Biomechanics and Modeling in Mechanobiology

, Volume 17, Issue 4, pp 1037–1052 | Cite as

A hybrid computational model for collective cell durotaxis

  • Jorge Escribano
  • Raimon Sunyer
  • María Teresa Sánchez
  • Xavier Trepat
  • Pere Roca-Cusachs
  • José Manuel García-AznarEmail author
Original Paper


Collective cell migration is regulated by a complex set of mechanical interactions and cellular mechanisms. Collective migration emerges from mechanisms occurring at single cell level, involving processes like contraction, polymerization and depolymerization, of cell–cell interactions and of cell–substrate adhesion. Here, we present a computational framework which simulates the dynamics of this emergent behavior conditioned by substrates with stiffness gradients. The computational model reproduces the cell’s ability to move toward the stiffer part of the substrate, process known as durotaxis. It combines the continuous formulation of truss elements and a particle-based approach to simulate the dynamics of cell–matrix adhesions and cell–cell interactions. Using this hybrid approach, researchers can quickly create a quantitative model to understand the regulatory role of different mechanical conditions on the dynamics of collective cell migration. Our model shows that durotaxis occurs due to the ability of cells to deform the substrate more in the part of lower stiffness than in the stiffer part. This effect explains why cell collective movement is more effective than single cell movement in stiffness gradient conditions. In addition, we numerically evaluate how gradient stiffness properties, cell monolayer size and force transmission between cells and extracellular matrix are crucial in regulating durotaxis.


Mechanics of cell migration Stiffness gradients Durotaxis Cell contractility Hybrid modeling approach Collective cell motion 



This work is supported by the Spanish Ministry of Economy and Competitiveness/FEDER (FPI BES-2013- 063684 to J.E., DPI201564221C21R to J.M.G.-A., BFU2016-79916-P and BFU2014-52586-REDT to PR-C, BFU2015-65074-P to XT), the Generalitat de Catalunya (2014-SGR-927 to XT and CERCA program), the European Research Council (StG 306571 to J.M.G.-A. and CoG-616480 to XT), European Commission (Grant Agreement SEP-210342844 to PR-C and XT). IBEC is recipient of a Severo Ochoa Award of Excellence from the MINECO.

Supplementary material

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of ZaragozaZaragozaSpain
  2. 2.Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute for Science and Technology (BIST)BarcelonaSpain
  3. 3.Centro Universitario de la DefensaZaragozaSpain
  4. 4.University of BarcelonaBarcelonaSpain
  5. 5.Center for Networked Biomedical Research on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN)BarcelonaSpain
  6. 6.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain

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