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Department of Psychology, Yale University, New Haven, Connecticut 06520-8205
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Blair, Hugh T., Brian W. Lipscomb, and Patricia E. Sharp. Anticipatory time intervals of head-direction cells in the anterior thalamus of the rat: implications for path integration in the head-direction circuit. J. Neurophysiol. 78: 145-159, 1997. Head-direction cells are neurons that signal a rat's directional heading in the horizontal plane. Head-direction cells in the anterior thalamus are anticipatory, so that their firing rate is better correlated with the rat's future head direction than with the present or past head direction. We recorded single-unit activity from head-direction cells in the anterior thalamus of freely moving rats. We measured the time interval by which each individual cell anticipated the rat's future head direction, which we refer to as the cell's anticipatory time interval (ATI). Head-direction cells in the anterior thalamus anticipated the rat's future head direction by an average ATI of ~17 ms. However, different anterior thalamic cells consistently anticipated the future head direction by different ATIs ranging between 0 and 50 ms. We found that the ATI of an anterior thalamic head-direction cell was correlated with several parameters of the cell's directional tuning function. First, cells with long ATIs sometimes appeared to have two peaks in their directional tuning function, whereas cells with short ATIs always had only one peak. Second, the ATI of a cell was negatively correlated with the cell's peak firing rate, so that cells with longer ATIs fired at a slower rate than cells with shorter ATIs. Third, a cell's ATI was correlated with the width of its directional tuning function, so that cells with longer ATIs had broader tuning widths than cells with shorter ATIs. These relationships between a cell's ATI and its directional tuning parameters could not be accounted for by artifactual broadening of the tuning function, which occurs for cells that fire in correlation with the future (rather than present) head direction. We found that when the rat's head is turning, the shape of an anterior thalamic head-direction cell's tuning function changes in a systematic way, becoming taller, narrower, and skewed. This systematic change in the shape of the tuning function may be what causes anterior thalamic cells to effectively anticipate the rat's future head direction. We propose a neural circuit mechanism to account for the firing behavior we have observed in our experiments, and we discuss how this circuit might serve as a functional component of a neural system for path integration of the rat's directional heading.
Head-direction (HD) cells are neurons that signal a rat's directional heading in the horizontal plane (Ranck 1984 Experimental procedures
SUBJECTS AND BEHAVIORAL TRAINING.
The subjects were 10 female Long-Evans rats, weighing 250-300 g at shipping. The animals were housed singly on arrival, and had a 12-h on:off (8:00 AM-8:00 PM) light:dark schedule. After RECORDING CHAMBER.
Recording sessions were conducted in the same cylindrical chamber as the training sessions. The recording environment was exactly the same as described in an earlier study of AHD cells (Blair and Sharp 1995 SURGERY AND DATA COLLECTION.
After behavioral training was completed, rats were deeply anesthetized with pentobarbital sodium, and the anterior thalamus of each hemisphere was implanted with an array of extracellular microelectrodes. A detailed description of the recording electrodes and surgical procedure has been presented elsewhere (Blair and Sharp 1995 CORRECTION FOR SYSTEM TIME DELAYS.
During a recording session, the signals from the electrode wire and the video tracking system traveled to the computer via separate pathways before they both arrived at the computer to be time stamped for storage. Because of the different types of signal processing that occur along these separate pathways in our system, the video tracking signal was always delayed by a constant time value of 15 ms with respect the electrode signal. Therefore a spike event and a position sample that occurred simultaneously did not arrive at the computer to be time stamped at the same time; instead, the position sample was time stamped 15 ms later than the spike event. To correct for this, our software subtracted 15 ms from the time stamp of each position sample. Extensive testing of our system has confirmed that this subtraction procedure accurately brings the position signal into temporal alignment with the electrode signal (Blair and Sharp, unpublished observations).
Data Analysis
DIRECTIONAL TUNING FUNCTIONS.
Each HD cell's directional tuning function was obtained by plotting the firing rate of the cell as a function of the rat's directional heading (Fig. 1A). We computed four parameters of the directional tuning function to describe the basic firing properties of HD cells (Fig. 1B): 1) the preferred firing direction, denoted as D, which indicates the average directional heading in which the cell tends to fire; 2) the peak directional firing rate, denoted as P, which indicates how fast the cell fires when the rat is facing in the cell's preferred direction; 3) the directional tuning width, denoted as W, which indicates the range (i.e., SD) of head directions over which the cell fires; and 4) the background firing rate, denoted as B, which indicates the cell's baseline firing rate when the rat is not facing near the cell's the preferred direction.
TURNING-VELOCITY-DEPENDENT DECOMPOSITION OF THE TUNING FUNCTION.
