The coordination of spindle‐positioning forces during the asymmetric division of the Caenorhabditis elegans zygote
2021; Springer Nature; Volume: 22; Issue: 5 Linguagem: Inglês
10.15252/embr.202050770
ISSN1469-3178
AutoresHélène Bouvrais, Laurent Chesneau, Yann Le Cunff, Danielle Fairbrass, Nina Soler, Sylvain Pastezeur, Thierry Pécot, Charles Kervrann, Jacques Pécréaux,
Tópico(s)Cellular Mechanics and Interactions
ResumoArticle26 April 2021free access Source DataTransparent process The coordination of spindle-positioning forces during the asymmetric division of the Caenorhabditis elegans zygote Hélène Bouvrais Corresponding Author Hélène Bouvrais [email protected] orcid.org/0000-0003-1128-1322 CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Laurent Chesneau Laurent Chesneau orcid.org/0000-0001-7042-443X CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Yann Le Cunff Yann Le Cunff orcid.org/0000-0002-3068-5675 CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Danielle Fairbrass Danielle Fairbrass CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Nina Soler Nina Soler orcid.org/0000-0002-6060-5461 CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Sylvain Pastezeur Sylvain Pastezeur CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Thierry Pécot Thierry Pécot orcid.org/0000-0003-0772-9753 INRIA, Centre Rennes - Bretagne Atlantique, Rennes, France Search for more papers by this author Charles Kervrann Charles Kervrann orcid.org/0000-0001-6263-0452 INRIA, Centre Rennes - Bretagne Atlantique, Rennes, France Search for more papers by this author Jacques Pécréaux Corresponding Author Jacques Pécréaux jacq[email protected] orcid.org/0000-0001-9998-4844 CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Hélène Bouvrais Corresponding Author Hélène Bouvrais [email protected] orcid.org/0000-0003-1128-1322 CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Laurent Chesneau Laurent Chesneau orcid.org/0000-0001-7042-443X CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Yann Le Cunff Yann Le Cunff orcid.org/0000-0002-3068-5675 CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Danielle Fairbrass Danielle Fairbrass CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Nina Soler Nina Soler orcid.org/0000-0002-6060-5461 CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Sylvain Pastezeur Sylvain Pastezeur CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Thierry Pécot Thierry Pécot orcid.org/0000-0003-0772-9753 INRIA, Centre Rennes - Bretagne Atlantique, Rennes, France Search for more papers by this author Charles Kervrann Charles Kervrann orcid.org/0000-0001-6263-0452 INRIA, Centre Rennes - Bretagne Atlantique, Rennes, France Search for more papers by this author Jacques Pécréaux Corresponding Author Jacques Pécréaux [email protected] orcid.org/0000-0001-9998-4844 CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France Search for more papers by this author Author Information Hélène Bouvrais *,1, Laurent Chesneau1, Yann Le Cunff1, Danielle Fairbrass1, Nina Soler1, Sylvain Pastezeur1, Thierry Pécot2, Charles Kervrann2 and Jacques Pécréaux *,1 1CNRS, IGDR - UMR 6290, University of Rennes, Rennes, France 2INRIA, Centre Rennes - Bretagne Atlantique, Rennes, France *Corresponding author. Tel: +33 2 23 23 40 08; E-mail: [email protected] *Corresponding author. Tel: +33 2 23 23 45 03; E-mail: [email protected] EMBO Reports (2021)22:e50770https://doi.org/10.15252/embr.202050770 PDFDownload PDF of article text and main figures. Peer ReviewDownload a summary of the editorial decision process including editorial decision letters, reviewer comments and author responses to feedback. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InMendeleyWechatReddit Figures & Info Abstract In Caenorhabditis elegans zygote, astral microtubules generate forces essential to position the mitotic spindle, by pushing against and pulling from the cortex. Measuring microtubule dynamics there, we revealed the presence of two populations, corresponding to pulling and pushing events. It offers a unique opportunity to study, under physiological conditions, the variations of both spindle-positioning forces along space and time. We propose a threefold control of pulling force, by polarity, spindle position and mitotic progression. We showed that the sole anteroposterior asymmetry in dynein on-rate, encoding pulling force imbalance, is sufficient to cause posterior spindle displacement. The positional regulation, reflecting the number of microtubule contacts in the posterior-most region, reinforces this imbalance only in late anaphase. Furthermore, we exhibited the first direct proof that dynein processivity increases along mitosis. It reflects the temporal control of pulling forces, which strengthens at anaphase onset following mitotic progression and independently from chromatid separation. In contrast, the pushing force remains constant and symmetric and