Elasticity of Lipid Vesicles
The first step to study the elasticity of cell membranes is to study lipid bilayers. Usually, the thickness of the lipid bilayer is much smaller than the scale of the whole lipid bilayer. It is reasonable to describe the lipid bilayer by a mathematical surface. In 1973, Helfrich recognized that the lipid bilayer was just like a nematic liquid crystal at room temperature, and then proposed the curvature energy per unit area of the bilayer
(1)where are bending rigidities. is called the spontaneous curvature of the membrane. and are the mean and Gaussian curvature of the membrane surface, respectively.
The free energy of a closed bilayer under the osmotic pressure (the outer pressure minus the inner one) as:
(2)where and are the area element of the membrane and the volume element enclosed by the closed bilayer, respectively. is the surface tension of the bilayer. By taking the first order variation of above free energy, Ou-Yang and Helfrich derived an equation to describe the equilibrium shape of the bilayer as:
(3)They also obtained that the threshold pressure for the instability of a spherical bilayer was
(4)where being the radius of the spherical bilayer.
Using the shape equation (3) of closed vesilces, Ou-Yang predicted that there was a lipid torus with the ratio of two generated radii being exactly . His prediction was soon confirmed by the experiment . Additionally, researchers obtained an analytical solution to (3) which explained the classical problem---the biconcave discoidal shape of normal red cells.
Read more about this topic: Elasticity Of Cell Membranes
Famous quotes containing the words elasticity of and/or elasticity:
“A submissive spirit might be patient, a strong understanding would supply resolution, but here was something more; here was that elasticity of mind, that disposition to be comforted, that power of turning readily from evil to good, and of finding employment which carried her out of herself, which was from Nature alone. It was the choicest gift of heaven.”
—Jane Austen (1775–1817)
“One of the reforms to be carried out during the incoming administration is a change in our monetary and banking laws, so as to secure greater elasticity in the forms of currency available for trade and to prevent the limitations of law from operating to increase the embarrassment of a financial panic.”
—William Howard Taft (1857–1930)