modelling cell-extracellular matrix interactions
DESCRIPTION
Modelling cell-extracellular matrix interactions. Luigi Preziosi. [email protected] calvino.polito.it/~preziosi. (degenerate parabolic). Tumours as multicomponent tissues. Dipartimento di Matematica. Dipartimento di Matematica. Mechanics in Multiphase Models. Growth. Stress. - PowerPoint PPT PresentationTRANSCRIPT
Modelling cell-extracellular matrix interactionsModelling cell-extracellular matrix interactions
Luigi Preziosi
[email protected]/~preziosi
Dipartimento di Matematica
Tumours as multicomponent tissuesTumours as multicomponent tissues
Dipartimento di Matematica
(degenerate parabolic)
Dipartimento di Matematica
Mechanics in Multiphase ModelsMechanics in Multiphase Models
Growth
Stress
Interaction force
Mechanical effects in:
(P. Friedl, K. Wolf)http://jcb.rupress.org/cgi/content/full/jcb.200209006/DC1
Cell-ECM interactionCell-ECM interaction
Dipartimento di Matematica
• Baumgartner et al. PNAS 97 (2000)
Dipartimento di Matematica
Sun et al. Biophys J. 89 (2005)
Human Brain Tumor
35 pN
Dipartimento di Matematica
Modelling the interaction between cells and ECMModelling the interaction between cells and ECM
Interaction forceAdhesion strength
- if cells are not pulled strong enough they stick to the ECM- otherwise they move relative to the ECM
vrel
cm
mcm
Darcy's-type law
• L.P. & A. Tosin, J. Math. Biol. 58, 625-656, (2009)
Dipartimento di Matematica
Modelling the interaction between cells and ECMModelling the interaction between cells and ECM
Interaction forceAdhesion strength
- if cells are not pulled strong enough they they stick to the ECM- otherwise they move relative to the ECM
Modelling the interaction between cells and ECMModelling the interaction between cells and ECMG. Vitale & L.P., M3AS, (2010)
Dipartimento di Matematica
Modelling the interaction between cells and ECMModelling the interaction between cells and ECM
Contribution due to porosity and tortuosity (in 3D)
Contribution due to adhesionv
Dipartimento di Matematica
Modelling the adhesive contributionModelling the adhesive contribution
Breaking length << cell diameterIn the limit: bond age << travel time
Evolution equation
Dipartimento di Matematica
F
If
Modelling the adhesive contributionModelling the adhesive contribution
FF0
If
Dipartimento di Matematica
FFm
FM
mD+m
ad
mad
Modelling the adhesive contributionModelling the adhesive contribution
Modelling the interaction between cells and ECMModelling the interaction between cells and ECM
Some concluding remarksSome concluding remarks
moves slows down stops
Adhesion depends on the amount of ECM,
Different clones have different thresholds
Different invasiveness
Dipartimento di Matematica
Modelling the interaction between cells and ECMModelling the interaction between cells and ECM
Interfacial forceVolume ratio
Dipartimento di Matematica
Cellular Potts Model Cellular Potts Model
Dipartimento di Matematica
Sub-Cellular Components in CPMSub-Cellular Components in CPMM. Scianna
M. Scianna & L.P., Multiscale Model. Simul. (2012)
Moving cell morphology with CPMMoving cell morphology with CPM
Dipartimento di Matematica
Effect of adhesion in 2DEffect of adhesion in 2D
Palecek et al., Nature 385, 537-540 (1997)
Effect of pore sizeEffect of pore size
M. Scianna, L.P., & K. Wolf, Biosci. Engng. (2012)
Effect of deformabilityEffect of deformabilityVarying fiber elasticity Varying nucleus elasticity
Dipartimento di Matematica
Direct and Inverse ProblemDirect and Inverse Problem
Dipartimento di Matematica
Dipartimento di Matematica
Dipartimento di Matematica
Dipartimento di Matematica
Cell TractionCell 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
Ambrosi, Peschetola,VerdierSIAM J. Appl. Math, (2006)
T24 cancer cells
Traction on a stiff gelTraction on a stiff gel
Dipartimento di Matematica
Traction on softer gelTraction on softer gel
Conclusions
• minor traction ability than fibroblasts• larger forces on stiffer gels
T24 cancer cells
Dipartimento di Matematica
Traction in 3DTraction in 3D
: f → u
Self-adjoint problem
Penalty function for the minimization problem
G. Vitale, D. Ambrosi, L.P., J. Math. Anal. Appl. 395,
788-801 (2012).Inverse Problems 28,
095013 (2012)
Dipartimento di Matematica
Traction in 3DTraction in 3D
D. Ambrosi
A. Tosin
G. Vitale
V. Peschetola
A. Chauviere
C. Verdier
S. Astanin
C. Giverso
M. Scianna