Main

Physical mechanisms have a fundamental role in establishing boundaries within living systems, from the intracellular level to collectives of organisms5,6,7,8. In early embryos, cell boundaries are established by rapid cleavage divisions that robustly organize the cytoplasm into progressively smaller cellular compartments1,2. The compartmentalization of the cytoplasm can occur before4,9 or without3,10 the formation of a new plasma membrane, raising the question of how boundaries between cytoplasmic compartments can be robustly maintained in the absence of physical barriers. Experiments using reconstituted cytoplasm have revealed that cytoplasmic compartments self-organize spontaneously3,4. The formation and division of these compartments rely on microtubule asters that define their boundaries11,12,13,14 and dynein activity that transports organelles towards the compartment centre15 (Extended Data Fig. 1a). Microtubule asters grow via self-amplifying microtubule growth or autocatalytic nucleation, the nucleation and branching of microtubules from existing microtubles13,16. Through branching nucleation, asters can explore a large volume of cytoplasm until they meet other asters. When asters enter in contact, the aster–aster interface is thought to be stabilized by components that provide local inhibition to microtubule nucleation and growth, creating robust boundaries that guide cytokinesis17,18,19. This process leads to a regular tessellation of the cytoplasm. However, it is unclear how local inhibition in combination with autocatalytic growth can lead to stable and robust boundaries20,21. To shed light on this problem, we combined theory with experiments in reconstituted cytoplasm and living zebrafish and Drosophila embryos. Starting from a theoretical prediction, we show that microtubule autocatalytic nucleation gives rise to aster invasion driving the coarsening of cytoplasmic compartments. By performing cell-cycle perturbations and biophysical measurements of microtubule dynamics, we found that the coarsening of cytoplasmic compartments is prevented either by synchronizing the cell-cycle oscillator to the dynamics of the asters or by reducing autocatalytic nucleation. Finally, we show that these mechanisms yield to divergent cytoplasmic organization strategies in embryos.

Cytoplasmic partitioning is unstable

We investigated cytoplasmic partitioning in live zebrafish embryos and Xenopus laevis egg extracts. In zebrafish embryos, cytoplasmic partitioning occurs before cytokinesis. During the first rounds of cell division, microtubule asters divide the cytoplasm into two distinct cytoplasmic compartments—denser regions of cytoplasm rich in organelles such as mitochondria—before the cell membrane ingresses (Fig. 1a–d, Extended Data Fig. 1b–d and Supplementary Video 1). This observation led us to test whether the embryo can divide its cytoplasm in the absence of cell membranes between cytoplasmic compartments. To this end, we inhibited the formation of cleavage furrows and cell membrane ingression by adding cytochalasin B22, an actin polymerization inhibitor. We observed low-density regions of microtubules and depolymerized actin between compartments over multiple cell cycles, indicating that the division of the cytoplasm in living zebrafish embryos does not require cytokinesis (Fig. 1e–h, Extended Data Fig. 1e and Supplementary Video 1). In frog extracts, undiluted cytoplasm obtained by crushing frog eggs at high speed self-organizes into distinct compartments that are not separated by cell membranes, similarly to syncytial systems3. These compartments form in the absence of cell membranes and divide over multiple cell cycles (Fig. 1i,j, Extended Data Fig. 1f–j and Supplementary Video 2). These results demonstrate that cytoplasmic partitioning is a fundamental process in cell division that precedes and is independent of cytokinesis.

Fig. 1: Robust compartmentalization is observed in vitro and in vivo, but theory and simulations predict a physical instability.

