PMC

Integration of velocity input by continuous attractor networks built from interacting excitatory and inhibitory neurons can generate grid firing fields. When the networks receive a theta modulated input they generate gamma frequency output that is modulated at theta frequency. A spatial input is required to oppose drift in the grid representation. Data are from Pastoll et al. ().

Spike rasters for E cells (red) and I cells (blue) during two theta cycles (grey). The excitatory synaptic input to a representative I cell is illustrated below. Note that a substantial residual inward current (blue shading) is maintained during the phase of the theta oscillation when spike activity of excitatory cells is reduced. The residual current enables the bump of activity to be maintained across theta cycles. Data are from Pastoll et al. () and Solanka et al. ().

A, schematic organisation of an E–I network with additional random place field inputs to each interneuron (left). Example firing fields of I cells (middle) and E cells (right) are shown adjacent to the schematised neurons. B, histograms of the spatial sparsity (upper) and gridness score (lower) for E–I networks simulated as in A. Note that most interneurons and many excitatory cells have grid scores <0.5. Data are from Solanka et al. . r in “r(Hz)” is spike rate.

A, In single bump models grid firing of excitatory cells can be generated by synaptic profiles that produce either surround excitation or surround inhibition. The surround connectivity is strongest for connections to neurons at a distance of about one‐half the width of the sheet. Each neuron makes divergent connections to many target neurons, and receives convergent input from many presynaptic neurons. B, In multi‐bump networks the strongest connections are onto neurons at a much shorter distance relative to the size of the sheet. The upper graphs plot synaptic strength as a function of position in the neural sheet, which is given a width of one. The plots below schematise the resulting E–I connectivity, illustrate the organisation of activity in the neural sheet and the organisation of excitatory cell activity in three dimensions. The connectivity profiles shown for the multi‐bump models are based on networks containing only inhibitory neurons, with either surround inhibition (Burak & Fiete, ) or local inhibition (Couey et al. ). The networks could be considered as having dedicated interneurons receiving input from each excitatory neuron.