Pulling forces in Cell Division

Transcription

1 Pulling forces in Cell Division Frank Jülicher Max Planck Institute for the Physics of Complex Systems Dresden, Germany

2 Max Planck Institute for the Physics of Complex Systems A. Zumdieck A. J.-Dalmaroni A. Hilfinger B. Friedrich N. Pavin V. Krstic Max Planck Institute of Molecular Cell Biology and Genetics J. Howard I. Riedel-Kruse J. Pecreaux J.C- Röper S. Diez C. Leduc A. Hyman G. Greenan C. Brangwynne S. Grill I.-M. Tolic Norrelykke S. Vogel N. Maghelli Institut Curie, Paris J.-F. Joanny J. Prost P. Martin M. Bornens M. Thery Amolf, Amsterdam M. Dogterom L. Laan

3 Cell division Organization of microtubules Mitotic spindle (A. Hyman)

4 From single molecules to integrated systems Single molecule behaviors Motor-filament systems collective behaviors movements and forces self-organized waves and patterns minus pushing pulling motor filament plus Spindles and Asters centering oscillations orientation and positioning Role of pulling forces

5 Spindles and Bundles mitotic spindle microtubules yeast microtubules Geometry and dynamics are determined by force balances

6 Microtubule pushing forces microtubule polymerization and buckling maximal force f pN buckling force f + 1 L 2 T.L. Hill (1967), Dogterom and Yurke, Science (1997), Jansen and Dogterom, PRL (2004)

7 Microtubule pushing forces microtubule polymerization and buckling maximal force f pN pushing force f + buckling force f + 1 L 2 T.L. Hill (1967), Dogterom and Yurke, Science (1997), Jansen and Dogterom, PRL (2004)

8 Centering by pushing centering force F net restoring force to the center (centering stiffness) long microtubules: F KX X spindle position weaker pushing (buckling) fewer microtubules T. Holy, M. Dogterom, B. Yurke, S. Leibler, PNAS (1997), J. Howard, Physical Biology 3 (2006) buckling force f + 1 L 2

9 Cortical pulling forces C. elegans embryo cortical pulling forces 10 µm S. Grill et al. Nature 409, 630 (2001), Grill and Hyman, Dev. Cell 8, 461 (2005)

10 Cortical pulling forces C. elegans embryo cortical pulling forces 10 µm force generators: dyneins pulling force f maximal force f 5pN S. Grill et al. Nature 409, 630 (2001), Grill and Hyman, Dev. Cell 8, 461 (2005)

11 Cortical pulling forces minus-end directed motors depolymerase activity cortical pulling forces minus plus force generators: dyneins pulling force f maximal force f 5pN S. Grill et al. Nature 409, 630 (2001), Grill and Hyman, Dev. Cell 8, 461 (2005)

12 Effects of pulling pushing centering force pulling no centering effect

13 Effects of pulling pushing centering force pulling off-centering F pulling can be destabilizing (negative stiffness) F +KX fewer long microtubules X spindle position

14 Aster positioning in vitro microfabricated chamber 2.6µm 10 or 15µm Liedewij Laan, Marileen Dogterom

15 Experimental results No dynein With dynein Rhodamine tubulin % of events % of events centered centered unreliable centering by pushing forces improved centering with pulling forces Liedewij Laan, Marileen Dogterom

16 Centering of asters: role of pulling forces isotropic aster: no net force due to pulling sliding of pushing MT at boundary: centering!

17 Mechanics of asters: theory n + t n t nucleation catastrophies motor binding = ν 2π k catn + k on n + φ (v φn + ) = k on n + k off n wall sliding density of pushing microtubules density of pulling microtubules n + (φ) n (φ) m F = dφ(n + f + n f )m

18 Microtubule distributions fast wall-sliding (low friction) medium wall-sliding slow wall-sliding (high friction) ξ = 10 5 Ns/m ξ = Ns/m ξ = Ns/m

19 Centering of asters Only pushing forces Only pulling forces

20 Experimental results No dynein With dynein Rhodamine tubulin % of events % of events centered centered unreliable centering by pushing forces improved centering with pulling forces Liedewij Laan, Marileen Dogterom

21 Effects of Geometry Circular geometry pushing forces pulling forces fast wall-sliding (low friction) medium wall-sliding slow wall-sliding (high friction) ξ = 10 5 Ns/m ξ = Ns/m ξ = Ns/m

22 Spindle movements Anterior Posterior x Anterior Posterior oscillations position (µm) x x displacement C. Elegans embryo Time (s) S. Grill et al. Nature 409, 630 (2001), Grill and Hyman, Dev. Cell 8, 461 (2005)

23 spindle positioning Spindle movements

24 Spindle movements Asymmetric distribution of pulling forces pulling forces spindle positioning force generators (dynein)

25 Spindle movements Asymmetric distribution of pulling forces spindle positioning oscillations? force generators (dynein)

26 Theory of spindle dynamics F l F r spindle position X λẋ = F l + F r friction left force right force pushing and pulling forces F r = n + r f + + n r f number of pushing MT number of pulling MT

27 Forces on individual MT f pulling f + pushing Force-velocity relationship v = v 0 (1 f/f s ) v v 0 stall force MT pushing v = v g = Ẋ f = f + MT pulling v = v p = Ẋ f = f load force f f s

28 Forces on individual MT f pulling f + pushing On- and off-rates pushing k on k off rate of motor binding (switch from pushing to pulling) rate of motor detachment pulling k off k on Load dependent off-rate k off = k 0 exp{ f/f c } detachment force f c = k B T/a

29 Antagonistic force generators Two groups of motors that act in opposition plus minus Tug of war plus Enhanced collective effects and instabilities

