Eukaryotes assemble a cytoskeletal structure of microtubules (MTs) called an ‘aster’, which is involved in critical cell functions including intracellular positioning and organelle transport. In metazoan cells, the aster acquires a radial shape in which MTs are focused by the centrosome and emanate toward the cell periphery (Wilson, 1986). Microtubules grow at the centrosome and at microtubule-based nucleation sites (Ishihara et al., 2016). The centrosome is also found at the two focus points of the mitotic spindle – the poles – linking the aster structurally and mechanically to the spindle, thus lending it a decisive role during cell division (Hinchcliffe and Sluder, 2001; Hoffmann, 2021). Positioning of the spindle by astral microtubules contacting the cell cortex determines the cell wall cleavage location in sand dollar and Xenopus eggs (Field et al., 2015; Mitchison et al., 2012; Rappaport, 1969; Rappaport, 1961). During fertilization, the maternal and paternal genomes are united by the assembly and migration of the sperm aster, which facilitates transport of the female toward the male pronucleus in sand dollar and Drosophila eggs (Chambers, 1939; Hamaguchi and Hiramoto, 1986; Riparbelli et al., 2000). Where the sperm aster positions inside the egg will roughly define the geometry of the first embryonic cleavage (Albertson, 1984; Hamaguchi and Hiramoto, 1980; Hirano and Ishikawa, 1979). Interestingly, in large egg cells, for example, from Xenopus, the aster migration can also occur without microtubules contacting the cell periphery (Wühr et al., 2010). Uninuclear cells contain one or, at most, two asters depending on the cell cycle stage.

The mechanics of aster movement has been a matter of long discourse, so far without any consensus on a unified biophysical model (Deshpande and Telley, 2021b). Disagreement remains likely because the experimental insight stems from different model organisms and cells which, by nature, have evolved divergent mechanisms of aster positioning. One fundamental question, whether asters position themselves by pulling on or by pushing at the rigid cell periphery, remains extensively debated (Garzon-Coral et al., 2016; Grill and Hyman, 2005; Meaders et al., 2020; Sulerud et al., 2020). Recently, an adaptation of the pulling model for cortex contact-free asters in large cells has gained new momentum (Hamaguchi and Hiramoto, 1980; De Simone et al., 2018; Tanimoto et al., 2018; Xie et al., 2022). In this model, the net force moving the aster originates from a balance of viscous drag forces of moving organelles along astral microtubules. Overall geometric asymmetry of the aster – caused by regional differences in microtubule lengths – is a key point of this model (Tanimoto et al., 2016).

An interesting yet understudied case of higher complexity is the positioning of multiple nuclei and their associated asters in multinucleated cells (coenocytes). In the syncytial embryo of insects, such as the fruit fly, the genome is rapidly proliferated and distributed without cell cleavage, leading to a single large cell with hundreds of nuclei (Donoughe and Extavour, 2016; Foe and Alberts, 1983; Sommer and Tautz, 1991). The positioning of these syncytial nuclei depends on the centrosome-nucleated microtubule aster (de-Carvalho et al., 2022; Megraw et al., 1999; Telley et al., 2012) and microtubule-associated crosslinking proteins (Deshpande et al., 2021a), because perturbation of these components causes aberrant nuclear movements, irregular nuclear distribution, and spindle aggregation. Therefore, nuclear positioning must be mechanistically linked to the separation of neighboring asters (i.e., not being part of the same mitotic spindle). Because these nuclei are not isolated by a cell wall, unlike in uninuclear cells, their positioning occurs relative to the cell cortex and each (direct) neighbor. Cell cortex pushing or pulling – whichever applies – is now combined with aster–aster interactions, adding considerable complexity to the mechanical system. Ultimately, a net force is required such that each aster is evenly and stably separated from its neighbors, of which there are on average six (Kanesaki et al., 2011). Recent work from us has suggested that short-ranged aster repulsion positions nuclei in a regular order within the syncytial embryo (de-Carvalho et al., 2022). However, experimental testing of these forces is still missing.

