Lipid bilayer shapes governed by bending rigidity and spontaneous curvature
The Helfrich free energy F = ∫[κ/2(2H−c₀)² + κ_G·K + σ]dA governs lipid membrane shape, where H is mean curvature, K is Gaussian curvature, c₀ is spontaneous curvature, and κ is bending rigidity. Cells exploit spontaneous curvature to drive budding, tubulation, and vesicle formation.