The standard tuning function of an HD cell plots the firing rate of the cell as a function of the rat's directional heading (see Fig. 1), regardless of the rat's angular head velocity when spikes occur. To examine how the rat's turning behavior influences the activity of an HD cell, we decomposed the cell's tuning function into three different components, corresponding to three different turning conditions. This is done by separating the spike data from the session into three categories-clockwise, counterclockwise, and straight-according to how the animal's head was turning at the moment when each spike occurred. By plotting a separate tuning function for the spikes in each turning category, three new tuning functions are generated: 1) a clockwise tuning function, which includes only spikes that occurred during clockwise head turns; 2) a counterclockwise tuning function, which includes only spikes that occurred during counterclockwise head turns; and 3) a straight tuning function, which includes only spikes that occurred when the head was not turning. The angular velocity of the head was measured by computing the angular difference in the rat's head direction between successive video frames. As explained by Blair and Sharp (1995) DEFINITION OF THE ATI.
It has been reported that the firing rate of HD cells in the anterior thalamus is better correlated with the rat's future head direction than with the rat's present head direction (Blair and Sharp 1995 MEASUREMENT OF THE ATI.
Blair and Sharp (1995) CRITERIA FOR DATA INCLUSION.
It was important to make certain that all recording sessions contained only well-discriminated spikes from a single HD cell. To ensure that this was the case, recording sessions had to meet three criteria for inclusion in the data set. First, spike histograms for the session had to clearly demonstrate that the cell had a refractory period of 1-2 ms. Second, the peak-to-baseline ratio of the directional signal (defined as the ratio P/B, using the parameters of Eq. 1) had to exceed 10/1 (for most sessions the peak-to-baseline ratio was much higher than 10/1, often exceeding 500/1). Third, the peak firing rate (P) of the cell had to exceed 20 Hz (previous studies have shown that anterior thalamic HD cells normally have peak firing rates in the range of 60-80 Hz, so any cell with a peak rate of <20 Hz was considered to be too poorly discriminated for inclusion). Sessions that did not meet these criteria were omitted from the study.
CELL IDENTIFICATION.
A primary aim of this study was to compare the specific tuning properties of different HD cells. Therefore it was absolutely essential to accurately identify when the same cell was being recorded over several sessions, and when a new cell was encountered that had not been recorded before. To determine this, we applied strict criteria for deciding which recording sessions had been performed on the same cell and which recording sessions had been performed on different cells. A pair of consecutive recordings was considered to be from the same cell if and only if the following three criteria were met: 1) the electrode array had not been advanced between the sessions, 2) both of the recordings were made from the same electrode wire, and 3) the preferred firing direction, D, from the two sessions did not differ by >30°. Similarly, a pair of recording sessions was considered to be from different cells if and only if the following two criteria were met: 1) the recordings were made from different electrode wires, and, if the array was advanced by <300 mm between the two recordings from different wires, then it was additionally required that the preferred direction of the cells differ by Cell sample
A total of 33 anterior thalamic HD cells was recorded during 73 recording sessions from 13 hemispheres of 10 rats. Histological examination revealed that most HD cells were localized to the anterodorsdal thalamic nucleus, in agreement with earlier reports on the anatomic distribution of HD cells (Taube 1995 Different anterior thalamic cells have different ATIs
The firing rate of HD cells in the anterior thalamus is better correlated with the rat's future head direction than with the rat's present or past head direction (Blair and Sharp 1995 DISTRIBUTION OF ATIS.
Figure 2A presents a bar graph that illustrates the range of ATI values obtained for different HD cells in our study. The height of each bar represents the ATI value for a single HD cell, averaged over all recording sessions conducted with that cell (with 1 ATI value obtained from each recording session). Bars are arranged from left to right in order of ascending ATI values, and error bars indicate the SE for cells that were recorded over multiple sessions (note that cells recorded for only 1 session do not have error bars). Figure 2 shows that the ATI values for individual cells ranged from a minimum of
ANALYSIS OF VARIANCE.
If it is true that individual anterior thalamic HD cells tend to anticipate the rat's future head direction by their own characteristic time intervals, then two observations should be expected: 1) different HD cells should exhibit different ATI values, and 2) a single HD cell, when recorded over multiple sessions, should exhibit very similar ATI values during each session. In other words, the between-cell variation in ATI values should be relatively large, and the within-cell variation in ATI values should be relatively small. One way of testing this hypothesis is to perform a one-way independent analysis of variance (ANOVA) test, where cell identity is defined as the independent variable and ATI is defined as the dependent variable. However, cells that were recorded for only one session cannot be included in such an ANOVA test, because there is no within-cell variation over sessions for these cells.
SUMMARY OF ATI DATA.
Table 1 summarizes the ATI values and preferred firing directions that were observed during each of the 73 recording sessions in our study. Table 1 also provides a record of how the electrodes were advanced between recording sessions.
CONTROL MEASURES.
