Impact of receptor-ligand distance on adhesion cluster stability

T. Erdmann and U. S. Schwarz

Eur. Phys. J. E 22: 123-137 (2007)

Cells in multicellular organisms adhere to the extracellular matrix
through two-dimensional clusters spanning a size range from very few
to thousands of adhesion bonds. For many common receptor-ligand
systems, the ligands are tethered to a surface via polymeric spacers
with finite binding range, thus adhesion cluster stability crucially
depends on receptor-ligand distance. We introduce a one-step master
equation which incorporates the effect of cooperative binding through
a finite number of polymeric ligand tethers. We also derive
Fokker-Planck and mean field equations as continuum limits of the
master equation. Polymers are modeled either as harmonic springs or as
worm-like chains. In both cases, we find bistability between bound and
unbound states for intermediate values of receptor-ligand distance and
calculate the corresponding switching times. For small cluster sizes,
stochastic effects destabilize the clusters at large separation, as
shown by a detailed analysis of the stochastic potential resulting
from the Fokker-Planck equation.