Head Direction Cell Activity in Mice: Robust Directional Signal Depends on Intact Otolith Organs

Subjects.

All experimental procedures were approved by the Dartmouth College Institutional Animal Care and Use Committee. The present study included wild-type mice [C57BL/6J (The Jackson Laboratory); 20–33 g; n = 7 males] and otoconia-deficient tilted mice homozygous for the Otop1^tlt mutation, which are maintained in the C57BL/6J background strain [B6.CG-Otop1^tlt/J (The Jackson Laboratory); 20–33 g; n = 4 males, 4 females]. All mice were group housed preoperatively and individually housed postoperatively within the same colony room. All mice received food and water ad libitum.

Before surgical and electrophysiological procedures, mice were screened for behavioral anomalies associated with otoconia agenesis as reported previously (Ornitz et al., 1998). Briefly, at ≥11 weeks of age, mice were dropped from a height of 10 cm into a pool of water. C57BL/6J mice immediately resurfaced and swam in an upright position, whereas tilted mice rolled onto their backs and swam underwater in an inverted spiral manner. Tilted mice usually did not resurface, and rescue by the researcher was required to prevent drowning. All tilted mice included in the present study were unable to maintain an upright swimming posture. Several additional tilted mice were excluded from the study before electrophysiological assessment because of their intermediate swimming ability, characterized by an upright swimming posture punctuated by back flips and somersaults.

Electrodes.

A miniature version of the multiple-electrode microdrive designed for rats (Kubie, 1984) was used. Each microdrive was constructed from 10 25-μm insulated nichrome wires (California Fine Wire) encased by a 26 gauge stainless steel cannula. Each wire contacted one gold pin of a modified 11-pin Augat connector. The finished electrode drive provides connections for 10 recording electrodes (tip impedance ∼2 MΩ) and one ground connection. Dental acrylic was used to encase the cannula, wires, and connector and to hold the heads of three drive screws. Tips of the drive screws were threaded into custom-built plastic cuffs, which were later cemented to the skull. These cuffs provided a fixed base into which the screws were advanced to lower the electrodes into the brain.

Surgery.

Mice were anesthetized with ketamine/xylazine (90 and 10 mg/kg, respectively) and positioned in a stereotaxic apparatus (David Kopf Instruments) with bregma and lambda in the same plane. The scalp was retracted, and a hole was drilled above the ADN. Additional holes were drilled in the frontal, parietal, and occipital bones into which jeweler's screws (Lomat Precision) were threaded. These screws were reinforced to the skull with a drop of superglue. The electrode bundle was sterilized and coated (except for the tips) with polyethylene glycol before being positioned dorsal to ADN (0.5 mm posterior, 0.70 mm lateral, 2.0 mm ventral to bregma). With the electrode bundle in position, the drive screw/cuff assemblies were fastened to the skull and jeweler's screws with Grip Cement (Dentsply International). The scalp was sutured around the electrode drive, and the animal was allowed to recover 1 week before recording. An implanted electrode drive is shown in supplemental Figure S1 (available at www.jneurosci.org as supplemental material). Buprenorphine (0.015 mg/kg) was administered as a postoperative analgesic.

Signal processing.

During recording sessions, the electrical signal from each electrode was conducted to a 10-channel head stage containing a unity gain operational amplifier. A flexible 25-conductor cable connected the head stage to an overhead commutator. After the commutator, electrical signals were amplified (P5 series; Grass Instruments) and bandpass filtered (300–10,000 Hz) before auditory and visual display on a loudspeaker and oscilloscope (model 2214; Tektronix). A dual time and amplitude window discriminator (model DDIS-1; BAK Electronics) was used to isolate single-unit spikes from background noise and triggered an electrical pulse during spike detection.

An overhead color video camera (Sony XC-711) was used to monitor the animal's HD at 60 Hz by tracking the position of one red and one green light-emitting diode (LED) attached to the animal's head stage, separated by 11 cm. Signals generated by the window discriminator at the occurrence of single-unit spikes and the concurrent LED positions were acquired by a computer [MacIntosh G4 (Apple Computers)] running Labview software (version 5.0; National Instruments). Data were analyzed with Labview, and graphs were generated with Microsoft Excel.

Apparatus.

A small black cylinder consisting of a wooden platform (40 cm diameter) surrounded by a black wall (40 cm height) contained a white cue card that covered ∼90° of the wall surface. For standard trials, the white cue card was centered at the 9:00 position as viewed by the camera. A black curtain extending from the ceiling to the floor surrounded the arena to discourage animals from using visual cues other than the white cue card. An overhead speaker controlled by a white noise generator was used to discourage the use of auditory cues. The wooden arena floor was cleaned with soap and water between sessions to discourage the use of olfactory cues.

Recording procedure.