Why should different anterior thalamic HD cells have different ATIs? One possibility is that these different ATIs are a functional property of the head-direction circuit, related to how anterior thalamic cells are connected to other cells. If this is true, then an analytic comparison of HD cells with different ATIs might provide insights into the architecture of the head-direction system (see DISCUSSION). Alternatively, it could be that variability in the ATI values of different cells resulted from uncontrolled variables specific to the animal or recording session in which the cell was observed. We conducted several analyses to control for possible influences of other anatomic, behavioral, and physiological variables that may have affected our measurement of the ATI.
Correlation between ATI and directional tuning function parameters
The results of the analyses in the previous section provide evidence that individual HD cells in the anterior thalamus have different ATIs. The varying ATIs of different cells cannot be accounted for by anatomic or behavioral factors. This suggests that the varying ATIs exhibited by different cells may be a functional property of the head-direction circuit. In this section, we analyze how the ATI of an HD cell is correlated with other directional tuning parameters, such as the tuning width and firing rate of the cell. As discussed later, the results of these analyses suggest insights into the circuit properties of the head-direction system.
DECOMPOSITION OF THE DIRECTIONAL TUNING FUNCTION.
As explained in the METHODS section, an HD cell's "standard" tuning function plots the firing rate of the cell as a function of the rat's directional heading, regardless of the rat's angular head velocity when spikes occur. The standard tuning function may be decomposed into three component tuning functions, corresponding to three different turning conditions: 1) a clockwise tuning function, 2) a counterclockwise tuning function, and 3) a straight tuning function. Each of these tuning functions provides a separate description of the directional tuning properties of the cell during a different state of the angular head velocity. Consequently, velocity-dependent influences on HD cell activity can be evaluated by comparing the parameters of the clockwise, counterclockwise, and straight tuning functions.
PEAK DIRECTIONAL FIRING RATE (P).
We define an HD cell's peak directional firing rate, P, as the peak firing rate (in Hz) of the cell's directional tuning curve. We compute the value of P by fitting the cell's directional tuning function to a Gaussian curve (see Eq. 1).3 It has been previously reported that for anterior thalamic HD cells, P is correlated with the angular velocity of head turns, such that the cell fires faster when the rat's head is turning than when the head is still (Blair and Sharp 1995 DIRECTIONAL TUNING WIDTH (W).
We define an HD cell's directional tuning width, W, as the width (in deg) of the cell's tuning function, which indicates the range of head directions over which the cell fires (see METHODS). Here we investigate how the value of W is correlated with the ATI of a cell.
Comparison of tuning widths under different turning conditions
We compared the widths of a cell's directional tuning functions under different turning conditions with the use of a series of paired, two-tailed t-tests. We found that for a given cell, the straight tuning function was broader than the standard tuning function by an average of 0.59 ± 0.32° (SE), a difference that was not quite statistically significant [t(32) = 1.84, P = 0.075]. The width of the clockwise tuning function was significantly narrower than the widths of both the standard [t(32) = 2.82, P = 0.008] and straight [t(32) = 2.65, P = 0.012] tuning functions. Likewise, the counterclockwise tuning width was narrower than both the standard [t(32) = 2.28, P = 0.030] and straight [t(32) = 2.38, P = 0.023] tuning widths. The clockwise and counterclockwise tuning widths did not differ significantly from one another [t(32) = 0.63, P = 0.54]. As explained in the DISCUSSION, this pattern of tuning widths for different turning conditions suggests that the tuning function of an HD cell changes its shape during head turns.
We have analyzed the anticipatory firing properties of HD cells in the anterior thalamus of the rat. We found that anterior thalamic HD cells anticipated the rat's future head direction by different time intervals, and that the ATI of a cell was correlated with the directional tuning parameters of the cell, such as the peak firing rate and directional tuning width. We now discuss the implications of these findings for the structure and function of the head-direction system.
Shape of the tuning function changes during head turns
As explained above (see METHODS), the preferred firing direction of an AHD cell must shift to the left during clockwise turns and to the right during counterclockwise turns. Figure 4 illustrates two possible ways that an AHD cell's tuning function might shift during head turns. The first possibility (Fig. 4A) is that the tuning peak might retain the same shape at all times, regardless of whether the head is turning or not. When the head is not turning, the peak would remain centered over the cell's preferred firing direction
Neural circuit for anticipatory firing
Figure 5 illustrates a hypothetical circuit to explain how anterior thalamic HD cells might show the firing properties we have reported in this study. The circuit contains two different types of HD cells: 1) AHD cells, which are assumed to possess the firing properties of anterior thalamic neurons that we have described in this study, and 2) turn-modulated HD (TMHD) cells, which are HD cells that fire faster when the rat's head turns in one direction and slower when the head turns in the other direction. There are two types of TMHD cells in the circuit: clockwise TMHD cells fire faster during clockwise turns and slower during counterclockwise turns, and counterclockwise TMHD cells behave in the opposite manner. Neurons that behave like TMHD cells have been observed in two brain regions that project strongly to the anterior thalamus: the postsubiculum (Markus et al. 1990
FUNCTIONAL CHARACTERISTICS.
