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Assembly and positioning of actomyosin rings by contractility and planar cell polarity.

Sehring IM, Recho P, Denker E, Kourakis M, Mathiesen B, Hannezo E, Dong B, Jiang D - Elife (2015)

Bottom Line: Intriguingly, rings always form at the cells' anterior edge before migrating towards the center as contractility increases, reflecting a novel dynamical property of the cortex.We develop a simple model of the physical forces underlying this tug-of-war, which quantitatively reproduces our results.We thus propose a quantitative framework for dissecting the relative contribution of contractility and PCP to the self-assembly and repositioning of cytoskeletal structures, which should be applicable to other morphogenetic events.

View Article: PubMed Central - PubMed

Affiliation: Sars International Centre for Marine Molecular Biology, University of Bergen, Bergen, Norway.

ABSTRACT
The actomyosin cytoskeleton is a primary force-generating mechanism in morphogenesis, thus a robust spatial control of cytoskeletal positioning is essential. In this report, we demonstrate that actomyosin contractility and planar cell polarity (PCP) interact in post-mitotic Ciona notochord cells to self-assemble and reposition actomyosin rings, which play an essential role for cell elongation. Intriguingly, rings always form at the cells' anterior edge before migrating towards the center as contractility increases, reflecting a novel dynamical property of the cortex. Our drug and genetic manipulations uncover a tug-of-war between contractility, which localizes cortical flows toward the equator and PCP, which tries to reposition them. We develop a simple model of the physical forces underlying this tug-of-war, which quantitatively reproduces our results. We thus propose a quantitative framework for dissecting the relative contribution of contractility and PCP to the self-assembly and repositioning of cytoskeletal structures, which should be applicable to other morphogenetic events.

No MeSH data available.


Related in: MedlinePlus

PCP participates in force balance to reposition actin rings.(A) Left: effect of a slow, 1.5-fold linear increase in contractility, for polarity-deficient mutants (no preferential flux on the edges). The ring forms directly at the center. Right: ring positioning for random uncoordinated polarity (preferential flux on the anterior, full red line, preferential flux on the posterior, dashed red line, and equal flux on anterior and posterior, full blue line). (B, C) Localization of Flag-Dsh (B), and Myc-Pk (C) in notochord cells. At early stages (19 and 20.8 hpf), Flag-Dsh localizes at the basal surface. At 20.8 hpf, it concentrates at the equator (white arrow). Subsequently, it shifts to both lateral surfaces, with a preference for anterior side of cells (yellow and blue arrows in B). Myc-Pk localizes at the anterior lateral surface of the cell at early stages and gradually concentrates to the center of anterior lateral surface (white arrow in C). (D) Myosin contractility antagonizes PCP to position a dynamic actin cytoskeleton. Anterior to the left. Scale bars, 10 μm.DOI:http://dx.doi.org/10.7554/eLife.09206.016
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fig7: PCP participates in force balance to reposition actin rings.(A) Left: effect of a slow, 1.5-fold linear increase in contractility, for polarity-deficient mutants (no preferential flux on the edges). The ring forms directly at the center. Right: ring positioning for random uncoordinated polarity (preferential flux on the anterior, full red line, preferential flux on the posterior, dashed red line, and equal flux on anterior and posterior, full blue line). (B, C) Localization of Flag-Dsh (B), and Myc-Pk (C) in notochord cells. At early stages (19 and 20.8 hpf), Flag-Dsh localizes at the basal surface. At 20.8 hpf, it concentrates at the equator (white arrow). Subsequently, it shifts to both lateral surfaces, with a preference for anterior side of cells (yellow and blue arrows in B). Myc-Pk localizes at the anterior lateral surface of the cell at early stages and gradually concentrates to the center of anterior lateral surface (white arrow in C). (D) Myosin contractility antagonizes PCP to position a dynamic actin cytoskeleton. Anterior to the left. Scale bars, 10 μm.DOI:http://dx.doi.org/10.7554/eLife.09206.016

