Cortical microtubule nucleation can organise the cytoskeleton of Drosophila oocytes to define the anteroposterior axis

  1. Philipp Khuc Trong
  2. Hélène Doerflinger
  3. Jörn Dunkel
  4. Daniel St Johnston
  5. Raymond E Goldstein  Is a corresponding author
  1. University of Cambridge, United Kingdom
  2. Massachusetts Institute of Technology, United States
8 figures

Figures

Figure 1 with 1 supplement
Models for the microtubule (MT) meshwork show local order in the cytoskeleton.

(A) 3D geometry of a stage 9 Drosophila oocyte (grey, anterior to the left, posterior to the right) containing more than 55,000 MT seeding points. From the corners to the centre, MT seeding density decreases weakly along the anterior (kA = 1000 μm, h0A=0.8) and strongly along the posterior-lateral cortex (kP = 150 μm, h0P=0, see ‘Materials and methods’ MT nucleation probability). Nucleated MT polymers are stiff random walks, initially pointing in a random direction. Only MT segments in a cross section are shown (green) to emulate confocal images. MT target lengths are chosen from a probability distribution that accounts for the MT aging process. The mean target length is set to a fraction ϵ of the anterior-posterior (AP) axis length, here ϵ = 0.5 (‘Material and methods’ MT growth). The inset shows the 3D angular distribution of 0.5% of all MT segments with 3D statistical bias. (B) Cross section through the MT cytoskeleton shown in A with 2D directional bias (top right). The inset shows 2D posterior bias (in percent) as function of depth (bottom right). (C) Local vector sum of MT segments from the cross section in panel B on a coarse-grained grid shown as streamlines that visualize local directionality. (D) Staining of α-tubulin (green) shows MT density distribution in a fixed stage 9 oocyte. Nuclei in blue (DAPI), scale bar is 30 μm. (E) Schematic detailing the work flow in the model and comparisons to experiments. (F) Local directionality of MT cross section as in panel C for an average over 50 independent realizations of the cytoskeleton. (G) Local directionality computed from the rod model with the same parameters as in panels A, B but shortened MT lengths (‘Material and methods’ Motor velocity field). Orange arrows show the separatrices between subcompartments. (H) MT density distribution computed from 50 realizations of the polymer model.

https://doi.org/10.7554/eLife.06088.003
Figure 1—figure supplement 1
Compartmentalization of the MT cytoskeleton is robust to changes in oocyte geometry.

(A) Alternative geometry for a stage 9 oocyte comprised of a posterior parabolic cap and an anterior disc. MT segments intersecting a cross section in one realization of the polymer model with nondimensional seeding density parameters kP = 150 μm, h0P=0,kA=1000μm, h0A=0.8 and MT length parameter ϵ = 0.5 from more than 55,000 seeding points are shown in green. Inset shows directionality of 0.5% of all MT segments with posterior bias. (B) Cross section through 3D MT cytoskeleton shown in panel A with 2D directional bias (top right). Inset shows 2D posterior bias (in percent) as function of depth (bottom right). (C) Local vectorial sum of MT segments visualized as a streamplot. One individual realization of the MT cytoskeleton shows poor spatial order. (D) α-tubulin staining of an early stage 9 oocyte. Scale bar is 25 μm. (E) Schematic of the work flow in our model. (F) Streamplot of the local vectorial sum of 50 realizations of the polymer MT cytoskeleton with parameters as in A, B. (G) Local net orientation of straight rod MTs in the rod model with parameters as in A, B but reduced mean MT target length ϵ = 0.28, showing the same compartmentalization of the oocyte as the average in the polymer model. (H) MT density distribution in the ensemble of 50 realization of the polymer MT cytoskeleton.

https://doi.org/10.7554/eLife.06088.004
Figure 2 with 1 supplement
Computed cytoplasmic flow fields capture key elements of in vivo flows.

