We present a minimal physical derivation of the natural angular frequency of radial oscillations (“osmotic breathing”) of a prebiotic vesicle. The vesicle radius R (t) is treated as the dynamical variable. By linearizing the pressure balance around equilibrium and introducing an effective radial stiffness, we obtain a simple scaling law for ω₀. The resulting expression shows that the oscillation frequency increases with membrane tension and decreases strongly with vesicle size, scaling as R₀^ (-3/2).
Peter Mikuláš (Sun,) studied this question.