Mentions: For the problem to be fully specified, we still need to impose the values of the boundary fluxes of actin . To begin, in order to expose the role of contractility only, we first assumed that they vanish. It should be noted that the actomyosin flux J encompasses both actin filament velocity, and an effective diffusive flux arising from actin polymerization (see Appendix 1: the model). Therefore, a vanishing total flux does not necessarily entail a vanishing velocity. Then, a linear stability analysis of Equations (1–3) predicts a threshold of actomyosin contractility above which, the homogeneous cortex loses stability and a mechanically stable central ring forms even in the absence of external signaling cues (see Appendix 3: steady states, and Figure 1 in Appendix 1: the model for the stability diagram and details on the boundary conditions). We can then interpret that the driving force positioning the ring at the equator is the contractility increase during the process of ring migration. Before finalizing the model, we check two of its key assumptions that (1) contractility increases smoothly as ring migration proceeds, and (2) the velocity gradient of actin filaments towards the center should depend linearly on the local contractility, indicated by local actomyosin concentration (as seen in Equation 3). To address the first assumption, we measure the angle between the lateral and basal side, from embryos at various stages (n > 20 angles for each embryo) (Figure 5B). As shown recently (Maître et al., 2012), this angle reflects a force balance between the tensions of the basal () and lateral () surfaces, and therefore can be used as a proxy for tension changes. Interestingly, the angle decreased smoothly and continuously during elongation and ring migration, indicative of an increased basal tension relative to lateral tension (Figure 5B), by roughly a factor of 2.5 during the elongation process, and 1.5 during the ring migration process. We assume at first order approximation that lateral tension is constant and set in the model that () increases by a factor 1.5. As we shall show later, such an increase enables a good fit to all of the available data (see Appendix 4: rough estimates of model parameters, and Appendix 5: model predictions for further details). To test the second assumption, we performed PIV analysis on high frequency movies of actin flows (Figure 5C), to measure local velocity gradients. When plotting these as a function of local actin concentration, we found a robust negative linear correlation (Figure 5D), which shows that flows are driven by differences in actomyosin concentration, validating quantitatively Equation 3 of our model. From the slope of the correlation, as well as from the characteristic of actin bundles measured above in the kymographs, we could extract the ratio (χ/η) of contractility and viscosity. Finally, we fixed the last parameters of our model through FRAP experiments (τ = 90 s) and through the width of the ring intensity profile (D = 2.10−12 m2/s) (see Appendix 4: rough estimates of model parameters for the details of parameter fitting). Under these assumptions and with these parameters, a central ring spontaneously forms at the center of the cell when contractility increases above the critical threshold , and contractility is self-sufficient to maintain the ring structure through actomyosin flows. However, the experimental data show the existence of a stage where the ring is positioned at the anterior side and also underlines the importance of PCP in the repositioning of actin rings. Our final model therefore incorporates polarity in the model in the simplest way possible: by assuming that it creates a small preferential polymerization of actin at the anterior side, that is, there is a non-zero flux at the anterior side, different from the flux at the posterior side. We considered that the flux on the posterior side was still zero, that is, and . We showed in Figure 7 in Appendix 5: model prediction that lifting this constraint does not qualitatively change our results, as the key parameter is the difference between anterior and posterior flux, but not their respective magnitude and our system is locally robust with respect to this type of perturbation. Assuming the existence of a preferential polymerization at one boundary due to PCP was supported by the well-studied link between PCP and actin polymerization (Wallingford and Habas, 2005). In particular, Disheveled (Dsh), one of the core member of the PCP pathway has been shown to activate key actin regulators such as Rho and Rac (Tahinci and Symes, 2003; Wallingford and Habas, 2005), as well as Daam1, a member of the formin protein family (Kida et al., 2007; Gao and Chen, 2010). It should be noted that as we are treating the actomyosin gel as a single species (with the assumption that bipolar filaments performing the contractile power stroke co-localize with actin), assuming that PCP localizes myosin anteriorly, as reported in Newman-Smith et al., 2015, would yield the same qualitative results. With these final boundary conditions, the dynamical system Equations (1–3) predicts a transition (which is now smooth, see Figure 1 in Appendix 1: the model) between two mechanically stable states of the actin ring: a central position if the contractility χ is large enough, and an anterior position when χ is small enough and the polarity-induced actin flux F dominates. We set the value of F using the filament velocity order of magnitude as well as the experimental actin density profiles when the contractility is impaired (blebbistatin experiments, see Appendix 5: model predictions).