Anticipatory cells with long ATIs. Figure 5A shows a circuit with three layers of cells: the top layer consists of clockwise TMHD cells, the bottom layer consists of counterclockwise TMHD cells, and the middle layer consists of AHD cells with long ATI values. In each layer there is one shaded cell, whose tuning curve is plotted in the graph at left. The shaded AHD cell in the center layer receives input from the shaded TMHD cells in the top and bottom layers. Consequently, the tuning function of the AHD cell in the center layer has two distinct peaks: the left peak is generated by input from the clockwise TMHD cell in the top layer, and the right peak is generated by input from the counterclockwise TMHD cell in the bottom layer. When the rat is not turning its head, both peaks of the AHD cell are of equal height. If the rat turns its head clockwise (i.e., to the right), then the left peak of the AHD cell grows and the right peak shrinks, which causes the preferred direction of the AHD cell to shift to the left during clockwise turns. Alternatively, if the rat turns its head counterclockwise (i.e., to the left), then the right peak of the AHD cell grows and the left peak shrinks, which causes the preferred direction of the AHD cell to shift to the right during counterclockwise turns. In summary, the two peaks in the AHD cell's tuning function change their relative sizes during head turns in such a way that the AHD cell's preferred direction shifts to the left during clockwise turns and to the right during counterclockwise turns. This shifting of the preferred direction is what gives the AHD cell its anticipatory firing properties (see METHODS, MEASUREMENT OF THE ATI).
ACCOUNTING FOR EXPERIMENTAL FINDINGS.
We now explain how the circuit of Fig. 5 can account for several of the findings we have reported in the present study.
Path integration
Figure 5 proposes a set of connections that might explain why anterior thalamic HD cells exhibit the properties we have described in this study. A very similar connective architecture has been proposed by several network models of the head-direction circuit to explain how directional path integration might occur (Blair 1996
Conclusions
In summary, we found that anterior thalamic HD cells anticipated the rat's future head direction by an average ATI of ~17 ms, but individual cells exhibited ATIs ranging between ~0 and 50 ms. We also found that the ATI of a cell was correlated with the directional tuning parameters of the cell, such as the peak firing rate and directional tuning width. We discovered that during head turns, anterior thalamic HD cells change the shape of their tuning function in a systematic way, and this change in the shape of the tuning function appears to provide an explanation for the anticipatory firing properties of anterior thalamic HD cells. We proposed a set of neural connections that could account for the firing properties we observed, and showed that these connections are similar to the connections that have been previously proposed by network models of path integration in the head-direction circuit. In conclusion, our experimental results provide empiric support for a connective architecture that could support path integration in the head-direction circuit.
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
; Taube et al. 1990). An HD cell fires action potentials only when the rat's head is facing in a particular direction with respect to the surrounding spatial environment, regardless of the rat's location within that environment. HD cells are not influenced by the position of the rat's head with respect to its body; they are only influenced by the direction of the head with respect to the fixed spatial surroundings. Each HD cell is tuned to have its own specific directional preference, so that together the entire population of cells provides a distributed representation of any direction the rat might face.
), a subregion of the subicular complex within the hippocampal formation (van Groen and Wyss 1990). They have since been found in several other brain regions, including the anterior thalamus (Taube 1995), laterodorsal thalamus (Mizumori and Williams 1993), limbic cortex (Chen et al. 1994b), striatum (Wiener 1993), and lateral mammillary nucleus (Leonhard et al. 1996). For a review of experimental data on HD cells, see Muller et al. (1996) and Taube et al. (1996).
proposed that the head-direction signal might be generated by a process of dead reckoning, or path integration. According to this hypothesis, HD cells might compute the directional position of the head by integrating the angular velocity of the head over time. McNaughton et al. (1991) suggested that HD cells might perform path integration by combining information about the rat's current head direction with information about the angular velocity at which the head is turning. This combined information could be used to predict which direction the rat's head would be facing next. Such a prediction could serve to update the head-direction signal during head turns, implementing a process of path integration.
). By contrast, the activity of HD cells in the postsubiculum is best correlated with the rat's present or recently past head direction (Blair and Sharp 1995).1 On the basis of these findings, it has been proposed that the anterior thalamus and postsubiculum might be part of a circuit for path integration of the rat's directional heading (Blair and Sharp 1995; Redish et al. 1996).
; McNaughton et al. 1991; Redish et al. 1996; Skaggs et al. 1995; Zhang 1996). Some of the results described here have been previously reported in abstract form (Blair et al. 1996).
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
1 wk of free feeding, rats were placed on a food deprivation schedule, under which they were reduced to 80% of their ad libitum weight through limited daily feeding. Rats were then trained to perform a simple pellet-chasing task (Muller et al. 1987), which required them to search for 20-mg food pellets (BioServe, Frenchtown, NJ) that were thrown into a cylindrical chamber at random locations at intervals of ~15 s. A total of six training sessions was given, and during this period rats acquired a pattern of nearly constant locomotion in the cylinder, repeatedly traversing the entire cylinder floor and frequently turning their heads to face in many different directions.
