How pinning influences the dynamics of cell membranes*

We simulate a membrane in thermal equilibrium, tethered to a flat surface at discrete random points.  We consider two cases, one where there is no correlation between randomly chosen tethered points and second where the tethered points appear in randomly placed clusters. We find that:

(a) for small frame tension the internal tension  decreases as pinning increases, 

(b) The internal tension and the fluctuating tension are approximately equal,   

(c) how the pinned points are distributed affects the spectrum  at small wavenumbers but has no significant effect on the internal tension.

Assuming small deformation we derive, theoretically, how the change in area varies with change in surface tension for a pinned membrane. This agrees with our simulations.  We use flicker imaging of HeLA cells to probe the same relation experimentally while we turn off the pinning of the cell membrane (partially) to the cytoskeleton by manipulating the protein ezrin.  Results of these experiments agree with both theory and numerical simulations showing that dynamics of the cell membrane is dominated by its pinning to the cytoskeleton.