Transition from curvature sensing to generation in a vesicle driven by protein binding strength and membrane tension.

The ability of proteins to sense and/or generate membrane curvature is crucial for many biological processes inside the cell. We introduce a model for the binding and unbinding of curvature inducing proteins on vesicles using Dynamic Triangulation Monte Carlo (DTMC) simulations. In our study, the interaction between membrane curvature and protein binding is characterised by the binding affinity parameter µ, which indicates the interaction strength. We demonstrate that both sensing and generation of curvature can be observed in the same system as a function of the protein binding affinity on the membrane. Our results show that at low µ values, proteins only sense membrane curvature, whereas at high µ values, they induce curvature. The transition between sensing and generation regimes is marked by a sharp change in the µ-dependence of the protein bound fraction. We present ways to quantitatively characterise these two regimes. We also observe that imposing tension on the membrane (through internal excess pressure for liposomes) extends the region of curvature sensing in the parameter space.

Thermal and active fluctuations of a compressible bilayer vesicle.

We discuss thermal and active fluctuations of a compressible bilayer vesicle by using the results of hydrodynamic theory for vesicles. Coupled Langevin equations for the membrane deformation and the density fields are employed to calculate the power spectral density matrix of membrane fluctuations. Thermal contribution is obtained by means of the fluctuation dissipation theorem, whereas active contribution is calculated from exponentially decaying time correlation functions of active random forces. We obtain the total power spectral density as a sum of thermal and active contributions. An apparent response function is further calculated in order to compare with the recent microrheology experiment on red blood cells. An enhanced response is predicted in the low-frequency regime for non-thermal active fluctuations.

Relaxation dynamics of a compressible bilayer vesicle containing highly viscous fluid.

We study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium. First we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers. Two types of instabilities are identified: a small wavelength instability and a larger wavelength instability. Considering the bulk fluid viscosity and the inter-monolayer friction as the dissipation sources, we next employ Onsager's variational principle to derive the coupled equations both for the membrane and the bulk fluid. The three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle. Most importantly, a higher fluid viscosity inside the vesicle shifts the crossover mode between the bending and the slipping to a larger value. As the vesicle parameters approach the unstable regions, the relaxation dynamics is dramatically slowed down, and the corresponding mode structure changes significantly. In some limiting cases, our general result reduces to the previously obtained relaxation rates.