For both the bilayer and the monolayer, the irst moment of the LLP π(z) gave the product of the bending rigidity and the spontaneous curvature. In order to obtain the spontaneous curvature, the values for the bending rigidity κ and κ ± were needed which in principle could be obtained by a buckling simulation. Here for simplicity we assumed κ ± = 12.5 k B T and κ = κ + + κ -= 25 k B T , which were the typical values for the plasma membrane made of POPC. Here we neglected the effect that the bilayer bending rigidity κ could be different for the two monolayers due to compositional asymmetry. In fact, the bending rigidity can be inluenced by the lipid composition, as well as ions in the external environment. If the membrane is made of a mixture of POPC and POPS (70:30), the surface charge might stiffen the membrane and increase the bending rigidity from 25 k B to 30 k B T . However, the presence of ions can counteract the effect of surface charge and soften the membrane. As a result of the complicated nature of the bending rigidity, the approximation κ ± = 12.5 k B T may affect the quantitative accuracy of the calculated spontaneous curvature, but not the sign of it (bending direction of membranes).