Here, by exploiting embryonic explants (Telley et al., 2013), which reduces complexity, and a cell cycle regulation mutant (Freeman et al., 1986; Lee et al., 2003) to uncouple microtubule organization from nuclear division, we have studied the dynamics of aster–aster interaction bottom-up. In this system, we uncover the physical principles of separation for simple aster arrays, reveal the positional autonomy of single asters, and derive the microtubule-associated mechanical separation potential. This work builds on our recent study (de-Carvalho et al., 2022) and reveals the underlying local mechanics between the structures that lend order to a rapidly proliferating embryonic system.

Asters are radial microtubule structures nucleated by the centrosome, which acts as microtubule organizing center (MTOC) as part of the mitotic spindle pole. In the early Drosophila embryo, the MTOC is physically connected to the nucleus throughout the cell cycle. We wanted to uncouple nucleus- and aster-associated forces and study isolated asters. To this end, we took advantage of giant nuclei (gnu) mutant Drosophila embryos, in which DNA endoreplication occurs without mitosis as the cell cycle is arrested in interphase. This results in the embryo having only one or just a few polyploid nuclei. Yet, centrosome maturation and duplication continue in gnu embryos (Freeman et al., 1986; Freeman and Glover, 1987; Lee et al., 2003; Figure 1A). We produced embryo explants from gnu mutant embryos (Telley et al., 2013; Figure 1B) and studied the positioning properties of individual or a small number of microtubule asters in the absence of nuclei. These explants exhibit a high aspect ratio with circular planar shape and <10 µm peak height. Thus, for the purpose of kinematic analysis we treated them as quasi-2D spaces.

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Single aster positioning is consistent with radially symmetric forces

Initially, we focused on explants containing a single aster to gain a deeper understanding of the aster–boundary interactions. Here, we note that the explant boundary likely does not have all the properties of a cell cortex, and likely acts more like a (semi) rigid barrier. In these experiments, a single aster consistently moved away from the explant boundary and eventually adopted a steady position (Figure 1C and Video 1, left). In a series of experiments, we deposited extract and waited 30 min, after which we measured the shortest distance b of the centrosome from the boundary at steady state. This distance varied between R/2 and R, with R being the explant radius (Figure 1D). Deviation from precise centering (b = R) may be due to yolk or lipid droplets (magenta circles in Figure 1C) forming exclusion zones. In large explants it is conceivable that aster centering is not achieved. We also note that in some explants the single aster was by chance already positioned near the center, and no further migration occurred. To obtain more detailed insight, we analyzed the kinematics of single asters located near the boundary after cytosol deposition (Figure 1E). Typically, they stayed for up to 10 min (Figure 1F, phase I), but they always eventually migrated (Video 1, left). Single asters moved rapidly after separation from the boundary, with a maximum velocity of 0.05 ± 0.02 µm/s (Figure 1F, phase II), at around 20% of its final distance from the explant boundary (Figure 1G), before decelerating (Figure 1F, phase III) and stopping 30–35 μm from the boundary at most (Figure 1E).

Video 1

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We then measured the radial intensity profile of single asters in explants as a proxy for aster size and microtubule length (Figure 1H, inset). We initially focused on asters near the center of the explants. Away from the MTOC, the distribution was well approximated with a mono-exponential decay with decay length of ~12 µm (Figure 1H). This value agrees with the size of asters associated to telophase and early interphase nuclei of wildtype embryo explants (Telley et al., 2012). The signal drops to background level at ~30 µm, suggesting that few microtubules are longer. We also looked at the microtubule distribution in asters positioned near the explant boundary. The microtubule signal toward the explant boundary was noticeably reduced (Figure 1—figure supplement 1, Figure 1) suggesting fewer microtubules reach a length equal to the boundary distance b. In some samples, we observed splay of microtubules when the aster was near the explant boundary (Figure 1I), consistent with microtubules pushing against the boundary.

