Requirements for a single cell mechanism of entorhinal "grid field" activity: role of dendritic oscillators and coupling

The responses of rat medial entorhinal cortical neurons form characteristic grid patterns as a function of the animal’s position. A recent model of grid fields proposes a mechanism based on intrinsic single cell properties. It relies on interference patterns emerging from multiple distinct and independent oscillations maintained in the dendritic tree of the cell. Here we examine the requirements necessary to implement this idealized mechanism in a biophysically realistic model. We find that appropriate grid field-formation by a single cell is exquisitely sensitive to intra-dendritic interactions. Mathematical analysis shows how these effects depend on properties of the dendritic oscillators and the (active) membrane segments that connect them. We provide requirements on the ion channel distributions that would be necessary for grid-fields. We implement these requirements in a compartmental model of a spiny stellate cell. We find that with realistic cell properties the intra-dendritic coupling is insufficiently weak to maintain grid field activity. Rather, the cell acts as a single oscillator as opposed to maintaining several independent oscillators. This work gives explicit requirements for a single cell implementation of grid-field activity and hints at a possible circuit level origin for grid pattern formation