Effects of visual inputs on neural dynamics for coding of location and running speed in medial entorhinal cortex

Neuronal representations of spatial location and movement speed in the medial entorhinal cortex during the ‘active’ theta state of the brain are important for memory-guided navigation and rely on visual inputs. However, little is known about how visual inputs change neural dynamics as a function of running speed and time. By manipulating visual inputs in mice, we demonstrate that changes in spatial stability of grid cell firing correlate with changes in a proposed speed signal by local field potential theta frequency. In contrast, visual inputs do not alter the running speed-dependent gain in neuronal firing rates. Moreover, we provide evidence that sensory inputs other than visual inputs can support grid cell firing, though less accurately, in complete darkness. Finally, changes in spatial accuracy of grid cell firing on a 10 s time scale suggest that grid cell firing is a function of velocity signals integrated over past time.


INTRODUCTION 24
The accompanied by a small, yet significant, decrease in the y-intercept (Pearson's R = -0.77, p = 142 0.0002) ( Figure 1J). In contrast, the y-intercept did not change significantly over time during the 143 dark condition (Pearson's R = -0.16, p = 0.5251) ( Figure 1J). In addition to those slow 144 components of change, analyzing the transition points between light and dark conditions, also 145 revealed fast components of changes in slope and y-intercept (Figs. 1K & L). Taken together, 146 transitioning from light to dark resulted in an initial fast decrease in slope followed by a further 147 slow decrease ( Figure 1K). Conversely, transitioning back from dark to light resulted in a fast 148 increase in slope followed by a further slow increase ( Figure 1K). Similarly, the y-intercept 149 showed a fast decrease with the transition from light to dark and a fast increase when 150 transitioning from dark to light. resembled the effects of transitioning from the dark to the light condition. Overall, increased 295 baseline firing rates due to stronger retinal stimulation were ~4 times more likely to be observed 296 than decreases in firing rates. In summary, these data demonstrate that the changes in retinal 297 stimulation due to changes in the amount of spatially non-informative light hitting the retina after 298 transitioning from dark to light and vice versa are sufficient to explain the observed changes in 299 firing rates of MEC neurons. 300

