  Cells exhibit qualitatively different behaviors on substrates with different
rigidities. The fact that cells are more polarized on the stiffer substrate
motivates us to construct a two-dimensional cell with the distribution of focal
adhesions dependent on substrate rigidities. This distribution affects the
forces exerted by the cell and thereby determines its motion. Our model
reproduces the experimental observation that the persistence time is higher on
the stiffer substrate. This stiffness dependent persistence will lead to
durotaxis, the preference in moving towards stiffer substrates. This propensity
is characterized by the durotaxis index first defined in experiments. We derive
and validate a 2D corresponding Fokker-Planck equation associated with our
model. Our approach highlights the possible role of the focal adhesion
arrangement in durotaxis.
