Vesicle formation induced by thermal fluctuations.

The process of fission and vesicle formation depends on the geometry of the membrane that will split. For instance, a flat surface finds it difficult to form vesicles because of the lack of curved regions where to start the process. Here we show that vesicle formation can be promoted by temperature, by using a membrane phase field model with Gaussian curvature. We find a phase transition between fluctuating and vesiculation phases that depends on temperature, spontaneous curvature, and the ratio between bending and Gaussian moduli. We analysed the energy dynamical behaviour of these processes and found that the main driving ingredient is the Gaussian energy term, although the curvature energy term usually helps with the process as well. We also found that the chemical potential can be used to investigate the temperature of the system. Finally we address how temperature changes the condition for spontaneous vesiculation for all geometries, making it happen in a wider range of values of the Gaussian modulus.

Red blood cells in low Reynolds number flow: A vorticity-based characterization of shapes in two dimensions.

Studies on the mechanical properties of red blood cells improve the diagnosis of some blood-related diseases. Some existing numerical methods have successfully simulated the coupling between a fluid and red blood cells. This paper introduces an alternative phase-field model formulation of two-dimensional cells that solves the vorticity and stream function that simplifies the numerical implementation. We integrate red blood cell dynamics immersed in a Poiseuille flow and reproduce previously reported morphologies (slippers or parachutes). In the case of flow in a very wide channel, we discover a new metastable shape referred to as 'anti-parachute' that evolves into a horizontal slipper centered on the channel. This sort of metastable morphology may contribute to the dynamical response of the blood.

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.