Computational model of cell migration through a viscoelastic extracellular matrix by local degradation and filopodia-based traction forces

Tommy Heck^a, Hans Van Oosterwyck^a^,^d, Herman Ramon^b, Bart Smeets^b, Paul Van Liedekerke^c

^aBiomechanics Section, Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300C - box 2419, Leuven, 3001

^bMeBioS, Department of Biosystems, KU Leuven, Willem de Croylaan 42 - box 2428, Leuven, 3001

^cInstitut National de Recherche en Informatique et en Automatique (INRIA), Domaine de Voluceau-Rocquencourt, B.P. 105, Le Chesnay Cedex, 8153

^dPrometheus, Division of Skeletal Tissue Engineering, KU Leuven, O&N 1, Herestraat 49 – box 813, Leuven, 3000, Belgium

Proceedings of New Advances in Probing Cell-ECM Interactions (CellMatrix)

Berlin, Germany, 2016 October 20th - 21st

Organizers: Ovijit Chaudhuri, Allen Liu and Sapun Parekh

Poster, Tommy Heck, 022
Publication date: 25th July 2016

Introduction

The extracellular matrix (ECM) is an important regulator of cell migration. Cells receive mechanical and chemical stimuli from the ECM, degrade the ECM and apply protrusive and contractile forces to it in order to migrate through the ECM. Computational models are being developed to improve the understanding of the role of cell-matrix interaction in cell migration.

Methods

A computational model has been developed of cell migration through a viscoelastic ECM. The ECM is modelled with a method called non-inertial smoothed particle hydrodynamics (NSPH) [1]. In this mesh-free numerical method the continuum laws of fluid and solid mechanics are implemented in a discrete way by convolution with a smoothing kernel. The mesh-free character allows to simulate large deformations of the ECM, cell-mediated ECM degradation and migration of a cell through the ECM without the need of time consuming remeshing. The cell is represented by a set of connected particles as either a rigid or a deformable cell and is embedded in the ECM model. The cell locally degrades the ECM, which is modelled as a phase transition accompanied by deviatoric stress dissipation, and applies filopodia-based contractile forces to it in order to migrate through.

Results and Discussion

Simulations are performed of a cell migrating through a viscoelastic ECM in 2D. The contractile force exerted by the filopodia, the number of filopodia and their orientation are varied in order to investigate their effect on cell migration. Further, the effect of the degradation rate and the local area in front of the cell where degradation takes place are investigated. Finally, also the effect of Young’s modulus, Poisson’s ratio and dynamic viscosity of the viscoelastic ECM are investigated. The results are compared to traction force microscopy results of fibroblasts embedded in a collagen gel. Altogether, this works presents a mechanically sound model of cell migration through a viscoelastic ECM that can aid in unravelling the mechanisms behind cell-matrix interaction during cell migration.

References

[1] Van Liedekerke P. et al., Computer Physics Communication, 184(7):1686-1696, 2013.

Acknowledgements

This research has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement no 308223), from FWO-Vlaanderen (grant number G.0821.13, Tommy Heck is a PhD fellow of FWO-Vlaanderen) and from IWT (Bart Smeets is a PhD fellow of IWT).

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