Using molecular simulations to parameterize discrete models of protein movement in the membrane

The work presented in this thesis centres on the development of a work-flow in which coarse-grained molecular dynamics (MD) simulations of a planar phospholipid bilayer, containing membrane proteins, is used to parameterize a larger-scale simplified bilayer model. Using this work-flow, repeat simulations and simulations of larger systems are possible, better enabling the calculation of bulk statistics for the system. The larger-scale simulations can be run on commercial hardware, once the initial parameterization has been performed.
In the simplified representation, each protein was initially only represented by the position of its centre of mass and later with the inclusion of its orientation. The membrane protein used throughout most of this work was the bacterial outer membrane protein NanC, a member of the KdgM family of proteins. To parameterize the motion and interaction of proteins using MD, the potential of mean force (PMF) for the pairwise association of two proteins in a bilayer was calculated for a variety of orientational combinations, using a modified umbrella sampling procedure. The relative orientations chosen represented extreme examples of the contact regimes between the two proteins: they approximately corresponded to maxima and minima of the solvent inaccessible surface area, calculated when the proteins were in contact. These PMFs showed that there was a correlation between the buried surface area and the depth of the potential well in the PMF; this is something that, to date, has only been observed in these relatively-'featureless' membrane proteins (but is seen in globular proteins), where the effect of the interactions with lipids in the bilayer plays a larger role. Features in the PMF were observed that resulted from the preferential organization of lipids in the region between the two proteins. These features were small wells in the PMF, which occurred at protein separations that corresponded to the intervening lipids being optimally packed between the proteins. This result further highlighted the role that the lipids in the bilayer played in the interaction between the NanC proteins.
The simplified bilayer model was parameterized using the PMFs and the relationship between buried surface area and potential well depth. The initial model included only the proteins' positions. A series of Monte Carlo simulations were performed in order to compare the system behaviour to that of an equivalent MD simulation. Initially, the MD simulation and our parameterized model did not show a good agreement, so a Monte Carlo scheme that incorporated cluster-based movements was implemented. The agreement between the MD simulation and the simulations of our model using the cluster-based scheme, when comparing diffusive and clustering behaviour, was good. Including the orientation-dependent features of the parameterization resulted in the emergence of behaviour that was not clearly detectable in the MD simulation.
Finally, attempts were made to parameterize the model using PMFs for the association of rhodopsin from the literature. Rhodopsin was a much more complicated protein to represent: there was not a clear correlation between surface area and the features of the PMF, and the geometry of the interaction between two rhodopsins was more complicated. Simulations of the 'rows-of-dimers' system of rhodopsin, observed in disc membranes, was not entirely well represented by the model; for such a closely packed system, where the number of lipids is much closer to the number of proteins, the use of an implicit-lipid model meant that the effect of the reduced lipid mobility was not adequately captured. However, the model accurately captures the orientational composition of the system. Future work should be focussed on incorporating explicit representations of the lipid in the system so that the behaviour of close-packed systems are better represented.

Advisor: Osborne, J
Gavaghan, D
Sansom, M