In summary, a single aster moves away from a cytoplasmic boundary and, provided sufficient space, reaches a boundary separation distance comparable to aster size. The motility displays three distinct dynamic phases: first, a very slow phase (at least along the radial axis) as they separate from the edge; second, a rapid motion away from the explant boundary; and finally, a gradually slowing down as they migrate toward the explant center (as evidenced in Figure 1D–F). The initial phase of separation may be due to splay of microtubules near the boundary edge (Figure 1I). In our movies (e.g., Video 1, left), we see random fluctuations in the movement of the aster and the surrounding cytoplasm while the aster is close to the explant boundary. These may be sufficient to release the aster eventually from the boundary (transition from phases I to II, Figure 1F). These observations are consistent with the asters generating a repulsive potential that decays to zero for distances >30 μm and is also inefficient at very short distances (<3 μm).

Lipid droplet movements in extract are consistent with a repulsive aster potential

Embryos contain high amounts of lipid droplets and yolk granules, which serve as fiduciary markers in our explants to study hydrodynamic flow (Monteith et al., 2016; Shamipour et al., 2023). Importantly for our later results, the spatial scale of such flows can define the length scale over which the forces generated by asters act. According to the hydrodynamic pulling model, cytoplasmic dynein moves small organelles along astral microtubules toward the MTOC (Hamaguchi and Hiramoto, 1986). Thus, we expect small droplets and spherical organelles to occupy the space of the aster and possibly accumulate at the MTOC.

We examined the localization and movement of droplets as the aster moved through the explant (small spheres in Video 1). We observed an approximately circular droplet exclusion zone of ~10 μm radius (Figure 2A, B), which maintained during aster migration (Figure 2B). This contrasts with the expected observation in the hydrodynamic drag model, and is suggestive of a repulsive interaction between the aster and yolk granules, at least over distances on the order of 10 μm. Next, we quantified the mobility of these yolk granules relative to the movement of the aster. As control, we calculated the mean-squared displacement (MSD) of the lipid droplets with and without an aster present in the explant (Figure 2C). The droplets clearly displaced further when an aster was present. The scaling of MSD with time is indicative of the dynamic mode, $x_{ms}~t^{\alpha }$ . For $\alpha \approx 1,$ the motion can be approximated as diffusion-like, whereas ${\displaystyle \alpha >1}$ implies directionality in the droplet movement. With and without an aster the mode of motion was $\alpha \approx 1.5\pm 0.1$ and $\alpha \approx 1.3\pm 0.1$, respectively.

Figure 2

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To better understand the dynamics, we quantified the movement of the yolk/lipid droplets relative to aster movement. The yolk granules streamed around the aster exclusion zone (Figure 2E) and consistently in the opposite direction, for particles in front of or behind the aster (Figure 2F). Again, this contrasts with the concentric movement pattern expected from the hydrodynamic pulling model. Overall, our particle motion analysis suggests a repulsion of small organelles from the aster center over a length scale of ~20 μm.

Aster–aster interactions are consistent with a repulsive potential involving short-ranged inhibition

Some explants contained a pair of asters that separated and adopted a steady-state inter-aster distance (Figure 3A and Video 1, right). At steady-state, the aster–aster interaction must balance with the forces involved in moving each aster away from the boundary. Here, we use our quantitative measurements of aster–aster dynamics to infer an effective interaction potential that we later use to develop our theoretical model.

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Our previous experiments indicate that this aster–boundary force decays with distance. From the perspective of the first aster, we may assume the second aster forms a local boundary – which is movable – and associate a similar force generation property between the first and the second aster. The resulting mechanical configuration is likely symmetric so that asters 1 and 2 are interchangeable. Force balance considerations (see Methods) provide a testable hypothesis: If the force occurring between the two asters (${\displaystyle F_{a\leftrightarrow a}}$) or between an aster and the boundary ($F_{a\leftrightarrow b}$) have identical mechanical properties, that is, the same amplitude and length parameters, we expect the asters to be positioned at half the diameter of the explant. Thus, we measured the final distance d between the centrosomes of the two asters, as well as the boundary distances b₁ and b₂ for asters 1 and 2, respectively, and the explant radius, R. Interestingly, we find that the two asters approximately partitioned the available space (${\displaystyle d=b_1=b_2=2R/3}$) (Figure 3—figure supplement 1A). From this result, we can conclude that from the viewpoint of one of the two asters, the periphery of the second aster cannot be viewed as a hard mechanical object. In other words, the steady-state force generation associated with an aster being a distance x away from the periphery of the second aster is lower than the force generated between the same aster and the explant boundary at distance x.

