Mechanical properties of cells and...

Mechanical properties of cells and tissues

J.F. Joanny

Physico-Chimie CurieInstitut Curie

Boulder Summer school, July 2015

Joanny (Institut Curie) Mechanics Boulder 1 / 45

Outline

1 Cell MechanicsActo-myosin cytoskeletonDynamics of cytokinesis

2 Mechanics and growth of tissuesMacroscopic theory of tissuesFluidization by cell division and apoptosis

3 Multicellular spheroidsTissue surface tensionSpheroid growth


Cell Mechanics

Outline





Cell Mechanics Acto-myosin cytoskeleton

Outline






Organelles and Cytoskeleton



Actin polymerization

Actin monomers

molecular weight 45kDasize δ = 5.5nmATP binding pocketpolar monomer

Actin polymers

2 protofilamentsright-handed helix, 72nmpitch, 24 monomers per turn



Actin in vivo

Actin interacting proteins

Revenu et al.



Molecular motors

Motor proteinsMuscle contraction (myosin II)Cilia and axonemes (Dynein)MitosisIntracellular transportInner ear hair cells (Myosin 1c)Rotating motors

General propertiesMotors consume ATPProcessive andnon-processive motors

Motor structure

ValeJoanny (Institut Curie) Mechanics Boulder 8 / 45


Cytoskeleton mechanics

Actomyosin gel

Treadmilling

Polar filament with + and − end



Violation of the fluctuation dissipation theorem

Fluctuations of acto-myosinnetworks

Mizuno et al.

Microrheology experiment:active and passiveSimilar experiment with cells



Red blood cells

Fluctuations of red blood cells

Betz et al.

Spectrin network needsto be prestressedNon-equilibriumreaction: binding andunbinding of spectrinsto the membrane



Active Systems

TissuesBacterial colonies Kessler, GoldsteinVibrated granular materials Menon et al.Active colloids, Active nematics Ramaswamy et al.Bird flocks, Fish shoals Vicsek, Toner, Chaté, Carere

Marchetti et al, Rev.Mod.Phys. 2013



Cell Cortex

Optical Imaging

CharrasActomyosin layerPolymerization from thesurface (formins)Treadmilling time ∼ 30sCortex tension

Electron microscopy

MedaliaDense actin layerThickness ∼ 1µmFilaments parallel to the cellsurface



Cell instabilities associated to cortical layer

Blebs Paluch

Detachments of themembrane form the corticallayerBleb lifetime 30s

Cell oscillations Pullarkat

Oscillations depend on actincontractilityOscillations depend oncalcium (threshold density)


Cell Mechanics Dynamics of cytokinesis

Outline






Final stages of cell division von Dassow

Final stage of cell division

Separation between daughtercellsSee urchin

Myosin contractility

Ring closure due to actincontractilityLocal enhancement of myosinactivity due to astralmicrotubules



Active gel theory of Cytokinesis

Cytokinesis driven by myosin contractility in the actin cortical layerExcess of contractility at the equator of the cell.Actin cortical layer described by active gel theory

Constant density in cortical layerIgnore polarization effectsViscoelastic actin layerActive stress ζ∆µ non homogeneous, increases at the equator

Cortical flow due to active stress gradientNumerical solution of active gel equations, using LagrangiancoordinatesImpose cylindrical symmetry of the cell



Dynamics of Cytokinesis

Cytokinesis completionCritical value of activity forcytokinesis completionLow activity of the ring:cytokinesis failureLarge activity of the ring:cytokinesis success



Kinetics of ring closure

Quasi-linear furrow constrictionRate of constriction increases with amplitude and width of inputsignalIf w ∼ R0 dRdt ∼ R0, Closure time Tc ∼ η/ζ∆µ independent of R0Good agreement with experiments



Qualitative interpretation

Cell tension T = eζ∆µ2Line tensionλ =

∫ds(T (s)− Tp) ∼ wδT

Dimensionless numberκ ∼ λ/(2TpR0)

Discontinuous closure transition

Linear constriction if dissipation dominated by cortical flow


Mechanics and growth of tissues

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Mechanics and growth of tissues Macroscopic theory of tissues

Outline






Multicellular spheroids

Intestinal epithelia



Epithelial tissues

Epithelial structureDividing cellsDifferentiated cellsApoptotic cells

Tissue mechanicsSolid-like behaviorLiquid-like behaviorViscoelastic liquid, relaxation time TPlastic behavior



Homeostatic pressure

Membrane permeable to interstitial fluidSteady State (kd = ka) defines homeostatic densityHomeostatic pressure



Cell proliferation and stress Cheng et al.



