Sen, R.; Posani, L.; Medoff, A.; Zhang, B.; Abbott, L.; Axel, R.; Fusi, S.

Navigation requires the brain to encode spatial relationships that support extrapolation from explored to unexplored regions of space. We identified a novel neural code for space in the mouse medial frontal cortex (mFC) that is well suited for this form of spatial generalization. Using calcium imaging of excitatory neurons in mFC, hippocampus (dorsal CA1), and lateroventral orbitofrontal cortex (lvOFC) as mice explored a square arena with landmarks, we found that mFC activity supports extrapolation. Linear regression of the animal's x or y coordinates trained in one region of the arena generalized to a completely different region. This property was observed in mFC but not in dCA1 or lvOFC. A model in which neurons encode the squared distance from the animal to multiple landmarks explains several properties of the geometry of the mFC representation, including extrapolation. The neural map that we observed in the frontal cortex may provide a basis for vector computation in navigation and complex route planning.