Assembly and positioning of actomyosin rings by contractility and planar cell polarity.

Sehring IM, Recho P, Denker E, Kourakis M, Mathiesen B, Hannezo E, Dong B, Jiang D - Elife (2015)

PCP participates in force balance to reposition actin rings.(A) Left: effect of a slow, 1.5-fold linear increase in contractility, for polarity-deficient mutants (no preferential flux on the edges). The ring forms directly at the center. Right: ring positioning for random uncoordinated polarity (preferential flux on the anterior, full red line, preferential flux on the posterior, dashed red line, and equal flux on anterior and posterior, full blue line). (B, C) Localization of Flag-Dsh (B), and Myc-Pk (C) in notochord cells. At early stages (19 and 20.8 hpf), Flag-Dsh localizes at the basal surface. At 20.8 hpf, it concentrates at the equator (white arrow). Subsequently, it shifts to both lateral surfaces, with a preference for anterior side of cells (yellow and blue arrows in B). Myc-Pk localizes at the anterior lateral surface of the cell at early stages and gradually concentrates to the center of anterior lateral surface (white arrow in C). (D) Myosin contractility antagonizes PCP to position a dynamic actin cytoskeleton. Anterior to the left. Scale bars, 10 μm.DOI:http://dx.doi.org/10.7554/eLife.09206.016
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fig7: PCP participates in force balance to reposition actin rings.(A) Left: effect of a slow, 1.5-fold linear increase in contractility, for polarity-deficient mutants (no preferential flux on the edges). The ring forms directly at the center. Right: ring positioning for random uncoordinated polarity (preferential flux on the anterior, full red line, preferential flux on the posterior, dashed red line, and equal flux on anterior and posterior, full blue line). (B, C) Localization of Flag-Dsh (B), and Myc-Pk (C) in notochord cells. At early stages (19 and 20.8 hpf), Flag-Dsh localizes at the basal surface. At 20.8 hpf, it concentrates at the equator (white arrow). Subsequently, it shifts to both lateral surfaces, with a preference for anterior side of cells (yellow and blue arrows in B). Myc-Pk localizes at the anterior lateral surface of the cell at early stages and gradually concentrates to the center of anterior lateral surface (white arrow in C). (D) Myosin contractility antagonizes PCP to position a dynamic actin cytoskeleton. Anterior to the left. Scale bars, 10 μm.DOI:http://dx.doi.org/10.7554/eLife.09206.016
Mentions: For the problem to be fully specified, we still need to impose the values of the boundary fluxes of actin . To begin, in order to expose the role of contractility only, we first assumed that they vanish. It should be noted that the actomyosin flux J encompasses both actin filament velocity, and an effective diffusive flux arising from actin polymerization (see Appendix 1: the model). Therefore, a vanishing total flux does not necessarily entail a vanishing velocity. Then, a linear stability analysis of Equations (1–3) predicts a threshold of actomyosin contractility above which, the homogeneous cortex loses stability and a mechanically stable central ring forms even in the absence of external signaling cues (see Appendix 3: steady states, and Figure 1 in Appendix 1: the model for the stability diagram and details on the boundary conditions). We can then interpret that the driving force positioning the ring at the equator is the contractility increase during the process of ring migration. Before finalizing the model, we check two of its key assumptions that (1) contractility increases smoothly as ring migration proceeds, and (2) the velocity gradient of actin filaments towards the center should depend linearly on the local contractility, indicated by local actomyosin concentration (as seen in Equation 3). To address the first assumption, we measure the angle between the lateral and basal side, from embryos at various stages (n > 20 angles for each embryo) (Figure 5B). As shown recently (Maître et al., 2012), this angle reflects a force balance between the tensions of the basal () and lateral () surfaces, and therefore can be used as a proxy for tension changes. Interestingly, the angle decreased smoothly and continuously during elongation and ring migration, indicative of an increased basal tension relative to lateral tension (Figure 5B), by roughly a factor of 2.5 during the elongation process, and 1.5 during the ring migration process. We assume at first order approximation that lateral tension is constant and set in the model that () increases by a factor 1.5. As we shall show later, such an increase enables a good fit to all of the available data (see Appendix 4: rough estimates of model parameters, and Appendix 5: model predictions for further details). To test the second assumption, we performed PIV analysis on high frequency movies of actin flows (Figure 5C), to measure local velocity gradients. When plotting these as a function of local actin concentration, we found a robust negative linear correlation (Figure 5D), which shows that flows are driven by differences in actomyosin concentration, validating quantitatively Equation 3 of our model. From the slope of the correlation, as well as from the characteristic of actin bundles measured above in the kymographs, we could extract the ratio (χ/η) of contractility and viscosity. Finally, we fixed the last parameters of our model through FRAP experiments (τ = 90 s) and through the width of the ring intensity profile (D = 2.10−12 m2/s) (see Appendix 4: rough estimates of model parameters for the details of parameter fitting). Under these assumptions and with these parameters, a central ring spontaneously forms at the center of the cell when contractility increases above the critical threshold , and contractility is self-sufficient to maintain the ring structure through actomyosin flows. However, the experimental data show the existence of a stage where the ring is positioned at the anterior side and also underlines the importance of PCP in the repositioning of actin rings. Our final model therefore incorporates polarity in the model in the simplest way possible: by assuming that it creates a small preferential polymerization of actin at the anterior side, that is, there is a non-zero flux at the anterior side, different from the flux at the posterior side. We considered that the flux on the posterior side was still zero, that is, and . We showed in Figure 7 in Appendix 5: model prediction that lifting this constraint does not qualitatively change our results, as the key parameter is the difference between anterior and posterior flux, but not their respective magnitude and our system is locally robust with respect to this type of perturbation. Assuming the existence of a preferential polymerization at one boundary due to PCP was supported by the well-studied link between PCP and actin polymerization (Wallingford and Habas, 2005). In particular, Disheveled (Dsh), one of the core member of the PCP pathway has been shown to activate key actin regulators such as Rho and Rac (Tahinci and Symes, 2003; Wallingford and Habas, 2005), as well as Daam1, a member of the formin protein family (Kida et al., 2007; Gao and Chen, 2010). It should be noted that as we are treating the actomyosin gel as a single species (with the assumption that bipolar filaments performing the contractile power stroke co-localize with actin), assuming that PCP localizes myosin anteriorly, as reported in Newman-Smith et al., 2015, would yield the same qualitative results. With these final boundary conditions, the dynamical system Equations (1–3) predicts a transition (which is now smooth, see Figure 1 in Appendix 1: the model) between two mechanically stable states of the actin ring: a central position if the contractility χ is large enough, and an anterior position when χ is small enough and the polarity-induced actin flux F dominates. We set the value of F using the filament velocity order of magnitude as well as the experimental actin density profiles when the contractility is impaired (blebbistatin experiments, see Appendix 5: model predictions).

