The self-assembly of lipid bilayer membranes to enclose functional biomolecules, thus defining a "protocell," was a seminal moment in the emergence of life on Earth and likely occurred at the micro-environment of the mineral-water interface. Mineral-lipid interactions are also relevant in biomedical, industrial and technological processes. Yet, no structure-activity relationships (SARs) have been identified to predict lipid self-assembly at mineral surfaces. Here we examined the influence of minerals on the self-assembly and survival of vesicles composed of single chain amphiphiles as model protocell membranes. The apparent critical vesicle concentration (CVC) increased in the presence of positively-charged nanoparticulate minerals at high loadings (mg/mL) suggesting unfavorable membrane self-assembly in such situations. Above the CVC, initial vesicle formation rates were faster in the presence of minerals. Rates were correlated with the mineral's isoelectric point (IEP) and reactive surface area. The IEP depends on the crystal structure, chemical composition and surface hydration. Thus, membrane self-assembly showed rational dependence on fundamental mineral properties. Once formed, membrane permeability (integrity) was unaffected by minerals. Suggesting that, protocells could have survived on rock surfaces. These SARs may help predict the formation and survival of protocell membranes on early Earth and other rocky planets, and amphiphile-mineral interactions in diverse other phenomena.