contributes to maintaining the spindle at the cell centre during metaphase. SYNOPSIS This study deciphers the temporal and spatial regulation of the spindle positioning forces during the nematode zygotic mitosis. Dynein persistence pulling increases with mitotic progression, augmenting the overall force. Polarity is encoded through an anteroposterior asymmetry in dynein on-rate and recapitulates the final spindle position. The pushing force opposes the spindle posterior displacement until late anaphase, maintaining the spindle at the cell centre during metaphase. Introduction During asymmetric division, the position of the mitotic spindle is accurately regulated. Its final position participates in the correct partition of cell fate determinants, which is crucial to ensure faithful division during developmental processes (Gönczy, 2008; Neumüller & Knoblich, 2009; Morin & Bellaïche, 2011; McNally, 2013; Kotak, 2019). Furthermore, its position at the late metaphase controls the pulling force burst (Bouvrais et al, 2018). In the one-cell embryo of the nematode Caenorhabditis elegans, the mitotic spindle is first oriented along the polarity axis and positioned at the cell centre. Then, the spindle is maintained at that position for a few minutes during metaphase. Finally, it is displaced towards the posterior before division (Gönczy, 2008; McNally, 2013). So far, cell-scale investigations revealed the forces at the core of this precise choreography but remained elusive in their regulation. In particular, force generators pull on astral microtubules from the cell periphery, corresponding to the cell cortex and cause the posterior displacement. The force generators are composed of the dynein/dynactin complex, the LIN-5NuMA protein and the G-protein regulators GPR-1/2LGN and are anchored at the membrane through Gα subunits (Gotta & Ahringer, 2001; Colombo et al, 2003; Srinivasan et al, 2003; Couwenbergs et al, 2007; Nguyen-Ngoc et al, 2007). This trimeric complex generates forces through dynein acting as molecular motor and/or tracking the plus-end of depolymerising microtubule (Schmidt et al, 2005; Kozlowski et al, 2007; Nguyen-Ngoc et al, 2007; O'Rourke et al, 2010; Laan et al, 2012a). Opposite to this cortical pulling, the centring force maintains the spindle at the cell centre during metaphase. Its mechanism is still debated with three major possibilities (Wühr et al, 2009; Wu et al, 2017): specific regulation of the cortical pulling forces (Tsou et al, 2002; Grill & Hyman, 2005; Kimura & Onami, 2007; Gusnowski & Srayko, 2011; Laan et al, 2012a); pulling forces generated by dynein localised at cytoplasmic organelles (Kimura & Onami, 2005; Kimura & Kimura, 2011; Shinar et al, 2011; Barbosa et al, 2017); and cortical pushing forces resulting from the growing of astral microtubules against the cortex (Garzon-Coral et al, 2016; Pécréaux et al, 2016), similarly to the mechanism found in yeast (Tran et al, 2001; Tolic-Nørrelykke et al, 2004). So far, these studies were all based on cell-scale measurements. How are the cortical pulling and pushing forces regulated and coordinated in space and time? The previous studies approached them separately, resorting to spatial or temporal averages. The cortical pulling forces are asymmetric, because of a higher number of active force generators—trimeric complexes engaged in pulling events with astral microtubules—at the posterior-most region of the embryo (Gotta et al, 2003; Grill et al, 2003; Pécréaux et al, 2006a; Nguyen-Ngoc et al, 2007; Rodriguez-Garcia et al, 2018), in response to polarity cues (Grill et al, 2001; Colombo et al, 2003; Tsou et al, 2003; Park & Rose, 2008; Krueger et al, 2010; Bouvrais et al, 2018). Besides, the physical basis of the progressive increase in the pulling force along the course of the division was inferred from cell-scale measurements, particularly during anaphase, and a molecular mechanism is still missing (Labbé et al, 2004; Pécréaux et al, 2006a; Campbell et al, 2009; Bouvrais et al, 2018). Furthermore, the spatiotemporal regulation of the centring force is still unknown, as well as its coordination with opposed pulling force. We here addressed this gap, through analysing the astral microtubules contacting the cortex. Astral microtubules are involved in generating all these forces. These semi-flexible filaments emanate from the spindle poles. They are dynamic, switching alternatively from growing to shrinking and back, at the catastrophe and rescue rates, respectively (Mitchison & Kirschner, 1984). At the cortex, astral microtubules can be in three different states: shrinking in coordination with cortex-anchored dynein that generates pulling force (Gonczy et al, 1999; Dujardin & Vallee, 2002; Grishchuk et al, 2005; Gusnowski & Srayko, 2011; Laan et al, 2012a; Rodriguez-Garcia et al, 2018); pushing by growing against the cortex, likely helped by stabilising associated proteins like CLASP (Faivre-Moskalenko & Dogterom, 2002; Dogterom et al, 2005; Howard, 2006; Espiritu et al, 2012); or stalled, clamped possibly by dynein tethering or other proteins (Labbé et al, 2003; Sugioka et al, 2018). Do the microtubule dynamics, especially their cortical residence times, reflect these different states? Interestingly, dynein tethering delays microtubule catastrophe, as shown in vitro and by computational studies (Hendricks Adam et al, 2012; Laan et al, 2012a). Oppositely, the larger the pushing force, the smaller the residence time (Janson et al, 2003). In C. elegans embryo, microtubules involved in pulling or pushing forces may display different cortical residence times (Pécréaux et al, 2006a; Pécréaux et al, 2016). They could thus reveal the corresponding force-generating events. For instance, previous studies uncovered anteroposterior variations in residence time. The microtubules would be more dynamic (lower lifetime) at the posterior cortex compared to the anterior (Labbé et al, 2003; Sugioka et al, 2018). However, the reported residence times are strikingly different between studies (Labbé et al, 2003; Kozlowski et al, 2007; O'Rourke et al, 2010; Hyenne et al, 2012; Schmidt et al, 2017; Sugioka et al, 2018). How the microtubule residence times evolve throughout mitosis is, however, yet to be studied. Indeed, the short duration of these cortical fluorescent spots of labelled microtubules (a few frames) and the low signal-to-noise ratio of the images made resolving both time and space variations hard until now. Recent developments in microscopy and image-processing tools call for revisiting this problem (Chenouard et al, 2014; Kervrann et al, 2016). Beyond imaging improvements, the statistical analysis of the durations of microtubule tracks at the cortex—resulting from following the same fluorescent spots over several images—could also be significantly refined in contrast to the classic fit with a mono-exponential distribution (Kozlowski et al, 2007; Sugioka et al, 2018). In particular, we here aim to distinguish several co-existing dynamical behaviours. Thus, we fitted the experimental distribution of the track durations with finite-mixture-of-exponential models and then used an objective criterion to choose the best one. Such an approach, although delicate, benefits from developments in applied mathematics (Grinvald & Steinberg, 1974; James & Ware, 1985; Vieland & Hodge, 1998; Jae Myung et al, 2000; Turton et al, 2003). Furthermore, in our case, the microtubule residence times could last only a few tenths of a second, i.e. a few frames. The discrete nature of the residence time histogram calls for specific analysis as performed in photon counting experiments. This field has designed appropriate fitting strategies that offer a firm starting point to analyse microtubule dynamics (Maus et al, 2001; Turton et al, 2003; Nishimura & Tamura, 2005; Laurence & Chromy, 2010). In the present paper, we aim to study the spatiotemporal regulation of the spindle-positioning forces during the first mitotic division of the C. elegans embryo. To do so, we measured the microtubule dynamics at the cell periphery. We designed the DiLiPop assay (Distinct Lifetime subPopulation) to disentangle several microtubule populations distinct by their cortical residence times. We found two of them, which we could associate with different microtubule functions. Equipped with this assay, we could investigate in time and space, and at the microscopic level, the regulation of the forces positioning the spindle during mitosis. We directly measured the force generator processivity increase that accounts for the pulling force regulation throughout mitosis. We showed that the three controls of pulling force (by polarity, spindle position and mitotic progression) act independently. We also identified which mechanism maintains the spindle at the cell centre during metaphase. Finally, we suggest how the two cortical forces, pushing and pulling, coordinate in space and time. Results The Distinct Lifetime (sub)Population (DiLiPop) assay reveals two populations of microtubules at the cortex To investigate the regulation of the forces exerted on the mitotic spindle during the first mitosis of the C. elegans zygote, we set to measure the dynamics of astral microtubules at the cortex. The microtubules were entirely fluorescently labelled using YFP::α-tubulin to view them in all their states. The thickness of the perivitelline space, about 250–500 nm, prevented the use of the TIRF microscopy without altering the embryo shape (Olson et al, 2012). We performed spinning disc microscopy at the cortical plane, at 10 frames per second similarly to Bouvrais et al, (2018) (Appendix Text §1.1.1). The high frame rate needed to resolve the brief cortical contacts led to images with a low signal-to-noise ratio (Fig 1A, top). We mitigated this issue by denoising using the Kalman filter (Fig 1A, middle; Movie