  Research on network mechanisms and coding properties of grid cells assume
that the firing rate of a grid cell in each of its fields is the same.
Furthermore, proposed network models predict spatial regularities in the firing
of inhibitory interneurons that are inconsistent with experimental data. In
this paper, by analyzing the response of grid cells recorded from rats during
free navigation, we first show that there are strong variations in the mean
firing rate of the fields of individual grid cells and thus show that the data
is inconsistent with the theoretical models that predict similar peak
magnitudes. We then build a two population excitatory-inhibitory network model
in which sparse spatially selective input to the excitatory cells, presumed to
arise from e.g. salient external stimuli, hippocampus or a combination of both,
leads to the variability in the firing field amplitudes of grid cells. We show
that, when combined with appropriate connectivity between the excitatory and
inhibitory neurons, the variability in the firing field amplitudes of grid
cells results in inhibitory neurons that do not exhibit regular spatial firing,
consistent with experimental data. Finally, we show that even if the spatial
positions of the fields are maintained, variations in the firing rates of the
fields of grid cells are enough to cause remapping of hippocampal cells.
