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

Cell polarity

PAR-6 / PAR-2

10 µm

Anterior Posterior

Par2Par6

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

Chirality

A chiral object is different from its mirror image.

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

A P

v

x

(x) vy(x)vx

vy

high contractilestress

vx vy

Chiral flow patterns fluorescent myosin motors

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

Anagha Datar, Stefan Münster

3D reconstruction

left-right symmetry breaking

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

R LRL

Left-right asymmetryof organisms

MammalWorm

cortical flows rotating cilia

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

Chirality in Biology

Molecules

Organisms

Cells

chiral filaments

chiral body plan

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