The preferred firing direction was also calculated by finding the directional bin with the highest average firing rate, and thus can be equated to the mode of the tuning curve. As the mode does not take into account all data points, the analysis in the results section uses the mean firing direction. In order to assess the degree to which the data deviated from the circular mean, resultant vector lengths were calculated on unsmoothed data.
Noise, multisensory integration, and previous response in perceptual disambiguation
In order to calculate the resultant vector length, the circular mean value of the angular data was calculated. This was done by transforming the angular data into vectors. A significant Rayleigh test indicates that the distribution is clustered around a particular direction.
Analysis of HD cell mean firing direction was performed using circular statistics, examining mean values of cells that had been recorded simultaneously, i. All circular analysis was also done using the CircStat Matlab toolbox [ 23 ], with a subset of trials checked by hand, yielding identical values.
Sensory cue integration
In order to analyse the rotation of HD cells between the standard and shifted-light conditions, the circular mean direction of cells in each light-shift trial was subtracted from the circular mean direction of cells in the preceding standard trial, to provide a measure of how far the ensemble rotated. The mean of these two rotations was taken to be the mean ensemble shift for that session. These mean shifts were then subtracted from the predicted angle of shift based on how much the light had rotated to produce absolute deviations from expected rotation.
The mean vector length of absolute deviations for each condition was calculated. The Rayleigh test [ 23 ] was then used to determine whether these absolute mean deviations clustered around a particular direction. Circular inferential statistics [ 23 ] were used to compare absolute mean deviation values against zero the predicted deviation given perfect light-following , using a one-sample test.
The Watson—Williams test the circular analogue of the one-way ANOVA was used to calculate the main effects of circular mean rotation across session. In order to measure the width of the HD tuning curve the firing rate versus HD plot the two sides of the curve were linearized using the method of Taube et al. This was done by selecting by eye a point adjacent to the peak and another point on the curve close to the base, and drawing a line through these that was extrapolated down to the x -axis. The distance between the x -intercepts of the two lines was taken to be the width of the tuning curve.
Once the experiments were finished, the rats were then deeply anaesthetized with isoflurane induction followed by sodium pentobarbital injection. The sections were then mounted and stained with Cresyl violet, and the slides were observed under a DM microscope Leica, UK in order to determine the site of the electrode track, which was verified using a rat brain atlas [ 24 ]. A total of 17 individual HD cells, in eight ensembles of one to three cells in each, were recorded from six rats during 54 sessions of trials.
These 17 HD cells met the inclusion criteria of having a peak firing rate of more than 1. Across all 17 cells, the average peak firing rate was When the light cue was moved, thus generating a conflict between the light and the background cues, cells generally rotated their mean firing direction in the same direction. If multiple cells were recorded in a session, the average mean shift was calculated, because HD cells from a single animal always act in concert and react together to environmental changes [ 1 ].
All subsequent analysis was performed on ensemble data using the CircStat Matlab toolbox. The pattern of response for the cells from the six animals, across the range of conflicts, is shown in figure 3. Separate plots indicate each of the six rats. Each data point represents the mean ensemble shift from one trial to the next.
Thus, there are two points for each light rotation two light shifts per session. The filled circles show rotations in the standard clockwise direction, while open triangles indicate the mean ensemble firing shift during the probe trials, when the landmark was rotated in the anticlockwise direction. These data showed an interesting relationship between the amount of conflict and the responses of the cells figure 3 and table 1. This suggests that all the recorded HD cells rotated their firing by similar amounts when exposed to a given light conflict.
The comparison between the actual mean ensemble shift for each session and the expected shift light rotation is illustrated in figure 4. Figure 4 also shows the mean firing rotation for each session when data from only the last 2 min of each trial were used. It can be seen that the mean firing shift for the latter half of each trial is very similar to the mean firing shift for the entire trial, indicating that the mean firing direction had stabilized within at least the first 2 min of each trial. The table shows the mean shift for all cells per session, expressed both in degrees and as a percentage of the actual light shift.
Plot showing the relationship between the expected shifts in degrees of the HD cells based on the light shift dashed line and the actual mean ensemble firing shift solid line; error bars show s.
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The dotted line represents the actual mean ensemble firing shift using data from only the last 2 min of each trial. This pattern in the data was quantified by calculating the amount of shift in the mean firing direction as a percentage of the actual light rotation table 1. Post hoc tests were then applied to these data, to determine i whether the mean firing direction rotated significantly less than the light and ii rotated significantly more than would be predicted by the background cues i. Calculations for each light rotation i. In comparing the mean firing shift with the unrotated background cues, we found that the mean firing shifts for all sessions were also significantly different from zero table 2 , column 5.