30 Friction generated by motors F ext Force-velocity relation of individual motors: Ẋ F ext ΓẊ Γ 2N f s v 0 Motor induced friction p f s p(1 p) f c Γ F ext p fraction of bound motors Grill et al., Phys. Rev. Lett. 94, (2005) Pecreaux et al. Current Biol. (2006) Riedel, Hilfinger, Howard, Jülicher, HFSP J. (2007)

31 Negative friction F ext Load-dependent off-rate : Ẋ F ext k off F ext ΓẊ Γ 2N f s v 0 Negative friction! p f s p(1 p) f c p fraction of bound motors Γ < 0 < 0 Grill et al., Phys. Rev. Lett. 94, (2005) Pecreaux et al. Current Biol. (2006) Riedel, Hilfinger, Howard, Jülicher, HFSP J. (2007)

32 Instability and bistability Ẋ Equal force on each side Unstable F ext

33 Instability and bistability Ẋ right side wins forward motion F ext

34 Instability and bistability Ẋ left side wins backward motion F ext

35 Spontaneous oscillations Centering stiffness K pushing Fraction of bound motors pulling p = k on k on + k off Nonlinear Oscillator m eff ẍ +(ξ Γ)ẋ + Kx + Bẋ 3 =0 delays due to on- and off-rates m eff 2N f s v 0 k on negative friction fs f c p 2 (1 p) nonlinear effects centering stiffness Pecreaux et al. Current Biol. (2006) Riedel, Hilfinger, Howard, Jülicher, HFSP J. (2007) Jülicher and Prost, PRL (1997)

36 Spindle movements Anterior Posterior x Anterior Posterior oscillations position (µm) x x displacement C. Elegans embryo Time (s)

37 Comparison to experiments d [µm] GPR-1/2 Reduce number of force generators spindle displacement fraction of bound motors A [µm] p on [s -1 ] Stable Oscillatory N motor number oscillation amplitude n=105 N t [hrs] N t [hrs] Pecreaux, et al., Current Biology 16, 2111 (2006)

38 Meiotic nuclear oscillations Yeast cell during meiosis Dynein (Dhc1-3GFP) Tubulin (mcherry-atb2) 2µm SPB: spindle pole body red: microtubules green: motors cell nucleus motors Cell nucleus microtubules pulling Iva Tolic-Norrelykke Nenad Pavin

39 Meiotic nuclear oscillations Oscillations driven by MT pulling Sven Vogel, N. Pavin, Nicola Maghelli, F. Jülicher Iva Tolic-Norrelykke, PLoS Biology 7 (2009)

40 Antagonistic motors F ext Ẋ Bistability F ext

41 Instability and bistability Ẋ left side wins backward motion F ext

42 Instability and bistability Ẋ right side wins forward motion F ext

43 Oscillations of the cell nucleus Stochastic simulation Dynamic redistribution of motors polymerization Cell nucleus depolymerization pulling Mechanically triggered attachment/detachment detachment attachment Iva Tolic-Norrelykke Nenad Pavin

44 Oscillations of the cell nucleus Stochastic simulation Yeast cell during meiosis red: microtubules green: motors 2µm Iva Tolic-Norrelykke Nenad Pavin

45 Comparison to experiments Oscillations involve dynamic redistribution of dynein in the cell Load-dependent off-rate Sven Vogel, N. Pavin, Nicola Maghelli, F. Jülicher, Iva Tolic-Norrelykke, PLoS Biology 7 (2009)

46 Spindle movements spindle displacement pulling forces spindle positioning force generators (dynein) spindle orientation centering oscillations

47 Spindle movements spindle displacement pulling forces spindle rotation spindle positioning force generators (dynein) spindle orientation centering oscillations

48 Spindle movements spindle displacement pulling forces spindle rotation spindle positioning force generators (dynein) spindle orientation centering oscillations

49 Spindle orientation during division Cell division on adhesive micropatterns (M. Thery, M. Bornens)

50 Spindle orientation during division Contraction of the cortical cytoskeleton actin Adhesion sites Retraction fibers actin DNA Cell rounding

51 Spindle orientation during division Cell division on adhesive micropatterns (M. Thery, M. Bornens)

52 Cortical motors and spindle orientation Retraction fibers actin actin Cortical motors DNA Cortical motors activated by signals from retraction fibers

53 Spindle torques φ f Torque on spindle τ(φ) = dψ R f Angular potential W (φ) = φ dφ τ(φ ) τ = dw dφ

54 Orientation dynamics φ Angular fluctuations η dφ dt = dw dφ + ζ(t) < ζ(t)ζ(t ) >= 2Dηδ(t t ) f Distribution of orientation angles noise strength D P (φ) e W (φ) D

55 Distribution of spindle orientations W P (φ) e W (φ) D P (φ) φ W (φ) P (φ) M. Thery, A. Jimenez-Dalmarony, M. Bornens, F. Jülicher, Nature 447, 493 (2007) φ

56 Distribution of spindle orientations W (φ) P (φ) e W (φ) D P (φ) φ W (φ) P (φ) M. Thery, A. Jimenez-Dalmarony, M. Bornens, F. Jülicher, Nature 447, 493 (2007) φ

57 Asymmetric division by spindle rotation W (φ) P (φ) φ W (φ) P (φ) M. Thery, A. Jimenez-Dalmarony, M. Bornens, F. Jülicher, Nature 447, 493 (2007) φ

58 Dynamics of cellular systems axoneme mitotic spindle sensory hair bundle Single molecules collective dynamics under control of signaling pathways and gene expression Spatiotemporal dynamics in cells are organized by active processes and force balances self-organized dynamics of cellular structures

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