), so it will only briefly be described here. All recording sessions were conducted in a 50.5-cm-high, 74.0-cm-diam cylindrical chamber, surrounded by a black curtain and flooded with white noise to minimize the influence of external cues. For most animals in the study (n = 7), the inner wall of the cylinder was painted with a series of eight alternating black and white vertical stripes. For the remaining animals (n = 3), the wall was painted with a pattern of four large stripes (1 white, 1 black, and 2 gray), each occupying 90° of arc. In agreement with previous reports (Blair and Sharp 1995), the difference in the wall's appearance had no discernible effect on the firing properties of the cells, and will not be considered further here. The floor of the cylinder was painted uniformly gray.
; Sharp and Green 1994). After recovery from surgery, animals were given screening/recording sessions, during which the rat performed the pellet-chasing task in the cylinder. To begin each screening/recording session, the rat was carried into the curtained enclosure (surrounding the cylinder) in an enclosed carrying cage, and the animal was held on the experimenter's shoulder while being attached to the recording cable. The animal was then placed into the cylinder (in the same position each time), and automatic delivery of food pellets was initiated. The signal from each recording wire was screened for single-cell activity, and if no single-cell activity was present, the electrode bundles were lowered slightly (between 0.022 and 0.044 mm) and the wires were checked again. On isolation of a single cell, a recording session was begun. The signal from the electrode wire was monitored by a recording system (Brainwave) that has been described elsewhere (Blair and Sharp 1995). Each recording session lasted between 15 and 30 min. At the end of the session, the animal was returned to its home cage in the enclosed carrying cage. Sessions were conducted on a daily basis for each animal until the electrodes had been lowered beyond the region where directional firing could be measured, indicating that the electrode tips were below the anterior thalamus.
), the position data from the tracking system was used to compute the animal's spatial location, directional heading, and angular head velocity every 1/60th of a second.
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FIG. 1.
Parameters of directional tuning function. A: tuning curve of a head-direction (HD) cell graphs cell's firing rate (Y-axis) as a function of rat's directional heading in horizontal plane (X-axis). Directional heading is plotted on a scale of 0-360°. B: to compute parameters of directional tuning function, a Gaussian function (see Eq. 1) is fitted to curve in A. Mean of Gaussian gives cell's preferred firing direction, D; SD of Gaussian is equal to half of cell's directional tuning width, W; peak height of Gaussian gives cell's peak directional firing rate, P; baseline of Gaussian gives cell's background firing rate, B.
where B, P, D, and W represent the tuning function parameters defined in the preceding paragraph (note that the square of the W parameter is divided by 2 in Eq. 1 because the cell's tuning width is defined as twice the SD of the fitted Gaussian). Each recording session's data were fitted to Eq. 1 by the method of least squares, with the use of a general-purpose iterative algorithm for curve fitting. The parameter values of the fitted curve were adopted as the estimates for the HD cell's tuning parameters during that recording session (see Fig. 1B).
![<IT>G</IT>(<IT>x</IT>) = <IT>B + P</IT>exp[−(<IT>x − D</IT>)<SUP>2</SUP>/(<IT>W</IT><SUP>2</SUP>/<IT>2</IT>)]](/content/vol78/issue1/fulltext/145/img001.gif)
(1)
; Taube et al. 1990). However, we have found that the tuning functions of anterior thalamic cells are better fit by a Gaussian function than a triangular function (unpublished observations). Recent theories of path integration in the head-direction circuit have described the shape of the directional tuning curve as a Gaussian rather than a triangle (Redish et al. 1996; Zhang 1996). For these reasons, we have chosen to estimate the tuning parameters of HD cells by a Gaussian function. It should be noted, however, that the main findings reported in this paper are robustly insensitive to the precise method that is used to estimate directional tuning parameters. We have confirmed this by reanalyzing the data with the use of a variety of different methods for estimating tuning parameters (see RESULTS).
, measurements of the rat's head direction were also interpolated between video frames to bring them into temporal alignment with measurements of the head velocity. For the analyses presented here, clockwise head turns were classified as angular head movements that exceeded a positive angular velocity of 120°/s, counterclockwise turns were classified as movements with a negative angular velocity of less than 
120°/s, and the head was considered to be straight when the angular velocity was zero, corresponding to moments when the rat's head was still or was moving straight forward or backward without turning.2 Head movements that did not fall into any of these three categories (that is, movements between 0 and ±120°/s), and spikes that occurred during such movements, were excluded from the analysis (on average, 8% of a session's data were discarded from the analysis in this way).