a, Schematic of an early zebrafish embryo, with microtubule asters in green and actin cortex in cyan (left), and a schematic of cytoplasmic compartmentalization (right). An aster–aster interaction can be described by a network of two self-amplifying loops interacting via local inhibition. b, Light-sheet fluorescence microscopy image of a live zebrafish embryo after the first division. Asters partition the cytoplasm before furrow ingression. Microtubules are shown in green with eGFP–Doublecortin and the actin cortex in cyan with utrophin–mCherry. c, Cell membrane (top) and microtubules (bottom) of a zebrafish embryo with PH-Halo and eGFP–Doublecortin. d, Mitochondria of a zebrafish embryo with mito–GFP. e,f, Live imaging of a syncytial zebrafish embryo. Asters coexist and form boundaries of low microtubule (e) and actin density (f). Cyto B, cytochalasin B. g, Cell membrane (top) and microtubules (bottom) of a syncytial zebrafish embryo. h, Mitochondria of a syncytial zebrafish embryo. i, Live imaging of cycling frog egg extract showing cytoplasmic partitioning. Microtubules are shown in green. j, Cytoplasmic compartments are visualized in magenta by labelling lipid organelles. k, Two asters interacting. l, Microtubule density profile of two interacting asters. ({x}) indicates the linear coordinates from the centre of one aster (0 µm) to the centre of the adjacent aster (approximately 200 µm). Experimental data are shown in black and green with s.e.m. (n = 8 independent samples), agent-based simulations are in grey with 95% confidence interval (n = 6 independent simulations) and one-dimensional theory is in orange. m, Numerical time evolution of microtubule densities. The inset shows the interface position over time. n, Top view of a 3D agent-based simulation of interacting asters in a slab showing boundary formation. Grey and green indicate microtubules of the two asters. The inset shows the interface details. o, Side view of temporal evolution of a 3D agent-based simulation showing invasion.

Source Data

The striking similarities in cytoplasmic partitioning between frog egg extracts and live embryos suggest that extract is a prime system to investigate this process, as it has the advantage that it is easy to manipulate and image. To quantify the formation of compartment boundaries, we measured the microtubule density profile using EB1–mApple, as it labels the growing plus ends of microtubules. We tracked individual EB1–mApple plus ends and reconstructed the density and polarity of microtubules of two compartments from the centre of one aster to the centre of the adjacent aster (Fig. 1l and Extended Data Figs. 1k and 2a–d and Supplementary Note 1). The two profiles corresponding to each compartment have an exponential increase close to their centre (around 0 and +200 µm in the x axis) consistent with autocatalytic growth. Near the interface (around 100 µm in the x axis), the microtubule profiles decay consistent with local inhibition at the antiparallel microtubule overlap17,18. These profiles suggest that the interaction between the two asters can be minimally described by a network of two autocatalytic, or self-amplifying, loops interacting via local inhibition (Fig. 1a, bottom). To test whether such a network can explain the robust formation of these compartments, we used a 1D continuum theory of aster–aster interaction (microtubules mostly grow into one direction in the midzone region; Extended Data Fig. 2h–j), incorporating autocatalytic growth, microtubule polymerization, microtubule turnover16,23 and local inhibition (Supplementary Note 2), resulting in the following equation:

$$\frac{{\partial \rho }_{i}}{\partial t}={\mp v}_{p}\frac{{\partial \rho }_{i}}{\partial x}+\alpha \frac{{\rho }_{i}}{1+({\rho }_{1}+{\rho }_{2})/{\rho }_{s}}-\theta {\rho }_{i}-\lambda \frac{{{\rho }_{1}\rho }_{2}}{{\rho }_{1}+{\rho }_{2}}$$

(1)

The first three terms describe the dynamics of the growth of one single aster16. The last term describes phenomenologically the local inhibition between the two asters that could result from crosslinking of antiparallel microtubules, decreasing microtubule polymerization by kinesins and increasing microtubule turnover17,18. In this equation, *i *= 1,2 and refers to the two asters, ({v}_{p}) is the polymerization velocity, (\theta ) is the microtubule turnover, (\alpha ) is a parameter related to the autocatalytic growth, (\lambda ) modulates the inhibition between asters, and ({\rho }_{s}) is a density of microtubules that indicates the saturation of microtubule nucleation due to depletion of nucleators as they bind to microtubule. We measured ({v}_{p}) by tracking the plus ends of the microtubules and (\theta ) using single-molecule microscopy of sparsely labelled tubulin dimers. We then globally fit the model to the density profiles to obtain the other parameters. A detailed description of the measurements and values of the parameters is reported in Supplementary Notes 1 and 2 and Supplementary Tables 4 and 6. The theoretical fit to the aster density profiles quantitatively agrees with the experiments (Fig. 1l, orange line). To take into account the geometry and microscopic details of microtubule branches, we validated the continuum theory using 3D agent-based simulations of two interacting asters, which also quantitatively recapitulate the aster density profiles (Fig. 1l, grey lines and Extended Data Fig. 3) and the microtubule organization in 3D (Fig. 1n). We found that both theory and simulations predict that the temporal evolution of these boundaries is unstable (Fig. 1m,o and Supplementary Video 3). Extending the 1D model to two and three dimensions shows that this instability is independent of dimensionality in our system (see Extended Data Fig. 2e–g and Supplementary Note 2.1). This instability is generally expected from local inhibition and self-amplification alone20; however, it disagrees with the robustness of cytoplasmic organization observed in embryos and cycling extracts3,4.

