Aurora A depletion reveals centrosome-independent polarization mechanism in C.elegans

How living systems break symmetry in an organized manner is an important question in biology. In C. elegans zygotes, symmetry breaking normally occurs in the vicinity of centrosomes, resulting in anterior-directed cortical flows and establishment of a single posterior PAR-2 domain. Here, we report that zygotes depleted of the Aurora A kinase AIR-1 or of centrosomes establish two posterior domains, one at each pole. Using transgenic animals and microfabricated triangular chambers, we establish that such bipolarity occurs in a PAR-2- and curvature-dependent manner. Furthermore, we develop an integrated physical model of symmetry breaking, establishing that local PAR-dependent weakening of the actin cortex, together with mutual inhibition of anterior and posterior PAR proteins, provides a mechanism for self-organized PAR polarization without functional centrosomes in C. elegans. One Sentence Summary We uncover a novel centrosome-independent mechanism of polarization in C. elegans zygotes

prevented PAR-2 domain formation in ~72% of embryos, demonstrating that cortical AIR-1 can prevent symmetry breaking. Taken together, these findings lead us to propose that AIR-1 plays a dual function: at the cortex, in preventing erroneous symmetry breaking, perhaps early in the cell cycle, and at centrosomes, in directing symmetry breaking in their vicinity, likely later on.
Why do embryos become bipolar upon AIR-1 depletion or without centrosomes? Because PAR-2 domains developed almost invariably at the poles, we hypothesized that membrane curvature might be important. To test this, we microfabricated equilateral triangular PDMS chambers ~40 To further analyze how membrane curvature cue can lead to bipolarization, we developed a physical model (Fig. 4E, Supp. Mat.). This model is based on known interactions between anterior and posterior PAR proteins (18) and accounts for preferential PAR-2 binding to regions of high curvature, as well as for coupling between PAR-2 and cortical actin. In this model, the wild type situation is simulated by locally weakening acto-myosin activity next to centrosomes ( Fig. 4F; Fig S4A, MovieS6). Independently of the location of the weakening, a posterior domain always establishes at one pole. Importantly, if acto-myosin activity is not weakened locally, as without functional centrosomes or upon AIR-1 depletion, then the corresponding phase diagram exhibits regions of coexisting polar and bipolar states (Fig 4G, 4H; Fig S4B, MovieS7).
Moreover, the fact that one domain forms more readily than two domains in the triangular geometry is captured by the model (Fig.4 I, 4J and Fig. 4A-D). We explored the validity of the physical model further by testing the impact of smaller embryo size, for which the model predicts a shift towards a single PAR-2 domain in air-1(RNAi) embryos (Fig. 4K). Accordingly, we found that smaller ani-2(RNAi) embryos (19) are bipolar in only ~29% of cases, with ~ 43% harboring a single PAR-2 domain, with a bias towards the anterior side (Fig. 4L,4M; Fig. S4C). Perhaps this bias arises from the maternal meiotic spindle being anteriorly localized, since this can promote PAR-2 loading in some circumstances (20). We conclude that our integrated physical model accounts for polarization in C. elegans zygotes in the absence of functional centrosomes, and supports the notion that the system can self-organize polarity in an autonomous manner.
In conclusion, our work reveals the mechanism through which AIR-1 normally orchestrates polarity establishment in C. elegans zygotes, and uncovers self-organizing properties that polarize embryos when centrosomes are missing, which could be of particular importance to establish embryonic axes in parthenogenetic species lacking centrioles. We propose that C. elegans AIR-1 normally acts through a dual-mechanism: prevention of erroneous symmetry breaking events through cortical localization and induction of a single symmetry breaking via centrosomal localization (Fig. 4N). In doing so, AIR-1 funnels the inherent self-organizing properties onto a single site, next to paternally contributed centrioles, thus ensuring spatial coupling between paternal and maternal contributions at the onset of development. It will be interesting to investigate whether such a dual-function extends to the human homologue Aurora A oncogene in polarized tumorigenic settings (21).  Table S1: list of worm strains posterior PAR proteins anterior PAR proteins cortex

Image processing and analysis
Images acquired at the spinning disk were processed by z-projecting the 4 cortical planes using maximum intensity (ImageJ software). Images acquired with the epifluoresence microscope (Zeiss ObserverD.1or Nikon Eclipse Ti-U) were processed as follows using ImageJ software: images underwent background subtraction using a "rolling ball" algorithm of 10 pixels, followed by a maximum intensity z-projection. Grey levels were set identically for all images within each experimental series.
For flow velocity analysis, heat maps were obtained using Particle Image Velocimetry (PIV) with a freely available PIVlab MATLAB algorithm (pivlab.blogspot.de). Using PIVlab, we performed a 4-step multi pass with a final interrogation area of 8 pixels with a step of 4 pixels.
2D velocity fields were obtained by averaging the x-component of velocity along the y-axis for each value in a single frame. All values were averaged over several embryos and represented in a heatmap using MATLAB. Prior to averaging all values across multiple embryos, embryos were aligned temporally using the best fit of the pronuclei growth curves. Pronuclear diameter was measured manually using ImageJ on DIC images.

