Time series of white-light pictures of the sunspot NOAA 7522, obtained at the Swedish Vacuum Solar Telescope (La Palma), were analyzed to study the proper motion of bright features in sunspots. For the first time, its relation with the dark nuclei present in the umbra is investigated. The bright features are visible in the penumbra as bright grains moving into the umbra. A few of them cross the penumbra/umbra boundary, becoming peripheral umbral dots, which move farther into the umbra until they meet dark nuclei, braking their motion and disappearing. In some cases the encounter with a dark nucleus produces a brightening of the central umbral dots placed on the opposite side of the nucleus. A similar phenomenon is observed in the grains of a faint light bridge, when bright penumbral grains collide with one of the edges of the bridge.