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We next turned to the analysis of the hypothesized speed signal by firing rate, in particular 302 "speed cells" in the MEC (Kropff et al., 2015) and asked if the speed modulation of firing rates in 303 MEC neurons is changed in complete darkness. Speed cell firing has previously been reported 304 to be affected by removal of visual inputs and this change in speed cell firing has been 305 interpreted as a change in the hypothesized speed signal by speed cells, which has further 306 been indicated to underlie changes in grid cell firing and path integration during darkness (Chen 307 et al., 2016; Pérez-Escobar et al., 2016). Importantly, previous studies have compared speed 308 tuning between conditions after normalization across conditions. An alternative approach, 309 however, compares speed tuning between conditions after normalization within conditions. It is 310 important to understand the difference between these two alternative approaches and to 311 understand the implications of these definitions for our interpretation of changes in speed tuning 312 curves. When speed modulation is analyzed after normalization across conditions, any change 313 in external or internal parameters affecting a neuron's mean firing rate will inevitably also affect 314 the speed tuning curve. For instance, a decrease in a neuron's mean firing rate will result in a 315 decrease of both the y-intercept and the slope of that neuron's speed tuning curve. In other 316 words, any change in firing rate will be interpreted as a change in speed modulation. In contrast, 317 analyzing speed modulation after normalization within conditions allows analyzing the speed 318 modulation of firing rate independently from changes in a neuron's mean firing rate. A change in 319 speed modulation would then present itself as a change in the slope of the speed tuning curve. 320 In this study, we do not present evidence for the validity of either approach but argue in favor of 321 the second approach-analyzing changes in speed modulation after normalization within 322 conditions-on the grounds that it is standard in the field to compare tuning of other parameters 323 such as head directional tuning by head direction cells or spatial tuning by place cells, grid cells, 324 or border cells after normalization within conditions. As shown above, the mean firing rates of 325 many neurons are responsive to changes in visual inputs. In addition, many speed cells show   and recorded grid cells during the initial dark session and a following light and dark session (10-390 20 min duration each). We found that spatial periodicity of grid cell firing was low-but not 391 completely eliminated-in the initial dark session and then strongly increased during the first 392 light session ( Figure 6A & B). Interestingly, after this initial orientation, spatial periodicity of grid 393 cell firing decreased again after removal of visual inputs, but remained significantly higher than 394 in the initial dark session (Chi-square = 10.89, p = 0.0043, n = 9 cells from two mice, Friedman 395 test; post hoc tests revealed p < 0.05 comparing initial dark and light, and initial dark and 396 second dark sessions). We next aimed to study the changes in grid cell spatial firing patterns 397 after transitioning from light to dark in more detail. Towards that aim, we recorded grid cells 398 during alternating light/dark epochs, always beginning with a light epoch followed by a dark 399 epoch. 28 cells from six mice were identified as grid cells based on their grid scores (see 400 Methods). To compare spatial firing properties of grid cells between light and dark conditions, 401 we concatenated all light and dark sessions to compute firing rate maps for light and dark 402 conditions. We found that grid cell field centers remained stable, but grid fields appeared wider 403 during complete darkness ( Figure 6C). Quantification of spatial periodicity and spatial precision 404 of grid cell firing by computing grid scores and spatial information (see Methods) revealed a 405 significant decrease in both spatial periodicity and spatial precision of spike locations ( Figure  406 6D & E). However, firing rate maps are the results of integrating firing rates of grid cells over 407 long time periods, thereby measuring only spatial variability, but not spatiotemporal variability of 408 grid cell firing. This distinction becomes important when considering two alternative hypotheses 409 13 with regard to the underlying cause for the observed broadening of grid fields in complete 410 darkness. Grid fields could appear wider because grid cells fire over a longer distance 411 throughout a single grid field traversal. Alternatively, grid fields could appear wider because grid 412 cell firing becomes less stable at the level of single grid field traversals. To distinguish between 413 these two alternative hypotheses, we used two complementary approaches, First, we computed 414 the spatiotemporal correlation between the observed firing rate over time and the firing rate  However, our data also show that the reduction in spatial accuracy of grid cell firing is 578 accompanied by a reduction of accuracy in head directional tuning and a reduction of spatial 579 accuracy of border cell firing (Figure 7). An alternative explanation for the observed reduction of 580 spatial accuracy in grid cell firing during darkness is therefore a reduction of accuracy in head 581 directional signals , boundary signals, or both due to the loss of 582 visual information. Another possibility is that the frequency of theta rhythmic firing of MEC 583 neurons serves as a speed signal that is integrated over longer time scales than previously 584 accounted for by computational models of grid cells (Dannenberg et al., 2019). In that scenario, 585 both the slope of the LFP theta frequency and spatial periodicity of grid cell firing would depend 586 on the history of a velocity signal, which would be consistent with the observed slow saturating 15mW into the medial septum during one or two test recording sessions did not show any 680 effects and we did not continue light delivery for the rest of the study. We did not notice any 681 differences between data recorded before those test stimulations and after those test 682 stimulations and also did not observe any differences between those mice which had and had 683 not been stimulated. No differences were observed between wildtype or transgenic mice. Prior 684 to surgery, mice were housed in Plexiglas cages together with their siblings. Turning that ceiling light off resulted in complete darkness, which was achieved by the following 720 measures. The open field environment was located at the end of the recording room surrounded 721 by three walls with no doors or windows and a thick laser-proof black curtain covering the front 722 side. All LED lights of all electrical equipment were completely shielded with black duck-tape. 723 Tracking of position and head direction of the mouse was achieved by using invisible infrared 724 LEDs. These infrared LEDs were additionally covered with tape to minimize their brightness and 725 preventing a potential spectral bleed into the visible spectrum. The slits around the door to the 726 recording room were covered with black shower curtain material to minimize light leaking into 727 the space within the recording room outside the laser-proof curtain. The computer monitors 728 outside of the curtain were also covered with black shower curtains. Importantly, the 729 experimenter frequently tested for any potential light sources within or light leaks into the space 730 around the open field environment. Recordings only began when it was completely dark from 731 the perspective of the human eye after having adopted to the dark condition for at least 5-min.

