Grid cell firing patterns may arise from feedback interaction between intrinsic rebound spiking and transverse traveling waves with multiple heading angles

Abstract

This article presents a model using cellular resonance and rebound properties to model grid cells in medial entorhinal cortex. The model simulates the intrinsic resonance properties of single layer II stellate cells with different frequencies due to the hyperpolarization activated cation current (h current). The stellate cells generate rebound spikes after a delay interval that differs for neurons with different resonance frequency. Stellate cells drive inhibitory interneurons to cause rebound from inhibition in an alternate set of stellate cells that drive interneurons to activate the first set of cells. This allows maintenance of activity with cycle skipping of the spiking of cells that matches recent physiological data on theta cycle skipping. The rebound spiking interacts with subthreshold oscillatory input to stellate cells or interneurons regulated by medial septal input and defined relative to the spatial location coded by neurons. The timing of rebound determines whether the network maintains the activity for the same location or shifts to phases of activity representing a different location. Simulations show that spatial firing patterns similar to grid cells can be generated with a range of different resonance frequencies, indicating how grid cells could be generated with low frequencies present in bats and in mice with knockout of the HCN1 subunit of the h current.

Rebound spiking in layer II medial entorhinal cortex stellate cells: Possible mechanism of grid cell function

“…Rebound spikes occur in response to release from hyperpolarizing current pulses and are dependent on the presence of the h-current ( I h , Alonso & Llinás, 1989; Klink & Alonso, 1993; Shay, Boardman, James, & Hasselmo, 2012). Recent models have simulated grid cell firing behaviors using phase interactions between theta oscillations and stellate cell rebound spikes (Hasselmo, 2013; Hasselmo & Shay, 2014). These rebound spiking models are similar to ‘hybrid’ grid cell models (Bush & Burgess, 2014; Navratilova et al, 2012; Schmidt-Hieber & Häusser, 2013) in that the generation of grid cells relies on the combination of recurrent network connectivity and intrinsic cellular properties.…”

“…The input phase preference was dependent on the presence of the h-current and both input and output phases changed with oscillation frequency and magnitude of inhibitory input. Simulation of a network of stellate cells with rebound spiking properties (Izhikevich, 2007) that also includes inhibitory feedback and oscillatory input regulated by the medial septum, showed that spatial periodicity resembling grid cell firing can be produced with rebound spiking (Hasselmo, 2013; Hasselmo & Shay, 2014). These results support the hypothesis that rebound spiking could contribute to the generation of grid cells.…”

If I had a million neurons

“…Another important part of this model is the proposal that neurons might be organized in ring attractors in which the spiking activity loops through a ring of cells (Blair et al, 2008(Blair et al, , 2013Welday et al, 2011). This activity corresponds to a traveling wave, and related models can use traveling waves with different direction and wave number to generate grid cells (Hasselmo and Brandon, 2012;Hasselmo and Shay, 2014). Large-scale population recording would allow analysis of the relative phase of spikes in different cells in medial septum to determine whether activity appears to propagate through neurons as a traveling wave that codes different movement directions.…”

“…Recent modeling suggests that the faster rebound spiking associated with higher resonance frequency could underlie the narrower spacing of grid cell firing fields in dorsal medial entorhinal cortex (Hasselmo, 2013;Hasselmo and Shay, 2014). Largescale recording of identified inhibitory interneurons in the medial entorhinal cortex could determine if they show systematic shifts in phase based on spatial location, and whether their summed input causes faster rebound spiking in stellate cells during higher velocity (Hasselmo, 2013;Hasselmo and Shay, 2014).…”

“…Largescale recording of identified inhibitory interneurons in the medial entorhinal cortex could determine if they show systematic shifts in phase based on spatial location, and whether their summed input causes faster rebound spiking in stellate cells during higher velocity (Hasselmo, 2013;Hasselmo and Shay, 2014). Intracellular recordings of entorhinal grid cells have already been used to evaluate predictions of grid cell models (Domnisoru et al, 2013;Schmidt-Hieber and Hausser, 2013).…”