Internal forces, tension and energy density in tethered cellular membranes.

We analyze tethered cellular membranes by considering the membrane resultants, tension and densities of two modes of energy, bending and adhesion. These characteristics are determined based on a computational (finite-difference) analysis of membrane shape. We analyze the relative contribution and distribution of the membrane characteristics in four typical zones of the membrane surface. Using an axisymmetric model, we found that the meridional and circumferential components of the resultant are different near the tether body and they converge to the value of membrane tension farther from the tether. At the beginning of the area of membrane detachment from the cytoskeleton, the density of bending energy is on the same order of magnitude as membrane tension (resultant). Away from the tether, the bending energy density quickly decreases and becomes of the same order as that of the adhesion energy in the membrane-cytoskeleton attachment area. In that area, both modes of energy are significantly smaller than the membrane tension. We also consider the effect of the membrane bending modulus on the distribution of the membrane characteristics. An increase in the bending modulus results in changing the length and position on the membrane surface of zone 1 characterized by significant evolution of the resultant components. It also results in shortening zone 2 that covers the rest of the area of membrane detachment. The obtained results can help in a better interpretation of the measurements of membrane mechanical properties as well as in analyses of proteins and channels in curved membranes.