In this chapter we have identified the lipid architecture and the parameter range where the lipids self-assemble in fluid planar bilayer. The input parameters of the model can be mapped into the macroscopic measurable values calculating the mechanical proper-ties of the planar membrane. We calculate at first the thickness profile of the membrane and the diffusivity of lipids to set the length and time scale of the system. Succes-sively, we have shown some relevant energetic contributions in shape deformation of bilayers. These values will be used in the next chapters as reference to study the local modification around the fusion objects and to map the continuous model calculations.
As a novel application we have used our solvent-free coarse-grained model to calculate the stiffness of liposomes and compare the results with finite elements calculations and experiments. We have shown the dependence of the final measurements on the indeter-mination of the environmental conditions and achieved a good qualitative agreement with the experiments.
conclusion
CHAPTER 4. MECHANICAL AND PHASE PROPERTIES OF PLANAR MEMBRANES
Chapter 5
stalk dynamics and morphology
The stalk is a lipid bridge between two lipid membranes and a fundamental inter-mediate structure in the process of membrane fusion. The formation and evolution of the stalk is a collective phenomenon, which involves the interaction and change of conformation of many lipids.
We use our coarse-grained solvent-free model to simulate a stalk between two op-posed membranes. The absence of solvent molecules avoids the non trivial problem of re-equilibrating the number of solvent molecules between the two bilayers present in ex-plicit solvent models and the hydration repulsion can be controlled via the interactions between the lipid head groups. Depending on the type and architecture of lipids we can change the stability and morphology of the stalk. Circular stalks are metastable and we calculate the average density profile and fluctuations of their radius. Small hydrophobic chains (oil) are added in the hydrophobic layer of the membrane prefer-entially go to the lower and upper ends of the stalk, where the membrane is slightly indented and the hydrophobic tails stretch to uniformly fill the space, and relax the total tension. Linear stalks formed by more asymmetric lipids are stable and span the simulation box over the periodic boundary conditions and we calculate their stiffness.
We compare the thickness profile and the bilayer repulsion with different models and experimental data. To compare the solvent-free model with the explicit solvent mod-els and experiments we change the head group interactions to mimic the hydration repulsion between the membranes. We estimate the bilayer repulsion depending on the hydration and lateral tension.
5.1 introduction
The adhesion and fusion between bilayer membranes gives rise to the mixing of lipids between the neighboring leaflets [Markvoort and Marrink (2011); Stiasny and Heinz (2004); Kozlovskyet al.(2004)]. This process involves the building of a lipid bridge, called stalk, where the lipids of the two opposed leaflets mix with each other.
The shape, the free-energy cost and stability and the mechanical properties of the stalk strongly depend on the lipid composition. We identify two lipid architectures that correspond to the inverted hexagonal or lamellar phase in the self-assembled aggregates (see fig:4.2). The second architecture has just one bead more in the head-group, this suggest us to call the first lipid type PE and the second PC recalling the different head-groups of the lipid membranes that correspond to the same self-assembled phases.
To create a stalk we prepare two opposed bilayers and induce a stalk using a cylindrical
Martini simulations
CHAPTER 5. STALK DYNAMICS AND MORPHOLOGY harmonic potential:
Uextexternal harmonic potential, (xext, yext) is the position of external potential,is the energy
prefactor. Uext= In case of PE lipid membranes the stalk, after eliminating the external potential, elongates linearly until the two opposed caps fuse together and the stalk expands along the whole box length (see fig:5.3). In case of a PC lipid membrane the stalk preserves the circular shape induced by the external field (see fig:5.4).
We develop two methods to describe the two stalk morphologies making use of the particular symmetry of the two stalks. In the case of PE membranes we study shape fluctuations reconstructing the linear shape of the stalk. In the case of PC membranes we construct the torus that at best envelop the hour glass shape of the stalk. The position of the center of mass of the stalk and shape fluctuations give us important information about the diffusion and the stiffness of the stalk.
We calculate the thickness profile in different models and compare the characteristic sizes of the stalk with the experiment. We associate profiles with similar hydration level that we quantify by the width of the water layer. In a solvent-free model the hydration level is represented by rescaling the virial coefficient of the head-group in-teractions, vBB. This virial coefficient changes effectively the interaction with the implicit water molecules and hence the hydration between the two bilayers. We show how the hydration layer works as parameter for the transition between the lamellar to the inverted hexagonal phase in experiments, explicit and implicit solvent models.
We quantify the energy change connected with the variation of vBB studying the bilayer repulsion between the two leaflets [Leikinet al. (1993); Rand and Parsegian (1989); Kozlovet al.(1994); McIntosh and S.A.Simon (1994); Rand et al.(1988)].We use the same method to calculate the bilayer repulsion between membrane with dif-ferent lateral tensions.
Between two opposed membranes stalk and pore formation are two competing pro-cesses that depend on the lateral tension and hydration. We observe that in the case of stalk formation preceding the pore formation the two bilayers fuse.