; Taube and Muller 1995). We define the ATI of an HD cell as the time displacement for which a cell's firing rate is best correlated with the directional position of the rat's head. That is, the ATI represents the average amount of time by which the cell's peak of activity precedes the arrival of the rat's head at a specific directional heading. For example, consider an HD cell that fires maximally 20 ms before the rat's head faces in a specific direction 
. The ATI for this cell would be +20 ms (the positive value indicates that the cell fires in correlation with the rat's future head direction, rather than the past head direction). Alternatively, if the cell fires maximally 10 ms after the rat's head has already faced in direction , then the ATI of the cell would be 10 ms (the negative value indicates that the cell fires in correlation with the rat's past head direction). If the cell fires maximally at the exact moment when the rat's head faces in direction , then the ATI would be 0 ms.
introduced a method for measuring the ATI of an HD cell recorded from a freely moving rat, based on comparing the cell's behavior during clockwise versus counterclockwise turns of the rat's head. To understand this method, consider an AHD cell with a preferred firing direction and an ATI of T ms. That is, the cell fires maximally T ms before the rat faces in the direction . If the rat's head is turning in the clockwise direction, approaching the direction from the left side, then the cell will fire maximally T ms before the head arrives at direction . Therefore the cell will fire maximally in a direction that is displaced to the left of , because the head will still be to the left of during the moments before arrival at . Conversely, if the rat's head is turning in the counterclockwise direction, approaching direction from the right side, then the cell will fire maximally in a direction that is displaced to the right of , because the head will still be to the right of during the moments before arrival at . It should therefore be expected that, if we plot the clockwise and counterclockwise tuning curves for an AHD cell (see TURNING-VELOCITY-DEPENDENT DECOMPOSITION OF THE TUNING FUNCTION, above), the clockwise tuning curve will be displaced to the left of and the counterclockwise tuning curve will be displaced to the right of . That is, we should expect to observe an angular separation (which we denote as S) between the preferred directions of the clockwise and counterclockwise tuning curves for an AHD cell.
for details). The time-displaced tuning function is then decomposed into its clockwise and counterclockwise components, allowing us to compute the angular separation, S, between them. Blair and Sharp (1995) showed that if the time displacement of the tuning function is exactly equal to the ATI of the HD cell, then the angular separation, S, should equal zero. Therefore we may estimate the ATI of an HD cell as the time displacement at which S = 0. See Blair and Sharp (1995) for a detailed presentation of this method.
90° (to eliminate cases in which the same cell might have been recorded on different wires); and 2) if the recordings were made from the same electrode wire, then the preferred directions of the cells had to differ by 90°, and the wire had to be advanced by 150 mm between the two recordings. If the identity of a cell could not be determined with certainty by these criteria, then the session was omitted from the study.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
). The preferred firing directions of different cells in the study were uniformly distributed over the 360° range of possible head directions. The average spike width (measured as the time interval between an action potential's initial departure from and subsequent return to baseline) was 223.9 ± 29.3 (SE) ms and the average peak-to-peak spike amplitude was 212.6 ± 25.1 (SE) mV. These spike parameters are similar to those that have been previously reported for extracellular recordings of HD cells in the anterior thalamus (Blair and Sharp 1995; Taube 1995). It should be noted that 21 of the 73 recording sessions in this study were also included in the study of Blair and Sharp (1995).
). A major objective of this study was to examine whether all HD cells in the anterior thalamus anticipate the rat's future head direction by a similar time interval, or whether individual HD cells might anticipate the rat's future head direction by different time intervals. The first step in addressing this question was to examine the distribution of ATI values from different HD cells in the anterior thalamus.
7.5 ms to a maximum of +47.6 ms (see METHODS for the meaning of positive and negative ATI values). The mean ATI for the entire set of cells (n = 33) was +17.0 ± 2.2 (SE) ms. This means that on average, the firing of anterior thalamic cells was best correlated with the direction the rat's head would be facing ~17 ms in the future. However, it does not appear that all of the cells anticipated the rat's future head direction by 17 ms. In many cases, the SE over multiple sessions for a cell is much smaller than the difference between the ATIs of that cell compared with another cell in the sample. This suggests that different HD cells in the anterior thalamus may have anticipated the rat's future head direction by different time intervals.
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FIG. 2.
A: bar graph of anticipatory time intervals (ATIs) for 33 anterior thalamic HD cells in our study. Height of each bar: ATI value (in ms) for an individual HD cell, averaged over all of recording sessions during which cell was recorded. Error bars: SE over sessions for cells that were recorded during multiple sessions (cells recorded for only 1 session do not have error bars). B: grouped frequency distribution of ATI values for anterior thalamic cells. ATI is grouped into 10-ms bins on abcissa, and number of cells falling into each 10-ms bin is plotted on ordinate. A large number of cells had ATIs near population mean, between 10 and 20 ms. There were relatively fewer cells with ATIs that were longer or shorter than population average.
View this table:
TABLE 1.
