  We investigate membrane-mediated interactions between transmembrane proteins
using coarse-grained models. We compare the effective potential of mean force
(PMF) between two proteins, which are always aligned parallel to the z-axis of
the simulation box, with those PMFs obtained for proteins with fluctuating
orientations. The PMFs are dominated by an oscillatory packing-driven
contribution and a smooth attractive hydrophobic mismatch contribution, which
vanishes if the hydrophobic length of the protein matches the thickness of the
membrane. If protein orientations are allowed to fluctuate, the oscillations
are greatly reduced compared to proteins with fixed orientation. Furthermore,
the hydrophobic mismatch interaction has a smaller range. Finally, we compare
the two-dimensional thickness profiles around two proteins with the predictions
from the elastic theory of two coupled monolayers, and find them to be in very
good agreement.