PAR-2 domain extent and intensity measurements
Images were processed as described above using ImageJ, following straightening of the embryo's outline for each time point using the ImageJ plugin "Straighten"

Mating experiments
SUCH-1 is a component of the anaphase promoting complex/cyclosome (APC/C) and its depletion causes, in addition to the paternal sperm phenotype, a maternally contributed delay in mitosis. Therefore, we used such-1(t1168) males to fertilize wild type females (fem-1(hc17)), thus ensuring that all embryos resulted from such-1(t1168) mutant sperm and that the maternal contribution is normal. To this end, gravid fem-1(hc-17) hermaphrodites expressing RFP::NMY-2; GFP::PAR-2; GFP::SAS-7 were shifted to the restrictive temperature (24°C) and L4 progeny were then mated with such-1(t1668) males at 20°C for 24h. Gravid adults were dissected and embryos were imaged as described above. Prior to and after imaging, each embryo was thoroughly screened for the absence of centrosomes as evaluated by the absence of focal GFP::SAS-7 signal.
Gravid adults were dissected and embryos imaged as described above. Only embryos that were fertilized, as evaluated by the presence of GFP::SAS-7, were imaged.

Immunofluorescence
Embryos were permeabilized by freeze-cracking followed by fixation in methanol at −20°C for

Triangular PDMS chambers
Micro-well structures were produced using standard soft-lithography methods. Using a custom lithography mask, a silicon waver coated with AZ 15nXT (MicroChemicals GmbH, Ulm, Germany) was illuminated with UV light to generate a casting mold of triangles with a side length of 40µm. Micro-well structures were generated by pouring poly(dimethylsiloxane) (PDMS; Sylgard 184, VWR) into these casting molds. Finally, these PDMS structures were cured for 1.5 hours at 75°C. Before each experiment PDMS chambers were treated with oxygen plasma for 90s to reduce its hydrophobicity. Worms were dissected as described above, and embryos were placed into the triangular chamber with an eyelash tool prior to symmetry breaking. Epifluoresence imaging was performed as described above.

Statistical analysis
Statistical significance for all shown quantification was performed using the non parametric two-sided Fisher's exact test, comparing a single category against the other pooled categories (e.g. posterior vs non-posterior) for two conditions (e.g. control versus air-1(RNAi)). The corresponding p-values for all experiments can be found in Table S2. A p-value <0.05 was considered as statistically significant. An experimentally constrained set of parameters for which the above behavior holds has been determined experimentally (18). Here, we will use similar values (see Table in  The velocity , of the cortical actin flow remains to be specified in this novel framework. In most previous work, flows were assumed to be directly linked to the action of centrosomes at the posterior pole and imposed ad hoc, even though the exact nature of this action and its temporal regulation remain unclear (18, 28, 29). In AIR-1 depleted embryos, weak cortical flows emanating from both poles can be observed despite non functional centrosomes, and it remains unknown how these cortical flow are initiated. We complement the above equations with an explicit description of the actin dynamics, which will notably yield an actin flow. Similar to Ref.

Theoretical description of symmetry breaking with and without external cue
(30), we base our description on actin conservation and force balance. Explicitly, we choose Π = −RB S + TB U with R and T > 0 so that the cortex is contractile for moderate densities and that the common positive pressure is recovered for high densities. The experiments suggest that PAR-2 loading affects actin mechanics; in particular, there are no flows in the absence of PAR-2 and AIR-1 (Fig. S2N). We assume that cortex contractility decreases with increasing PAR-2 concentration and account for this by setting R = R E − W". In contrast, we choose the passive coefficient T to be uniform. In our phenomenological description, we do not specify a molecular mechanism through which " reduces contractility, as this is irrelevant for the qualitative behavior of the system. Previous work suggests that posterior PAR proteins decrease the concentration of active myosin through the RHO-1 pathway. However, since we focus here on the essential parts of the physical mechanism underlying symmetry breaking, we chose not to include these molecular details. Likewise, we do not consider the actin network and the myosin distributions separately, even though this distinction might be relevant in other situations.
Similar to equations (1) and (2), the full set of equations (1)-(4) has an !-dominant and a "-dominant stationary state. Due to the dependence of " binding on the curvature, however, they are not completely homogenous. For a sufficiently strong preferential attachment rate I or decrease of contractility W, these states are not stable: " will bind preferentially to the membrane in a curved region, which generates a small gradient of " along the membrane. This protein gradient leads to a gradient of contractility, which in turn generates an actin flow directed away

Smaller embryo
When considering an embryo with the same aspect ratio and a reduced length of 40 µm, one obtains the phase diagram shown in Fig. 4L. While qualitatively similar to the one above, it is clear that the polar phase (green) is larger, with the frontier with the bipolar phase shifted to the right. Hence, some embryos that were mainly in the bipolar phase are now in the coexistence of the polar and bipolar phases, in agreement with the experimental results. This shift is due to two effects. First, the curvature difference between the poles and the equator is higher, so that the enhanced rate of PAR-2 attachment at poles is higher. This effect globally shifts phases to the left. Note that we get a similar effect by increasing the aspect ratio. The other dominant effect is due to the reduced area/volume ratio, which enables less PAR-proteins to attach to the membrane, and consequently diminishes the coupling with acto-myosin contractility. This globally moves phases to the top of the phase diagram.

Triangles
Finally, we apply our description to embryos squeezed in triangular chambers. Contour length is now approximately 120 µm, and the area/volume ratio is 0. 22Z[ \] . We model the curvature function as J(8) = J E 1 − 0.6cos(3=8/c) ) \d with J E = 0. 05Z[ \] . This gives rise to phenotypes with one, two or three domains, depending on the parameters I and W . Due to increased PAR-2 domain extension in this triangular shape the bipolar phenotype appears to be unstable, leading to a shift towards a single PAR-2 domain in this scenario. Kymographs in Fig.4 J,K were obtained with I = 0.9 and W = 20.

C) Parameters
Parameters for the advection-reaction-diffusion system are chosen following Goehring et al.