Excess area dependent scaling behavior of nano-sized membrane tethers

Thermal fluctuations in cell membranes manifest as an excess area (${\cal A}_{\rm ex}$) 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 ${\cal A}_{\rm ex}$ in live cells. 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 along with experiments of tether extraction in 15 different cell types collapse onto two unified scaling relationships mapping tether force, tether radius, bending stiffness $\kappa$, and membrane tension $\sigma$. We show that $R_{\rm bead}$, the size of the wetting region, is an important determinant of the radius of the extracted tether, which is equal to $\xi=\sqrt{\kappa/2\sigma}$ (a characteristic length scale of the membrane) for $R_{\rm bead}<\xi$, and is equal to $R_{\rm bead}$ for $R_{\rm bead}>\xi$. We also find that the estimated excess area follows a linear scaling behavior that only depends on the true value of ${\cal A}_{\rm ex}$ for the membrane, based on which we propose a self-consistent technique to estimate the range of excess membrane areas in a cell.