Distance Mapping and Variable-Specific Geometry of Goal-Relevant Frames in the Retrosplenial Cortex

Goal-directed navigation requires animals to continuously update their position relative to an unmarked goal. Here, we recorded retrosplenial cortex (RSC) activity in freely moving rats during goal-directed navigation and random foraging. We found that RSC neurons encoded the Euclidean distance to the goal, and that this distance representation was selectively biased toward the goal during navigation. This goal-biased signal could not be explained by non-uniform behavioral sampling alone. Task engagement selectively enhanced allocentric head-direction representations anchored to a landmark cue, whereas egocentric boundary-bearing signals showed no detectable task-related enhancement and no detectable goal-centered spatial organization in this task context. Mixed-selective RSC population activity further exhibited variable-specific separability--smoothness geometry: distance-to-goal showed high local smoothness and decoding performance, whereas egocentric boundary bearing showed stronger macro-scale separability. These task-related spatial representations persisted under reduced visual input, suggesting contributions from memory and self-motion signals. Together, these findings indicate that RSC organizes goal-relevant spatial representations in a task-dependent manner.