  We illuminate the many-body effects underlying the structure, formation, and
dissolution of cellular adhesion domains in the presence and absence of forces.
We consider mixed Glauber-Kawasaki dynamics of a two-dimensional model of
nearest-neighbor interacting adhesion bonds with intrinsic binding-affinity
under the action of a shared pulling or pushing force. We consider adhesion
bonds that are immobile due to being anchored to the underlying cytoskeleton as
well as adhesion molecules that are transiently diffusing. Highly accurate
analytical results are obtained on the pair-correlation level of the
Bethe-Guggenheim approximation for the complete thermodynamics and kinetics of
adhesion clusters of any size, including the thermodynamic limit. A new kind of
dynamical phase transition is uncovered -- the mean formation and dissolution
times per adhesion bond change discontinuously with respect to the
bond-coupling parameter. At the respective critical points cluster formation
and dissolution are fastest, while the statistically dominant transition path
undergoes a qualitative change -- the entropic barrier to complete
binding/unbinding is rate-limiting below, and the phase transition between
dense and dilute phases above the dynamical critical point. In the context of
the Ising model the dynamical phase transition reflects a first-order
discontinuity in the magnetization-reversal time. Our results provide a
potential explanation for the mechanical regulation of cell adhesion, and
suggest that the quasi-static and kinetic response to changes in the membrane
stiffness or applied forces is largest near the statical and dynamical critical
point, respectively.
