Practice question

Spontaneous curvature stems from imbalance between optimal headgroup repulsion and hydrocarbon chain pressure described by Israelachvili packing parameter P equals v divided by a times l. When headgroup area a large relative to volume v molecule resembles inverted cone P less than one yielding positive curvature forming micelles as lysophosphatidylcholine with one chain generating outward bulges. Small headgroup like PE PA DAG yields cone P greater than one favoring negative curvature invaginations and HII tubes needed for fusion fission. PC sphingomyelin balanced a and v give cylinder P about one stabilizing flat bilayers low curvature elastic stress. Cells manipulate curvature enzymatic remodeling PC to PA via phospholipase D reducing head size or insertion ENTH BAR amphipathic helices wedging into leaflet creating asymmetry. Cholesterol modestly increases order but near cylindrical shape contributes little curvature per se. Glycolipid large oligosaccharide exerts steric pressure outside. Linking head size to curvature clarifies tubular ER reticulons caveolae caveolin scaffolding and budding mechanisms examined in cell biology and biophysics exams requiring shape understanding and bending energetics quantitative analysis for vesicle formation.