Theory for the bending rigidity of protein-coated lipid membranes

We study the bending rigidity of protein-coated lipid bilayer membranes by a continuum Landau theory. For up-down symmetric membrane proteins, the bending rigidity (κ) of the membrane is found to increase linearly with protein fraction (φ) and coupling strength (λ) due to the coupling between membrane curvature and local protein fraction. We estimate the coupling strength as λ ∝ κa_p²/a_l², where a_p and a_l are the lateral sizes of proteins and lipids, respectively. Estimated values of λ/κ are given for various combinations of membrane proteins and lipids. We show that the presence of membrane proteins leads to thinning of the effective membrane thickness and reduces the mean layer spacing of a stack of bilayers.