A model for protein-lipid interactions in bilayer membranes where the proteins are very dilute is extended to higher protein concentration, where appreciable lipid-mediated protein-protein interactions occur. It is found that proteins may change the lipid phase transition temperature. and tat they weaken the phase transition. There exists a critical protein concentration above which the sharp lipid phase transition is abolished. The model also qualitatively reproduces several experimental observations on the physical behavior of bilayers formed from mixtures of cholesterol and phosphatidylcholines.The study of.the interactions between phospholipids and intrinsic membrane proteins in cell membranes and model bio.-logical membranes continues to be an active area of research (1-4). Much of the impetus for these studies comes from the fact that protein-lipid interactions can control some functions of biological membranes. For example, the physical state of the membrane lipids modulates the activity of membrane-bound enzymes (e.g., ref. 5) and affects the lateral distribution of proteins in the membrane surface (6).In an earlier paper (7),. we presented a simple, qualitative model of protein-lipid interactions for the case where the protein lateral concentration was low enough that proteinprotein interactions were negligible. Proteins make up a substantial fraction of the surface area of membranes, though, and it is important to take, this into account theoretically. Therefore, we now extend the model to allow for large protein concentration. These results were presented at the 1979 Annual Meeting of the Biophysical Society (8). The reader is referred to ref. 7 for a more thorough discussion of the basic theory than that presented below, as well as for more.details about other work in the field. DESCRIPTION OF THEORY Basic Idea. The following are the basic steps we have taken in developing the theory. (0) We adopt the point of view that the protein is a rigid body in the membrane. The perturbation it produces in the structure of the membrane smoothly decays away from the protein.(ii) The perturbation is identified with a change in the order of the lipid molecules, and an order parameter is defined as a numerical measure of order. (iii) The order parameter is related to the free energy of the system. (iv) For given conditions, the spatial dependence of the order parameter about the protein is taken to be that which minimizes the free energy of the system. Order Parameter; The order parameter is defined in terms of the geometrical properties of the bilayer. When a phosphatidylcholine bilayer is warmed through its phase transition, its thickness decreases by about 20-30% (9). Because volume changes are comparatively small (10), the surface area varies in a reciprocal manner by about the same amount. We define the order parameter u as u = (Af-A)/(Af-As), . [1] in which Af and A, refer to the molecular areas in the "fluid" and "solid" states at the transition temperature in a bilayer without proteins. Thus, u goe...