Using soft to build living matter : mechanical modeling of a developing tissue Cyprien Gay (MSC UMR 7057 Paris-Diderot)
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1 Using soft to build living matter : mechanical modeling of a developing tissue Cyprien Gay (MSC UMR 7057 Paris-Diderot) biochemistry mechanically active molecules mechanics V. Fleury SOFT V. Fleury LIVING deformability growth / contractility cellularity SPEC - 22 octobre 2014 page 1 / 24
2 Why simulations? Vary parameters independently Determine which parameters should be varied Show large scale role of local scale parameters Understand the effect of parameters inaccessible to theory Length scales: cytoskeleton continuum Suggest parameter values SPEC - 22 octobre 2014 page 2 / 24
3 Mechanics: the system and its environment length and force : two variables length = specified or force = specified or f (length, force, t) = 0 constitutive equation mechanical equilibrium SPEC - 22 octobre 2014 page 3 / 24
4 Cellularity: from fluid to solid air + water + surfactant = solid pressure tension V. Leroy crystal amorphous pressure tension SPEC - 22 octobre 2014 page 4 / 24
5 Cytoskeleton: contractile, elastic, viscous elastic viscous contractile M. Tortora J. Étienne et al G* tissue cortex SPEC - 22 octobre 2014 page 5 / 24
6 Cell-cell adhesion: dynamical model tensile force bonding at low tension or angle debonding at high tension or angle SPEC - 22 octobre 2014 page 6 / 24
7 Sub-cellular simulation Dynamics Equilibrium Rheology Laplace-Young Plateau Adhesion SPEC - 22 octobre 2014 page 7 / 24
8 Une cellule entre deux plaques A. Asnacios M. Tortora force (t) force (t) SPEC - 22 octobre 2014 page 8 / 24
9 Adhesion causes contraction of cellular aggregate Magnetic cells Magnetic contraction => elasticity Spontaneous contraction => adhesion Frasca et al. Soft Matter 2014 Next step: dynamics SPEC - 22 octobre 2014 page 9 / 24
10 From cell to tissue one cell connective tissue no cell-cell detachments to be included: rearrangements shape vs. volume (tensors) growth SPEC - 22 octobre 2014 page 10 / 24
11 Large deformations: cell deformation vs. rearrangements very large deformations and yet cells remain round T1 rearrangements intercalation cell scale: deformation large scale: rearrangements SPEC - 22 octobre 2014 page 11 / 24
12 Growth or apoptosis: cell deformation / change in number growth relieves stretching / apoptosis relieves compression cell scale: change in volume large scale: change in number of cells SPEC - 22 octobre 2014 page 12 / 24
13 Mechanical arrangement: cell / tissue and shape / volume intra inter shape cell shape cell arrangement volume cell volume number of cells SPEC - 22 octobre 2014 page 13 / 24
14 Mechanical arrangement: cell / tissue and shape / volume shape intra (visco) elasticity contractility inter rearrangements fluidification (cytokinesis, apoptosis) (anisotropic) cytokinesis volume swelling -cytokinesis +cytokinesis -apoptosis SPEC - 22 octobre 2014 page 14 / 24
15 Mechanical arrangement: cell / tissue and shape / volume intra viscoelasticity inter rearrangements ck shape fluidization volume - ck apoptosis swelling + ck SPEC - 22 octobre 2014 page 15 / 24
16 Mechanical arrangement: cell / tissue and shape / volume intra viscoelasticity inter rearrangements ck shape fluidization volume - ck apoptosis swelling + ck SPEC - 22 octobre 2014 page 16 / 24
17 System of continuum equations incompressible volume conservation mechanical equilibrium constitutive equation individual responses + topology SPEC - 22 octobre 2014 page 17 / 24
18 Confined growing aggregate PDMS wall PDMS wall 100 m Desmaison et al, PLoS One 2013 SPEC - 22 octobre 2014 page 18 / 24
19 Coupling with cell biochemistry growth factors, morphogens + growth rate intercalations and cortex anisotropy pressure Rauzi, Nat Cell Bio 2008 SPEC - 22 octobre 2014 page 19 / 24
20 Dissipation function formalism mechanical fields coupled mechanical and non-mechanical fields SPEC - 22 octobre 2014 page 20 / 24
21 Measurable detailed kinematics SPEC - 22 octobre 2014 page 21 / 24
22 Eulerian description with local deformation memory no memory tissue: huge deformations memory no memory SPEC - 22 octobre 2014 page 22 / 24
23 Large deformations: objective derivatives tensors rotate with material tensors are stretched with material our tensors are built on vectors attached to the material => upper-convected derivative (no choice) SPEC - 22 octobre 2014 page 23 / 24
24 Using soft to build living matter : mechanical modeling of a developing tissue Cyprien Gay (MSC UMR 7057 Paris-Diderot) Tissus S. Tlili F. Graner Ph. Marcq F. Molino P. Saramito M. Tortora V. Boudara F. Molino G. Frasca V. Du D. Fayol J.C. Bacri F. Gazeau M. Reffay C. Wilhelm Mousses liquides S. Bénito C.-H. Bruneau T. Colin F. Molino Subcellular simulation mechanically active molecules: cortex + adhesion Continuum theory tissue-scale mechanics cellularity liquid / solid rearrangements / large deformations growth / apoptosis cell number => volume change slow viscous behaviour SPEC - 22 octobre 2014 page 24 / 24
Mechanical modeling of a developing tissue as both continuous and cellular
Mechanical modeling of a developing tissue as both continuous and cellular Modélisation mécanique d'un tissu en développement : en quoi un matériau cellulaire diffère d'un matériau continu Cyprien Gay
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