Mice were screened daily for HD cells as reported previously (Taube, 1995). Briefly, electrodes were connected to the head stage, and the mouse was placed in the arena. Each of the 10 channels was evaluated for single-unit activity with >2:1 signal-to-noise (S/N) ratio. During visual or audible detection of single-unit spikes, the window discriminator was adjusted to isolate these spikes from background noise. For all cells, only records in which the cellular waveforms were well isolated from background noise throughout the recording session were included in analyses.

The occurrence of spikes was visually assessed for directional modulation, after which cell activity was recorded across several conditions using a protocol developed previously (Fig. 1). This procedure includes monitoring HD cell responses during five consecutive sessions: (1) standard (8 min), white cue card is positioned in the standard position; (2) rotation (8 min), white cue card is rotated 90° clockwise (CW) or counterclockwise (CCW) from the standard location; (3) standard (8 min), white cue card is returned to the standard location; (4) darkness (16 min), white cue card is removed and the overhead lights are extinguished; and (5) standard (8 min), white cue card is replaced at the standard location and lights are turned on. Before the beginning of each session, the mouse was placed in an opaque container and the experimenter slowly carried the animal around the outside of the arena in both directions while rotating the container to disorient the animal. For two cells in C57BL/6J mice, the recording procedure included additional rotation sessions, and the dark/no cue session was only 8 min in length, instead of 16 min. No differences in HD cell activity were observed between these mice and those that were assessed using the procedure described above. Therefore, data obtained during rotation and dark/no cue conditions from these cells were included in all analyses.

Note that, although the overhead lights were extinguished to eliminate the use of visual cues during session 4, the red and green tracking LEDs could have provided a small amount of ambient illumination within the arena. This illumination was presumably unusable for HD perception however, because the black featureless walls of the cylinder did not appear to provide any visual landmark information. This presumption is supported by the results reported here, which are consistent with previous findings with blindfolded rats (Goodridge et al., 1998).

Data analysis.

HD was determined by calculation of the angle between the positions of the anterior (red) and posterior (green) LEDs within a 256 × 256 pixel field at 60 Hz. HD during each 16.667 ms epoch was then sorted into 60 6° bins. The average firing rate as a function of HD within a session was calculated by dividing the total number of spikes by the amount of time the HD was within the limits of each bin. Data from cells that appeared to exhibit an increased firing rate as a function of HD were subjected to Rayleigh's test (Batschelet, 1981) to determine whether firing occurred randomly or clustered in a particular direction. Although a significance criterion of 0.20 ≤ r < 0.40 indicates directional modulation that is significantly different from a random distribution, these cells were not classified as HD cells because their tuning curves did not resemble classical tuning curves of HD cells found in rats. Therefore, we adopted a significance criterion of r ≥ 0.40 for a cell to be considered an HD cell.

Additional cell discharge characteristics were derived from the raw data and triangular model, as reported previously (Taube et al., 1990a). For the triangular model, linear positive and negative slopes were manually fit to the raw data to form a triangle with the x-axis as base. From the triangular model, five characteristics of cell activity were calculated: (1) background firing rate (mean firing rate in all directions 18° away from the x-intercept of each triangle leg); (2) peak triangular firing rate (y-coordinate of the apex of the triangle); (3) triangular preferred firing direction (x-coordinate of the apex of the triangle); (4) directional firing range (the difference, in degrees, between the x-coordinates of the base of triangle legs); and (5) asymmetry score (the left leg slope divided by the absolute value of the right leg slope). The S/N ratio was computed as the peak firing rate divided by the background firing rate.

For comparison with data from the triangular model, observed peak firing rate and preferred direction were also calculated. A Gaussian curve was fit to the raw data, with the Gaussian mean corresponding to the preferred firing direction. A correlation coefficient was then calculated between a Gaussian curve and the raw data, as reported previously (Zhang, 1996).

The anticipatory time interval (ATI) was calculated for each HD cell using a time-shift analysis, as reported previously (Blair and Sharp, 1995). In the original study, cellular activity during angular head velocities (AHVs) >90°/s were used for ATI analyses. However, because bidirectional sampling at >90°/s was insufficient for two C57BL/6J HD cells, this lower limit was reduced to 60°/s. With this limit, all 24 C57BL/6J HD cells were included in the analysis. For tilted mice, the 60°/s lower limit allowed inclusion of eight HD cells (vs six HD cells with the 90°/s limit). Although the mean ATI for C57BL/6J HD cells was not significantly different when using the 60°/s versus 90°/s velocity limit (p = 0.968), it is important to note differences between our methodology and that of previous studies.

Directional information content (IC) was calculated for each cell as reported previously (Stackman and Taube, 1998): IC = Σp_i (λ_i/λ) log₂(λ_i/λ), where p_i is the probability of the head pointing in the ith bin, λ_i is the firing rate when the head is pointed within the ith bin, and λ is the overall mean firing rate of the cell for all bins. An information content value of 0 indicates no relation between HD and firing rate, and a value ≥1 indicates a strong relation between HD and firing rate. In cases in which multiple HD cells were recorded on the same electrode, directional IC scores were not calculated because λ is potentially biased by the spikes of additional cell(s).

