Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Mathematical modeling of mechanical cell-extracellular matrix interactions
Elisabeth Geraldine Rens, Roeland Merks

Last modified: 2014-03-28


Cell shape, migration and adhesion properties
are important factors during many biological processes, such as
tissue formation, angiogenesis and tumor growth. A good understanding
of cell behavior is vital for medicine and tissue engerineering.
Computer models can be of assistance, because by simulation we can
infer important parameters for the inhibition and promotion of
crucial cell properties and examine different mechanisms that are
involved more thoroughly. Cell behavior depends on various chemical and
mechanical factors, such as chemotaxis towards growth factors within
the extracellular matrix, adhesion of cells to the extracullular
matrix and more. Also, the compliancy of the extracellular matrix is
considered to account for different cell shapes and migratory
properties. It has been shown that cells sense and respond to the
mechanical properties of the extracellular matrix. In addition, cells
can remodel the substrate that they adhere to. This provides cells
with the ability of cell-cell mechanical communication, which turns
out to be important during morphogenesis. In this work we use the Cellular Potts Model, a
cell-based model with dynamics based on Hamiltonian minimization, to
study this mechanical cell-substrate interaction. We model cells that
apply a force on the substrate which depends on the shape of the
cell. With a finite element method we can calculate the deformations
in the substrate. Subsequently, the cells respond to the strain in
the matrix. We assume that cells preferentially adhere to the
substrate in the direction of higher strain. This is a reasonable
assumption, as it has been shown that cells align in the direction of
strain. With this model we are able to reproduce cell
behavior as observed in vitro. Similar to experiments, cells in our
model become small and round on compliant substrates, elongate on
substrates of intermediate compliancies and spread on stiff
substrates. Remarkably, simulated cells elongate and round in a
pulsating manner, which has recently been observed with melanoma
cells as well. In the model, this oscillating behavior seems to
depend on the random motility of the cells. The model is of help in
elucidating the cell shape and migration properties on different
substrate stiffnesses. Furthermore, with just this mechanical
cell-substrate feedback in the Cellular Potts Model, simulations show
higher level collective behavior of cells, such as the formation of
vascular patterns. Current research focuses on the effect of changing
the adhesivity of the substrate.