Coarse grained simulations
Membranes are important in all organisms as the plasma membrane of cells forms the protective barrier between the cytosol and the exterior. Membranes, which constitute mainly of lipids and proteins, exhibit interesting phenomena on a wide range of scales. For each problem, the appropriate modeling technique should be chosen.
The main constituent of these membranes are phospholipids, which are aggregated in a bilayer. A nice review of simulations using various techniques is given in [Curr. Top. Membr. in Membrane Fusion 68, 259-294 (2011)]. We show that even using a relatively simple model for lipids many properties of such bilayers can be elucidated, like their self-assembly, the spontaneous formation of vesicles, the fusion of such vesicles as well as the occurrence of diverse vesicle shapes and different fission pathways.
Our coarse grained (CG) lipids are based on lipids of the glycerophospholipids class, dipalmitoylphosphatidyl-choline (DPPC) being a typical example. In our CG model (extensively described in [A.J. Markvoort, et al., J. Phys. Chem. B, 109, 22649-22654 (2005)]) three types of coarse grained particles are used to describe the chemically relevant groups in phospholipids and water. The apolar tails of the phospholipids are represented by T particles (green), whereas the polar head groups are represented by H particles (white) and water by W particles (blue). The interactions between the particles are described by truncated shifted Lennard-Jones, harmonic bond, and angle potentials. For all simulations we use the in-house developed molecular dynamics PumMa code.
Spontaneous vesicle formation
When 128 lipids are dispersed in a simulation box which is filled for the remaining part with water, the lipids spontaneously aggregate into a bilayer.
When 512 lipids are dispersed in a larger water box, they spontaneously form a vesicle. Lipids dispersed in water (far left) first form micelles and bicelles, which aggregate into a larger bilayer (center) that, once sufficiently large, starts to curl and finally closes to a vesicle (far right). This process follows the pathway as suggested by Leng et al. from experimental studies.
Such a vesicle can also be formed starting from a 'periodic' bilayer that has been placed in a larger water box. In this way larger vesicles can be made.
Many different hypotheses on the molecular mechanisms of vesicle fusion exist. Whereas these mechanisms cannot be readily asserted experimentally, our simulations show the fusion at a molecular level. When two spherical vesicles are placed next to each other, the vesicles come together by random Brownian motion. The outer monolayers fuse and the two inner monolayers form a hemifusion diaphragm. When this hemifusion diaphragm breaks fusion is reached.
The fusion process follows various discrete stages. The advantage of simulations is that they allow to zoom in on these details, both in time and in space, in order to study different stages in the fusion process in detail. For example, initial contact and stalk formation [J. Phys. Chem. B 110, 13212-13219 (2006) ] or anisotropic stalk expansion.
Catalogue of vesicle shapes
When the two leaflets of the bilayer have an equal composition, the membrane preferentially forms a flat sheet or a spherical vesicle. However, a difference between the composition of the two leaflets or a difference in vesicle interior and exterior may result in a curved bilayer or in a wide variety of vesicle shapes.
To introduce asymmetry, two types of lipids are used with slightly different headgroups. Compared to the original lipid, one lipid has a slightly higher and the other lipid a slightly lower water-headgroup interaction (given as a percentage change from the original parameters), making it slightly more and less hydrophilic, respectively.
In a bilayer, domains of such lipids with small differences in this water-headgroup interaction already result in bilayers with a notable spontaneous curvature.
Similarly, a spontaneous curvature in the membrane of a vesicle has a large effect on the vesicle shape. By only changing the water-headgroup interaction strengths, a vesicle can adopt a wide variety of vesicle shapes. These shapes are comparable with theoretically predicted shapes from energy minimization of continuous curves and with experimentally shown vesicle shapes [J. Phys. Chem. B 110, 22780-22785 (2006), J. Phys. Chem. B 113, 8731-8737 (2009)].
When taking the lipids with the more hydrophilic headgroups in the outer monolayer and the original lipids in the inner monolayer (instead of the less hydrophilic ones), the vesicle reshapes to a budded form as well. However, as the neck is in this case less stable, the vesicle is now able to complete fission.
A completely different way of fission can be reached by using two types of lipids that phase separate. However, the changes in the interaction parameters need to be much larger than for the above pathway, since this mechanism constitutes a local mechanism only contributed to by the lipids at the interface, whereas in the above mechanism all lipids contribute [J. Phys. Chem. B 111, 5719-5725 (2007)].
As both fusion and fission have been observed, the vesicle fusion and vesicle fission pathways can be compared. Although vesicle fusion and fission are each others inverse processes, their pathways are not simply each others reverse, as can be seen from the schematically depicted pathways below. Where fusion proceeds via stalk expansion and a hemifusion diaphragm (perpendicular to symmetry axis), fission proceeds via a narrow neck (parallel to symmetry axis). This can also explain why fusion is often leaky and fission is not.
A third fission mechanism is formed by the uptake of newly added lipids in an existing vesicle. This new material, when externally added, is taken up in the outer leaflet of the bilayer. When this uptake is faster than the relaxation by means of flip-flop, the outer leaflet grows faster than the inner monolayer. The resulting area difference is then relaxed by a deformation of the vesicle, which ultimately results in fission.
A combined experimental and simulation study showed that this mechanism explains for the so called Matrix Effect in vesicle replication of fatty acid vesicles [Biophys. J. 99, 1520-1528 (2010)].
Apart from lipids alone, we are also interested in the role of membrane proteins. Because of the increased length and time scales reachable with coarse graining, we like to use for this coarse grained models as well. In this way we for instance studied hydrophobic matching, protein aggregation, and their effect of proteins on flip flop as well as membrane fusion using simple model proteins [J. Phys. Chem. B 110, 13614-13623 (2006)] and a more detailed model [Int. J. Mol. Sci. 11, 2393-2420 (2010)].
Encapsulation of solute molecules in nano and micrometer scale liposomes composed of fatty acids or phospholipids is of interest for applications ranging from drug delivery, food technology, (biomimetic) microreactors, the origin of life/protocells and artificial living cells, to the fundamental biophysical and molecular biological study of individual biomolecules or protein networks. For many of these applications a predictable loading of the vesicles with a small number of the molecules of interest is essential, as well as a high efficiency with which those target molecules are encapsulated. Intriguingly, experimental studies on encapsulation of macromolecules by liposomes have showed that the concentration of entrapped material does not always correspond to the concentration in the buffer. Often the concentration of entrapped macromolecules is below the buffer concentration, whereas for other systems an overall enhanced encapsulation of proteins and RNA in vesicle formation has been observed. We have used our coarse grained model to elucidate the underlying molecular mechanisms of encapsulation during vesicle formation [J. Phys. Chem. B 116, 12677-12683 (2012)].
The more different chemical groups present in the system of interest, the more coarse grained particle types are necessary. To be able to perform a molecular dynamics simulation, the interactions between also these particle types need to be specified. Therefore, we are also working on a multi-scale approach to derive interactions between coarse grained particles directly from underlying atomistic simulations [J. Phys. Chem. B 115, 10001-10012 (2011)].