  We consider the lateral diffusion of a protein interacting with the curvature
of the membrane. The interaction energy is minimized if the particle is at a
membrane position with a certain curvature that agrees with the spontaneous
curvature of the particle. We employ stochastic simulations that take into
account both the thermal fluctuations of the membrane and the diffusive
behavior of the particle. In this study we neglect the influence of the
particle on the membrane dynamics, thus the membrane dynamics agrees with that
of a freely fluctuating membrane. Overall, we find that this curvature-coupling
substantially enhances the diffusion coefficient. We compare the ratio of the
projected or measured diffusion coefficient and the free intramembrane
diffusion coefficient, which is a parameter of the simulations, with analytical
results that rely on several approximations. We find that the simulations
always lead to a somewhat smaller diffusion coefficient than our analytical
approach. A detailed study of the correlations of the forces acting on the
particle indicates that the diffusing inclusion tries to follow favorable
positions on the membrane, such that forces along the trajectory are on average
smaller than they would be for random particle positions.
