M. Basan A. Basu A. Callan-Jones J.F. Joanny F. Julicher K. Kruse T. Risler G.Salbreux K. Sekimoto...

transcript

M. BasanA. BasuA. Callan-JonesJ.F. JoannyF. JulicherK. KruseT. RislerG.SalbreuxK. SekimotoR. Voituriez

C. Sykes

E. Paluch

P. Pullarkat

M. Bornens

X. Sastres

J.P. Henry

E. Karatekim

From cell to tissue dynamics?

QuickTime™ et undécompresseur Cinepak

sont requis pour visionner cette image.

QuickTime™ et undécompresseur Cinepak Codec by Radiussont requis pour visionner cette image.

Fibroblast FragmentsDepolymerized Microtubules

E. Paluch et al, E.480Bornens et al, 1988

QuickTime™ et un décompresseurCinepak sont requis pour visualiser

cette image.

Filament array in lamellipodia

(T. Svitkina and G.G. Borisy, 1999; Blanchoin et al.; Pantaloni et al., 2000, Ishiwata et al 2000)

Arp 2/3

Actin Intrinsic Treadmilling

ADP ATP

Actin-based motility

QuickTime™ et un décompresseurCinepak sont requis pour visualiser

cette image.

MYOSIN

QuickTime™ et undécompresseur Video

(R. Vale)

Muscles: Actin and Myosin Filaments

Conserved quantities, Broken symmetries

• Actin (monomer+polymer)• Myosin (bound, unbound)• Momentum (force)• Polarization

Harvard ChoiceP.C. Martin et al

Conservation laws

Jρ = ρv

Dissipative

Reactive

+λa pα Δμ

+λm pα Δμ

A. Simha, S. Ramaswamy; T. Liverpool, C. Marchetti, H. Chaté

+λ2ζΔμpβ∂β pα

K. Takiguchi,1991G. H. Koenderink 2006

F. Nedelec et al 1997, K. Kruse, F. Jülicher, 2000, T. Liverpool, C. Marchetti 2002, I. Aranson2005, B. Mulder et al 2005

2ηuαβ = .....+ ζΔμpα pβ + ...

Nematic Hydrodynamics(F.M. Leslie, F. Brochard, P.G. de Gennes, P.

Pieranski, E. Guyon)

Dt= ........+ ωαβ pβ + ....= .....+ ν 1uαβ pβ + ....

cos(2Ψ0) =1/ν 1

Spontaneous Frederiks transition

R. Voituriez

∂α∂t

∂ 2α

∂z2+ (1+ ν 1)uzx

2 ˜ η uzx ≈ σ zx − ˜ ζ Δμ sin(2α ) + ν 1K∂ 2α

K˜ γ 1

∂ 2α

∂z2− Δμ ˜ ˜ ζ α

(Δμ ˜ ˜ ζ )c = K(π

Remains to be seen!

+λ2ζΔμpβ∂β pα =1

2λ 2ζΔμ sin(2θ )

L. Giomi, C. Marchetti, J.F. Joanny, J.P.

δK > 0

δK < 0

δK = 0

Topological Singularities

Spontaneously moving topological singularity

QuickTime™ et undécompresseur GIF

State Diagram

ζ Δμ =R2 ˜ ζ Δμ /K

δK = δK /K

EXPERIMENT(François Nedelec et al)

QuickTime™ et undécompresseur H.263

Allow for density variation:d=2

R. GoldsteinB. subtilis

S. Ramaswamy, G. Menon et al

Fluctuations?

Thermal noise

Non thermal fluctuations

Long time limit

Traveling waves M. Sheetz, H.G. Dobereiner

Always unstable at long wavelength!

Gel regime: non thermal noise importantFluid regime: nematic coupling important

Particle (Vesicle), Diffusion

Short time: F. MacKintosh

< (x(t) − x(t' ))2 >= 2d 3q

(2π )3(< (u(q,t)∫ u(−q,t) > − < u(q,t)u(−q,t' ) >)

< (x(t) − x(t' ))2 >= 2d 3q

(2π )3

Eq2∫ (1− e−

t−t '

τ m )

t << τ m

< (x(t) − x(t' ))2 >=Δ2qc

πEτ m

t − t '

t >> τ m

< (x(t) − x(t' ))2 >=Δ2qc

L= ζΔμθ

⟨θ 2⟩=kT

KL;⟨θ⟩= 0

v =ζΔμ

Short − time : t⟨γ1

⟨(δx)2⟩≅ v2t2

Long− time : t⟩γ1

KL2 = τ nem

⟨(δx)2⟩≅ (v2τ nem2 )(

τ nem

) = δDt

“balistic”

“diffusive”

τnem =γ1L

Kπ 2≈

ξ 2Eπ 2≈ τ M (

πξ)2

“diffusive”

D ≈ kBT(ζΔμ )2γ1

(ηK )2

F. MacKintosh

New material Science

• Transitions toward moving sates

• “Ramaswamy waves”

• Unconventional diffusion

• Long wavelength unstable

• Similar to bacterial motion, flocks etc…

Questions• Shape (profile)

• Relation thickness/force/velocity and flow

• Substrate, membrane tension

• What determines Length?

• A. Verkhovsky symmetry breaking?