Given the above observation, we predicted that the dynamics between aster pairs will differ from the single aster dynamics. Using live imaging, we tracked the dynamics and separation of aster doublets. The velocity profile of the doublets is distinct from the single aster case (Figure 3—figure supplement 1B). We noticed that the peak separation velocity was always near half the final aster separation distance (Figure 3B), independent of final separation distance. This suggests that the resulting magnitude of the forces are similar in the initial phase of separation and the eventual reaching of the equilibrium position.

Given the eccentric movement of two asters, the aster separation could be driven by overlap and sliding of astral microtubules (Baker et al., 1993; Deshpande et al., 2021a; Lv et al., 2018; Vukušić et al., 2021; Vukušić et al., 2017), or by mutual contact leading to repulsion by microtubules of both asters. Thus, we quantified the microtubule intensity between the separating asters (Figure 3C, left) and generated kymographs of the microtubule fluorescence intensity along the separation axis (Figure 3C, right). The intensity at half the separation distance decayed exponentially (Figure 3D), consistent with models of dynamic microtubule length distribution (Howard, 2001; Jeune-Smith and Hess, 2010). When aster separation ceased there was almost no detectable microtubule signal between the asters.

Viscous forces dominate at the cellular scale, and we expect that the net force causing aster separation is related to the velocity of separation, because it must balance the drag force caused by their movement through the bulk cytoplasm. For a viscous material, the velocity, $v$, of a submerged object depends on the applied force $F$: $v\approx \gamma F$, where $\gamma$ is the effective viscous drag coefficient. Naively interpreting the microtubule distribution as the resulting force profile does not match with the observed separation velocity profile. However, multiplying the microtubule distribution by a short-ranged inhibitory term, $f_{inhib}=f_0\frac{x^2}{x_0^2+x^2}$ (${\displaystyle x_0\approx 15\text{µm}}$), results in an excellent fit to our observed aster separation velocities (Figure 3E). The nature of such a short-ranged inhibition in the action of microtubules is expanded on in the Discussion.

Overall, we see that aster–aster and aster–boundary dynamics both appear to involve repulsive interactions with a degree of inhibition at very short distances. The difference in the apparent steady-state positioning of aster pairs suggests that aster–aster interactions are weaker than those between the asters and the boundary. Below, we use these results to define length scales and relative interactions strengths to simulate an effective potential between asters to explain the observed dynamics.

The two asters may mechanically interact via crosslinking of microtubule overlaps (Bieling et al., 2010; Deshpande et al., 2021a; Lv et al., 2018; Subramanian et al., 2013; Wijeratne and Subramanian, 2018), while astral microtubules may simply hit against the boundary interface, which acts as an immovable hard wall. However, we note that this conclusion is based on inference from the aster positions; we have not been able to quantitatively test this observation.

Perturbations of aster interaction are consistent with a microtubule-mediated repulsive force potential

To further explore the nature of microtubule aster interaction, we performed a series of inhibitory treatments to chemically perturb the interaction. Since small-molecule inhibitors for candidate molecular motors have no effect in Drosophila (Firestone et al., 2012; Maliga et al., 2002), we targeted microtubules and ATPases in general. We generated explants with two asters during separation and pulse injected a defined volume of 200 µM colchicine, which causes acute depolymerization of microtubules. Upon injection the asters stopped separating and sometimes inverted their direction of motion (Figure 4A and Video 2, right). We then tested whether ATP-dependent molecular machinery was the sole process leading to aster repulsion, by inhibiting ATP consumption with sodium azide. We injected a series of concentrations of sodium azide into explants that contained a separating pair of asters (Video 2, middle). Adding sodium azide decreased the initial recoil velocity (dashed lines in Figure 4A) and resulted in a considerable reduction in aster separation distance. However, even at very high concentrations of sodium azide, we still observed residual motion, suggesting that both ATP-driven microtubule-mediated separation and passively driven separation, for example, through entropy minimization, occur here.

