11Neuronal representations of spatial location and movement speed are important for a broad 12 range of cognitive functions, including spatial self-localization and memory-guided navigation. 13Two possible speed signals, by theta frequency or by firing rate, have been hypothesized to 14 provide the velocity signal needed for generating the spatially periodic grid cell firing pattern. 15However, which of these speed signals is utilized by the brain remains unknown. By 16 manipulating visual inputs and analyzing the time-courses of evoked changes, we demonstrate 17 that changes in spatial stability of grid cell firing correlate in time with changes in speed coding 18 by local field potential theta frequency. In contrast, visual inputs do not affect speed coding by 19 firing rate even if baseline firing rates are changed. Moreover, grid cells maintain a spatially 20 periodic firing pattern, though less stable, in complete darkness. These data suggest that mice 21 use an oscillatory speed signal to perform path integration. 22 23 ( Supplementary Fig. 1B & C). 126
127Local field potential activity in the MEC primarily reflects the summed activity of synaptic inputs 128 to the MEC, which is likely to be correlated with firing patterns of MEC neurons. Many neurons 129 in the MEC show a theta rhythmic firing pattern and-similarly to the LFP theta frequency-the 130 frequency of theta rhythmic firing increases with running speed (Hinman et al., 2016). In our 131 data set, we identified a total of n = 342 neurons from 14 mice as theta modulated based on 132 their autocorrelograms. We asked if and how theta rhythmic firing in these theta modulated 133 MEC neurons is affected by removing and reinstating all visual inputs. Towards that aim we 134 used an MLE approach (Climer et al., 2015) to fit a model of theta spiking rhythmicity to the 135 observed spike train autocorrelations and identify the frequency and magnitude of theta 136