A model for semi-solid membrane: Anomalous diffusion and effective shear modulus

The basic architecture of the cell membrane is best described by the `Fluid Mosaic' model, proposed by Singer and Nicolson [Science 175, 720–731 (1972)]. In the model, the membrane is composed primarily of bi-layer lipids and houses domains of embedded proteins. From the perspective of physical properties, the cell membrane exhibits fluid-like characteristics with lipid molecules diffusing on the surface, while also demonstrating solid-like attributes, evidenced by a non-zero shear modulus. We introduce a model for a semi-solid membrane which mimics the described physical properties of the cell membrane. We conduct Monte Carlo simulations to study the diffusion and the mechanical properties of this semi-solid membrane. The fraction of the solid regions ($Phi$) can be varied. For a non-zero Φ, we recover the sub diffusive nature of the trajectories as found in cell membrane. We also show that our model semi-solid membrane have a non-zero shear modulus for Φ≥0.1.