One possible explanation for this apparent inconsistency between theory and experiments is that the time needed to develop such instability may be larger than the cell-cycle time, which drives the disassembly of the microtubule asters before the assembly of mitotic spindles. Close to the unstable point, the time to develop the instability can become arbitrarily large. Indeed, our numerical solutions suggest that the time to develop this instability can easily be up to 40 min (Fig. 1m), which is comparable with the cell-cycle time in both frog extracts and frog embryos, which are equal to about 40 min and 30 min, respectively24,25. To test whether the cell cycle prevents the development of the instability, we arrested cytoplasmic extracts in interphase by blocking translation of cyclin B1 with cycloheximide3. Cycloheximide did not affect the speed of microtubule polymerization, turnover (Supplementary Table 4) and overall compartment growth (Supplementary Video 4). We observed that compartments that initially formed with a well-defined boundary as in the control condition, started coarsening by means of the microtubule asters invading each other and fusing, consistent with the aster invasion predicted by our theory (Fig. 2a and Supplementary Video 5). This coarsening can continue for several hours, leading to compartments of few millimetres in size, in contrast to hundreds of microns in the cycling extract. During the coarsening, dynein motors relocated nuclei to the new centre of the larger compartments (Fig. 2a, bottom). However, dynein activity does not hinder the invasion process because invasions occur before active transport of nuclei and organelles, as well as when dynein is inhibited (Extended Data Figs. 4–6 and Supplementary Video 6). Dynein inhibition enhances invasion by leading to splayed asters, presumably due to the lack of proper pole formation26 (see dynein-inhibited cycling extract in Supplementary Video 6).

Fig. 2: Cytoplasmic partitioning is intrinsically unstable, but the cell-cycle duration can avoid the instability leading to robust compartmentalization.

a, Live imaging of interphase-arrested cytoplasmic extract showing microtubule aster invasion. Microtubules are shown in green. Aster invasion results in the fusion of cytoplasmic compartments and dynein-induced relocation of sperm nuclei. Cytoplasmic compartments are shown in magenta and nuclei in cyan with GFP-nuclear localization signal (NLS). b, High-resolution timelapse of an invasion event. c, Top view of 3D agent-based simulations of two asters showing the invasion process over time. d, Invasion time plotted against initial mass difference between the asters, showing that asters with small mass differences take longer to invade than asters with large mass differences (40 invasion events from n = 20 independent samples). Error bars are s.e.m. Cell-cycle time of the frog embryo25 is plotted for comparison. Simulations are shown in grey (n = 78 independent simulations), experimental data in blue and theory in orange. The error bars are s.d. e, Phase portrait of the average area of the compartments for arrested (magma; n = 6 independent samples) and cycling extract (viridis; n = 6 independent samples) normalized (norm) for the initial area equal to 1 (dashed line). (\tau ) = 8 min. Although the area of compartments in arrested extract grows freely, the area of compartments in cycling extract oscillates and maintains a small size, even though some invasion events are present. A is the compartment area. f, Zoomed graph of the phase portrait of the cycling extract. The average cell-cycle time varies from 39 to 65 min (n = 6 independent samples). g, Normalized average compartment area over time. Shades of blue refer to the different cell-cycle times reported in the caption of panel h. Experimental data are shown as dots and binned data with error bars (s.d.). n = 6 independent samples. h, Probability density function (PDF) of normalized average compartment area (n = 6 independent samples).

