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. 2014 Apr 2;34(14):5065–5079. doi: 10.1523/JNEUROSCI.4017-13.2014

Figure 3.

Figure 3.

A hybrid OI and CAN model. a, In the absence of rhythmic input from VCOs, uniform feedforward excitatory input to the grid cell network, combined with recurrent inhibitory connectivity, produces a stable network state that is characterized by a single activity bump across the topographically organized sheet of cells. b, The power spectrum of the spike train autocorrelogram averaged across all active cells (i.e., those with mean firing rate >1 Hz over the 10 s simulation) illustrating the lack of rhythmicity in the spike trains during formation and maintenance of the activity bump in the absence of VCO inputs. c, In the hybrid model, spatially tuned rhythmic input from VCOs breaks the input symmetry of uniform feedforward excitation to the grid cell network so that the single, stable activity bump is more rapidly generated in a location dictated by the interference pattern. d, The power spectrum of the spike train autocorrelogram averaged across all active cells illustrating theta rhythmicity in the spike trains during formation and maintenance of the activity bump in the presence of VCO inputs. e, Simulations of the hybrid OI/CAN model in a 2D arena. Input from VCOs determine the location of the activity bump and integrate movement over time, thereby shifting its location according to self-motion. ei, Path taken by the animal (gray) and the location of spikes fired by a typical grid cell (red). eii, Smoothed firing rate map. eiii, Smoothed spatial autocorrelation. eiv, Mean temporal autocorrelation, illustrating that burst-firing frequency is higher than baseline theta frequency (marked by red lines), which suggests that phase precession is present in these simulations. f, Simulations of the hybrid OI/CAN model on a 1D track. fi, Mean grid cell firing rate. fii, Membrane potential of a typical grid cell. fiii, Mean low-frequency (<3 Hz) “ramp” amplitude in the membrane potential. fiv, Mean 5–11 Hz theta amplitude in the membrane potential. fv, Phase of firing relative to LFP theta. fvi, Phase of firing relative to theta-band membrane potential oscillations. g, Group data averaged across 50 independent simulations on the 1D track. gi, Mean increase in theta amplitude (ΔTheta) and ramp depolarization (ΔRamp) inside the grid field. gii, Pooled phase of grid cell firing relative to LFP theta.