Elasticity of Cell Membranes
A cell membrane is simplified as lipid bilayer plus membrane skeleton. The skeleton is a cross-linking protein network and joints to the bilayer at some points. Assume that each proteins in the membrane skeleton have similar length which is much smaller than the whole size of the cell membrane, and that the membrane is locally 2-dimensional uniform and homogenous. Thus the free energy density can be expressed as the invariant form of, and :
(10)where is the in-plane strain of the membrane skeleton. Under the assumption of small deformations, and invariant between and, (10) can be expanded up to second order terms as:
(11)where and are two elastic constants. In fact, the first two terms in (11) are the bending energy of the cell membrane which contributes mainly from the lipid bilayer. The last two terms come from the entropic elasticity of the membrane skeleton.
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