To determine the response of a cell to cue card rotations, the cross-correlation between sessions 1 and 2 were calculated as described previously (Taube et al., 1990b). Briefly, the firing-rate/head-direction function for session 1 was shifted clockwise in 6° steps, and the cross-correlation between the curves was recalculated at each step. The angular shift of each cell was defined as the angle at which the cross-correlation was maximal. Previous studies indicate that, when multiple HD cells are simultaneously recorded, the preferred firing directions for all HD cells rotate in register (Taube et al., 1990b). Therefore, for recording sessions during which multiple HD cells were recorded, the average shift of the preferred directions for simultaneously recorded cells was used for statistical calculations.

A firing rate × HD × time analysis was used to plot preferred direction stability throughout a single session. This analysis calculates the average HD and firing rate for bins of 10 consecutive (160 s) samples, for an effective temporal resolution of 16 s. When the firing rate for any bin reaches 75% of the maximum firing rate for all bins within a session, an HD × time point is generated. From the plots of cells that showed a constant preferred direction shift <360° throughout the recording session, a regression line was fit to the HD × time points to quantify the preferred direction drift (degrees) over time (seconds). For plots that showed >360° of drift throughout the session, the plot was divided into time segments, each of which contained a single slope. The preferred direction drift for these cells was calculated as the mean absolute slope across all time segments. To quantify the drift for sessions in which the preferred direction shifted one direction for a portion of a session and then shifted the other direction for another portion of the session, we divided the sessions into primary and secondary portions that corresponded to the individual drifts. The absolute values of the CW and CCW drifts were then calculated, and the mean of these absolute values was used to define the drift of preferred direction for each cell.

The spike train of HD cells generally includes periods of low activity punctuated by periods of high activity that resemble bursts. Because the occurrence of bursts is determined by the animal's HD, the bursts of activity appear nonperiodic and of indefinite duration. Therefore, we developed a measure, referred to as the burst index, to represent the proportion of time during which a cell fired in high-frequency bursts or was inactive relative to the time during which action potentials occurred at a relatively constant rate. For this measure, spikes were sorted into 1 s bins from the beginning to the end of a recording session. The burst index was defined as follows:

where FR represents the mean firing rate over the entire session, and bins_Total represents the total number of bins during the session. Burst index values can range between 0 and 1, with a value of 0 indicating a firing rate that remains near the mean rate for the entire session and a value of 1.0 indicating the cell is bursty and either remains silent or fires near its maximal rate for the entire session.

For all analyses, means are reported along with SEM. Group comparisons were conducted on a personal computer with statistical software (Statview, version 5.0.1; SAS Institute).

Several terms are used in Results to describe HD cell properties. “Signal degradation” indicates that the HD cell provides a less robust representation of direction, as indicated by a reduced Rayleigh's r value calculated from the tuning curve. “Stability” refers to the consistent firing of an HD cell in relation to HD. This stability can occur within or between sessions. “Within-session stability” refers to the ability of a cell to maintain a consistent preferred firing direction throughout a single recording session. “Between-sessions stability” refers to the ability of a cell to reliably represent the same preferred firing direction relative to the environment. A cell becomes unstable when the preferred firing direction of a cell changes over time, which can be classified in one of two different ways: “drift” or “shift.” Drift occurs when the preferred firing direction of a cell gradually and continuously changes within a session. A shift occurs when the preferred firing direction switches rapidly to a new direction within a session or between sessions. The key difference between a drift and a shift is time: a drift occurs continuously, whereas a shift occurs abruptly. The specific conditions in which stability or instability occurred are noted in Results, along with the occurrence of drift or shift. Signal degradation and instability are not mutually exclusive, because within-session instability can lead to signal degradation. However, between-sessions instability does not lead to signal degradation.

Histology.

After electrophysiological recording, mice received an overdose of sodium pentobarbital (150 mg/kg), and electrode tip locations were marked with iron deposited by anodal current (15 μA, 20 s). Mice were killed by transcardial perfusion with normal saline, followed by 10% Formalin. Brains were then postfixed in 10% Formalin containing 2% potassium ferrocyanide for 24–48 h to produce a Prussian blue reaction at electrode tip locations. Brains were removed from Formalin and placed in 20% sucrose for cryoprotection before being sectioned at 50 μm on a cryostat. Brain sections containing ADN were mounted on gelatin-coated microscope slides. Brain tissue was rehydrated before being stained with thionin and then dehydrated and covered with glass before examination under light microscopy. Electrode position in ADN was verified by electrode tracks through ADN and Prussian blue reaction ventral to ADN.