(A) Streamlines (light blue lines) visualize the 3D cytoplasmic flow field computed from the realization of the cytoskeleton shown in Figure 1A. The horizontal plane shows a 2D cross-section through the 3D field. Anterior to the left, posterior to the right. (B) Cross-section through the 3D field shown in panel A with arrows indicating flow directions and colouring indicating flow speeds. (C) Confocal image of a live stage 9 oocyte. Arrows show the flow field computed from particle image velocimetry (PIV) of streaming yolk granules and averaged over ≈5 min. Scale bar is 25 μm. (D) Same as A, but showing the mean flow organization for an average of 100 individual 3D flow fields, analogous to the mean organization of the MT cytoskeleton in Figure 1F. (E) Same as B for the average in panel D. (F) Mean fluid flow speeds were obtained by PIV (red, 13.7 ± 0.8 nm/s, mean ± sem) and automatic particle tracking (orange, 15.3 ± 0.7 nm/s, mean ± sem) from 48 oocytes. Experimentally measured flow speeds were used to calibrate the forces f in the Stokes Equation 2 such that the computed mean speeds in 3D (blue, mean: 14.5 nm/s) or in 2D cross sections (green, mean: 14.8 nm/s) match the measured values. The larger spread in experimental flow speeds may reflect greater variability of motor activity, cytoplasmic composition, geometry or age in vivo.

https://doi.org/10.7554/eLife.06088.005
Figure 2—figure supplement 1
The oocyte nucleus covers a negligible fraction of the oocyte volume and disturbs the flow field only locally.

(A) Streamlines visualizing the flow field computed in the 3D oocyte geometry with additional no-slip boundary condition on a sphere representing the nucleus. Same forces as in Figure 2A,B, main text. The nucleus occupies 2.2% of the oocyte volume. Horizontal plane shows a cut through the flow field. (B) Young stage 9 oocyte stained with DAPI (blue), phalloidin (red) and showing oskar MS2 GFP (green) in the process of reaching the posterior pole. Scale bar is 25 μm. (C) Extracted and rotated shape of the oocyte in panel B (red), and symmetrized geometry resulting from averaging the shape above and below the AP-axis (blue). Black circle indicates the nucleus. (D) Ratio of nucleus volume to oocyte volume computed for Ne = 9 early (red) and Nm = 7 mid stage 9 oocytes (blue). Arrowhead marks the oocyte shown in panel B. (E, F) Cross sections through the 3D flow fields for the same forces as in panel A with (F) and without (E) nucleus. (G, H) Same as E and F, but vertical cross section that does not contain the nucleus.

https://doi.org/10.7554/eLife.06088.006
The model recapitulates oskar and bicoid mRNA transport, implying dominance of cytoskeletal transport.

(AC) Shown are fixed oocytes with oskar MS2 GFP (green) and stained with DAPI (blue) and Phalloidin (red). oskar mRNA forms a central cloud at late stage 8 (A), a collimated channel while moving to the posterior (B), and a posterior crescent at stage 9 (C). Scale bars are 25 μm. (D) 3D oocyte showing the initial oskar mRNA cargo distribution. (E, F) Cross sections through a simulation of oskar mRNA transport with diffusion, motor-transport and flows showing the distribution of total cargo cb + cu at the indicated time points. No posterior anchor is present. Simulations of three 6 hr cycles through 50 (vm,u)-pairs in random order once (twice, see Figure 4). For simulations of 1.5 hr, 25 (vm,u)-pairs were chosen at random. Compare to experimental observations in panels B and C. (G) Same simulation as in DF, but without cytoplasmic flows, showing largely identical localisation as in F. (H) Simulation of bicoid mRNA transport shows the mRNA quickly accumulating at the nearest cortex (arrowheads) when injected in the posterior (inset), corresponding to the behavior of naive bicoid. (I) Same as in H, corresponding to naive bicoid mRNA injection at the anterior-dorsal region (inset). (J) Same as in H for injection at the anterior middle (inset), showing that over long times simulated bicoid mRNA localises to the anterior corners (arrowheads). Localization to the anterior depends on sufficient proximity of the injection site as observed for injections of naive bicoid mRNA. (K) Same simulation for oskar mRNA as in DF, but with a posterior anchor (arrowhead) and without active motor-driven transport. Compare to panels F and G.

https://doi.org/10.7554/eLife.06088.007
Figure 4 with 2 supplements
The cortical MT seeding density determines sites of mRNA localisations and gives rise to a bifurcation in the cytoskeleton.

