Bulletin of Mathematical Biology

, Volume 80, Issue 5, pp 1017–1045 | Cite as

How Nucleus Mechanics and ECM Microstructure Influence the Invasion of Single Cells and Multicellular Aggregates

  • Chiara Giverso
  • Alessandro Arduino
  • Luigi Preziosi
Special Issue : Mathematical Oncology


In order to move in a three-dimensional extracellular matrix, the nucleus of a cell must squeeze through the narrow spacing among the fibers and, by adhering to them, the cell needs to exert sufficiently strong traction forces. If the nucleus is too stiff, the spacing too narrow, or traction forces too weak, the cell is not able to penetrate the network. In this article, we formulate a mathematical model based on an energetic approach, for cells entering cylindrical channels composed of extracellular matrix fibers. Treating the nucleus as an elastic body covered by an elastic membrane, the energetic balance leads to the definition of a necessary criterion for cells to pass through the regular network of fibers, depending on the traction forces exerted by the cells (or possibly passive stresses), the stretchability of the nuclear membrane, the stiffness of the nucleus, and the ratio of the pore size within the extracellular matrix with respect to the nucleus diameter. The results obtained highlight the importance of the interplay between mechanical properties of the cell and microscopic geometric characteristics of the extracellular matrix and give an estimate for a critical value of the pore size that represents the physical limit of migration and can be used in tumor growth models to predict their invasive potential in thick regions of ECM.


Cell migration Cancer invasion Metastasis 

Mathematics Subject Classification

92B05 92C15 92C42 92C17 


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.Istituto Nazionale di Alta Matematica “F. Severi”Città UniversitariaRomeItaly
  2. 2.Department of Mathematical SciencesPolitecnico di TorinoTurinItaly
  3. 3.Department of EnergyPolitecnico di TorinoTurinItaly
  4. 4.Istituto Nazionale di Ricerca MetrologicaTurinItaly

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