An Analytical Model for Orientation-Dependent Membrane–Substrate Interactions in Supported Lipid Bilayers

Supported lipid bilayers (SLBs) adhered to solid substrates provide an important model system for studying membrane mechanics and for developing biomimetic membrane platforms. In this work, we examine the mechanical response of SLBs supported on cylindrical substrates, with particular emphasis on the role of membrane–substrate contact angle. Classical membrane–substrate interaction models restricted to normal-incidence contact are extended through a linearized representation of the membrane unit normal at the interaction boundary, enabling orientation-dependent boundary conditions while preserving analytical tractability. Closed-form analytical solutions are derived for membrane shape and curvature within the prescription of small incremental deformations superposed on a finite initial configuration. The results demonstrate that decreasing the contact angle strengthens adhesion, increases curvature, and enhances membrane deformation, whereas larger contact angles yield weakly adhered, near-planar membrane configurations. These trends establish contact angle as an effective geometric control parameter governing membrane–substrate interactions on cylindrical supports. The proposed analytical framework advances existing membrane–substrate theories and provides a mechanics-based foundation for interpreting and tuning supported lipid bilayer behavior in applications involving biosensing interfaces and lipid-based drug delivery systems.