Table 1.

Description of cells recorded from C57BL/6J and otoconia-deficient tilted mice while the electrode tips were located within the dorsoventral bounds of ADN

HD cells

Histological analysis revealed that recording electrodes penetrated the ADN of eight tilted mice. The waveforms of 79 cells were isolated from background noise while the electrode bundle was located between the dorsal and ventral bounds of ADN. The number of cells recorded from the ADN per tilted mouse was not significantly different from control mice (χ²₍₁₎ = 0.726; p > 0.05). Of the 79 ADN cells in tilted mice, nine (11.4%) were classified as HD cells, indicated by a significantly increased firing rate as a function of HD (Rayleigh's r ≥ 0.40). The directional tuning curve of a representative tilted HD cell is depicted in Figure 3B. All nine HD cells were recorded from four mice, and the tuning curves of HD cells not shown in the text are depicted in supplemental Figure S3 (available at www.jneurosci.org as supplemental material). In the other four mice, single-unit activity was recorded while the electrodes were within the dorsoventral bounds of ADN, but none of these cells reached the significance criterion to be classified as HD cells. Additional tuning curves of ADN cells in tilted mice that showed directional modulation, but did not reach the significance criterion to be classified as HD cells, are also illustrated in supplemental Figure S3 (available at www.jneurosci.org as supplemental material). The number of ADN cells that were significantly modulated by HD was lower in tilted mice compared with controls (11.4 vs 22.0%; χ²₍₁₎ = 4.586; p < 0.05). HD cell frequencies for C57BL/6J and tilted mice are described in Table 1. For one cell with significant directional activity during session 1, recording was terminated after loss of significant directional firing during session 2, although the waveform continued to be isolated from background noise. For all other HD cells in tilted mice, recording continued for five sessions and all waveforms were well isolated from background noise.

Bursty cells

In seven of the eight tilted mice, 23 cells that did not reach the Rayleigh's significance criterion for classification as HD cells were subjectively classified as “bursty” cells. These cells fired in bursts with little accommodation, and the bursts did not correspond to a single HD; thus, the average tuning curve of each cell showed a relatively uniform spike distribution (Fig. 4A). These bursts of activity were not periodic but instead appeared to occur at random intervals throughout the recording session, independent of the animal's HD. The pattern of burst activity observed in these nondirectional cells differs from that of unstable C57BL/6J cells in darkness (described below and depicted in Fig. 9D), which showed a unidirectional preferred firing direction drift throughout the recording session. The cell depicted in Figure 4 was recorded as the mouse navigated primarily in a CW direction throughout the recording session, resulting in bursts of activity that also shifted primarily in a CW direction (Fig. 4B). For this cell, bursts occurred during long CW head turns as well as during brief CCW head turns. This burst activity is best exemplified by the firing rate versus time plots in Figure 4C. Compare the activity pattern of the bursty cell (top graph) with the similar type of burst activity for an HD cell (middle graph) and the different pattern seen for a non-HD, non-bursty cell (bottom graph). In particular, note that the bursty cell becomes virtually silent between the prominent bursts of activity. This lack of activity between bursts is distinct from the moderate baseline firing rate of most nondirectional C57BL/6J cells, which showed considerable rate variability but did not cease firing between periods of high firing rates.

Several analyses were conducted to determine whether bursty cells show unique firing characteristics relative to HD and non-directional ADN cells. First, a burst analysis was conducted to determine whether the spike trains of the cells in question included discrete bursts of activity similar to those of HD cells. HD cell spike trains consist of long periods of inactivity, punctuated by bursts of activity with variable frequency and duration that depend on the animal's behavior. To compare spike train features between cell types, we calculated a burst index for each HD and nondirectional cell (see Materials and Methods). For HD cells, the mean burst index was 0.620 ± 0.0327 (range, 0.375–0.915). For nondirectional cells, the mean burst index was 0.017 ± 0.030 (range, 0.000–0.410). To provide a conservative estimate of the number of bursty cells recorded from tilted mice, we adopted a burst index criterion of 0.400. For the 23 tilted cells that were subjectively categorized as bursty, the mean burst index was 0.450 ± 0.042 (range, 0.077–0.752). We eliminated one cell from this analysis because of an abnormally low mean firing rate that resulted in a burst index of 1.000. Of the 22 remaining cells, 13 cells had burst index values greater >0.40. These 13 cells were therefore quantitatively categorized as having bursty spike patterns similar to those of HD cells. Importantly, only 3 nondirectional cells in two of seven C57BL/6J mice versus 13 nondirectional cells in six of eight tilted mice met the quantitative criterion to be classified as bursty. The probability of recording a bursty cell was significantly greater in tilted mice than in C57BL/6J mice (χ²₍₁₎ = 11.046, p < 0.001).