Source Data

To rule out possible artefacts due to global inhibition of protein translation by cycloheximide, we also specifically blocked the translation of cyclins selectively by using morpholinos following existing protocols27,28 and observed an increase of the cell-cycle duration and aster invasion events (Supplementary Video 7). With a closer examination using higher-resolution imaging (Supplementary Video 8), we observed that an invading aster gained mass, consistent with continuous autocatalytic growth, at the expense of the invaded aster, that eventually disappeared (Fig. 2b). The aster invasion and compartment fusion are accompanied by disassembly of the chromosomal passenger complex at the aster–aster interface. This indicates that inhibition between the asters is present at the beginning of the interaction, consistent with previous experiments15,17,18,19, but is disrupted by autocatalytic nucleation over longer timescales (Extended Data Fig. 6e). This invasion dynamics was also reproduced in the 3D agent-based simulations (Fig. 2c). In the simulations, the asters are confined in a rectangular slab, and the invasion occurs laterally, as also seen in the experiments, often with deformations of the interface in a finger-like manner (Supplementary Video 8). Together, our results show that cytoplasmic partitioning is an intrinsically unstable mechanism.

Cell cycle can prevent the instability

Our results suggest that the cell-cycle duration can determine whether invasion events occur and thus regulate the patterns of cytoplasmic partitioning. To further investigate this dependence, we experimentally quantified the invasion time as a function of the aster mass difference, ({\Delta {\rm{{\rm M}}}}_{i}). We experimentally introduce differences in aster mass by exploiting local variations of sperm nucleus densities in the imaged sample. We calculated the mass of the asters from the area under the curve of 1D profiles of microtubule density (Extended Data Fig. 7a–d). We defined the invasion time (\tau ) as the time for the initial mass difference between the asters ({\Delta {\rm{{\rm M}}}}_{i}) to decrease by a factor (e) (Fig. 2d). The invasion time decays as the mass difference between the asters increases. This trend was also perfectly captured by a parameter-free prediction of the theory (Fig. 2d, orange line) and simulations (Fig. 2d, grey points and Extended Data Fig. 7f–p). Asters with large mass differences invade in a few minutes. Asters with small mass differences — that represent the situation in living embryos where compartments are highly uniform — have an invasion time comparable with the cell-cycle time.

The time dependence of the invasion events allows the cell-cycle duration to prevent aster invasion, and therefore the runaway growth of asters, if compartments are similar in size. Conversely, for slow cell-cycle times, invasion events may lead to increasing differences between compartments that may amplify the instability, leading to divergent compartment size distributions. This process can be visualized by means of a phase portrait, showing that while in the arrested extract, the compartment size monotonically increases, whereas in the cycling extract, it oscillates around a characteristic compartment size, despite some invasion events (Fig. 2e,f). To further explore the effect of the cell-cycle duration on the compartment size, we systematically delayed the cell-cycle time by titrating cycloheximide amounts in extracts. These experiments showed that the cell-cycle duration directly affects the average compartment size and therefore patterning of the cytoplasm (Fig. 2g and Supplementary Video 9). Moreover, we observed that although for shorter cell-cycle times the distribution of compartment sizes is peaked, as the cell cycle slows down, the compartment size distribution becomes increasingly broader (Fig. 2h). This monotonously increasing variation in compartment size is in contrast with the heterogeneity of stable compartment sizes (with bounded sizes) that naturally arises in embryos and cytoplasmic extracts as a function of the density of asters3,29. These results show that a delicate balance between the cell-cycle time and compartment growth is necessary to achieve a uniform and robust cytoplasmic partitioning.

Microtubule dynamics regulate the instability

Our data show that changes in cell-cycle timing can have dramatic consequences in the precision of cytoplasmic partitioning, from extremely regular partitioning when matching autocatalytic growth, to system-size coarsening. We wondered whether there were regimes in the parameter space that could prevent this instability, independently of the cell-cycle timing. To this end, we performed a linear stability analysis of equation (1) (Supplementary Note 2.1), leading to the stability criterion:

$$\theta > \frac{\alpha }{1+2{\rho }_{\mathrm{int}}/{\rho }_{s}}$$

(2)

