Thermodynamics and dynamics of the formation of spherical lipid vesicles

Abstract

We propose a free energy expression accounting for the formation of spherical vesicles from planar lipid membranes and derive a Fokker-Planck equation for the probability distribution describing the dynamics of vesicle formation. We find that formation may occur as an activated process for small membranes and as a transport process for sufficiently large membranes. We give explicit expressions for the transition rates and the characteristic time of vesicle formation in terms of the relevant physical parameters.

Fig. 1

Schematic representation of vesicle formation from a planar membrane

Fig. 2

Dimensionless free energy as a function of θ for δ = 0.1, 1.8, 2.8, 4.1

Fig. 3

a Dimensionless transition rate r_p as a function of δ for different values of a = κ_b/k_BT = 2, 15, 25, 50 at room temperature. The vertical lines indicate the limit of validity of the activation dynamics approximation. b Dimensionless transition rate r_v as a function of δ for different values of a = 2, 5, 15, 25 at room temperature

Fig. 4

Angle θ as a function of the dimensionless time τ = 2πκ_bαt for the following values of δ: 15, 25, and 60 obtained by solving numerically (21). The solid circles represent an analytical solution given in the text for δ = 15. The inset shows a log–log plot of vesicle formation time τ_c vs δ for δ = 10, 15, 25, 60, and 400. The slope of the straight line is ∼ − 1.07

Fig. 5

Probability distribution P as a function of angle and dimensionless time τ obtained by numerically solving (13) with an initial condition given by a Gaussian distribution centered at θ = π. At short times (τ < 1), diffusion dominates, spreading the distribution. For times τ > 1, the drifting force dominates and the distribution becomes narrow close to θ = 0