To further determine the spiking characteristics of bursty cells, interspike interval histograms were constructed to determine whether the firing patterns of quantitatively categorized bursty cells were more similar to HD cells or to nondirectional cells. However, no distinguishing characteristics of bursty cells were found compared with other nondirectional cells or to HD cells (supplemental Fig. S4, available at www.jneurosci.org as supplemental material). To determine whether tilted mice locomoted more or less during sessions in which bursty cells were recorded relative to sessions in which HD cells were recorded, we calculated the overall distance the rat traversed during the 8 min recording session. Each session was counted only once, whether single or multiple bursty cells were recorded during the session. For the 11 sessions during which the 13 bursty cells were recorded, the mean overall distance traveled was 1037.94 ± 106.64 cm (range, 651.93–1853.69 cm). During sessions in which HD cells were recorded from tilted mice, the mean total distance traveled was 1333.90 ± 211.06 cm (range, 789.86–2532.00 cm). The total distance traveled by tilted mice was not significantly greater during sessions in which HD cells were recorded relative to those sessions in which bursty cells were recorded (t₍₁₆₎ = 1.39; p = 0.185).

If bursty cells in tilted mice are indeed similar to HD cells, which appear to be part of an attractor network, the bursts of activity of one cell would remain in register with those of other bursty cells. This prediction also suggests that, during head turns, the order of bursts would depend on the direction of head turn. In the present study, two bursty cells were simultaneously recorded from one tilted mouse on two occasions. For each head turn during these sessions, we determined the burst order, as indicated by the onset time for each burst, along with the associated turn direction. For one pair of cells, the animal made eight CW turns and five CCW turns. In every CW turn, the bursts of cell 2 preceded the bursts of cell 1, and, in every CCW turn, the bursts occurred in the reverse order. For the second pair of cells, the animal made four CW turns and five CCW turns. For every CW turn, cell 2 preceded cell 1, and, for every CCW turn, cell 1 preceded cell 2 (Fig. 5). Thus, the fact that these bursty cells remain in register is consistent with the hypothesis that these bursty cells are similar to HD cells in C57BL/6J mice. Furthermore, the consistent order of burst activity found in these cells is similar to that of nondirectional bursty ADN cells in chinchillas after bilateral occlusion of their semicircular canals (Muir et al., 2004; Brown et al., 2006).

Assuming that HD cell activity is based on a ring attractor network, rhythmic burst activity could arise if a network becomes disconnected from its external inputs, and the activity hill drifts around the ring network at a fixed rate. In this scenario, one would expect to observe activity bursts at fixed intervals when recording from a single cell that is part of the disconnected network. The firing rate versus time plot for the bursty cell in Figure 4B appears somewhat rhythmic and would provide support for this view. However, the bursts appear rhythmic because of the timescale used in the graph. When the time intervals between burst onsets are analyzed for this cell, they generally did not occur at fixed intervals and varied more than is apparent from the plot in Figure 4B. The interburst interval of this cell is shown labeled in red on supplemental Figure S5 (available at www.jneurosci.org as supplemental material), which plots the time intervals between burst onsets for the 13 cells classified as bursty. Other bursty cells also did not generate bursts at a particular rhythm. The nonflat curves for each cell indicates that activity bursts did not occur at regular intervals. However, because the semicircular canals, along with proprioceptive and motor efference signals, are still intact in tilted mice, it is possible that, if the nature of their movements is taken into account, especially the directions they are turning their heads, the onset of bursts might be more predictable.

Bursty cells were found in two of the four tilted mice in which HD cells were identified on different days. In fact, one of the bursty cells in a tilted mouse had been recorded on the previous day and showed significant directional activity on the first day of recording. These findings, along with the fact that HD cells and bursty cells were not recorded simultaneously, suggest that the HD system of tilted mice may maintain a stable HD representation during some trials but fails to maintain this stable HD representation across trials. Thus, these bursty ADN cells could be HD cells that failed to maintain directionality across trials, and this failure appears to have resulted from the absence of an otolithic signal. This failure to maintain directionality could be interpreted as perceptual disorientation. However, there was a trend for tilted mice to locomote less during trials in which bursty cells were recorded relative to trials in which HD cells were recorded, and this result is not consistent with previous studies suggesting increased movement after vestibular inactivation (Ossenkopp et al., 1990). Alternatively, it is possible that two types of HD cells exist: one that relies heavily on otolithic input and another that relies predominantly on non-otolithic inputs, although this explanation would have difficulty accounting for the finding that HD and bursty cells were never encountered together during a single recording session. Another possible explanation for the presence of bursty cells in tilted mice is that these cells are similar to C57BL/6J cells, which appeared to be directionally modulated but did not reach the Rayleigh's significance criterion to be classified as HD cells (range, 0.177–0.383). However, the spike trains of only two of these C57BL/6J cells showed discrete bursts of activity, and bursty cells in tilted mice were, in this way, dissimilar to most nondirectional cells of C57BL/6J mice. Table 1 summarizes the percentage of HD and bursty cells found in C57BL/6J and tilted mice.

