On Gaussian curvature and membrane fission

We propose a three-dimensional mathematical model to describe dynamical processes of membrane fission. The model is based on a phase field equation that includes the Gaussian curvature contribution to the bending energy. With the addition of the Gaussian curvature energy term numerical simulations agree with the predictions that tubular shapes can break down into multiple vesicles. A dispersion relation obtained with linear analysis predicts the wavelength of the instability and the number of formed vesicles. Finally, a membrane shape diagram is obtained for the different Gaussian and bending modulus, showing different shape regimes.

Incorporation of Soft Particles into Lipid Vesicles: Effects of Particle Size and Elasticity

The interaction between particles and lipid biomembranes plays an essential role in many fields such as endocytosis, drug delivery, and intracellular traffic. Here we conduct a theoretical study on the incorporation of elastic particles of different sizes and rigidities into a lipid vesicle through adhesive wrapping. It is shown that while the incorporation of relatively small particles involves smooth shape evolution, the vesicle wrapping of large particles exhibits a discontinuous shape transition, followed by a protrusion of the vesicle membrane at infinitesimal cost of elastic deformation energy. Moreover, softer particles require stronger adhesion energy to achieve successful internalization and delay the onset of discontinuous shape transition to a higher wrapping degree. Depending on the adhesion energy, particle-vesicle size, and rigidity ratios, and the spontaneous curvature of the vesicle, a rich variety of wrapping phase diagrams consisting of stable and metastable states of no-wrapping, partial-wrapping, and full-wrapping are established. The underlying mechanism of the discontinuous shape transformation of the vesicle and the relation between the uptake proneness and uptake efficiency are discussed. These results shed further light on the elasticity effects in cellular uptake of elastic particles and may provide rational design guidelines for controlled endocytosis and diagnostics delivery.