Abstract
In a biological cell, the cell membrane is coupled to the actin cortex. This forms an outer layer that determines much of the mechanics of the cell. Since scientists discovered the flickering phenomena in red blood cells in the nineteenth century, biophysicists constructed models that were expected to explain the dynamics of cell membranes. In this thesis, I present theoretical models to investigate the dynamics of a membrane coupled to an actin cortex. The main feature of our lastest model is that the contractility provided by the myosin motors in the actin cortex is included. This provides a distribution of active force dipoles in the actin cortex. We found that the contractility from the myosin becomes significant in the long wavelength limit, bringing the membrane into non-equilibrium states. The crossover wavelength is proportional to the inverse square root of myosin concentration. Also, the characteristic time scale for the cell membrane dynamics shows crossover from purely viscous to contractility-dominant regimes. Last but not the least, the physical meaning of the crossovers are discussed in details. Keywords: actin cortex, biomembrane, soft matter, active matter. 1