(AE) Simulations of oskar (AC) and bicoid (D) mRNA transport with diffusion, cytoskeletal transport and flow for the cytoskeletal architectures shown in panels EH, and their corresponding flow fields. For oskar mRNA, simulations reproduce wild-type localisation (A, same as Figure 3F), and partial (B) or complete mislocalisation (C). Initial condition as in Figure 3D. Simulation times were occasionally increased to 6 hr (B) to rule out transient concentration patterns. For bicoid mRNA, simulations capture mislocalisation to both anterior and posterior as in gurken/torpedo/cornichon mutants and in strong par-1 hypomorphs (D, arrowheads). Time points as indicated. The inset in D shows initial condition. (EH) Average local MT orientations in ensembles of 50 realizations of the polymer model for varying MT seeding densities along arclength s (see panel E) of the posterior-lateral cortex (insets). A MT seeding density that increases from a wild-type gradient (E, h0P=0,kP=150μm) laterally towards the posterior (F, h0P=0,kP=17.5μm) to a near-uniform distribution (G, h0P=0,kP=1μm) shows a saddle-node bifurcation by creating a pair of stable (green) and unstable (red) fixed points. (H) A MT seeding density that is slightly lower at the posterior pole (h0P=0.7,kP=40μm) produces mean MT orientations virtually indistinguishable from uniform seeding density (compare to G). (IK) Vector field of the mathematical normal form of the 2D saddle-node bifurcation (‘Materials and methods’ Bifurcation normal form). Values of the bifurcation parameter λ as indicated. Fixed points are located at positions x=±λ. (L) Fluorescence in-situ hybridization to bicoid mRNA in a strong par-1 hypomorph. The mRNA (red) localises around the cortex, with most accumulation at the anterior corners and at the posterior pole (compare to panel D, arrowheads). Scale bar is 25 μm.

https://doi.org/10.7554/eLife.06088.008
Figure 4—figure supplement 1
Either the MT seeding density or the MT length can act as bifurcation parameter.

(AJ) Each panel shows the mean local MT orientations for an ensemble of 50 realizations of the polymer MT cytoskeleton under variations of the seeding density parameter kP and MT length parameter ϵ as indicated. Approximate location of the stable fixed point is shown in green, with region of attraction in blue, and domain of attraction of the posterior pole in red. The point on the AP-axis between red and blue arrow region marks the unstable fixed point. Percentages indicate the ensemble-averaged 3D directional bias. Experimentally, the directional bias was measured as 57.97%:42.03% (Parton et al., 2011). Cytoskeleton in panel I was used as wild-type cytoskeleton (Figure 1F, main text). Anterior seeding density is unchanged in all panels kA = 1000 μm, h0A=0.8. (KO) Same as panels AJ but for ensembles with 100 realizations of the cytoskeleton to ensure reliable visualization of vector field even when fewer MTs reaching the oocyte center. (PT) Vector fields computed from a saddle-node bifurcation normal form. The critical bifurcation point is λ = 0, and for λ < 0, fixed points are located at x±=±λ.

https://doi.org/10.7554/eLife.06088.009
Figure 4—figure supplement 2
Lateral MT growth produces the clone-adjacent-mislocalisation phenotype (see main text).