Table 2.

HD cell firing properties in mice and rats

Background firing rate

The background firing rate for HD cells recorded from C57BL/6J mice was low (mean, 1.83 ± 0.28 spikes/s). In tilted mice, the mean background firing rate was 2.89 ± 0.92 spikes/s. Background firing rates did not differ between C57BL/6J and tilted mice (t₍₃₁₎ = 1.49; p = 0.147).

Peak firing rate

The mean peak firing rates for C57BL/6J and tilted HD cells were 35.17 ± 4.72 spikes/s (range, 4.29–110.77 spikes/s) and 37.24 ± 6.80 spikes/s (range, 11.13–64.40 spikes/s), respectively. Peak firing rates of HD cells of tilted mice did not differ from those of C57BL/6J mice (p > 0.05). Peak firing rates were correlated with background firing rates for both groups: C57BL/6J, r = 0.732, p < 0.0001; tilted, r = 0.670, p < 0.0001. As in previous studies with rats, high and low peak firing rates were observed for different HD cells within the same animal for both groups. The physiological importance of peak rate variability between cells within the same animal is presently unknown. The mean S/N ratios for HD cells in C57BL/6J and tilted mice were 68.58 ± 43.07 and 23.19 ± 8.12, respectively. Although the S/N ratio appears much larger in C57BL/6J than tilted mice, this difference was not statistically significant (p > 0.05).

Directional firing range

The mean directional firing range in C57BL/6J mice was 141.58 ± 8.83°, which, as noted above, is considerably larger than the ∼90° value observed in rats (Taube, 1995). In tilted mice, the mean directional firing range was 124.25 ± 9.23°. The directional firing range of tilted mice did not differ from that of C57BL/6J mice (p > 0.05). Using the firing rate × HD × time analysis to calculate the SD of the HDs when the cell fired ≥75% of its maximum firing rate (as described above), we found no difference between C57BL/6J HD cells (mean, 39.62 ± 4.23°) and tilted HD cells (mean, 35.29 ± 5.92°) (t₍₃₁₎ = 0.554; p = 0.58).

Gaussian r

With the preferred firing direction for each cell centered on the mean, a Gaussian distribution was fit to recorded data. The mean correlation between the data and best-fit Gaussian curve was 0.941 ± 0.011 for C57BL/6J mice and 0.846 ± 0.040 for tilted mice. The Gaussian r for HD curves from tilted mice was significantly lower than for HD curves from C57BL/6J mice (t₍₃₁₎ = 3.15; p = 0.0036).

Directionality measures

The mean directional information content for C57BL/6J HD cells was 0.918 ± 0.103 bits, whereas this measure was 0.519 ± 0.095 bits for tilted mice. Although the information content score was much lower for tilted mice than C57BL/6J mice, this comparison did not quite reach significance (t₍₂₉₎ = 1.999; p = 0.055). An accurate information content score could not be calculated for two HD cells recorded from a tilted mouse because both cells were recorded simultaneously on the same electrode.

Another method for measuring the extent of directional information represented by HD cell activity is to analyze the Rayleigh's r values calculated from tuning curves. Across HD cells that met the directional criterion of Rayleigh's r > 0.4, the mean r values for C57BL/6J and tilted mice were 0.686 ± 0.024 and 0.528 ± 0.020, respectively. Figure 6A (left) plots the distribution of r values across both groups of mice and shows that there was a strong trend for tilted mice to have smaller r values. Together, the Rayleigh r and directional information content analyses suggest that the directional tuning of tilted HD cells is lower than that of C57BL/6J mice.

Anticipatory time interval

As previously reported in the rat ADN, HD cell activity in the mouse ADN usually predicts impending HD during head turns by showing the highest firing rate several milliseconds before the head actually faces the preferred direction of the cell (Fig. 7A) (Blair and Sharp, 1995; Blair et al., 1997; Taube and Muller, 1998). Because of insufficient sampling in both directions that potentially biased the ATI value, one HD cell from a tilted mouse was excluded from the analysis. ATI values for all other HD cells are presented here and in Figure 7B. For C57BL/6J mice, the mean ATI was 39.76 ± 6.63 ms (range, −12.55 to 110.25 ms). In two HD cells, the ATI was negative, indicating that the preferred direction of the cells during head turns lagged behind the average preferred direction of the cells. For one pair of simultaneously recorded cells in tilted mice, session 3 was used for the ATI analysis because within-session stability was greater in session 3 than in session 1. Across tilted HD cells, the mean ATI was 30.48 ± 13.27 ms (range, −16.14 to 92.95 ms), with two HD cells showing negative ATI values. The mean ATI did not differ between C57BL/6J and tilted mice (t₍₃₀₎ = 0.674; p = 0.506), indicating that the ATI does not depend on otolith signals.

