,y\left(\theta \right)-v\right)-\overline{I_t\left(u,v,\theta \right)}\right]}^2\right\}}^{\frac{1}{2}}}$$ 1

where $I_{ref}\left(x,y\right)$ is the fluorescence intensity of the reference image (typically at the initial time frame) at pixel x and y, $\overline{\cdot }$ is the spatial average of $\cdot$, and $I_t$ is the modified image at time t. We applied an exhaustive search for the optimal set $\left(u_{opt},v_{opt},{\theta }_{opt}\right)$, which minimizes the normalized cross-correlation function.

Using the improved CN, we first extracted cell contours from the raw data for all the image sequences using binarization in Fiji (Supplementary Fig. 1a, b). Next, we applied the Voronoi diagram (Supplementary Fig. 1c), which evaluates the skeleton inside the contour as previously analyzed¹⁶. As this method may create lateral branches, we defined the part of the centerline as the longest skeleton neglecting all the branches shorter than the longest one (illustrated with the red line in Supplementary Fig. 1d). We then smoothly extended the ends to the contour (the dashed green line in Supplementary Fig. 1d). We quantified the growth rate dL/dt and tip shape (r_e, r_a) by measuring the cell length L and the ellipse fitting with the horizontal radius r_e and the vertical radius r_a (Supplementary Fig. 1e).

Detection of MT band using truncated Gaussian fitting

Based on the cell shape and centerline described above (Supplementary Fig. 1f), we projected the fluorescence intensity of MT marker within the cell to the centerline (Supplementary Fig. 1g). We then plotted the MT signal intensity as a function of the position z along the centerline (Supplementary Fig. 1h). We fitted the intensity with the truncated Gaussian distribution using parameters ($\mathrm{\alpha },\beta ,\mu ,\sigma ,b$) with average $\mu$ and standard deviation $\sigma$ of the distribution as follows.

$$P\left(z\right)=\frac{1}{\sigma }\frac{\phi \left(\frac{x-\mu }{\sigma }\right)}{\psi \left(\frac{\beta -\mu }{\sigma }\right)-\psi \left(\frac{\alpha -\mu }{\sigma }\right)}+b$$ 2

Here, the Gaussian probability density function is $\mathrm{\phi }\left(x\right)=\frac{1}{\sqrt{2\pi }}\exp \left(-\frac{1}{2}{x}^2\right)$, and the cumulative distribution function is $\psi \left(x\right)=\frac{1}{2}\left(1+\mathrm{erf}\left(\frac{x}{\sqrt{2}}\right)\right)$. We then defined the MT band by $\sigma$ from the average, $2\sigma$ in width. Using the extracted $\mu$ and $\sigma$, we could plot the line segment of the MT band as shown as the magenta line in Supplementary Fig. 1i. The coefficient of determination ($r^2$) is calculated as follows.

$$r^2=1-\frac{{\sum }_i{\left(I_i\left(z\right)-P_i\left(z\right)\right)}^2}{{\sum }_i{\left(I_i\left(z\right)-Ī\right)}^2}$$ 3

where $I_i\left(\mathrm{z}\right)$ stands for the i-th fluorescent intensity at the position z along the cell centerline greater than $b$, and $\overline{\cdot }$ is the spatial average of $\cdot$.

Construction of model zygote based on viscoelasto-plastic deformation model

We constructed a mechanical model for a zygote elongation based on the model previously developed for root hairs as schematically illustrated in Supplementary Fig. 5a^16,17. This model describes the degree of surface stress derived from the pressure on the input shape (curvature $\mathrm{\kappa }$ and cell wall thickness $\mathrm{\delta }$) as shown in the arrow from shape to stress. Then, it calculates the strain rate $\stackrel{°}{\mathrm{\epsilon }}$, which is the consequence of the wall yield beyond the yield stress ${\sigma }_y$ (the arrow from stress to strain). Finally, the next shape is achieved by applying the displacement vector $v$ on the current shape (the arrow from strain to shape).

Cell surface mechanical stresses in the meridional and circumferential directions were formulated as,

$${\mathrm{\sigma }}_{\mathrm{s}}=\frac{P}{2\delta {\kappa }_{\theta }}$$ 4

$${\mathrm{\sigma }}_{\mathrm{\theta }}=\frac{P}{2\delta {\kappa }_{\theta }}\left(2-\frac{{\kappa }_s}{{\kappa }_{\theta }}\right)$$ 5

respectively. Here, the circumferential curvature ${\kappa }_{\theta }$ was calculated by ${\kappa }_{\theta }=\frac{1}{r_{\theta }}$ where the radius $r_{\theta }$ is the curvature of the surface lying on the plane perpendicular to the meridional coordinate (Supplementary Fig. 5b). On the other hand, the meridional curvature ${\kappa }_s$ was calculated by ${\kappa }_s=\frac{1}{r_s}$ where the radius $r_s$ is the curvature perpendicular to the meridional coordinate $S$ (Supplementary Fig. 5c).

