Proefschrift
Mathematical modelling of cell behaviour in fibrous extracellular matrices: multiscale mechanics of shape, patterning, and motilit
Cells interact with the extracellular matrix (ECM), a fibrous scaffold surrounding cells that provides mechanical support and mediates signaling between cells.
- Auteur
- K.A.E. Keijzer
- Datum
- 03 juli 2026
- Links
- Thesis in Leiden Repository
Mechanical strains and stress in the ECM influence cell shape and affects cell migration. In turn, cells deform and reorganize the ECM fibers through their contractile forces. In this thesis, we study the mechanical reciprocity between cells and fibrous ECM, and how this two-way interaction affects cellular shape and motility. To this end, we develop a hybrid mathematical model that combines three scales: the cellular scale, the fibrous network scale, and the mechanosensitive adhesions linking the two. Together, these scales are represented through a hybrid mathematical model that couples a lattice- based stochastic model for cell shape, the Cellular Potts Model (CPM), with a particle– spring representation of a discrete, bendable fibrous ECM and a set of ordinary differential equations describing the mechanosensitive focal adhesions that connect the cell to the ECM.
In Chapter 2, we ask how local variations in ECM stiffness due to anisotropy of ECM fibers affect cell shape. To this end, we apply the hybrid model and find that, consistent with experimental observations, cells sense the anisotropy of fibers and change their shape accordingly. We also find that cellular contractile forces remodel and realign the local fibrous matrix, and that this remodeling precedes and guides new protrusions, establishing a feedback loop in which cells first create anisotropy and then follow it.
In Chapter 3, we study, together with a direct colleagueworking in the wet lab, how ECM proteins laminin and fibronectin present in the intersegmental space can guide the growth of intersegmental blood vessels (ISVs) in the zebrafish embryo. Here, the hybrid mathematical model is used to study how ECM stiffness, density, and chemical signaling together can regulate the correct development of ISVs and how perturbations in either factor could affect the patterning of the final vessels.
In Chapter 4, we study the relationship between cell contraction and ECM elasticity in 3D. While previous chapters studied 2D systems, this chapter extends parts of the model into 3D and investigates the effect of cellular contraction on the deformation of the ECM and the effect of elastic ECM-derived restoring forces on the contracting cell.
In the final chapter, we study how cell contraction and ECM deformation can influence cell migration. In Chapter 2, we found that cells remodel the matrix before extending over it. Here, we examine this feedback loop in more detail and find that the model predicts a preparatory phase in which the cell deforms the ECM, after which the induced anisotropy biases and facilitates migration.
In summary, this thesis aims to contribute to our understanding of the reciprocal interaction between cells and the fibrous environment. The model developed in this thesis shows that the mechanosensitivity of the adhesion between cell and ECM can reproduce several of the mechanical effects of the ECM on morphology, morphogenesis, and migration.