Deduce the area compressibility KA of the lipid bilayerSolut

Deduce the area compressibility KA of the lipid bilayer.

Solution

Mechanics of lipid bilayer includes study of physical material properties which classify lipid bilayer with stress and strain.

Area compressibility modulus is defined as,   KAA(/A)_T,V^,   

Here^, KA isarea expansion modulus,A is the area of the system and is the surface tension. Here we consider that the surface tension is zero.

Here,Area compressibility possess two contributions as, one intrinsic K_A^trueas there is change in area per lipid along the curved membrane surface, and another is projected area which changes due to undulation of the bilayer.

Area compressibilities exhibit a considerable system size-dependence due to the difference between the projected area of the lipid bilayers and the true area that follows the undulating surface. Fluctuations may occur in membrane surface due to undulation of lipid bilayer. Such kind of undulation is well described by Helfrich type of theory.