The strain rates $\stackrel{°}{\mathrm{\epsilon }}$ on the surface in the meridional and circumferential directions were formulated as,

$$\stackrel{°}{{\mathrm{\epsilon }}_{\mathrm{s}}}=\Phi \left({\sigma }_e-{\sigma }_y\right)\frac{{\sigma }_s-\nu {\sigma }_{\theta }}{K},\mathrm{for}{\sigma }_e\ge {\sigma }_y$$ 6

$$\stackrel{°}{{\mathrm{\epsilon }}_{\mathrm{\theta }}}=\Phi \left({\sigma }_e-{\sigma }_y\right)\frac{{\sigma }_{\theta }-\nu {\sigma }_s}{K},\mathrm{for}{\sigma }_e\ge {\sigma }_y$$ 7

respectively, where $\mathrm{\Phi }\left(S\right)$ is the surface extensibility defined as $\mathrm{\Phi }\left(S\right)={\mathrm{\Phi }}_0\cos \left(\frac{S\pi }{2l_g}\right)$, ${\sigma }_e=\frac{1}{\sqrt{2}}{\left[{\left({\sigma }_s-{\sigma }_{\theta }\right)}^2+{\left({\sigma }_{\theta }-{\sigma }_n\right)}^2+{\left({\sigma }_n-{\sigma }_s\right)}^2\right]}^{1/2}$ with ${\sigma }_n$ standing for the stress perpendicular to the surface, $K={\left[\beta {\sigma }_s^2+\beta {\sigma }_{\theta }^2+\left(\beta -6\nu \right){\sigma }_s{\sigma }_{\theta }\right]}^{1/2}$ and $\beta =2{\nu }^2-2\nu +2$. Here, $l_g$ is the range of extensible area (extensibility range), and ${\mathrm{\Phi }}_0$ is the magnitude of extensibility at $S=0$. We note that the strain rate becomes zero for ${\sigma }_e<{\sigma }_y$, and ${\sigma }_n$ makes the cell wall thinning due to stretching with $\nu \le 1$, but we assumed that the new wall material maintains wall thickness in this study. Since we found that the zygote tips are hemispherical², we utilized the cosine function to describe surface extensibility based on the knowledge in the case of a hemisphere-like shape^49,50. The extensibility means the degree of deformability as shown in Supplementary Fig. 5c. The displacement vectors in the tangential direction and in the perpendicular direction were,

$$v_t\left(\mathrm{s}\right)=\sin \phi \left(s\right){\int }_S^s\frac{1}{\sin \phi \left(s\right)}\left({\stackrel{°}{\epsilon }}_s-\frac{{\kappa }_s}{{\kappa }_{\theta }}{\stackrel{°}{\epsilon }}_{\theta }\right)ds$$ 8

$$v_n\left(\mathrm{s}\right)=\frac{{\stackrel{°}{\epsilon }}_{\theta }}{{\kappa }_{\theta }}-\cos \phi \left(s\right){\int }_S^s\frac{1}{\sin \phi \left(s\right)}\left({\stackrel{°}{\epsilon }}_s-\frac{{\kappa }_s}{{\kappa }_{\theta }}{\stackrel{°}{\epsilon }}_{\theta }\right)ds$$ 9

The initial configuration is based on the hemispherical shape with a radius larger than the data. The simulation step was smaller than the data time interval 20 min and we solved the above equations per simulation step. Depending on the parameter $P$ and $l_g$, the growth speed and cell shape were altered as summarized in Supplementary Fig. 5d.

Parameter estimation of turgor pressure $\mathit{P}$ and range of extensible area ${\mathit{l}}_{\mathit{g}}$

We estimated the parameter set $\left(P,l_g\right)$ through the quantification of growth and tip radius (Supplementary Fig. 5e). Plotting analyzed data on the so-called morphospace $\left({\frac{dL}{dt}}^{data},r_e^{data}\right)$ summarizing the characteristic features of the zygote cell shape, we exhaustively searched for the best fitted model parameters $\left(P,l_g\right)$ and resulting $\left({\frac{dL}{dt}}^{model},r_e^{model}\right)$ that minimizes the error function $E=\sqrt{{\left({\frac{dL}{dt}}^{data}-{\frac{dL}{dt}}^{model}\right)}^2+{\left(r_e^{data}-r_e^{model}\right)}^2}$. This fitting process was applied to each two sequential time frames.

