Excess area dependent scaling behavior of nano-sized membrane tethers

Thermal fluctuations in cell membranes manifest as an excess area (Aex) which governs a multitude of physical process at the sub-micron scale. We present a theoretical framework, based on an in silico tether pulling method, which may be used to reliably estimate Aex in live cells. We perform our simulations in two different thermodynamic ensembles: (i) the constant projected area and (ii) the constant frame tension ensembles and show the equivalence of our results in the two. The tether forces estimated from our simulations compare well with our experimental measurements for tethers extracted from ruptured GUVs and HeLa cells. We demonstrate the significance and validity of our method by showing that all our calculations performed in the initial tether formation regime (i.e. when the length of the tether is comparable to its radius) along with experiments of tether extraction in 15 different cell types collapse onto two unified scaling relationships mapping tether force, tether radius, bending stiffness., and membrane tension s. We show that Rbead is an important determinant of the radius of the extracted tether, which is equal to the characteristic length xi = root kappa/2 sigma for R-bead < xi, and is equal to R-bead for R-bead > xi. We also find that the estimated excess area follows a linear scaling behavior that only depends on the true value of Aex for the membrane, based on which we propose a self-consistent technique to estimate the range of excess membrane areas in a cell.