Data from individual recording sessions
0.17, P = 0.34]. The number of recording sessions per cell varied between one and seven. There was not a significant correlation between the average ATI of a cell and the number of sessions over which the cell was recorded to obtain the average ATI [r(32) = 0.27, P = 0.13]. We conclude that the ATI measurement was not influenced by the length of the recording session or by the number of recording sessions conducted with the cell.
0.08, P = 0.66].
0.06, P = 0.74] of action potentials measured from the extracellular recording electrode.
). For some cells (e.g., cell 30), these changes in the sizes of the peaks cause a clear change in the shape of the cell's tuning function when the rat's head is turning. This behavior might provide insight into possible mechanisms for anticipatory firing of anterior thalamic HD cells (see DISCUSSION). In the remainder of this section, we compare the parameters of the clockwise, counterclockwise, and straight tuning functions, and analyze how these parameters are correlated with the ATI of a cell.
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FIG. 3.
Tuning functions for cells (n = 16) that were recorded for 2 recording sessions. Three tuning curves are shown for each cell: a clockwise (· · ·), counterclockwise (thin line), and straight (thick line) tuning curve. Cells with long ATIs tend to have broader tuning widths and slower peak firing rates than cells with short ATIs. Also, some cells with long ATIs (such as cells 30, 26, and 2) appear to have 2 peaks in their tuning function, whereas cells with short ATIs always have only 1 peak.
; Taube 1995). We now verify this finding for the present data set, and investigate how the influence of the angular velocity on P is correlated with the ATI of the cell.
0.43, P = 0.012]. The average peak directional firing rate of the straight tuning function was 61.5 ± 4.8 (SE) Hz, and the peak rate of a cell's straight tuning function was also inversely correlated with the cell's ATI value [r(32) = 0.43, P = 0.012]. The average peak directional firing rates of the clockwise and counterclockwise tuning functions were 65.8 ± 4.9 (SE) Hz and 65.7 ± 4.9 (SE) Hz, respectively. A cell's peak rate was inversely correlated with its ATI for both the clockwise [r(32) = 0.41, P = 0.019] and counterclockwise [r(32) = 0.40, P = 0.02] turning conditions.
; Taube 1995). In agreement with this, we found that the peak directional firing rate was higher by an average of 4.4 ± 0.6 (SE) Hz when the rat was turning than when it was not turning. The firing rate when the head was not turning was significantly lower than when the head was turning clockwise [t(32) = 4.72, P < 0.0001] or counterclockwise [t(32) = 5.81, P < 0.0001], but there was no significant difference in the firing rate during clockwise versus counterclockwise turns [t(32) = 0.13, P = 0.89]. The amount by which a cell's firing rate increased during turns was not correlated with the ATI value of the cell [r(32) = 0.13, P = 0.49].
; Taube and Muller 1995). We time displaced the standard tuning function of each cell in our study by a time interval equal to the cell's ATI. This time displacement reduces S to near zero, and therefore the width of the time-displaced standard tuning function should be narrower than the width of the undisplaced standard tuning function. In agreement with this prediction, we found that the widths of the time-displaced tuning functions were significantly narrower than the widths of the undisplaced tuning functions as determined by a one-tailed paired t-test [t(25) = 3.88; P < 0.0001].4 However, even though most of the angular separation between clockwise and counterclockwise turning conditions had been removed, the correlation between the tuning width and the ATI of the cell was not reduced by the time displacement of the standard tuning function [r(32)=0.70, P < 0.001]. This suggests that the correlation of the ATI with the cell's tuning width cannot be accounted for simply by the increased angular separation between clockwise and counterclockwise tuning functions. Further evidence for this is presented in the following paragraph.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
. During clockwise turns, the peak would shift to the left along the directional axis, and during counterclockwise turns, the peak would shift to the right along the directional axis (Fig. 4A, bottom). Notice that in Fig. 4A, bottom, the clockwise, counterclockwise, and straight tuning functions all have the same shape, and thus they have approximately the same tuning width. The standard tuning function (top) includes all three turning conditions and is thus broader, spanning the width across all three of the component tuning functions.
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FIG. 4.
Two possible explanations for why an HD cell shifts its preferred firing direction during head turns. A: 1st possibility is that clockwise, counterclockwise, and straight tuning functions all have same shape, and therefore, same tuning width (bottom). Clockwise tuning function is shifted to left on directional axis, and counterclockwise tuning function is shifted to right, which results in a broadening of width of standard tuning function (top). Pattern of tuning widths in A does not match our experimental observations. B: 2nd possibility is that shape of tuning function changes during head turns, becoming skewed to left during clockwise turns and skewed to right during counterclockwise turns (bottom). This does not cause any significant broadening of standard tuning function. Pattern of tuning widths in B matches our experimental observations.
have implemented a computational model of the head-direction circuit, which predicts such a skew in the tuning function of AHD cells during head turns. We now discuss a neural circuit mechanism that could explain why an AHD cell's tuning function changes its shape during head turns.