where ({\rho }_{\mathrm{int}}) is the density of microtubules where the two asters intersect. We confirmed this stability criterion by numerically solving equation (1) (Fig. 3a). The stability of the compartment boundaries critically depends on a competition between the autocatalytic rate and microtubule turnover, and not on the strength or the shape of the local inhibition term or dimensionality (Extended Data Fig. 2a–f and Supplementary Note 2.1). When the autocatalytic term dominates over turnover, microtubule density profiles feature exponential growth from the centre of the compartment (Fig. 3b, (2)). Although this density will go down as the asters interact, the boundary they form will always be unstable. Conversely, if turnover dominates over autocatalytic growth, the density of microtubules decreases from the centre of the compartment (Fig. 3b, (1)). In this regime, the boundary created as the two asters interact will be stable, but the compartments will be generally smaller with a size defined by the decay length scale of the microtubule density. Consistent with the instability that we measured, extracts fall in the unstable region of the phase diagram (Fig. 3a). These results show that the stability of compartments can be achieved by modulating microtubule nucleation and dynamics, independently of cell-cycle timing.

Fig. 3: Microtubule dynamics can regulate the stability of cytoplasmic partitioning.

a, Stability phase diagram of (\alpha {\prime} ) − (\theta ) versus (\theta ) showing a stable and unstable region. The blue and orange dots correspond to numerical solutions of equation (1). The black line represents the stability criterion (\alpha {\prime} ) = (\theta .) The error bars represent the 95% confidence interval of the mean. The numbers of independent tracks, lifetimes and regions of interest analysed are reported in Supplementary Tables 1–3. b, Schematics of microtubule asters and 1D density from close to the centre to the boundary. In stable asters, the microtubule density decreases from the centre. In unstable asters, the microtubule density increases from the centre because of the exponential nature of branching. c, Microtubule density profile of two AurkA asters measured as the density of plus ends of the microtubule. Experimentally measured profiles are shown in green and dark grey (n = 7 independent samples) and 1D global fit is in orange. d, Confocal microscopy time sequence of AurkA asters in interphase-arrested cytoplasmic extract showing that the asters are stable and regularly partition the cytoplasm. e, Microtubule density profile of two AurkA–Ran(Q69L) asters. Experimentally measured profiles are shown in green and dark grey (n = 5 independent samples) and the 1D global fit is in orange. f, Confocal microscopy time sequence of AurkA–Ran(Q69L) asters in interphase-arrested cytoplasmic extract showing that the asters are unstable. g, Microtubule density profile of two sperm nuclei asters with MCAK-Q710. Experimentally measured profiles are shown in green and dark grey (n = 5 independent samples) and the 1D fit is in orange. h, Confocal microscopy image of a MCAK-Q710 sperm nucleus aster. i, Comparison of aster organization dynamics with and without MCAK-Q710, showing an overall smaller aster size in the perturbed case due to a decrease of invasion events. All error bars in the profiles are s.e.m. (c,e,g).

Source Data

To investigate the possibility of stabilizing cytoplasmic compartments by changing microtubule dynamics, we fabricated asters with a decreasing microtubule density profile13. These asters can be obtained by adding Aurora kinase A antibody-coated (AurkA) beads to extracts14,15,17 (Fig. 3c) instead of sperm nuclei. The AurkA beads act as artificial centrosomes. AurkA beads trigger the nucleation of microtubules13,30, but to a lesser extent than chromatin-associated centrosomes. In this condition, we measured that the microtubule density profile decays from the beads (Fig. 3c), consistent with a decrease of microtubule nucleation and a stable system according to the theory. We confirmed this shift to the stable regime by measuring the turnover rates and polymerization velocity of microtubules and fitting the nucleation parameters. As expected, these asters fall into the stable regime of the phase diagram (Fig. 3a, orange area). We then tested whether the system is stable when the cell cycle is arrested. As predicted by the stability criterion, asters formed by addition of AurkA beads in arrested cytoplasm do not invade, and partition the cytoplasm with surprising regularity similar to asters in Drosophila extract and embryos31 (Fig. 3d, Extended Data Fig. 8i–k and Supplementary Video 10). We showed that the stability does not depend on the size of these asters by using a lower bead concentration (Supplementary Video 10). These results are consistent with previous experiments performed in extract with AurkA beads14,15,17. Experiments with purified centrosomes from HeLa cells and Drosophila embryos in extract also led to stable asters (Extended Data Fig. 8c–g). To confirm that the effect on the stability was solely due to changes in microtubule nucleation, we supplemented extracts in the presence of AurkA beads with constitutively active Ran(Q69L) to increase microtubule nucleation16 (Fig. 3e). In this situation, nucleators in the cytoplasm are activated and drive the formation of microtubule branches in AurkA bead asters. This branching results in the increase of the density of microtubules from the centre of the compartments similar to the case asters from chromatin-associated centrosomes. Moreover, cell-cycle arrest reveals that AurkA–Ran(Q69L) asters became unstable and invaded as in the sperm aster case (Fig. 3f and Supplementary Video 10), consistent with theory.

