symmetry breaking of biological cells · cliff brangwynne surface active processes drive a cellular...
TRANSCRIPT
Frank Jülicher
Max Planck Institutefor the Physics of Complex Systems
Dresden
Symmetry breaking ofbiological cells
Max Planck Institute for the Physics of Complex Systems
Max Planck Institute of Molecular Cell Biology and Genetics
Justin BoisSaroj Nandi
Stephan GrillSundar NaganathanMasatoshi NishikawaPeter Gross
Maria StrempelSebastian FürthauerVijay K. Krishnamurthy
Anthony HymanNate Goehring
TU Dresden - Biotec
Miriam MayerStefan MünsterAnagha Datar
From a single cell to an organism
fertilized egg organism
anterior posterior
dorsal
ventral
right
left
Cell polarity and chiralityCell asymmetries guide morphogenesis of tissues and organs
Cell chirality
Cell polarity
asymmetric distribution of molecules
asymmetric flows
fertilized egg
adult roundworm Caenorhabditis elegans
Anterior Posterior
Asymmetric cell division
Anthony Hyman, Stephan Grill
Polarized hydrodynamic flows
Par2Par6
10µm PAR-6/PAR-2
Cliff BrangwynneSurface active processes drive a cellular flow pattern
Anterior Posterior
Par2Par6
flows contribute tocell polarization
Cell polarity and flows
Flow generationChemical signaling
contraction
A P
PAR-6 / PAR-2
Par6 Par2
Mechano-chemical patterning
P
Par6 Par2
force generation
chemicalsignals
flows
activation
active processes andpattern formationtightly integrated
contraction
A P
contraction
The cell cortex
Cell membrane
Cell cortex(active gel)
Cell cytoplasm
(Gary Borisy)
A thin active material generates flows
Active gels
molecules
motor complex
active gelactive bundle
Cytoskeletal networks
Active stresses
Spontaneous flows
Dynamic patterns
ATP
ADP+P�µ = µATP � µADP � µP
motor
plusminus
force dipole
actin network (A. Ott)
Force dipoles
f �f
shear rateshear stress active stress (axial)
constitutive relation of active gel
Kruse, Joanny, Jülicher, Prost, Sekimoto (2004,2005,2007)Hatwalne, Ramaswamy, Rao, Simha (2004)
�⇣�µ(p↵p� � 1
3p�p��↵�)�tot
↵� = 2⌘v↵�
active stress: density of force dipoles
Active gels
shear rateshear stress active stress (axial)
constitutive relation of active gel
p�
local polar or nematic orderdeformation rate
force balance
@�(�↵� � P �↵�) = 0tot
�⇣�µ(p↵p� � 1
3p�p��↵�)
v↵� =1
2(@↵v� + @�v↵)
�tot
↵� = 2⌘v↵�
�↵�
Kruse, Joanny, Jülicher, Prost, Sekimoto (2004,2005,2007)Hatwalne, Ramaswamy, Rao, Simha (2004)
cortical tension
T =
Zd
0dz�
xx
active tension
hydrodynamic equation
characteristic length ⇤ = (⇥/�)1/2 = (d⇥/�)1/2
Tact =
Zd
0dz�act
xx
@x
Tact = �⌘@2x
vx
+ �vx
layer of active gel below cell membrane
d
x
z
polaritypolarity
vx
x
Thin active film
tot
Par6 Par2
P
contraction
A P
contraction
Tact Tact
Step change of active tension
Mayer et al., Nature 467 (2010)
Hydrodynamic length scale
vzTact Tact
x
@x
Tact = �⌘@2x
vx
+ �vx
vx
= v0e�|x|/`
⇤ = (⇥/�)1/2 = (d⇥/�)1/2Tact
�vx
vz
= �d(@x
vx
+ @y
vy
) Mayer et al., Nature 467 (2010)
Cell polarity and active flows
Par2Par6
diffusion interactionsadvection
@t
c6
= D6
@2
x
c6
� @x
(v c6
) + kon,6
c6,cyto
� ko↵,6
c6
� kc,6
c↵22
c6
@t
c2
= D2
@2
x
c2
� @x
(v c2
) + kon,2
c2,cyto
� ko↵,2
c2
� kc,2
c2
c↵66
⇤x
Tact
= �⇥⇤2x
v + �v
active hydrodynamics
active stress regulation
Tact = T0f(c6)c2c6
Nate Goering, Justin Bois, Peter Gross, Vijay Krishnamurthy
on and off rates
Par6 Par2
Pe =u⇥
D=
T0
�DPeclet number
PAR-2
PAR-6
flow velocitymembrane concentration
Anterior AnteriorPosterior Posterior
A mechano-chemical switch
Peter Gross, Vijay Krishnamurty, Justin Bois
symmetric polar
Quantitative description
Vijay Krishnamurthy, Peter Gross
Par6 Par2
Observed and calculated spatiotemporal molecular distributions along the cortex
Par6
[µm
�2]
Par2
[µm
�2]
Myosin
[µm
�2]
Flow
[µm/m
in]
Distance from pole [µm]
theoryexperiment
A P
v
x
(x) vy(x)vx
vy
Chiral flow patterns
high contractilestress
vx
vy
chiral flows
fluorescent myosin motors
Enhanced chiral flows
Tact
v
Tactchiral flowsincreased ina csnk-1 mutant
n
vkv? v?