Figure 4

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Video 2

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Both effective pushing or pulling forces can cause aster separation and centering (Grill et al., 2003; Laan et al., 2012; Zhu et al., 2010). Though our above results appear more consistent with effective pushing forces, this is based on analysis of the aster dynamics and the aster positioning within the explant; that is, we have not directly tested the nature of the effective force. Pulling within the cytoplasm requires aster asymmetry (Kimura and Kimura, 2011; Tanimoto et al., 2016). Thus, we performed targeted UV photo-ablation experiments in larger explants containing one or two asters, thereby inducing shape change or inhibiting interaction of the asters (Figure 4B, see Methods). First, we generated ellipse-shaped ablations positioned asymmetrically around one steady-state aster, affecting microtubules on the left side more than on the right side of the aster (Figure 4C). If pulling on the boundary (Grill et al., 2003) or hydrodynamic effects from vesicle transport along microtubules (Tanimoto et al., 2016) drives aster motion, we expect a displacement to the right (positive) after ablation. Conversely, if the net force applied on microtubules favors pushing on the MTOC, we expect a displacement to the left (negative). Indeed, asters consistently moved to the left, supporting a dominating effect of microtubule-driven pushing (Figure 4D and Video 3). As a control, we performed the same perturbation in explants that were injected with the microtubule inhibitor colchicine (Figure 4E). Under this condition, asters moved very slowly to the right (positive), which is consistent with a weak hydrodynamic effect from other contractile sources (e.g., actomyosin) (Kinneret, 2016). We conclude that a single aster moves and positions within Drosophila explants by microtubule-dependent pushing force.

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To challenge these conclusions, we performed two types of UV ablation in explants containing two asters (Figure 4F): (1) light pulses emitted along an ellipse around both asters, while they separate, to destroy microtubules in the periphery; (2) light pulses emitted along a line between the two asters, either in steady state or while separating, to destroy microtubules between asters. If forces are attractive, then ablation type 1 will stop separation while ablation type 2 will lead to an acceleration. If forces are repulsive, we predict the opposite response. We found a slight but significant acceleration for peripheral ablation in two out of three experiments (Figure 4G, type 1 and Video 4). We observed a strong deceleration or movement inversion with subsequent recovery for central ablation (Figure 4F, type 2) in all three experiments. Separation recovered likely because of fast re-growth of microtubules after ablation (in the range of µm/min) (Rogers et al., 2002). In summary, the dynamic behavior of asters in our explants is consistent with a model of radially symmetric microtubule-based repulsion.

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Simple repulsive model of aster interactions can replicate the observed aster behavior ex vivo

We formulated a physical model of aster repulsion from our experimental insights. We considered the asters as generating a radially symmetric repulsive potential, embedded within a 2D circular environment (Figure 5A). The repulsive potential is taken to be exponentially decaying with length scale 15 μm (based on Figure 1H). We also include a short-ranged inhibitory term when asters are close to the boundary or each other, of the form $\frac{x^2}{x^2+x_0^2}$ , where $x_0=18\mu m$ (aster–boundary) and $x_0=25\mu m$ (aster–aster). To match our observations on one- and two-aster cases, the repulsion from the explant boundary was 40% larger than the aster–aster repulsion (Methods). We also include a noise term due to the inherent stochasticity in the system.

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We tested whether this 2D model could replicate the observed dynamics and positioning in the one-aster case. The model reproduced the dynamics of a single aster moving away from the boundary (Figure 5B). Likewise, we can solve the 1D equation of motion stochastically for the one-aster case (Methods); the final aster position scaled with droplet size up to around 50 μm (Figure 5C).