This indicates that on average cells showed some rotation during all sessions and were not controlled completely by either cue. Taken together, these results suggest that the HD cells used a combination of both the light landmark and the background cues at all conflict sizes. The weighting of this information was, however, dependent on the session.
This pattern showed some variation between animals, with cells in rat showing more of a tendency to steadily pull away from the light as conflict increased figure 3. Examination of the pattern of responding in individual rats revealed that this compromise between cues occurred within single cells and was not just a population average. The majority of cells adopted intermediate mean firing directions with the exception of those in rat , which showed a more abrupt switch. The progressively increasing under-rotation of the firing directions may be due to one or both of two factors.
The first is that perhaps the system learned about a steadily increasing uncertainty concerning the location of the light, based on the repeated conflicts with the background cues: in other words, it learned that the light could not be trusted as a reliable indicator of direction, so that the light failed to capture the cells. The other is that perhaps the system always trusted the light, but gradually learned a new association between the light and the directional system.
That is, perhaps the light always captured the cells but the relationship between the light and the cells changed across time. We tested this possibility by introducing probe trials in three animals in which the light was unexpectedly moved in the opposite direction, anticlockwise instead of the usual clockwise. If the cells had simply learned that the light was uncertain had a broad variance , they should under-rotate in these probes just as they under-rotated following rotations in the usual direction.
If they had learned a new mapping, then on these reverse trials they should over-rotate, to maintain the same position with respect to the light. The results of these probes are shown by the open triangles in figure 3. It is evident that in these counter-rotation probes, the cells show the amount of under-rotation that would be predicted on the basis of the data points on either side.
Thus, it seems unlikely that the cells learned a new mapping—rather, they seem to have simply learned a weaker influence. This is discussed further in the next section. Using the same inclusion criteria as for Experiment 1, we selected for analysis a total of five individual HD cells, in four ensembles of one and two cells in each. These five cells were recorded from three rats during seven sessions of 35 trials.
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Across all five cells, the average peak firing rate was The present experiment examined how HD cells responded to a conflict between two cue sets: background cues including self-motion cues and uncontrolled environmental cues versus a highly salient landmark cue. The weighting of the background cues was much less in naive animals, suggesting a contribution of experience to the decision process.
Sensory Cue Integration
In the original study of cue control of HD cells by Taube et al. A number of more recent studies have found similar results [ 3 , 4 , 7 , 11 — 18 ]. A summary of the studies in which responding to a rotated cue has been examined is presented in table 3. Although the amount of under-rotation varies, presumably as a function of other factors like whether and how much the rats were disoriented, or how salient the other cues were, it is nevertheless a highly consistent finding that rotation of a cue rarely results in complete cue-following.
Summary of the literature on cue conflict experiments with HD cells. The additional contribution made by our study is that under-rotation is not constant but varies as a function of the experience of the animal; in animals exposed to repeated and gradually increasing cue conflicts the cells suddenly began to increase their under-rotation, while a similar degree of conflict in naive animals yielded much less undershoot figure 5 , indicating plasticity in the system. It is not fully straightforward to explain these findings.
On the one hand, it seems natural that when there are conflicting cues, a sensory system should respond in a compromise manner, expressing contributions from both sets of cues. On the other hand, how could such integrative dynamics arise from an attractor network? Why does the signal rotate partly towards the cue but then stop? Or conversely, if the competing cues are very strong, fail to drag it at all? The settling of the HD system to a position short of complete reorientation suggests that some kind of plasticity must have occurred, reweighting the visual cue dynamically during the trial, so that by the end it has a slightly different relationship with the HD signal.
In the electronic supplementary material, and also in the companion paper to this one [ 10 ], we explore this issue in detail, outlining how plasticity in an attractor network can lead to integrative behaviour and presenting some simulations of this process. According to our hypothesis, rapid intratrial reweighting of the inputs from the landmark onto the putative ring attractor would result in the activity of the HD network stabilizing at a point intermediate between the two excitatory drives onto the ring the one from the landmark via the visual system and the other from the background cues; electronic supplementary material, figure S2.
The amount of integration would depend on the speed of reorientation, which in turn would depend on the strength of the sensory drive.