; Taube et al. 1990) and the lateral mammillary nucleus (Leonhard et al. 1996). TMHD cells may be particularly abundant in the lateral mammillary nucleus(R. W. Stackman and J. S. Taube, unpublished observations).
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FIG. 5.
Proposed mechanism for anticipatory firing properties of HD cells in anterior thalamus. Arrows: connections between cells in circuit. Left: graphs show clockwise (· · ·), counterclockwise (thin line), and straight (thick line) tuning functions for corresponding shaded cell on right. A: anticipatory HD (AHD) cell with a long ATI (shaded circle) receives input from turn-modulated HD (TMHD) cells with distant preferred firing directions. B: AHD cell with a short ATI (shaded square) receives input from TMHD cells with nearby preferred directions. See text for a more detailed explanation.
; McNaughton et al. 1991; Redish et al. 1996; Skaggs et al. 1995; Zhang 1996). Figure 6 illustrates one such model, which was proposed by Skaggs et al. (1995). The circuit of Fig. 6 contains three types of neurons.5
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FIG. 6.
Network model of head-direction circuit, originally proposed by Skaggs et al. (1995) . HD cells excite their neighbors via indirect connections through TMHD cells, which function as excitatory interneurons. When rat is not turning, excitation through TMHD cells is equal in both clockwise (clk) and counterclockwise (cnt) directions, causing a stable pattern of activity that represents a fixed directional heading. When rat turns its head in clockwise direction, excitation through clockwise TMHD cells exceeds excitation through counterclockwise TMHD cells, causing activity to propagate in clockwise direction through HD cell layer. A similar (but reversed) process occurs for counterclockwise turns. See Skaggs et al. (1995) for more details.
) and limbic cortex (McNaughton et al. 1994).
; Taube et al. 1990), but they may be more abundant in the lateral mammillary nucleus (Leonhard et al. 1996; R. W. Stackman and J. S. Taube, unpublished data).
; Redish et al. 1996; Zhang 1996).
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ACKNOWLEDGEMENTS |
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The authors acknowledge T. Carew, I. Lidsky, J. Junior, and the Yale Neuroengineering and Neuroscience Center (NNC) for assistance in preparing the manuscript. We thank B. Skaggs for assistance with adapting Fig. 6 and K. Zhang and D. Redish for helpful comments on the manuscript.
This work was supported by National Institute of Mental Health National Research Service Award Fellowship 1 F31 MH-11102-01A1 to H. T. Blair and by Whitehall Foundation Grant A94-06 to P. E. Sharp.
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FOOTNOTES |
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1
Blair and Sharp (1995) reported that the activity of postsubicular HD cells was best correlated with the present direction of the rat's head, whereas the activity of anterior thalamic HD cells was best correlated with the direction in which the rat's head would be facing 37 ms in the future. Preliminary findings reported by Taube and Muller (1995) were nearly identical. However, both of these studies failed to compensate for a 15-ms time delay in the video signal used to track the rat's head direction. H. T. Blair and P. E. Sharp (unpublished observations) have performed a corrected analysis of their original data and have found that the ATI for postsubicular cells was 15.7 ms and the ATI for anterior thalamic cells was +24.7 ms. J. S. Taube and R. U. Muller (personal communication) have reported corrected figures of 6.1 ms for postsubicular cells and +23.2 ms for anterior thalamic cells.
2
During the pellet-chasing task, the rat rarely moves backward, and it does not maintain a perfectly straight forward trajectory for extended periods of time. Therefore most of the data in the "head-straight" turning condition come from periods when the head was still.
3
We repeated our analyses of the peak firing rate with the use of several other methods for measuring the peak firing rate of a cell, including fitting the tuning curve to a triangular function instead of a Gaussian and taking the peak directional firing rate from the raw data without fitting it to any function. We obtained similar results with each method of estimating the peak firing rate. Thus the relationships we have observed between the peak directional firing rate, the angular head velocity, and the ATI value are not artifacts of the Gaussian method for estimating the peak firing rate.
4
Because of the limited temporal resolution of our 60-Hz video tracking system, the ATI of each cell had to be rounded to the nearest multiple of 16.6 ms for time displacement analysis. Seven cells had ATIs that rounded to an ATI of 0 ms, and these seven cells had to be omitted from the paired t-tests comparing time-displaced tuning widths against undisplaced tuning widths. Thus the reader may note that these paired t-tests have 25 degrees of freedom, rather than 32.
5
Our terminology for the cell types differs slightly from that of Skaggs et al. (1995). What we refer to here as AV cells were referred to by Skaggs et al. (1995) as "vestibular cells," and what we refer to as TMHD cells were referred to by Skaggs et al. (1995) as "rotation cells."
Address for reprint requests: H. T. Blair, Dept. of Psychology, Yale University, PO Box 208205, Yale Station, New Haven, CT 06520-8205.
Received 16 October 1996; accepted in final form 14 March 1997.
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REFERENCES |
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Abstract
Introduction
Methods
Results
Discussion
References
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