We next introduced a second aster into the 2D model. We had to account for interactions between aster–boundary and aster–aster. The two-aster scenario was defined by allowing a single aster to divide, then following the positions of each sister aster. We can reproduce the experimentally observed aster dynamics, with a more symmetric speed profile as compared with the one-aster case (Figure 5D). Again, solving the equivalent 1D equation of motion stochastically, we found that this provides a good approximation of the aster positions (compare Figure 5E and Figure 5F).

Our model closely matches experimental observations in one- and two-aster scenarios. What about systems with greater than two asters? We previously showed that multi-aster samples form symmetric structures, for example, equilateral triangles with three asters and square-like distributions with four asters (de-Carvalho et al., 2022). Can our model replicate these observations? We ran our dynamic simulations with three of four initial asters randomly placed, until the asters reached equilibrium positions. In the three-aster scenario, most simulations resulted in the asters distributed such that they (approximately) formed the vertices of an equilibrium triangle. Subsequently, the asters were distributed with angle 60° between each other (Figure 5G). Likewise, most four-aster simulations resulted in the asters (approximately) forming the vertices of a square, with angle distribution 90° (Figure 5H). These results are similar to those observed experimentally (de-Carvalho et al., 2022). Consistent with experiment, in a small subset of simulations the four asters formed a triangle with the fourth aster positioned away from the other three (upper right inset, Figure 5H). In conclusion, our simple repulsive model can reproduce both the observed equilibrium aster distributions and the quantified aster dynamics in a range of scenarios.

We have characterized the mechanics of microtubule aster positioning using an ex vivo model of the cellular context where, naturally, hundreds of these cytoskeletal structures co-exist and define the regular positioning of nuclei in a multinucleated cell. We generated single embryo explants from mutant Drosophila syncytial embryos in which mitosis is inhibited but centrosomes duplicate and divide, each giving rise to a radial microtubule array. This experimental reductionist approach of generating a proliferative aster system ex vivo has several advantages (de-Carvalho et al., 2022). First and foremost, it enables the study of the mechanics of single aster positioning (the ‘atomic’ structure) under boundary conditions, and the canonical interaction between two structures. Our experiments support a mechanical model where asters generate a radially symmetric, repulsive force potential. Given the positioning of asters relative to each other and to the boundary, we posit that the repulsive interaction toward the boundary is about twice as strong as compared to the repulsion between two asters. However, we note that we have been unable to directly measure this force. The range of action between asters is finite and productive for positioning only up to ~35 µm. We note that two asters positioned close (<3 µm) to each other, for example after centrosome disengagement, show dynamics of weak attraction. We highlight that, by design, our experiments in embryo explants resolve the canonical aster–aster interaction whereas additional cell cortex interactions and more complex boundary conditions imposed by the cell membrane may occur in the intact embryo (Foe et al., 2000; Postner et al., 1992; Winkler et al., 2015). Importantly, embryo explants do not reconstitute a compartmentalized f-actin cortex (de-Carvalho et al., 2022) as typically seen in embryos (Foe et al., 2000). Potentially, the boundary force in embryos may be different, with cortical attachment leading to net pulling between boundary and aster.

There has been substantial discussion over the nature of aster force potentials (Garzon-Coral et al., 2016; Meaders et al., 2020; Minc et al., 2011; Mitchison et al., 2012; Pelletier et al., 2020; Sulerud et al., 2020; Tanimoto et al., 2018): are they repulsive or attractive; what range do they act over; and are there different regimes of action depending on temporal or spatial constraints? Here, we show that asters derived from the syncytial embryo of Drosophila display a short-range repulsive potential. At very short distances, this potential tends to zero (or arguably even attractive), likely due to microtubules being unable to form linearly. A simple model can replicate our observations without requiring additional assumptions. It is worth noting that the length scales here (typically 3–10 μm between asters in the embryo) are substantially smaller than those in other model systems used to explore aster dynamics, such as the sea urchin (>50 μm, Tanimoto et al., 2018; Meaders et al., 2020). In that system, effective pulling forces generated by hydrodynamic processes dominate the aster positioning (Tanimoto et al., 2018).

