  Understanding mechanosensitivity, i.e. how cells sense the stiffness of their
environment is very important, yet there is a fundamental difficulty in
understanding its mechanism: to measure an elastic modulus one requires two
points of application of force - a measuring and a reference point. The cell in
contact with substrate has only one (adhesion) point to work with, and thus a
new method of measurement needs to be invented. The aim of this theoretical
work is to develop a self-consistent physical model for mechanosensitivity, a
process by which a cell detects the mechanical stiffness of its environment
(e.g. a substrate it is attached to via adhesion points) and generates an
appropriate chemical signaling to remodel itself in response to this
environment. The model uses the molecular mechanosensing complex of latent
TGF-$\beta$ attached to the adhesion point as the biomarker. We show that the
underlying Brownian motion in the substrate is the reference element in the
measuring process. The model produces the closed expression for the rate of
release of active TGF-$\beta$, which depends on the substrate stiffness and the
pulling force coming from the cell in a subtle and non-trivial way. It is
consistent with basic experimental data showing an increase in signal for
stiffer substrates and higher pulling forces. In addition, we find that for
each cell there is a range of stiffness where a homeostatic configuration of
the cell can be achieved, outside of which the cell either relaxes its
cytoskeletal forces and detaches from the very weak substrate, or generates an
increasingly strong pulling force through stress fibers with a positive
feedback loop on very stiff substrates. In this way, the theory offers the
underlying mechanism for the myofibroblast conversion in wound healing and
smooth muscle cell dysfunction in cardiac disease.