Stability within the same day

The preferred firing direction of some C57BL/6J HD cells remained quite stable across standard sessions, whereas other cells showed considerable variability. Stability within the same day was assessed by determining the amount of directional shift in the firing rate versus HD function required to obtain the greatest correlation between sessions 1 and 3 (Fig. 8B) and between sessions 1 and 5 (Fig. 8C). As with the cue rotation analysis, we used the mean preferred firing direction shift of all simultaneously recorded cells for statistical calculations. For C57BL/6J HD cells, the preferred direction showed some variability across standard sessions 1 and 3, with the mean shift of 1.31 ± 7.80° (range, −57 to 60°), and the mean shift between sessions 1 and 5 of −13.50 ± 7.79° (range, −63 to 24°). A paired comparison test reveals that the shift of preferred direction between sessions 1 and 3 was similar to the shift between sessions 1 and 5 (t₍₁₀₎ = 1.303; p = 0.222).

For tilted HD cells that remained significantly directional through session 3, the preferred direction showed some variability between standard sessions 1 and 3 (mean, 21.00 ± 1.73°; range, 18–24°) but was not significantly different compared with C57BL/6J mice (t₍₁₅₎ = 1.366; p = 0.192). For cells that remained stable through session 5, the mean preferred direction shift between sessions 1 and 5 was 56.00 ± 14.42° (range, 36–84°), and a paired comparison test of the shifts between sessions 1 and 3 revealed no significant difference (t₍₂₎ = 2.268; p = 0.152). However, the shift of the preferred direction between session 1 and 5 in tilted HD cells differed from that of C57BL/6J mice (t₍₁₆₎ = 5.204; p < 0.0001). In general, the preferred firing direction of HD cells in C57BL/6J mice appeared to be fairly stable across environmentally similar conditions separated by tens of minutes, but HD cells in tilted mice became less stable over time and recording sessions.

To compare HD cell stability in mice with previously reported values from rats, we computed the absolute value of the deviation in the preferred firing direction between sessions 1 and 3 (an absolute deviation ≠ 0° indicates a CW or CCW deviation from the preferred firing direction in session 1). In rat ADN HD cells, the mean absolute deviation between the first two standard recording sessions was 4.71 ± 1.80° (range, 0–18°) (Taube, 1995) (Table 3). In contrast, C57BL/6J mice showed a mean absolute deviation of 18.85 ± 5.61° (range, 0–60°) and was significantly greater than that of rats (t₍₂₅₎ = 2.475; p = 0.021). Thus, although the mouse HD signal remains relatively stable across recording sessions, the rat HD signal appears to be a more stable representation of actual head direction.

Stability across days

The waveforms of eight C57BL/6J HD cells were isolated from background noise across 2 d. Although the activity of most of these cells was not recorded on both days, all HD cells subjectively appeared to remain directional across both days. The preferred direction of these HD cells remained relatively constant across both days, although a small deviation was present that was similar to the deviation observed between standard sessions recorded on the same day (described above).

HD signal degradation in tilted mice

In general, most C57BL/6J HD cells that were directional in session 1 remained directional throughout all standard sessions, whether the standard sessions occurred on the same day or across days. Exceptions include one HD cell that became nondirectional during session 3 and two HD cells that became nondirectional during session 5. In contrast, most HD cells from tilted mice that were directional in session 1 showed decreased directionality across subsequent recording sessions, despite the fact that the waveforms of the cells remained well isolated with no apparent change in spike amplitude. As a quantitative indicator of this decreased directionality in tilted mice, we computed the Rayleigh's r values from the tuning curves of HD cells recorded during the three standard sessions (Fig. 6A). Across these sessions, the number of HD cells in C57BL/6J mice with significant directional activity for sessions 1, 3, and 5 was 24 of 24 (100%; mean Rayleigh's r = 0.69), 19 of 20 (95%; mean Rayleigh's r = 0.64), and 17 of 19 (89%; mean Rayleigh's r = 0.62), respectively (Fig. 6B). The decrease in the total number of cells recorded across sessions resulted from lost isolation of unit activity. In contrast to C57BL/6J HD cells, a greater percentage of tilted HD cells became nondirectional across sessions. For tilted mice, nine of nine cells (100%; mean Rayleigh's r = 0.53) were directional during session 1, and each successive recording session resulted in a lower percentage of cells remaining directional. For session 3, five of nine cells (56%; mean Rayleigh's r = 0.39) remained directional, and three of eight cells (38%; mean Rayleigh's r = 0.34) remained directional during session 5. Thus, HD cells in tilted mice showed reduced directionality across sessions within the same day relative to HD cells in C57BL/6J mice. Two simultaneously recorded HD cells from C57BL/6J and tilted mice are presented in Figure 9 to illustrate HD signal degradation in tilted mice across sequential sessions.