(AD) Addition of lateral MTs reproduces the clone-adjacent-mislocalisation phenotype. (A) Cross section through one realization of the wild-type MT cytoskeleton in the polymer model (h0A=0.8,kA=1000μm, h0P=0,kP=150μm). Additional MTs have been added dorsal to the posterior pole (black arrow) to mimick posterior follicle cell clones (RASΔC40b MARCM) that overexpress dystroglycan (Poulton and Deng, 2006). (B) Density of MTs for 50 realizations of the cytoskeleton shows enrichment on one side of the posterior pole (white arrow). (C) Streamplot showing the local vectorial orientation averaged over 50 realizations of the cytoskeleton. Note the upwards tilt away from the central posterior pole. (D) Simulations of oskar mRNA transport by diffusion, cytoskeletal transport and corresponding cytoplasmic flows show that cargo is repelled from the site of additional MT nucleation on one side of the posterior pole, thereby capturing the CAM phenotype (Poulton and Deng, 2006).

https://doi.org/10.7554/eLife.06088.010
The parameter space of the rod model shows the relation and interconversion between all three distinct cytoskeletal architectures.

(A) The regions corresponding to wild-type (red), weak par-1 hypomorph (blue) and strong par-1 hypomorph topologies (green, arrowhead at far left) are shown as a function of the mean MT length ϵ and extent of the posterior seeding density kP. The bifurcation line between wild-type and weak par-1 hypomorph topologies can be crossed by either changing the seeding density laterally (horizontal dashed arrow), or by shortening the MTs (vertical dashed arrow). (B, C) Parameter spaces as in A for increasing MT nucleation at the posterior pole (B: h0P=0.03,C:h0P=0.1). Inset in panel C shows a magnification of the triple point at which small changes in parameters can convert each cytoskeletal architecture into any other. (D) Local net orientations of MT rods for parameter values indicated in the inset of panel C (yellow circles). In all panels, parameter values for anterior MT nucleation were kept constant (h0A=0.8,kA=1000μm).

https://doi.org/10.7554/eLife.06088.011
Seeding point density in the polymer model.

Shown are N randomly drawn seeding points on the posterior cap of the standard oocyte geometry, according to Equation 15 distributed either (near-)uniformly on the cap (A, G) or in a parabolic gradient from the posterior pole to the anterior corners (F, L). Between uniform and parabolic distribution, the seeding density can vary either by laterally reducing the density (B, CE, parameter kP), or by reducing the density at the posterior pole (H, IK, parameter h0P). Total number of points is calculated with a fixed number of anterior points NA = 4000 (Equation 20). For actual computations of wild-type cytoskeletons (kP=3,h0P=0,kA=20,h0A=0.8, see main text for dimensional parameters), more than 55,000 seeding points are used.

https://doi.org/10.7554/eLife.06088.012
The cortical MT density increases approximately parabolically from the posterior pole towards the anterior corners.

(A) α-tubulin staining of a stage 9 oocyte (green) with DAPI staining of DNA (blue). Arrows indicate arclengths sP from the posterior pole to the anterior corners and analogously sA at the anterior. (B) Fluorescence intensity profile (green) with moving average (red) extracted from a 10 pixel wide line along sP indicated in panel A. Arclength was normalized to one, and the minimum intensity of the moving average was subtracted from both fluorescence profiles. (C) Average intensity profiles (red) of cortical MT density as in panel B from N = 15 oocytes. The minimum intensity value across all profiles was subtracted from each. Blue line shows a parabolic fit. (D) Probability densities for the distribution of MT seeding points along anterior arclength (top) and posterior arclength (bottom) used for the wild-type cytoskeleton (blue lines). Black dashed line in bottom panel shows exact parabola. Arclengths are nondimensional lengths with scale L = 50 μm.

https://doi.org/10.7554/eLife.06088.013
von Mises-Fisher parameter κ determines MT stiffness.

Shown are three cross sections through MT cytoskeletons for indicated values of κ. MTs become stiffer with increasing values of κ. Insets show angular distribution for 3 × 103 points drawn from von Mises-Fisher distribution around mean direction μ^=e^z.

https://doi.org/10.7554/eLife.06088.014

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  1. Philipp Khuc Trong
  2. Hélène Doerflinger
  3. Jörn Dunkel
  4. Daniel St Johnston
  5. Raymond E Goldstein
(2015)
Cortical microtubule nucleation can organise the cytoskeleton of Drosophila oocytes to define the anteroposterior axis
eLife 4:e06088.
https://doi.org/10.7554/eLife.06088