Abstract
Lipid membranes, which are fundamental to cellular function, undergo various mechanical deformations. Accurate modeling of these processes necessitates a thorough understanding of membrane elasticity. The lateral shear modulus, a critical parameter describing membrane resistance to lateral stresses, remains elusive due to the membrane's fluid nature. Two contrasting hypotheses, local fluidity and global fluidity, have been proposed. While the former suggests a zero local lateral shear modulus anywhere within lipid monolayers, the latter posits that only the integral of this modulus over the monolayer thickness vanishes. These differing models lead to distinct estimations of other elastic moduli and affect the modeling of biological processes, such as membrane fusion/fission and membrane-mediated interactions. Notably, they predict distinct local stress distributions in cylindrically curved membranes. The local fluidity model proposes isotropic local lateral stress, whereas the global fluidity model predicts anisotropy due to anisotropic local lateral stretching of lipid monolayers. Using molecular dynamics simulations, this study directly investigates these models by analyzing local stress in a cylindrically curved membrane. The results conclusively demonstrate the existence of static local lateral shear stress and anisotropy in local lateral stress within the monolayers of the cylindrical membrane, strongly supporting the global fluidity model. These findings have significant implications for the calculation of surface elastic moduli and offer novel insights into the fundamental principles governing lipid membrane elasticity.