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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
Joanny (Institut Curie) Mechanics Boulder 2 / 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
Joanny (Institut Curie) Mechanics Boulder 2 / 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
Joanny (Institut Curie) Mechanics Boulder 2 / 45
Cell Mechanics
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
Joanny (Institut Curie) Mechanics Boulder 3 / 45
Cell Mechanics Acto-myosin cytoskeleton
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
Joanny (Institut Curie) Mechanics Boulder 4 / 45
Cell Mechanics Acto-myosin cytoskeleton
Organelles and Cytoskeleton
Joanny (Institut Curie) Mechanics Boulder 5 / 45
Cell Mechanics Acto-myosin 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
Joanny (Institut Curie) Mechanics Boulder 6 / 45
Cell Mechanics Acto-myosin cytoskeleton
Actin in vivo
Actin interacting proteins
Revenu et al.
Joanny (Institut Curie) Mechanics Boulder 7 / 45
Cell Mechanics Acto-myosin cytoskeleton
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
Cell Mechanics Acto-myosin cytoskeleton
Cytoskeleton mechanics
Actomyosin gel
Treadmilling
Polar filament with + and − end
Joanny (Institut Curie) Mechanics Boulder 9 / 45
Cell Mechanics Acto-myosin cytoskeleton
Violation of the fluctuation dissipation theorem
Fluctuations of acto-myosinnetworks
Mizuno et al.
Microrheology experiment:active and passiveSimilar experiment with cells
Joanny (Institut Curie) Mechanics Boulder 10 / 45
Cell Mechanics Acto-myosin cytoskeleton
Red blood cells
Fluctuations of red blood cells
Betz et al.
Spectrin network needsto be prestressedNon-equilibriumreaction: binding andunbinding of spectrinsto the membrane
Joanny (Institut Curie) Mechanics Boulder 11 / 45
Cell Mechanics Acto-myosin cytoskeleton
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
Joanny (Institut Curie) Mechanics Boulder 12 / 45
Cell Mechanics Acto-myosin cytoskeleton
Cell Cortex
Optical Imaging
CharrasActomyosin layerPolymerization from thesurface (formins)Treadmilling time ∼ 30sCortex tension
Electron microscopy
MedaliaDense actin layerThickness ∼ 1µmFilaments parallel to the cellsurface
Joanny (Institut Curie) Mechanics Boulder 13 / 45
Cell Mechanics Acto-myosin cytoskeleton
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)
Joanny (Institut Curie) Mechanics Boulder 14 / 45
Cell Mechanics Dynamics of cytokinesis
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
Joanny (Institut Curie) Mechanics Boulder 15 / 45
Cell Mechanics Dynamics of cytokinesis
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
Joanny (Institut Curie) Mechanics Boulder 16 / 45
Cell Mechanics Dynamics of cytokinesis
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
Joanny (Institut Curie) Mechanics Boulder 17 / 45
Cell Mechanics Dynamics of cytokinesis
Dynamics of Cytokinesis
Cytokinesis completionCritical value of activity forcytokinesis completionLow activity of the ring:cytokinesis failureLarge activity of the ring:cytokinesis success
Joanny (Institut Curie) Mechanics Boulder 18 / 45
Cell Mechanics Dynamics of cytokinesis
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
Joanny (Institut Curie) Mechanics Boulder 19 / 45
Cell Mechanics Dynamics of cytokinesis
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
Joanny (Institut Curie) Mechanics Boulder 20 / 45
Mechanics and growth of tissues
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
Joanny (Institut Curie) Mechanics Boulder 21 / 45
Mechanics and growth of tissues Macroscopic theory of tissues
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
Joanny (Institut Curie) Mechanics Boulder 22 / 45
Mechanics and growth of tissues Macroscopic theory of tissues
Multicellular spheroids
Intestinal epithelia
Joanny (Institut Curie) Mechanics Boulder 23 / 45
Mechanics and growth of tissues Macroscopic theory of tissues
Epithelial tissues
Epithelial structureDividing cellsDifferentiated cellsApoptotic cells
Tissue mechanicsSolid-like behaviorLiquid-like behaviorViscoelastic liquid, relaxation time TPlastic behavior
Joanny (Institut Curie) Mechanics Boulder 24 / 45
Mechanics and growth of tissues Macroscopic theory of tissues
Homeostatic pressure
Membrane permeable to interstitial fluidSteady State (kd = ka) defines homeostatic densityHomeostatic pressure
Joanny (Institut Curie) Mechanics Boulder 25 / 45
Mechanics and growth of tissues Macroscopic theory of tissues
Cell proliferation and stress Cheng et al.
