Interactions between two sheets of a bilayer membrane and its internal lateral pressure

We have modelled a phospholipid bilayer as two monolayer sheets which interact with each other by a coupling which depends upon the states of the lipid hydrocarbon chains in each sheet. We make use of a model (Georgallas and Pink 1982a) and its parameters, already used to study monolayer phase changes at the LC-LE transition, in order to study the lipid main transition. Although the monolayer coexistence curve can be calculated exactly, we have made use of high-temperature series expansions to calculate the critical point of the bilayer. We also present the results of computer simulations on triangular lattices for the pressure-area isotherms. We find: (i) the interaction between the sheets of a DPPC bilayer is about 1.5-2% of the maximum interaction within the plane of each sheet; (ii) the internal lateral pressure of a DPPC bilayer is about 30.5 dyne/cm; (iii) the bilayer transition enthalpy depends sensitively upon the coupling between the sheets. Should this coupling vary from sample to sample (due, possibly, to its preparation) then very different values of transition enthalpy may be measured. (iv) We present a rough rule-of-thumb for estimating the internal lateral pressure of a bilayer from a knowledge of the corresponding monolayer pressure-area isotherms.