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Nano-scale mechanical probing of supported lipid bilayers with atomic force microscopy

We present theory and experiments for the force-distance curve $F(z_0)$ of an atomic force microscope (AFM) tip (radius $R$) indenting a supported fluid bilayer (thickness $2d$). For realistic conditions the force is dominated by the area compressibility modulus $κ_A$ of the bilayer, and, to an excellent approximation, given by $F= πκ_A R z_0^2/(2d-z_0)^2$. The experimental AFM force curves from coexisting liquid ordered and liquid disordered domains in 3-component lipid bilayers are well-described by our model, and provides $κ_A$ in agreement with literature values. The liquid ordered phase has a yield like response that we model by hydrogen bond breaking.