What is the mechanism underlying the reduction in microtubule-mediated force at very short distances, both for aster–aster and aster–boundary interactions? We observed splay in the microtubule distribution near the boundary. If microtubules are generating a mechanical pushing force (i.e., like a rod being pushed against a wall), such splay would be expected. Microtubule polymerization at a boundary generates forces against the boundary in the range that can lead to buckling (Holy et al., 1997; Howard, 2001). Conversely, it is challenging to reconcile this observation with astral microtubules (and linker proteins) transmitting a local pulling force (Grill et al., 2003). However, when two asters are very close, there may occur molecular crosslinking both between microtubules orientated (anti-) parallel – and perpendicular – to their axis of separation. Crosslinking between the perpendicular orientated microtubules at the periphery could act to generate a local pulling force between the asters at very short distances. As asters separate, sliding of antiparallel orientated microtubules will dominate, driving further aster separation. To test this hypothesis, super resolution microscopy may be necessary to gain sufficient spatial resolution to distinguish the relative population of parallel and perpendicular aligned microtubule bundles.

Between two asters, force inhibition may be attributed to molecular friction between microtubules (Forth et al., 2014). Single-molecule experiments showed that antiparallel microtubule crosslinking, and their sliding by molecular motor activity or entropic effects (Lansky et al., 2015), results in viscoelastic properties of the microtubule pair as a mechanical element (Shimamoto et al., 2015). At the level of two asters, hundreds of such elements in parallel accumulate to a ‘softened’ repulsion, overcoming any opposing forces on each aster (boundary constraints, viscosity of cytoplasm), leading to aster separation.

We emphasize that the molecular mechanism underlying the generation of the pushing forces remains unclear, in part due to the lack of suitable reagents for targeted perturbation of molecular motors in Drosophila. However, our finding that aster separation occurs despite inhibition of ATPases (e.g., motors) is both interesting and intriguing. It is unlikely due to mutual contact between microtubules growing from opposite asters since the probability for such encounters to happen and to be mechanically effective is extremely low. In our view, this ‘passive’ repulsion force is likely caused by entropy-driven microtubule sliding by ATP-independent crosslinkers (Forth et al., 2014). If possible, targeted inhibition of candidate microtubule-associated proteins should give further insight.

All original data are available on a data repository of Zenodo (CERN), https://doi.org/10.5281/zenodo.8090780. Codes are available on GitHub (copy archived at Tim Saunders Lab, 2023).

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Author details

1. Jorge de-Carvalho

   Instituto Gulbenkian de Ciência, Fundação Calouste Gulbenkian, Oeiras, Portugal

   Contribution

   Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing – original draft

   Competing interests

   No competing interests declared

2. Sham Tlili

   Mechanobiology Institute and Department of Biological Sciences, National University of Singapore, Singapore, Singapore

   Present address

   Aix-Marseille Université | AMU · Institut de Biologie du Développement de Marseille-Luminy (UMR 7288 IBDML), Marseille, France

   Contribution

   Conceptualization, Software, Formal analysis, Investigation, Methodology

   Competing interests

   No competing interests declared

3. Timothy E Saunders

   1. Mechanobiology Institute and Department of Biological Sciences, National University of Singapore, Singapore, Singapore
   2. Institute of Molecular and Cellular Biology, A*Star, Proteos, Singapore, Singapore
   3. Centre for Mechanochemical Cell Biology, Warwick Medical School, University of Warwick, Warwick, United Kingdom

   Contribution

   Conceptualization, Software, Formal analysis, Supervision, Visualization, Methodology, Writing – original draft, Project administration, Writing – review and editing

   For correspondence

   timothy.saunders@warwick.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-5755-0060

4. Ivo A Telley

   Instituto Gulbenkian de Ciência, Fundação Calouste Gulbenkian, Oeiras, Portugal

   Contribution

   Conceptualization, Resources, Data curation, Formal analysis, Supervision, Funding acquisition, Investigation, Visualization, Methodology, Writing – original draft, Project administration, Writing – review and editing

   For correspondence

   itelley@igc.gulbenkian.pt

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4444-1046

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