Joanny (Institut Curie) Mechanics Boulder 26 / 45
Mechanics and growth of tissues Macroscopic theory of tissues
Competition between two tissues
Tissue with larger homeostatic pressure invades the other oneFinal state: homeostatic densityNumerical simulation of tissue invasion
Joanny (Institut Curie) Mechanics Boulder 27 / 45
Mechanics and growth of tissues Fluidization by cell division and apoptosis
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
Joanny (Institut Curie) Mechanics Boulder 28 / 45
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
Joanny (Institut Curie) Mechanics Boulder 29 / 45
Multicellular spheroids
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
Joanny (Institut Curie) Mechanics Boulder 30 / 45
Multicellular spheroids
Multicellular spheroids
Tissue spheroids in micropipettes Guevorkian,Brochard
Joanny (Institut Curie) Mechanics Boulder 31 / 45
Multicellular spheroids Tissue surface tension
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
Joanny (Institut Curie) Mechanics Boulder 32 / 45
Multicellular spheroids Tissue surface tension
Surface tension of Tissues
Relaxation measurementsSteinberg et al., F. Montel
Relaxation measurementsSteinberg et al.Neural Retina relaxation
Joanny (Institut Curie) Mechanics Boulder 33 / 45
Multicellular spheroids Tissue surface tension
Interfacial tension
Interfacial tension between tissuesSteinberg
Adhesion between cellsInterfacial tension depends onadhesion molecules Steinbergdepends on actomyosincytoskeleton and contractilityLaplace law Pch − P
hh =
2γr
Joanny (Institut Curie) Mechanics Boulder 34 / 45
Multicellular spheroids Tissue surface tension
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
Joanny (Institut Curie) Mechanics Boulder 35 / 45
Multicellular spheroids Spheroid growth
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
Joanny (Institut Curie) Mechanics Boulder 36 / 45
Multicellular spheroids Spheroid growth
Spheroid growth F.Montel, M.Delarue
Growth experiments
Indirect experimentsDialysis bagPressure exerted by dextran
Direct experimentsSpheroid in contact withdextran solutionsNo penetration of dextran inspheroid
Joanny (Institut Curie) Mechanics Boulder 37 / 45
Multicellular spheroids Spheroid growth
Surface growth
Pressure dependence
∂tV = (kd − ka)V + 4π(3
4π)2/3δksλV 2/3
Nutrient effectCrowding effectNegative homeostatic pressure Elgeti
Joanny (Institut Curie) Mechanics Boulder 38 / 45
Multicellular spheroids Spheroid growth
Cell flow
Injection of fluorescent nano-particles
IncompressiblefluidVelocity field∇ · v = k(r)
Joanny (Institut Curie) Mechanics Boulder 39 / 45
Multicellular spheroids Spheroid growth
Particle distribution
Transport by cell flow ∂tρ+∇ vρ = 0Negligible diffusion
Joanny (Institut Curie) Mechanics Boulder 40 / 45
Multicellular spheroids Spheroid growth
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
Joanny (Institut Curie) Mechanics Boulder 41 / 45
Multicellular spheroids Spheroid growth
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
Joanny (Institut Curie) Mechanics Boulder 42 / 45
Multicellular spheroids Spheroid growth
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
Joanny (Institut Curie) Mechanics Boulder 43 / 45
Multicellular spheroids Spheroid growth
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
Joanny (Institut Curie) Mechanics Boulder 44 / 45
Multicellular spheroids Spheroid growth
Curie Theory Group
Thomas Risler Philippe Marcq Morgan Delarue
Pierre Recho Jonas Ranft C. Erlenkamper
Edouard Hannezo Hervé Turlier Alexandre Mamane
Joanny (Institut Curie) Mechanics Boulder 45 / 45
Cell MechanicsActo-myosin cytoskeletonDynamics of cytokinesis
Mechanics and growth of tissuesMacroscopic theory of tissuesFluidization by cell division and apoptosis
Multicellular spheroidsTissue surface tensionSpheroid growth