EV1, right) (Kalman, 1960). However, we did not correct any bleaching to avoid artefact, preferring to work out the imaging conditions. We then tracked the microtubule contacts using the u-track algorithm (Fig 1A, bottom; Appendix Table S1; Appendix Text §1.1.2) (Jaqaman et al, 2008). This image-processing pipeline is further named KUT. During metaphase and anaphase, the microtubule tracks appeared as fluorescent spots, suggesting that the microtubules did not slide or bend along the cortex (Movie EV1). The tracks were classified mainly as diffusive-like, based on the asymmetry in the position scatter along each trajectory (Huet et al, 2006; Jaqaman et al, 2008). Besides, each microtubule visited a limited cortical region (< 1 μm2 in average, Appendix Text §1.1.2), in agreement with microtubule end-on cortical-interaction (Laan et al, 2012a). We estimated that it enabled us to capture at least 2/3 of the microtubule contacts (Appendix Fig S1A) by comparing with electron tomography (Redemann et al, 2017). Figure 1. Microtubule dynamics at the cortex of the Caenorhabditis elegans embryo encompass two distinct residence time behaviours during the first zygotic division The typical workflow of the DiLiPop (Distinct Lifetime subPopulation) assay disentangles microtubule populations. (Top) Bright spots are the plus-ends of the fluorescently labelled microtubules. (Middle) Spots are enhanced after denoising by a Kalman filter. (Bottom) The trajectories of the microtubules (yellow lines) are obtained using the u-track algorithm (Appendix Text, §1.1.2). The parameters used are in Appendix Table S1. Scale bar represents 10 μm. Experimental distribution of the microtubule track durations for an embryo imaged from nuclear envelope breakdown to late anaphase. (Insets) Spatial distributions of the tracks lasting 0.3 s (brown), 1 s (orange) and 3 s (pink). The above experimental distribution (open circles) was fitted using various exponential models: (dashed blue line) mono-exponential, (plain red line) double exponential, (dash-dotted green line) triple-exponential, (dashed purple line) stretched exponential and (dash-dotted brown line) a diffusion with drift model (Appendix Text, §1.2.1). The double exponential model was the most satisfactory visually. This was confirmed applying the approach described in (D). Flow diagram of the advanced statistical analysis used in the DiLiPop assay (Appendix Text, §1.2). (White boxes) Exemplar distributions (histograms), depicting the count ci,j per duration-bin (indexed by i), j indexing the embryo. (Grey shadings) The experimental distributions of the microtubule track durations for N embryos were individually fitted using different exponential models (Appendix Text, §1.2.1) and assuming a Poisson distribution (Appendix Text, §1.2.2). (Green shading) We maximised the global likelihood L, computed as the product of embryo likelihoods Lj (Appendix Text, §1.2.3). (Orange shadings) We thus obtained the model parameters for each studied model. (Blue shadings) The best model was selected as the one minimising the Bayesian Inference Criterion (BIC) (Appendix Text, §1.2.4). (Purple shadings) We estimated the standard deviations on the best model parameters by using either a bootstrap approach (Appendix Fig S1D) or the likelihood-based confidence intervals (Appendix Fig S1E) (Appendix Text, §1.2.5). Microtubule track durations of N = 25 untreated embryos (same condition as in (B, C)) were subjected to DiLiPop global fit. The best-fitting model was the double exponential (black line). Dotted green and dashed orange lines highlight the separate contributions of each exponential component, respectively, short- and long-lived. The BIC values for each model are reproduced in Appendix Table S2. Corresponding fit parameters and error bars, which are standard deviations (SD) obtained by bootstrapping. Data information: Imaging of YFP::α-tubulin-labelled embryos was performed at a frame acquisition rate of 10 Hz. KUT and statistical analyses are illustrated with a one-cell untreated embryo. The data set composed of N = 25 untreated C. elegans embryos is also used in the Figs 2A, 4A and B, and 6A, in Appendix Figs S1A, S4, S6C and D, S12A and B, and S14 and Appendix Table S2. Source data are available online for this figure. Source Data for Figure 1 [embr202050770-sup-0004-SDataFig1.xlsx] Download figure Download PowerPoint To ensure that fluorescent spots were associated with microtubule contacting the cortex and not with free tubulin in the cytoplasm, we permeabilised embryos by perm-1(RNAi) and performed a nocodazole treatment as in (Carvalho et al, 2011) (Appendix Fig S2A) (Appendix Text §1.1.3). After microtubule depolymerisation, we obtained a negligible number of tracks at the cortex, about 1 or 2 per frame, which was ten to forty times less than in untreated embryos (Appendix Fig S2B). The control embryos treated with DMSO appeared