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Pulling forces in Cell Division
Frank JülicherMax Planck Institute
for the Physics of Complex SystemsDresden, Germany
Max Planck Institute for thePhysics of Complex Systems
Max Planck Institute of Molecular Cell Biology and Genetics
B. FriedrichN. PavinV. Krstic
J. HowardI. Riedel-KruseJ. PecreauxJ.C- Röper
I.-M. Tolic NorrelykkeS. VogelN. Maghelli
S. Grill
S. DiezC. Leduc
A. HymanG. GreenanC. Brangwynne
J.-F. JoannyJ. ProstP. Martin
A. ZumdieckA. J.-DalmaroniA. Hilfinger
Institut Curie, Paris Amolf, AmsterdamM. DogteromL. Laan
M. BornensM. Thery
From single molecules tointegrated systems
Motor-filament systems
Single molecule behaviors
Spindles and Asters
filament
motor
collective behaviors
self-organized waves and patterns
minus plus
movements and forces
centeringoscillationsorientation and positioning
pulling
pushing
Role of pulling forces
Spindles and Bundlesmitotic spindle
yeast microtubules
Geometry and dynamics are determined by force balances
microtubules
microtubule polymerization and buckling
f+ ∼ 1L2
buckling force
maximal force f+ � 5− 10pN
T.L. Hill (1967), Dogterom and Yurke, Science (1997), Jansen and Dogterom, PRL (2004)
Microtubule pushing forces
f+ ∼ 1L2
buckling force
maximal force f+ � 5− 10pNmicrotubule polymerization and buckling
Microtubule pushing forces
pushing force f+
T.L. Hill (1967), Dogterom and Yurke, Science (1997), Jansen and Dogterom, PRL (2004)
Centering by pushing
f+ ∼ 1L2
buckling force
long microtubules:
weaker pushing (buckling)
fewer microtubules
net restoring force to the center (centering stiffness)
centering force
F
F � −KX
X spindle position
T. Holy, M. Dogterom, B. Yurke, S. Leibler, PNAS (1997), J. Howard, Physical Biology 3 (2006)
Cortical pulling forces
10 µm
S. Grill et al. Nature 409, 630 (2001), Grill and Hyman, Dev. Cell 8, 461 (2005)
C. elegans embryo cortical pulling forces
Cortical pulling forces
10 µm
C. elegans embryo cortical pulling forces
pulling force f−
force generators: dyneins
f− � 5pNmaximal force
S. Grill et al. Nature 409, 630 (2001), Grill and Hyman, Dev. Cell 8, 461 (2005)
Cortical pulling forces
minus-end directed motorsdepolymerase activity
cortical pulling forces
pulling force f−
force generators: dyneins
f− � 5pNmaximal force
minus plus
S. Grill et al. Nature 409, 630 (2001), Grill and Hyman, Dev. Cell 8, 461 (2005)
Effects of pullingpushing
pulling
pulling can be destabilizing (negative stiffness)
fewer long microtubules
centering force
off-centering
F
F � +KX
X spindle position
Experimental results
Rhodamine tubulin
unreliable centering by pushing forces improved centering with pulling forces
% o
f eve
nts
centered centered%
of e
vent
s
No dynein
With dynein
Liedewij Laan, Marileen Dogterom
Centering of asters:role of pulling forces
isotropic aster: no net force due to pulling sliding of pushing MT at boundary: centering!
