Pulling forces in Cell Division - IITKhome.iitk.ac.in/~debch/IITKGJ/Julicher2.pdf · Pulling forces in Cell Division Frank Jülicher Max Planck Institute for the Physics of Complex

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

Cell divisionOrganization of microtubules

Mitotic spindle

(A. Hyman)

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


10 µm

C. elegans embryo cortical pulling forces

pulling force f−

force generators: dyneins

f− � 5pNmaximal force



minus-end directed motorsdepolymerase activity

cortical pulling forces

pulling force f−

force generators: dyneins

f− � 5pNmaximal force

minus plus


Effects of pullingpushing

pulling

no centering effect

centering force

Effects of pullingpushing

pulling

pulling can be destabilizing (negative stiffness)

fewer long microtubules

centering force

off-centering

F

F � +KX

X spindle position

Aster positioning in vitromicrofabricated chamber

2.6µm

15µm10 orLiedewij Laan, Marileen Dogterom

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

Only pushing forces Only pulling forces

Centering of asters

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


spindle positioning

Spindle movements

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

Unstable

Equal force on each side

Instability and bistability

−Fext

X

forward motion

right side wins

−Fext


X

backward motion

left side wins

−Fext


X

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

Bistability

Antagonistic motors

−Fext

X

Fext

backward motion

left side wins

−Fext


X

forward motion

right side wins

−Fext


X

attachment

depolymerization

detachment

pullingCell nucleus

Mechanically triggered attachment/detachment

Dynamic redistribution of motors

polymerization

Oscillations of the cell nucleus Stochastic simulation


Oscillations of the cell nucleus Stochastic simulation


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



centering oscillations

spindle rotation

Spindle movements


pullingforces




Spindle movements


pullingforces


spindle rotationspindle displacement


Spindle orientationduring division

(M. Thery, M. Bornens)

Cell division on adhesive micropatterns

actin

actin

DNARetraction fibers

Adhesionsites

Contraction of the cortical cytoskeleton


Cell rounding

(M. Thery, M. Bornens)


Cell division on adhesive micropatterns

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)


P (!) ! e!W (!)

D

!

W (φ)

W (φ)

!

P (φ)

P (φ)

Distribution of spindle orientations

Asymmetric divisionby spindle rotation


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

Documents

Pulling forces in Cell Division - IITKhome.iitk.ac.in/~debch/IITKGJ/Julicher2.pdf · Pulling forces in Cell Division Frank Jülicher Max Planck Institute for the Physics of Complex