Analysis of theta-frequency phase locking. The analysis of theta-frequency phase 818
locking is only valid when LFP theta rhythm is present and a sufficiently large number of spikes 819 is present to estimate the phase distribution. We therefore restricted our analysis to time points 820 where the running speed of the mouse was larger than 5 cm/s and where the sample size was 821 larger than 30 spikes. LFP theta phase and the mean resultant length were computed as 822 described in detail in Dannenberg et al. (2015). In short, the instantaneous LFP theta phase was 823 computed from the Hilbert transform of the LFP signal filtered within the theta-range (6-10 Hz). 824 For higher accuracy, the boundaries of this theta range were adjusted separately for each where is the animal's location, is the ℎ spatial bin, is the number of spatial bins and 861 ( | ) is the probability that = when a spike is observed.
can then be understood 862 as an increase in the amount of order in the distribution of spike locations relative to a 863 completely random (uniform) distribution of spike locations. 864 Spatial correlation. Firing rate map similarities were quantified by the spatial correlation 865 between two firing rate maps. To compute the spatial correlation, the spatial bins of the firing 866 rate maps were transformed into a single vector. The spatial correlation was then computed as 867 the Pearson's correlation coefficient between two of those spatially binned firing rate vectors. firing rates were computed from the next 10 s of data and centered to the spatial bin at the time 876 of the spike. All those firing rate maps were then averaged and smoothed with a Gaussian 877 kernel (SD = 3 cm) to create the spike-triggered firing rate map. To compute the occupancy-878 normalized firing rate as a function of radial distance, the circumferences of circles with 879 increasing radii ranging from zero to 95 cm were overlaid with the spike-triggered firing rate 880 map. For each of those circles, the spatial firing rates of all bins falling on the circle's 881 circumference were then averaged to compute the spatial firing as a function of radial distance. 882

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The location of the first peak in the plot of the firing rate as function of radial distance defined 883 the spacing of the grid cell. 884

Border score and border cells.
A border score was computed as described in 885 detail by Solstad et al. (2008). Border scores ranged from -1 for cells with central firing fields to 886 +1 for cells with firing fields that perfectly aligned with at least one entire wall of the open field 887 environment. Cells with a border score larger than 0.68 were defined as border cells. 888 Computation of head direction firing rate maps. Head directional firing rate maps 889 were generated by dividing the head directional parameter space into six-degree bins and 890 computing the occupancy-normalized firing rate as the total number of spikes falling into that bin 891 divided by the total time the animal spent in that bin. Cells were classified as head direction cells if each of the following was true. First, the inverse of 896 the circular standard deviation was greater than 1 in either the light or the dark condition; 897 second, the p-value of the Rayleigh test was smaller than 0.001 in either the light or the dark 898 condition; third, the peak firing rate in the head directional field was larger than 1 Hz in either the 899 light or the dark condition. showed stable firing across the whole recording session. Cells, whose mean firing rates were 905 below 1-Hz or whose mean firing rates differed more than by a factor of two between the first 906 and second halves of the recording session, were excluded from the analysis. To compare 907 speed modulation of firing rates on the population level, we fitted the data with a quadratic 908 polynomial curve (poly2 fit, MATLAB) and clustered neurons into positively and negatively 909 speed-modulated neurons using hierarchical clustering (clustergram, bioinformatics toolbox, 910

MATLAB). 911
Speed score. The speed score was calculated as the Pearson's product moment 912 correlation between instantaneous firing rate and running speed (Kropff et al., 2015).