Cell Adhesion and Reorganization in Tumour Growth Modelling. Luigi Preziosi calvino.polito.it/~preziosi

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1 Cell Adhesion and Reorganization in Tumour Growth Modelling Luigi Preziosi calvino.polito.it/~preziosi

2 Tumours as Multicomponent Tissues deformable and degradable ECM extracellular liquid (P. Friedl, K. Wolf) host cells and tumour cells

3 Tumours as Multicomponent Tissues + saturation + diffusion of nutrients & chemical factors H. Byrne & L.P., Math. Med. Biol. 20, (2004)

4 Mechanical effects Mechanical effects in: Growth Stress Interaction force Mechanotransduction Contact inhibition of growth M. Chaplain, L. Graziano, & L.P., Math. Medicine Biol. 23, (2006) J. Galle, & L. P., A. Tosin, Appl. Math. Letters, 22, (2009) Growth and cell re-organisation D. Ambrosi, L.P., Biomech. Modeling in Mechanobiology 8, (2009). L. P, D. Ambrosi, C. Verdier, J. Theor. Biol. 262, (2010).

5 Mechanics in Multiphase Models Mechanical effects in: Growth Stress Interaction force Cell aggregates as fluids (viscous or inviscid) mcm Darcy's-type law vrel (J. Guch)

6 Modelling the interaction between cells and ECM - if cells are not pulled strong enough they stick to the ECM - otherwise they move relative to the ECM I Adh nt e r a esion c t i on stren force gt h mcm Darcy's-type law σ cm vrel L.P. & A. Tosin, J. Math. Biol. 58, , (2009)

7 Cell-ECM interaction Baumgartner et al. PNAS 97 (2000)

8 Human Brain Tumor 35 pn Sun et al. Biophys J. 89 (2005)

9 Interfering with the adhesion mechanisms Disrupts actin cytoskeleton removes hyaluronan backbone from membrane see also Canetta et al. (2004)

10 Modelling the interaction between cells and ECM G. Vitale & L.P., M3AS, (2010)

11 Modelling the interaction between cells and ECM Contribution due to porosity and tortuosity (in 3D) Contribution due to adhesion v

12 Modelling the adhesive contribution Evolution equation In the limit: bond age << travel time Breaking length << cell diameter

13 Modelling the adhesive contribution If ζ ζ0 F If ζ ζ0 F0 F

14 Modelling the adhesive contribution ζ md+mad Fm FM F mad

15 Modelling the interaction between cells and ECM

16 Modelling the interaction between cells and ECM Different clones have different thresholds Different invasiveness Adhesion depends on the amount of ECM, moves slows down stops

17 Modelling the interaction between cells and ECM Volume ratio Interfacial force

18 Modelling the interaction between cells and ECM

19 Plastic re-organisation during growth (T. Demuth, M. Berens) jcs.biologists.org/cgi/content/abstract/116/21/4409 (B. Ribba)

20 Cell re-organisation Forgacs et al., Biophys. J. 74: (1998)

21 Cell re-organisation Foty et al., PRL 72: (1996) Fig. 4. A spherical heart aggregate on the lower compression plate (A) before compression, (B) after initiation of compression and (C) released from compression after a few seconds behaves as an elastic solid, springing back to its original, spherical shape. Fig. 5. A spherical heart aggregate on the lower compression plate (A), compressed for 3.5 hours (B), and then released (C), temporarily retains flat upper and lower surfaces. Behaving as a viscous liquid, it slowly rounds up again (D,E) when incubated for an additional few hours.

22 Stress relaxation G(s) = relaxation kernel } surface tension λ1 λ2 Forgacs et al., Biophys. J. 74: (1998) Winters et al., Int. J. Cancer, 114: ,(2005)

23 Stress relaxation Forgacz et al. (1998)

24 Spheroids are Viscoplastic Iordan, Duperray, Verdier, Phys. Rev. E 77, (2008)

25 Spheroids are Viscoplastic Yield stress using Herschel Bulkley s model Iordan, Duperray, Verdier, Phys. Rev. E 77, (2008)

26 Hypothesis σ2 fluid-like region When and where the stress is large enough some bonds break cells re-organise stress relaxes bonds don t break cells deform elastic recovery solid-like region yield surface σ1

27 Evolving Natural Configurations. D. Ambrosi & L.P., Biomech. Modeling Mechanobiol., (2009) Invariant measure of the stress (e.g., maximum shear stress)

28 Limit case: small elastic deformation

29 Limit case: small elastic deformation

30 Limit cases: small elastic deformation strain stress = t t strain stress cell re-organisation τ τ Unrecovered deformation t t

31 Steady shear rate. at low shear rates apparent viscosity goes like γ. 1

32 strain Stress relaxation stress t } yield stress t regardless of imposed strain strain Winters et al., Int. J. Cancer, 114: Dipartimento di Matematica ,(2005)

33 Foty's cell reorganisation test If deformation is not too large

34 A Voigt-Kelvin generalization C. Giverso & L.P. (2010)

35 Foty's cell reorganisation test Imposing a deformation and then releasing the stress

36 Forgacz et al. (1998) Stress relaxation

37 Stress relaxation

38 Modelling the interaction between cells and ECM

39 Conclusions - Describing tumours as remodeling solids requires some care - Final constitutive equation simple to be used - Constitutive model able to explain different types of experiments - Possibility of linking constitutive model with microscopic measurements

40 A. Chauviere C. Verdier S. Astanin C. Giverso M. Scianna D. Ambrosi A. Tosin G. Vitale V. Peschetola

41 Istituto per la Ricerca e la Cura del Cancro Divisione di Angiogenesi Molecolare F. Bussolino E. Giraudo G. Serini E. Medico Ospedale Molinette Laboratorio di Immunogenetica A. Funaro N. Lo Buono Università di Torino Dipartimento di Biologia Animale e dell'uomo L. Munaron

42 Understanding cell traction deformation D. Ambrosi J.Math.Biol 58, 163 (2009) Where in Ωc the force is exerted?

43 Direct and Inverse Problem

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47 Measured deformation Evaluated traction

48 Traction on a stiff gel Ambrosi, Peschetola,Verdier SIAM J. Appl. Math, (2006) T24 cancer cells

49 Traction on softer gel T24 cancer cells Conclusions minor traction ability than fibroblasts larger forces on stiffer gels

50 Invasion of Ovary Cancer Cells

51 Invasion of Ovary Cancer Cells Top view Side view C. Giverso, M. Scianna, L.P., N. Lo Buono & A. Funaro Math. Model. Nat. Phenom. 5 (2010)

52 Invasion of Ovary Cancer Cells

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55 Invasion of Ovary Cancer Cells

56 Invasion of Ovary Cancer Cells

57 Invasion of Ovary Cancer Cells Top view Side view Bottom view

58 Invasion of Multicellular Spheroids

59 Invasion of Multicellular Spheroids

60 Invasion of Ovary Cancer Cells