Competition between two tissues

Tissue with larger homeostatic pressure invades the other oneFinal state: homeostatic densityNumerical simulation of tissue invasion


Mechanics and growth of tissues Fluidization by cell division and apoptosis

Outline





Mechanics and growth of tissues Fluidization by cell division and apoptosis

Stress relaxation in a tissue Ranft, Julicher

Force dipoles induced by division and apoptosisDividing or apoptotic cells exert a force dipole fαdβForce dipole density Qαβ =

∑d iαβδ(r− ri)

Force balance ∂βσelαβ +∑

f iαδ(r− ri) = 0Total stress σαβ = σelαβ −Qαβ so that ∂βσαβ = 0

Internal stress in a tissue σinαβ = −QαβChange in internal stress due to division and apoptosisCell division coupled to stress Fink, Cuvelier

ddtσint = −ρpdkd − ρpaka

ddtσ̃intαβ = −ρp̃dkd < nαnβ −

13δαβ >= −

1τaσ̃αβ



Outline







Tissue spheroids in micropipettes Guevorkian,Brochard


Multicellular spheroids Tissue surface tension

Outline






Surface tension of Tissues

Relaxation measurementsSteinberg et al., F. Montel

Relaxation measurementsSteinberg et al.Neural Retina relaxation



Interfacial tension

Interfacial tension between tissuesSteinberg

Adhesion between cellsInterfacial tension depends onadhesion molecules Steinbergdepends on actomyosincytoskeleton and contractilityLaplace law Pch − P

hh =

2γr



Metastatic Inefficiency

0 5 10 15 20 25 30

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20

Critical Cell Number

Prob

abili

ty Prob

abili

ty

Time [d]

nc3

0

20

40

60

80

100

120

10 50 90 130 170 210 250 290 330 370 More

Size Interval

Num

ber o

f Tum

ors

nc10

t10 d

0.08

0.06

0.04

0.02

t14 d


Multicellular spheroids Spheroid growth

Outline






Spheroid growth F.Montel, M.Delarue

Growth experiments

Indirect experimentsDialysis bagPressure exerted by dextran

Direct experimentsSpheroid in contact withdextran solutionsNo penetration of dextran inspheroid



Surface growth

Pressure dependence

∂tV = (kd − ka)V + 4π(3

4π)2/3δksλV 2/3

Nutrient effectCrowding effectNegative homeostatic pressure Elgeti



Cell flow

Injection of fluorescent nano-particles

IncompressiblefluidVelocity field∇ · v = k(r)



Particle distribution

Transport by cell flow ∂tρ+∇ vρ = 0Negligible diffusion



Volume change after a pressure step

Growing spheroid with no applied pressurePressure step 5000 Pa after 4 daysVolume and anisotropy from correlations between nuclei position



Hydrodynamic calculation

Isotropic liquid SpheroidConstant pressure both in outer dividing layer and in inner layerPressure jump, larger pressure in the outer layerUpon pressure jump, cell contraction in the outer layer

Cell orientationViscoelastic spheroid. Elastic short time responseActive stress because of cell orientation σaαβ = ζ∆µpαpβActive stress depends on pressure



Active hydrodynamics of tissues

Radially polarized cell cellsActive gel hydrodynamics with active stress depending onpressure

Power law decay of density δnn =∆P(3+βe)

3K

(r

R0

)βeβe = −0.6



Volume decrease and cell division

Decrease in cell division rate,no change in apoptosis

Decrease in cell diameter atcenter after 5 min.P27 Overexpression after 1dayDecrease in cell divisionafter 4 daysCell proliferation arrest in G1phase



Curie Theory Group

Thomas Risler Philippe Marcq Morgan Delarue

Pierre Recho Jonas Ranft C. Erlenkamper

Edouard Hannezo Hervé Turlier Alexandre Mamane


Cell MechanicsActo-myosin cytoskeletonDynamics of cytokinesis

Mechanics and growth of tissuesMacroscopic theory of tissuesFluidization by cell division and apoptosis

Multicellular spheroidsTissue surface tensionSpheroid growth

Mechanical properties of cells and...

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