For cells to function properly, membrane proteins must be able to diffuse within biological membranes. The functions of these membrane proteins depend on their position and also on protein-protein and protein-lipid interactions. However, so far, it has not been possible to study simultaneously the structure and dynamics of biological membranes. Here, we show that the motion of unlabelled membrane proteins can be characterized using high-speed atomic force microscopy. We find that the molecules of outer membrane protein F (OmpF) are widely distributed in the membrane as a result of diffusion-limited aggregation, and while the overall protein motion scales roughly with the local density of proteins in the membrane, individual protein molecules can also diffuse freely or become trapped by protein-protein interactions. Using these measurements, and the results of molecular dynamics simulations, we determine an interaction potential map and an interaction pathway for a membrane protein, which should provide new insights into the connection between the structures of individual proteins and the structures and dynamics of supramolecular membranes.