Measuring biomembrane undulations at sub-µm lengthscales using single gold nanorods

We measure the orientation of gold nanorods bound to a lipid membrane to probe its undulation dynamics on sub-µm lengthscales. Using high-speed polarimetric microscopy we measure the time dependent mean-squared displacement of the out-of-plane rotation of the nanorod. Fitting the results to a theoretical model allows us to determine various mechanical properties of giant unilamellar vesicles including their bending rigidity, surface tension, and the inter-monolayer friction coefficient. Probing membrane fluctuation in angular space rather than height space makes our approach sensitive to the short wave-length undulations which previously had only been accessible via measurement techniques like small-angle X-ray scattering and neutron spin echo spectroscopy on model membranes. We validated our approach by comparison to a simulation of the motion of a nanorod on a model membrane, using a Monte Carlo realization of the membrane at different states of tension. Motion of single GNRs on the plasma membrane of cultured cells reveals its complex physics. Our findings for the time dependent motion of the plasma membrane normal vector reveal sub-µm wavelength Brownian undulations expected for a lipid membrane coupled to a cell cortex undergoing active undulations at longer time-scales.