Small scale membrane mechanics.

Large scale changes to lipid bilayer shapes are well represented by the Helfrich model. However, there are membrane processes that take place at smaller length scales that this model cannot address. In this work, we present a one-dimensional continuum model that captures the mechanics of the lipid bilayer membrane at the length scale of the lipids themselves. The model is developed using the Cosserat theory of surfaces with lipid orientation, or 'tilt', as the fundamental degree of freedom. The Helfrich model can be recovered as a special case when the curvatures are small and the lipid tilt is everywhere zero. We use the tilt model to study local membrane deformations in response to a protein inclusion. Parameter estimates and boundary conditions are obtained from a coarse-grained molecular model using dissipative particle dynamics (DPD) to capture the same phenomenon. The continuum model is able to reproduce the membrane bending, stretch and lipid tilt as seen in the DPD model. The lipid tilt angle relaxes to the bulk tilt angle within 5-6 nm from the protein inclusion. Importantly, for large tilt gradients induced by the proteins, the tilt energy contribution is larger than the bending energy contribution. Thus, the continuum model of tilt accurately captures behaviors at length scales shorter than the membrane thickness.

Robust driving forces for transmembrane helix packing.

The packing structures of transmembrane helices are traditionally attributed to patterns in residues along the contact surface. In this view, besides keeping the helices confined in the membrane, the bilayer has only a minor effect on the helices structure. Here, we use two different approaches to show that the lipid environment has a crucial effect in determining the cross-angle distribution of packed helices. We analyzed structural data of a membrane proteins database. We show that the distribution of cross angles of helix pairs in this database is statistically indistinguishable from the cross-angle distribution of two noninteracting helices imbedded in the membrane. These results suggest that the cross angle is, to a large extent, determined by the tilt angle of the individual helices. We test this hypothesis using molecular simulations of a coarse-grained model that contains no specific residue interactions. These simulations reproduce the same cross-angle distribution as found in the database. As the tilt angle of a helix is dominated by hydrophobic mismatch between the protein and surrounding lipids, our results indicate that hydrophobic mismatch is the dominant factor guiding the transmembrane helix packing. Other short-range forces might then fine-tune the structure to its final configuration.

Molecular simulation of the DMPC-cholesterol phase diagram.

In this paper, we present a coarse-grained model of a hydrated saturated phospholipid bilayer (dimyristoylphosphatidylcholine, DMPC) containing cholesterol that we study using a hybrid dissipative particle dynamics-Monte Carlo method. This approach allows us to reach the time and length scales necessary to study structural and mechanical properties of the bilayer at various temperatures and cholesterol concentrations. The properties studied are the area per lipid, condensation, bilayer thickness, tail order parameters, bending modulus, and area compressibility. Our model quantitatively reproduces most of the experimental effects of cholesterol on these properties and reproduces the main features of the experimental phase and structure diagrams. We also present all-atom simulation results of the system and use these results to further validate the structure of our coarse-grained bilayer. On the basis of the changes in structural properties, we propose a temperature-composition structure diagram, which we compare with the experimental phase and structure diagrams. Attention is paid to the reliability and interpretation of the model and simulation method and of the different experimental techniques. The lateral organization of cholesterol in the bilayer is discussed.