Kinetics of particle wrapping by a vesicle.

We present theoretical results on kinetics for the passive wrapping of a single, rigid particle by a flexible membrane. Using a simple geometric ansatz for the shape of the membrane/particle complex we first compute free energy profiles as a function of the particle size, attraction strength between the particle and vesicle, and material properties of the vesicle--bending stiffness and stretching modulus. The free energy profiles thus computed are taken as input to a stochastic model of the wrapping process, described by a Fokker-Planck equation. We compute average uptake rates of the particle into the vesicle. We find that the rate of particle uptake falls to zero outside of a thermodynamically allowed range of particle sizes. Within the thermodynamically allowed range of particle size, the rate of uptake is variable and we compute the optimal particle size and maximal uptake rate as a function of the attraction strength, the vesicle size, and vesicle material properties.