Mechanics of asters: theory
density of pushing microtubules
nucleation
catastrophieswall sliding
motor binding
n+(φ)density of pulling microtubules n−(φ)
F = −�
dφ(n+f+ − n−f−)m
m
∂n−
∂t= konn+ − koffn−
∂n+
∂t=
ν
2π− kcatn
+ − konn+ − ∂
∂φ(vφn+)
Microtubule distributions
fast wall-sliding (low friction)medium wall-slidingslow wall-sliding (high friction)
ξ = 10−5 Ns/mξ = 5 · 10−5 Ns/mξ = 2.5 · 10−4 Ns/m
Experimental results
Rhodamine tubulin
unreliable centering by pushing forces improved centering with pulling forces
% o
f eve
nts
centered centered%
of e
vent
s
No dynein
With dynein
Liedewij Laan, Marileen Dogterom
Effects of Geometry
Circular geometrypushing forces
pulling forces
fast wall-sliding (low friction)medium wall-slidingslow wall-sliding (high friction)
ξ = 10−5 Ns/m
ξ = 5 · 10−5 Ns/m
ξ = 2.5 · 10−4 Ns/m
Spindle movements
PosteriorAnterior
displacement
xx
position (µm)
Time (s)C. Elegans embryo
Anterior Posterior
xoscillations
S. Grill et al. Nature 409, 630 (2001), Grill and Hyman, Dev. Cell 8, 461 (2005)
spindle positioning
Spindle movements
pullingforces
force generators (dynein)
Asymmetric distribution of pulling forces
spindle positioning
Spindle movements
oscillations ? force generators (dynein)
Asymmetric distribution of pulling forces
Theory of spindle dynamics
spindle position X
left forcefriction
pushing and pulling forces Fr = −n+r f+ + n−r f−
right force
λX = Fl + Fr
Fl Fr
number of pushing MT
number of pulling MT
Forces on individual MT
Force-velocity relationshipv
stall force
load force
pulling
pushingf+
f−
v = vg = −X v = vp = X
f = f+ f = f−
MT pushing MT pulling
v = v0(1− f/fs)
f
v0
fs
Forces on individual MT
pulling
pushingf+
f−
Load dependent off-rate
On- and off-rates
kon rate of motor binding (switch from pushing to pulling) koff
rate of motor detachment
detachment force fc = kBT/a
koff = k0 exp{−f/fc}
kon
koff
pushing
pulling
Antagonistic force generatorsTwo groups of motors that act in opposition
Enhanced collective effects and instabilities
“Tug of war”
plusminusplus
Friction generated by motors
−Fext
Motor induced friction
Γ � 2Nfs
v0
�p− fs
fcp(1− p)
�
Fext
Pecreaux et al. Current Biol. (2006)Riedel, Hilfinger, Howard, Jülicher, HFSP J. (2007)
Grill et al. , Phys. Rev. Lett. 94, 108104 (2005)
Fext � ΓX
ΓX
Force-velocity relation of individual motors:
p fraction of bound motors
Negative friction
−Fext
Fext
< 0
< 0X
Pecreaux et al. Current Biol. (2006)Riedel, Hilfinger, Howard, Jülicher, HFSP J. (2007)
Grill et al. , Phys. Rev. Lett. 94, 108104 (2005)
Negative friction !Load-dependent off-rate :
Γ � 2Nfs
v0
�p− fs
fcp(1− p)
�Fext � ΓX
Γkoff
p fraction of bound motors
Spontaneous oscillationsKCentering stiffness
Nonlinear Oscillator
Pecreaux et al. Current Biol. (2006) Riedel, Hilfinger, Howard, Jülicher, HFSP J. (2007)
meff � 2Nfs
v0kon
�fs
fcp2(1− p)
�
meff x + (ξ − Γ)x + Kx + Bx3 = 0negative frictiondelays due to
on- and off-ratesnonlinear effects
Jülicher and Prost, PRL (1997)
centering stiffness
pulling
pushing
p =kon
kon + koff
Fraction of bound motors
Spindle movements
PosteriorAnterior
displacement
xx
position (µm)
Time (s)C. Elegans embryo
Anterior Posterior
xoscillations
0 10 20 30 40 500