To determine whether the decreased directionality of HD cells in tilted mice was related to the amount of movement exhibited by the mouse during a recording session, we calculated the total distance traveled during sessions 1, 3, and 5 for C57BL/6J and tilted mice. These measures are plotted in Figure 6C. Although sessions 1 and 5 show less movement in tilted mice, a repeated-measures ANOVA indicated there was no significant difference between C57BL/6J and tilted mice in the amount of total movement across sessions (F_(1,16) = 2.154; p = 0.16) or in the group × session interaction (F_(2,32) = 2.52; p = 0.096). Furthermore, we conducted a correlation analysis to determine whether total distance was associated with the Rayleigh's r value. For C57BL/6J mice, total distance was not well correlated with Rayleigh's r value during session 1 (r = −0.028; p = 0.92), session 3 (r = 0.144; p = 0.55), or session 5 (r = 0.326; p = 0.18). Similarly for tilted mice, total distance traveled was not well correlated with Rayleigh's r values during session 1 (r = 0.019; p = 0.97), session 3 (r = −0.146; p = 0.72), or session 5 (r = 0.349; p = 0.41). Thus, although differences in the amount of movement were observed between C57BL/6J and tilted mice, these differences did not predict the degree of the direction-specific firing of the cell.

In summary, the directional firing of C57BL/6J HD cells remained robust across recording sessions. Furthermore, most HD cells had a preferred firing direction that remained fairly consistent across standard recording sessions within the same day and across days. In contrast, most HD cells in tilted mice became nondirectional over the course of recording. For tilted mouse HD cells that remained directional across sessions, an increasing amount of variation was observed between the preferred direction established during session 1 and that of subsequent recording sessions.

“Visual” versus “nonvisual” HD cells

In rats, ADN HD cells typically remain stable in darkness over time intervals on the order of minutes (Blair and Sharp, 1995; Goodridge et al., 1998). The present results from C57BL/6J mice indicate that some HD cells become unstable in darkness. One possibility is that some HD cells in mice could be influenced primarily by visual afferents, whereas others are influenced primarily by vestibular afferents. However, if there are different HD cell subtypes within the ADN, there is no topological organization to them because both stable and unstable HD cells were recorded throughout the dorsoventral axis of ADN. If “visual” HD cells are influenced primarily by visual information, then these cells would (1) become unstable when visual information is not available and (2) show strong influence of visual cue rotation. Conversely, if “nonvisual” HD cells depend primarily on self-movement information, then these cells should (1) remain stable whether or not visual information is present and (2) may show less influence of cue card rotation. To address these predictions, we evaluated the probability that visual HD cells (cells that responded well to cue card rotation) became unstable in darkness and that nonvisual HD cells remained stable in darkness. This analysis was conducted according to session; therefore, if more than one HD cell was recorded simultaneously, responses for both (or all three) HD cells were averaged to obtain a single value. Although not exclusive, these predictions were observed in the present study, in which 7 of 13 (54%) visual HD cells became unstable in darkness and a greater percentage (5 of 5; 100%) of nonvisual HD cells remained stable in darkness (χ² = 4.41; p < 0.05). Thus, consistent with the hypothesized predominant reliance of some HD cells on visual information, the HD cells that demonstrated good cue control in rotation experiments were more likely to become unstable in dark sessions than were cells that displayed poor cue control. However, a second prediction from the visual versus nonvisual hypothesis is that, when multiple HD cells are simultaneously recorded, a percentage of these cells should become unstable in darkness whereas others should remain directional. This prediction was not observed, because all simultaneously recorded HD cells either remained stable or became unstable during a given recording session, whether in light or darkness. Therefore, the most likely explanation for visual versus nonvisual dependence of some HD cell recording sessions is variation in the spatial information detected and/or perceived by the mouse across recording sessions.

Tilted mice

In tilted mice, only five HD cells had sufficiently stable preferred firing directions at the end of session 3 to enable assessment in the dark/no cue session. The preferred direction of four of these HD cells remained stable throughout session 4. Only one HD cell, which remained stable through session 3, showed extreme instability during darkness and then regained directionality during session 5. For stable HD cells in tilted mice, the mean absolute value of the drift in preferred direction during darkness was 0.015 ± 0.003°/s (range, 0.009–0.021°/s). The absolute value of preferred direction drift did not differ between C57BL/6J and tilted mice (t₍₉₎ = 1.513; p = 0.165). Tilted mice showed a higher percentage of HD cells that remained stable during darkness than did C57BL/6J mice. This greater percentage of stable cells may have resulted from a general reduced stability of HD cells in tilted mice; the HD cells that would have become unstable during darkness may have become unstable in light before assessment during darkness.