Statistical Mechanics of Biological Membranes: Protein Aggregation and Lipid Ordering

It is known that membrane proteins are surrounded by a halo of perturbed lipids. When two protein particles approach one another, their effects are superimposed. This produces a force between them. We construct a Landau model of the membrane order parameter, and use it to calculate the interaction potential. Protein aggregation is predicted to be inherently favorable, though sometimes opposed by a barrier. Because experiments can be done only in large populations of particles, the theory is generalized to that situation. This allows us to calculate the protein chemical potential, and to study how the interaction between two given particles is modified by proximity to others. The protein diffusion equation predicts when the lipid-mediated forces lead to protein precipitation rather than a slight clustering tendency. Next we turn to experimental tests, based on the protein pair correlation function. We describe its relation to the potential and develop a method for measuring it. We find a repulsion between protein particles, extending several nm beyond their apparent edges, and an attraction, extending 10 to 20 nm. The prediction of when precipitation occurs is shown to be at least qualitatively accurate. The preceding analysis is primarily thermodynamic, and thus neglects molecular details. We next study them, discovering that the behavior of our order parameter coincides with that of membrane thickness. On a molecular level, it can be controlled by either lipid conformation or tilt. After deriving the model from statistical mechanics, we find the former to be implausible, suggesting that tilt mediates protein interactions. Lastly, the model is supplemented with a general description of lipid phase transitions. We find that it correctly predicts the phase behavior of protein-lipid systems. It also reveals that the usual analysis underestimates the amount of lipid perturbed by each protein particle. Furthermore, we demonstrate that those lipids are usually constrained between the disordered and ordered states, closer to the former.