Bottom Line: Intriguingly, rings always form at the cells' anterior edge before migrating towards the center as contractility increases, reflecting a novel dynamical property of the cortex.We develop a simple model of the physical forces underlying this tug-of-war, which quantitatively reproduces our results.We thus propose a quantitative framework for dissecting the relative contribution of contractility and PCP to the self-assembly and repositioning of cytoskeletal structures, which should be applicable to other morphogenetic events.

View Article: PubMed Central - PubMed

Affiliation: Sars International Centre for Marine Molecular Biology, University of Bergen, Bergen, Norway.

ABSTRACT
The actomyosin cytoskeleton is a primary force-generating mechanism in morphogenesis, thus a robust spatial control of cytoskeletal positioning is essential. In this report, we demonstrate that actomyosin contractility and planar cell polarity (PCP) interact in post-mitotic Ciona notochord cells to self-assemble and reposition actomyosin rings, which play an essential role for cell elongation. Intriguingly, rings always form at the cells' anterior edge before migrating towards the center as contractility increases, reflecting a novel dynamical property of the cortex. Our drug and genetic manipulations uncover a tug-of-war between contractility, which localizes cortical flows toward the equator and PCP, which tries to reposition them. We develop a simple model of the physical forces underlying this tug-of-war, which quantitatively reproduces our results. We thus propose a quantitative framework for dissecting the relative contribution of contractility and PCP to the self-assembly and repositioning of cytoskeletal structures, which should be applicable to other morphogenetic events.

No MeSH data available.


Related in: MedlinePlus