Modelling cell-extracellular matrix interactions
Luigi Preziosi
[email protected]
calvino.polito.it/~preziosi
Tumours as multicomponent tissues
Dipartimento di
di Matematica
Matematica
Dipartimento
(degenerate parabolic)
Mechanics in Multiphase Models
Mechanical effects in:
Growth
Stress
Interaction force
(P. Friedl, K. Wolf)
http://jcb.rupress.org/cgi/content/full/jcb.200209006/DC1
Dipartimento di Matematica
Cell-ECM interaction
• Baumgartner et al. PNAS 97 (2000)
Dipartimento di Matematica
Dipartimento di Matematica
Human Brain Tumor
35 pN
Sun et al.
Biophys J.
89 (2005)
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
mcm
Darcy's-type law
scm
vrel
• L.P. & A. Tosin, J. Math. Biol. 58, 625-656, (2009)
Dipartimento di Matematica
Modelling the interaction between cells and ECM
- if cells are not pulled strong enough
they they stick to the ECM
- otherwise they move relative to the
ECM
Dipartimento di Matematica
Modelling the interaction between cells and ECM
G. Vitale & L.P., M3AS, (2010)
Modelling the interaction between cells and ECM
Contribution due to porosity and tortuosity (in 3D)
Contribution due to adhesion
Dipartimento di Matematica
Modelling the adhesive contribution
Evolution equation
In the limit:
bond age << travel time
Breaking length << cell diameter
Dipartimento di Matematica
Modelling the adhesive contribution
If
z
z0
F
If
z
z0
F0
F
Dipartimento di Matematica
Modelling the adhesive contribution
z
mD+mad
mad
Fm
FM F
Dipartimento di Matematica
Modelling the interaction between cells and ECM
Some concluding remarks
 Different clones have different thresholds
Different invasiveness
Adhesion depends on the amount of ECM,
moves
slows down
stops
Modelling the interaction between cells and ECM
Volume ratio
Interfacial force
Dipartimento di Matematica
Cellular Potts Model
Dipartimento di Matematica
Sub-Cellular Components in CPM
M. Scianna
M. Scianna & L.P., Multiscale Model. Simul. (2012)
Dipartimento di Matematica
Moving cell morphology with CPM
Dipartimento di Matematica
Effect of adhesion in 2D
Palecek et al., Nature 385, 537-540 (1997)
Effect of pore size
M. Scianna, L.P., & K. Wolf, Biosci. Engng. (2012)
Effect of deformability
Varying fiber elasticity
Varying nucleus elasticity
Direct and Inverse Problem
Dipartimento di Matematica
Dipartimento di Matematica
Dipartimento di Matematica
Dipartimento di Matematica
Cell Traction
V. Peschetola, V. Laurent, A. Duperray, L. Preziosi, D. Ambrosi, C. Verdier,
Comp. Methods Biomech. Biomed. Engng. 14, 159-160 (2011).
time
Dipartimento di Matematica
Traction on a stiff gel
Ambrosi, Peschetola,Verdier
SIAM J. Appl. Math, (2006)
T24 cancer cells
Dipartimento di Matematica
Traction on softer gel
T24 cancer cells
Conclusions
• minor traction
ability than
fibroblasts
• larger forces
on stiffer gels
Dipartimento di Matematica
Traction in 3D
:f→u
G. Vitale, D. Ambrosi, L.P.,
J. Math. Anal. Appl. 395,
788-801 (2012).
Inverse Problems 28,
095013 (2012)
Penalty function for the minimization problem
Self-adjoint problem
Dipartimento di Matematica
Traction in 3D
Dipartimento di Matematica
A. Chauviere
C. Verdier
S. Astanin
C. Giverso
M. Scianna
D. Ambrosi
A. Tosin
G. Vitale
V. Peschetola