Calculation of Green Function for the Problem of Mechanical Indentation of Supported Lipid Bilayer

We considered the bilayer lipid membrane deposited onto a solid support. The lipid membrane is a quasi-3D elastic medium. We derived the exact Green function for the response of the membrane shape to an arbitrary applied force field, accounting for membrane deformations of splay, tilt, lateral stretching, twist, Gaussian splay, and lateral tension. The effect of the support was explicitly taken into account. The results were illustrated for the force fields arising in typical experiments of atomic force microscopy. The Green function can be utilized to determine the elastic parameters of lipid bilayers.