0.1
0.2
0.3
0.4
0.5
N
Stable
Oscillatory
on [s
-1]
Comparison to experiments
spindle displacement
Reduce number of force generators
GPR-1/2
N N
0 10 20 30 400
1
2
3
4
5
6
0 10 20 30 400
1
2
3
4n=105
t [hrs]
d [µ
m]
A [µ
m]
t [hrs]
Pecreaux, et al., Current Biology 16, 2111 (2006)
p
oscillation amplitude
fraction of bound motors
motor number
Nenad Pavin
red: microtubulesgreen: motors
2µm
pullingCell nucleus
Meiotic nuclear oscillations
Iva Tolic-Norrelykke
Yeast cell during meiosis
cell nucleus microtubules
motors
Nenad PavinIva Tolic-Norrelykke
SPB: spindle pole body
Dynein (Dhc1-3GFP)Tubulin (mCherry-Atb2)
Meiotic nuclear oscillations
Sven Vogel, N. Pavin, Nicola Maghelli, F. Jülicher Iva Tolic-Norrelykke, PLoS Biology 7 (2009)
Oscillations drivenby MT pulling
attachment
depolymerization
detachment
pullingCell nucleus
Mechanically triggered attachment/detachment
Dynamic redistribution of motors
polymerization
Oscillations of the cell nucleus Stochastic simulation
Nenad PavinIva Tolic-Norrelykke
Oscillations of the cell nucleus Stochastic simulation
Nenad PavinIva Tolic-Norrelykke
red: microtubulesgreen: motors
2µm
Yeast cell during meiosis
Oscillations involve dynamic redistribution of dynein in the cell
Comparison to experiments
Sven Vogel, N. Pavin, Nicola Maghelli, F. Jülicher, Iva Tolic-Norrelykke, PLoS Biology 7 (2009) Load-dependent off-rate
Spindle movements
spindle positioning spindle orientation
pullingforces
force generators (dynein)
spindle displacement
centering oscillations
spindle rotation
Spindle movements
spindle positioning spindle orientation
pullingforces
force generators (dynein)
spindle displacement
centering oscillations
Spindle movements
spindle positioning spindle orientation
pullingforces
force generators (dynein)
spindle rotationspindle displacement
centering oscillations
actin
actin
DNARetraction fibers
Adhesionsites
Contraction of the cortical cytoskeleton
Spindle orientationduring division
Cell rounding
Cortical motors andspindle orientation
actin
actin
DNA
Retraction fibers
Cortical motors
Cortical motors activated bysignals from retraction fibers
Spindle torques
W (!) = !
! !
d!!"(!!)
Torque on spindle
!(") =
!
!
!
!
"
d# $R ! $f
!
!
!
!
Angular potential
!
!f
τ = −dW
dφ
Orientation dynamics
!
!f
P (!) ! e!W (!)
DDistribution of orientation angles
noise strength D
ηdφ
dt= −dW
dφ+ ζ(t) < ζ(t)ζ(t�) >= 2Dηδ(t− t�)
Angular fluctuations
Distribution of spindle orientations
M. Thery, A. Jimenez-Dalmarony, M. Bornens, F. Jülicher, Nature 447, 493 (2007)
P (!) ! e!W (!)
DW (φ)
!
P (φ)
!
P (φ)
W (φ)
M. Thery, A. Jimenez-Dalmarony, M. Bornens, F. Jülicher, Nature 447, 493 (2007)
P (!) ! e!W (!)
D
!
W (φ)
W (φ)
!
P (φ)
P (φ)
Distribution of spindle orientations
Asymmetric divisionby spindle rotation
M. Thery, A. Jimenez-Dalmarony, M. Bornens, F. Jülicher, Nature 447, 493 (2007)
φ
φ
W (φ)
W (φ)
P (φ)
P (φ)
collective dynamics under control of signaling pathways and gene expression
Spatiotemporal dynamics in cells are organized by active processes and force balances
Singlemolecules
self-organized dynamics of cellular structures
Dynamics of cellular systems
sensory hair bundle
axoneme mitotic spindle