Traveling Theta Waves and the Hippocampal Phase Code

Hippocampal place fields form a neuronal map of the spatial environment. In addition, the distance between two place field centers is proportional to the firing phase difference of two place cells with respect to the local theta rhythm. This consistency between spatial distance and theta phase is generally assumed to result from hippocampal phase precession: The firing phase of a place cell decreases with distance traveled in the place field. The rate of phase precession depends on place field width such that the phase range covered in a traversal of a place field is independent of field width. Width-dependent precession rates, however, generally disrupt the consistency between distance and phase differences. In this paper we provide a mathematical theory suggesting that this consistency can only be secured for different place field widths if phase precession starts at a width-dependent phase offset. These offsets are in accordance with the experimentally observed theta wave traveling from the dorsal to the ventral pole of the hippocampus. Furthermore the theory predicts that sequences of place cells with different widths should be ordered according to the end of the place field. The results also hold for considerably nonlinear phase precession profiles.