To further test the stability criterium, we aimed at perturbing intrinsically unstable asters by modifying microtubule dynamics. To this end, we added purified MCAK-Q710 (ref. 32) to extracts in the presence of sperm DNA, as in the control situation. Previous work has shown that MCAK-Q710 alters microtubule turnover and dynamics in metaphase33 and interphase14. We measured microtubule growth and turnover as in control, and observed a decrease of microtubule polymerization by approximately 20%, whereas turnover remained unchanged14 (Supplementary Table 4). These results imply a change in microtubule length, which according to our model directly influences ({\rho }_{s}) and (\alpha ). We then used the predicted change on these parameters while keeping the value of inhibition unchanged, to predict the density profile (up to the absolute value of the density close to the centre, which we fit). The spatial dependence of the density profile in both theory and experiments agree quantitatively (Fig. 3g), and the predicted changes in ({\rho }_{s}) and (\alpha ) match the global fit to the profiles (Extended Data Fig. 8h). The change of these parameters also predicts a shift in the stability of these compartments: from unstable to stable (Fig. 3a). To test this prediction experimentally, we compared the aster organization over time with and without MCAK-Q710. We observed an overall smaller compartment size in the perturbed case due to a decrease in invasion events (Fig. 3i and Supplementary Video 10). In summary, robust compartmentalization of the cytoplasm can be achieved in a parameter regime where microtubule turnover dominates over autocatalytic nucleation rate, independently of the cell-cycle time.

Divergent partitioning strategies

To investigate the in vivo relevance of the stability prediction, we turned to zebrafish and Drosophila embryos. We chose these embryos because of their drastically distinct aster structure despite a comparable embryo size (approximately 700 µm in diameter for zebrafish and approximately 500 µm for the long axis of Drosophila). In zebrafish embryos, the density of microtubules in interphase asters increases from the centrosome until microtubules reach the entire cell (Fig. 4a,e). By contrast, in Drosophila embryos, microtubule density decreases from the centrosomes (Fig. 4b,k) and microtubule asters do not reach the boundary of the whole syncytium (cortex of the embryo). These asters slowly fill up the embryo volume in subsequent cell divisions. On the basis of the theory and results in extract, we predicted that the cytoplasmic compartments in zebrafish should be unstable and by contrast stable in Drosophila. To test this prediction, we first confirmed where these embryos lie in the phase diagram (Fig. 4c). To this end, we quantified microtubule dynamics in embryos by measuring the polymerization velocity as the speed of plus ends, and the microtubule turnover as half-time recovery from photobleaching (for zebrafish) and photoconversion (for Drosophila) experiments. We estimated the parameters associated to autocatalytic growth and the local inhibition similarly to the data of microtubule asters in extract. In the stability phase diagram, zebrafish falls into the unstable region, whereas Drosophila lies in the stable region, consistent with the shape of the density profiles. The microtubule turnover that we measured in extracts, zebrafish and Drosophila is very similar, whereas the shift from the stable to unstable regime is mainly driven by changes in autocatalytic nucleation (Fig. 4d).

Fig. 4: Test of the (in)stability prediction in zebrafish and Drosophila embryos.

a,b, Confocal microscopy image of microtubule asters in zebrafish (a) and Drosophila (b) embryos with enlargement in the inset. Asters were visualized by a time projection over 20 frames of growing plus ends shown by EB1 (b). c, Phase diagram of ({\alpha }^{{{\prime} }-\theta ) versus (\theta ) for frog cytoplasm and zebrafish and Drosophila embryos. The black line represents the stability criterion ({\alpha }}{{\prime} }) = (\theta .) Sample numbers are reported in Supplemen