Calculation of the time change of the circumferential stress

We calculated the time change of circumferential surface tension (Dσ_θ/Dt) using a moving coordinate system of surface points, since a time partial derivative ($\partial {\sigma }_{\theta }/\partial t$) using a fixed coordinate system does not reflect the temporal change in surface tension of the point of interest. The time change of the circumferential stress was calculated as,

$$\frac{D{\sigma }_{\theta }}{Dt}=\frac{\partial {\sigma }_{\theta }}{\partial t}+v_t\frac{\partial {\sigma }_{\theta }}{\partial S}$$ 10

where $v_t$ is the displacement vector in the tangential direction. We note that the time partial change is corrected with the tangential displacement depending on the Lagrangian flow of the point on the cell surface.

Cortical MTs agent-based model

We constructed an agent-based model of the cortical MTs (CMTs) where we took the CMTs as agents (elements) and analyzed the collective behavior of the agents based on the previous works^51,52. We accounted for the following three main dynamics: single MT growth and shrinkage, MTs interaction, and orientational modification based on a given large surface tension as an external directional cue⁵³.

For single MT growth and shrinkage, we used the growth speed of the plus end $v^{+}$ = 0.08 µm/s, the shrinkage speed of the plus end $v^{-}$ = 0.16 µm/s, and the shrinkage speed of the minus end (so-called treadmilling speed) $v^{tm}$ = 0.01 μm/s. The switching rate from shrinkage to growth at the plus end (so-called rescue rate) is r_r = 0.007 1/s, and the switching rate from growth to shrinkage (so-called spontaneous catastrophe rate) r_c is in the range [0.001–0.01] 1/s. The nucleation rate of CMTs on the surface r_n = 0.001 1/s.

For MTs interaction, we considered the interactions between CMTs based on the previous studies^52,54. First, we took into account the zippering effect where the growing CMT changes the direction of the growing front parallel to another CMT with the colliding angle less than 40 degrees. Second, we took into account the induced catastrophe where it begins to depolymerize from the growing front with a probability 50% with the colliding angle more than 40 degrees. Third, we took the account for crossover where the growing CMT crosses another CMT with a probability 50%, with the colliding angle more than 40 degrees.

For orientational modification by a directional cue, we defined the directional cue zone (DCZ) where the newly added CMT is biased in a circumferential direction with weight b_d.

$${\mathbf{r}}_{\mathbf{n}\mathit{+}\mathbf{1}}=\frac{\left(1-b_d\right){\mathbf{r}}_{\mathbf{n}}+b_d\mathbf{u}}{∣\left(1-b_d\right){\mathbf{r}}_{\mathbf{n}}+b_d\mathbf{u}∣}$$ 11

where ${\mathit{r}}_{\mathit{n}}$ and ${\mathit{r}}_{\mathit{n}\mathit{+}\mathit{1}}$ are the current and next unit vector of CMT plus end, respectively, $\mathit{u}$ is a unit vector in the circumferential direction and $\mid \cdot \mid$ is the standard norm of $\cdot$.

Based on the typical spatial scale of a zygote, 5 µm in radius, we set the cylindrical geometry with radius 5 µm. We set the unit of the length of the CMT segment as 8 nm, the width of a ring of tubulin as the same as the previous study⁵⁵. We set the speed of growth at the plus end as 4.8 µm/min⁵². The simulation time step is 0.2 s. Most of the simulation iterates 12000 times, corresponding to 40 min in reality. We note that we also implemented the finite tubulin-pool effect, as same as in the previous study⁵¹.

Quantification and statistical analysis

Statistical analysis was performed using R. The methods used for the statistics and the number of samples are described in the respective legend.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

S.T. and M.U. designed the research; S.N., H.M., and Y.H. carried out the experiments; Z.K., Y.I., and T.N. performed image analysis and modeling; and Z.K., S.T., and M.U. wrote the manuscript.

Peer review

Peer review information

Nature Communications thanks Chris Ambrose and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

Source data are provided with this paper. Data supporting the findings of this work are available within the paper and its Supplementary Information files. Plasmids and transgenic lines generated in this study are available upon request to the corresponding authors. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-72280-4.