similar to non-treated. It confirmed that the tracks studied here corresponded to astral microtubules contacting the cortex. We furthermore computed the count of instantaneous contacts in untreated embryos. They increased around anaphase onset (Appendix Fig S1A) similarly to the microtubule dynamics (Srayko et al, 2005). They also increased with the centrosome approaching the cortex (Bouvrais et al, 2018) (Appendix Text §1.1.3). Importantly, the instantaneous count of microtubule contacts at the posterior cortex oscillated during anaphase as in (Kozlowski et al, 2007). The period was comparable to the one of the posterior centrosome oscillation. These oscillations depended on GPR-1/2 (Appendix Fig S3) (Appendix Text §1.1.3). We overall concluded that the investigated spots corresponded to astral microtubules reaching the cortex. We computed the duration distributions of the microtubule tracks for each embryo separately (to avoid averaging artefacts) (Fig 1B). When all the microtubules have the same catastrophe rate, this distribution follows an exponential decay (Kozlowski et al, 2007; Floyd et al, 2010). However, we also envisaged that multiple mechanisms are superimposed, leading to distinct catastrophe rates. Therefore, we fitted the duration distribution with finite-mixture-of-exponential models, in particular, double- and triple-exponential models (Appendix Text §1.2.1). The double exponential appeared to fit better, suggesting that we observed at least two populations of microtubules contacting the cortex of C. elegans embryo, distinct by their residence times (Fig 1C). These populations might offer the opportunity to visualise the various force-generating mechanisms. To finely characterise them, we implemented an advanced statistical analysis of the track-duration distribution (Fig 1D), described in details in Appendix Text §1.2. In a nutshell, because we fitted a histogram with few counts in some bins, we modelled the data point errors using a Poisson law. We designed the objective function correspondingly to fit the histogram (Fig 1D, grey shading) (Appendix Text §1.2.2) (Laurence & Chromy, 2010). To distinguish between multiple populations within each embryo from a single population per cell with parameters varying between embryos, we fitted each embryo individually. However, to gain certainty, we imposed the same model parameters on each embryo of a given data set, by global fitting, i.e. maximising the product of the embryo-wise likelihoods (Fig 1D, green) (Appendix Text §1.2.3) (Beechem, 1992). We performed an unbiased selection of the best mixture-of-exponential model using the Bayesian Inference Criterion (BIC) (Fig 1D, blue) (Appendix Text §1.2.4) (Schwarz, 1978). Finally, we computed the confidence intervals on the fitted parameters using bootstrapping (Fig 1D, purple; Appendix Fig S1D) (Appendix Text §1.2.5) (Efron & Tibshirani, 1993). We validated this approach using the likelihood ratio (Appendix Fig S1E) (Bolker, 2008; Agresti, 2013). Applying this approach to untreated embryos of C. elegans, we found two populations within the microtubules residing at the cortex (Fig 1EF, Appendix Table S2). Their distinct dynamics, whose lifetimes were in the range of the second, were in agreement with residence time measurements performed with high enough image acquisition rate (Kozlowski et al, 2007; O'Rourke et al, 2010; Lacroix et al, 2016; Schmidt et al, 2017; Sugioka et al, 2018). It suggested that the microtubules could be involved in two different mechanisms. In contrast, performing the DiLiPop assay on embryos treated with nocodazole, we found a very-short-lived population, whose lifetime was briefer than the short-lived one, and no long-lived population (Appendix Fig S2C). Control embryos (DMSO) showed a two-population behaviour similar to non-treated ones (Appendix Fig S2C compared to Fig 1F). Therefore, the few remaining tracks upon nocodazole treatment corresponded likely to detection noise (Appendix Text §1.1.3). In conclusion, our analysis reflected astral microtubule dynamics out of the noise. We firstly asked how dependent on imaging conditions were the results (Appendix Text §1.1.4). We applied our DiLiPop analysis to untreated α-tubulin-labelled embryos acquired at 20 Hz and compared the result to our untreated embryo data set, comprising 25 embryos acquired at 10 Hz. We observed fewer tracks due to the reduced sensitivity linked to the shorter exposure time (Appendix Fig S4A). However, we found two populations with lifetimes similar to the reference data set ones (Appendix Fig S4B). We performed a converse analysis and simulated a 2 frames per second acquisition through a running sum of 5 images on our reference data set. We obtained fewer tracks, since those below 0.5 s were not resolved (Appendix Fig S4C). The recovered-tracks analysis resulted in a single population with a lifetime close to the long-lived one measured at 10 Hz (Appendix Fig S4D). In conclusion, our results were independent of the frame rate provided it is fast enough to resolve the short-lived population. We secondly ensured that our complex pipeline could not create the two dynamically distinct populations through artefacts. We built images containing particles with a single dynamical behaviour (Appendix Fig S5A, black; Appendix Table S3; Materials and Methods) (Costantino et al, 2005). By DiLiPop analysis, we recovered a single population with the correct lifetime (Appendix Fig S5A, red). In contrast, a similar simulation with two dynamical populations led to the double exponential as the best model (Appendix Fig S5B, blue) and accurate lifetimes (Appendix Fig S5B, right). Overall, the KUT image-processing pipeline did not cause artefacts. However, and to gain certainty, we repeated the analysis of in vivo data using an image-processing pipeline based on different hypotheses. This pipeline, named NAM, encompasses the ND-SAFIR denoising (Appendix Fig S6B, middle) (Boulanger et al, 2010), the ATLAS spot-detecting (Basset et al, 2015) and the MHT linking (Multiple Hypothesis Tracker) (Appendix Fig S6B, right) (Chenouard et al, 2013), with settings listed in Appendix Table S4 (Appendix Text §1.1.5). Applied to untreated C. elegans embryos, the NAM pipeline combined to DiLiPop statistical analysis recovered the two populations distinct by their dynamics (Appendix Fig S6A, green). Furthermore, the lifetimes were close to the ones obtained using the KUT pipeline (Appendix Fig S6A, right). We, therefore, excluded that the two dynamically distinct populations could be artifactual. We estimated that we analysed about 2/3 of the microtubule contacts at the cortex compared to the theoretical expected ones. While this proportion was high, we wondered whether the remaining 1/3 could correspond to a particular population. Firstly, we reused the fabricated images containing particles displaying two dynamical behaviours and compared the recovered population-proportion with the assigned one. Both proportions were similar. Therefore, our KUT pipeline introduced no bias analysing fabricated images (Appendix Fig S5B, right). Secondly, to investigate this point on real images, we compared the recovered proportions obtained through the KUT and NAM analysis pipelines applied to untreated embryos. We observed similar populations, both in lifetimes and proportions (Appendix Fig S6A, right), which suggested again that viewing 2/3 of expected microtubules introduced no bias. Furthermore, the similarity of the results obtained using two pipelines different by their approaches made unlikely that the remaining 1/3 of contacts would correspond to an additional population. Along a similar line and before investigating the biological relevance of these populations, we wondered whether there might be even more than two populations in general. We reasoned that the number of data points, typically ~20,000 microtubule tracks per embryo, may be insufficient to support a triple-exponential model. We addressed this question in silico and simulated distributions of microtubule track durations creating "simulated embryos", with three dynamical populations of lifetimes 0.4, 1.5 and 4 s, and proportions set to 55, 40 and 5%, respectively. These values correspond to experimental estimates on untreated embryos (Appendix Table S2). To mimic the experimental conditions of untreated embryos, we generated "fabricated datasets" composed of 25 simulated embryos and analysed them using the DiLiPop assay. We repeated 10 times this simulation procedure to get certainty about the results. We further considered only the sample sizes, for which a majority of fabricated data sets led to the simulated model, here triple-exponential, being the best model according to Bayesian criterion. Among valid conditions, we averaged the recovered model parameters over the data sets, where the recovered best model was correct. It suggested that 20,000 tracks per embryo were necessary and also sufficient to support the triple-exponential model if applicable (Appendix Fig S7A). We reckoned that a third and very-long-lived population might be in such a low proportion that the amount of experimental data did not allow identifying it. Keeping with our in silico approach and using 20,000 tracks per embryo, we fixed the short-lived proportion to 55% and the very-long-lived one from 2.5 to 10%. We found that 5% was enough to support the triple-exponential model (Appendix Fig S7B). We concluded that in untreated embryos, there is less than 5% or no very-long-lived population of astral microtubules. Being confident in the biological origin of the two microtubule populations, we wondered whether two well-defined microtubule populations exist or whether the numerous molecular motors and microtubule-associated proteins (MAPs) could lead to a
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