Sundar Naganathan
Active chiral processes
force dipole
torque dipole
f �f
�⌧⌧Fürthauer, Strempel, Grill, Jülicher, EPJE (2012)
Angular momentumconservation
Momentum conservation
Angular momentum conservation
�tot
↵� = �↵� + �act
↵�
@��tot
↵� = 0
M tot
↵�� = M↵�� +Mact
↵��
@�Mtot
↵�� = 2�tot,a↵�
force dipole density
torque dipole density
active antisymmetricstress
momentumflux
flux of intrinsic angular momentum
Fürthauer, Strempel, Grill, Jülicher, EPJE (2012)
active filament meshworkbelow cell membrane cortical tension
active tension and torque
Hydrodynamic equations
@x
Tact = �⌘@2x
vx
+ �vx
vx
chiral coupling
d
x
z
polaritypolarityx
vy
Fürthauer, Strempel, Grill, Jülicher, Phys. Rev. Lett. (2013)
✏ =⌧actTact
T actij = Tact�ij + ⌧act✏ij
Tij =
Z d
0dz�ij
Naganathan, Fürthauer, Nishikawa, Jülicher, Grill, eLife (2014)
✏@x
Tact = � ⌘
2@2x
vy
+ �vy
Thin chiral active gel
Myo
sin:
:GFP
inte
nsity
(a.
u.)
Anterior Posteriorx
Tact(x) ⇠ c(x)
v(x)flow velocity
myosin motor distribution
Tact(x) ⇠ c(x)
myosin motor distribution
flow velocity
11µm` = (⌘/�)1/2' ✏ ' 0.5
vy
vx
Naganathan, Fürthauer, Nishikawa, Jülicher, Grill, eLife (2014)
Active stress and chiral flowsve
loci
ty (μm
/min
)
mot
or c
once
ntra
tion
(a.u
.)
Left-right symmetry breakingin the worm C. elegans
left-right asymmetric organism
Worm left-right symmetric egg
4-cell stage (top view)
R
L
A PP2
ABa ABp
1-cellstage
2-cellstage
4-cellstage
8 cells
P0 P1AB PABp2ABa
EMS
left-right asymmetric organism
Worm left-right symmetric egg
third division: 4-6 cells
R
L
A PP2
ABar ABpr
ABal ABpl
Left-right symmetry breakingin the worm C. elegans
1-cellstage
2-cellstage
4-cellstage
8 cells
P0 P1AB PABp2ABa
EMS
R
L
A PP2
ABar ABpr
ABal ABpl
left-right asymmetric organism
Worm left-right symmetric egg
rotation of cell division axisbreaks left-right symmetry
Left-right symmetry breakingin the worm C. elegans
1-cellstage
2-cellstage
4-cellstage
8 cells
P0 P1AB PABp2ABa
EMS
rotation of cell division axisbreaks left-right symmetry
R
L
A PP2
ABar ABpr
ABal ABpl
Rotation of cell division axis
Anagha DatarSundar Naganathan
Tubulin
R
L
A PP2
ABar ABpr
ABal ABpl
L
R
1-cellstage
2-cellstage
4-cellstage
8 cells
P0 P1AB PABp2ABa
EMS
Saroj Nandi
contractile ring
y
x
vx
Tact
vy
Left Right
@x
Tact = �⌘@2x
vx
+ �vx
✏@x
Tact = � ⌘
2@2x
vy
+ �vy
Dividing cell
chiral coupling✏ =⌧actTact
notorque ⌧ =
ZdA�(r⇥ v) = 0
Symmetric division: chiral flows
Chiral flows rotate division axis
Chiral cortical flow
S. Grill, S. Naganath
R
L
A PP2
ABar ABpr
ABal ABpl
Friction force �vx
Chiral cortical flow
S. Grill, S. Naganath
R
L
A PP2
ABar ABpr
ABal ABpl
Friction force �vx
Chiral flows rotate division axis
Y. Okada et al. Cell, 121(4): 633 (2005)S. Nonaka et al. Cell, 95 (6): 829 (1998)
Left-right asymmetry in mammals
chiral cilium
Mammal (mouse)
microtubules
dynein
Hilfinger and Jülicher, Phys. Biol. 5 (2008)
Cilia-driven chiral flows
Active mechanical processes generate flows
Chemical patterns
force generation
chemicalsignals
activation
Mechano-chemical patterning
flows
ATP
ADP+P
A P
Max Planck Institute for the Physics of Complex Systems
Max Planck Institute of Molecular Cell Biology and Genetics
Justin BoisSaroj Nandi
Stephan GrillSundar NaganathanMasatoshi NishikawaPeter Gross
Maria StrempelSebastian FürthauerVijay K. Krishnamurthy
Anthony HymanNate Goehring
TU Dresden - Biotec
Miriam MayerStefan MünsterAnagha Datar