Leading EdgeGlycoprotéine

GlycolipideProtéine Oligosaccharide

Cholestérol

Pore protéique

Phospholipides

Leading edge and membrane dynamics

Fi = dsm∫ Φ(δ − δ0 )

0 =δF

∂t= vp(δ) − vT ,l

Steady motion

∂t= U →→ δ = δ∗

Peff = P +d

dδΦ(δ∗− δ0 )

Peff = P +vp

o − (U + vT ,l )

σ eff = σ + Φ(δ∗− δ0 )€

λa =dvp

dδ/d2φ

2σ€

σPeff

Threshold

Peff ≈ 103 −102 Pascal

Peff hl =vp

0 − (U + vl )

hl = σ +σ '+Flext = − fl

(U + vl ) = vp = vp0 − λ a

σ +σ '+Flext

Leading edge

vp( peff ) = U + vl = vp0 − λ a peff

2ηvαβ = (1+ τD

Dt)(σ αβ +ζΔμpα pβ )

∂α(σαβ−Pδαβ)=0

Thin slab U

2η∂v

∂x= σ +ζΔμ

fx = σh

∂σh

∂x= ξv

d2 = 2ηh /ξ

d2 ∂2σ

∂x2− σ = ζΔμ

v = hξ −1 ∂σ

L/2-L/2

v=0 v<0v>0

Free ends

€ €

2) = σ (−

2) = 0

σ = −ζΔμ (1−ch(

v =ζΔμ

U = vp − v(−L

U = vdp − v(L

U =vp + vdp

Screening!

Lamellipodium shape and motion?

ρh(x)(U + v(x)) = const

2η∂v

∂x= (1+ τU

dx)σ +ζΔμ

∂hσ

∂x= ξv

d2 = 2ηh /ξ

Keratocyte:

In most cases d « L:

ζΔμ ≈103 Pa

ξ ≈ 31010 Pa.s /mGrowth cone:

ζΔμ ≈50Pa

ξ ≈ 108 Pa.s / m

A. Verkhovsky et al

T. Betz

+ Stick-Slip!

What determines Length?

ρvphl = ρvdphL = D∂c

∂xh(x)

vp = kp(δ)cl

ρvph = ρvdph = DcL − cl

(kpccell

kp(δ)ccell ⟩⟩vdp →→ L⟩⟩d

kp(δ)ccell ≈ vdp →→ L⟨⟨d

Fragment

n =1 Actin KinaseRho Kinase

QuickTime™ et undécompresseur TIFF (LZW)

P. Pullarkat, K. Jacobson

Cortical Actin?

σ zz = 0

ξ1 = τvt = τakp

Steady − state : kp = kdp = kdp0 exp(−p /σ 0 )

Intrinsically unstable!

Spherical symmetry:Threshold!

T = σ xx0

∫ dz = (−ζΔμ )(e∗− vtτ (1− exp(−e∗

vtτ))

2T / R ≈ δπ

T ≈ 103 ×10−6 ≈ 10−3 N /m

δπ ≈ 102 Pascal

R ≈ 10μm

Pramod Pullarkat

Frequency

Activity Parameter Calcium sensitivity

Activity parameter

QuickTime™ et undécompresseur TIFF (non compressé)

Frequency

QuickTime™ et undécompresseur Aucune

Mitosis?

D. Bray, J. Spudich et al

Stability of an active Shell

Cell oscillations: M. Bornens et al, P. Pullarkat, K. Jacobsen

Tissue Dynamics

4) Metastatic Inefficiency

Cameron et al., Cancer Research (2000)

Measurement of Active Tissue Homeostatic Pressure

Lamellipodium :

peff ≅ 103 pascalNumbers?

σ =−p(ρ ,Δμ ) +η∂vx

∂x= 0

∂t+ ρ

∂x= (kd − ka )ρ

σ + k(x − x0 ) = 0

dt= vx(x)

Stationary State:

vx = 0

kd (ρ s ,Δμ ) = ka (ρ s ,Δμ )

vx (xs ) = 0

p(ρ s ,Δμ ) = k(xs − x0 )

Tissue Fight for Space

3) Tumor Growth Dynamicsa) Compartment Competition

• Force balance:

(Liquid limit: )

• Constitutive eqns :

Highest Stationary pressure wins again!

4) Metastatic Inefficiency

•Surface tension for at tumor boundary:

Tumor grows

Tumor shrinksCritical Radius!

p2 − p1 =2γ

If const

If faster than r « Benign » steady state

Small tumors are monoclonal

How do you reach the critical radius?

Nutrition/Signalization: millimeter size Steady State

QuickTime™ et undécompresseur TIFF (non compressé)

Stability versus Angiogenesis?

Duplicating cells

Migrating cells

Necrosed cells

• rc a few cell diameter• Very sensitive on • Preferential nucleation at rigid interfaces• Seed and soil (Stephen Paget 1889)• Papillomas virus• But many other steps…

Messages :

• Quantitative cell dynamics

• Signalization, Fluctuations

• Axones, synapses and Alzheimer

• Tissue dynamics: new concepts, new experiments

• Much to do!

M. Basan A. Basu A. Callan-Jones J.F. Joanny F. Julicher K. Kruse T. Risler G.Salbreux K. Sekimoto...

Documents