Mathematical modeling of dynamic behavior of fluid bilayer membranes under the effect of density asymmetry

Shape transformations in biological membranes are crucial in a variety of cellular processes such as transport in the Golgi apparatus and endoplasmic reticulum, shaping the cell organelles and signaling in neuronal synapses. Dynamic analysis of lipid bilayer membranes is popular among researchers as valuable information about cell functions can be retrieved. There are several limitations in experimental tests and simulations such as computational and implementation cost while in theoretical studies, different phenomena can be modeled and the effect of each parameter can be investigated. In this paper, a continuum model including elastic energies and dissipation functions is utilized with energy approach to obtain the governing equations of an enclosed lipid bilayer membrane. The governing equations are solved numerically for vesicles initially disturbed and the relaxation dynamics is studied. The stationary shape of the vesicles for different values of reduced volume and reduced area difference is obtained to explore the phase diagram and verify the governing equations. Then, the density asymmetry in bilayers caused by the change in the density or the equilibrium density of the outer monolayer is studied. This leads to the formation of buds, tubules, and pearls. This can be observed in the recruitment of proteins to the outer monolayer or pH gradients of the environment of a vesicle. The effect of density difference and curvature on creation and growth of tubules are investigated. An interesting metastable state in the adsorption of the final bud due to the increase in the density of the outer monolayer is observed in which the shape of the vesicle is almost unchanged. A prolate vesicle relaxes toward an oblate or a stomatocyte vesicle when the equilibrium density of the outer monolayer increases.