  Area per molecule in a DPPC-Cholesterol bilayers depends non-linearly on the
cholesterol concentration. Using flexible strings model of lipid membranes we
calculate area per molecule in DPPC-Cholesterol mixtures in the biologically
relevant concentrations range. Few parameters of the model are optimized for a
perfect agreement with the area per lipid data available from molecular
dynamics simulations. Lateral pressure at the hydrophilic interface, {\gamma},
is taken to be proportional to the cholesterol concentration. Non-linearity
arises as a consequence of the non-linear dependence of thermodynamical
equilibrium area of molecules on {\gamma}. DPPC lipid is modeled as flexible
string of finite thickness and a given bending rigidity, while cholesterol
molecule is modeled as rigid rod with finite thickness and infinite rigidity.
Using parameters fitted to reproduce area per molecule dependence on
cholesterol concentration, we had further calculated our model predictions for
the NMR order parameter of DPPC lipid chains and coefficient of thermal area
expansion. The microscopic nature of the model allows to consider a broad range
of thermodynamic phenomena.
