Minimal driving of hippocampal theta by the supramammillary nucleus during water maze learning

Animals

Five male Sprague-Dawley rats were obtained from the Department of Laboratory Animal Sciences at the University of Otago. Surgery and WM testing procedures are described in detail elsewhere (McNaughton et al., 2006) where the animals analyzed in this study formed the behavioral control group. Briefly, animals were anesthetized with ketamine/medetomidine, and bipolar stainless steel electrodes were implanted in CA1/dentate layers of the hippocampus (AP −3.8 mm, ML −2.5 mm, DV −3.5 mm, tip separation 1.0 mm) and the supramammillary nucleus (AP −4.8 mm, ML −0.9 mm, DV −9.4 mm, tip separation 0.5 mm, 6.0° from vertical). A stimulating electrode aimed at the fornix and a 26 GA cannula guide aimed at the medial septum were also implanted for a different study. Antisedan (2.5 mg/kg, 5 mg/ml, Novartis Animal Health Australia Limited) was administered to facilitate recovery from anesthesia, and this was followed by postoperative analgesic administration. The rats were then allowed to recover for at least 10 days before any electrophysiological or behavioral testing. The University of Otago Animal Ethics Committee approved these manipulations, and the experimental procedures described below.

Behavior and Electrophysiology

Local field potentials (LFPs) were recorded through a source follower, amplified (Grass P511K, 1–30 Hz bandpass filter), and digitized at 100 Hz for subsequent analyses. The data were acquired and stored by Spike2 (CED, UK) for offline analysis. The WM testing followed the single-day protocol of Pan and McNaughton (1997). Briefly, the WM consisted of a rigid black plastic pool (150 cm in diameter, 35 cm high) and was filled to a 25-cm depth with 26°C (±2°C) water. A black plastic platform (15-cm square) was placed 1.5 cm beneath the water surface in the center of the southeast quadrant. Animals were prehandled and allowed 40 s to find the platform and were then guided to the platform if they failed to locate it. The animals were then left on the platform for 15 s, which also served as the intertrial interval as the next trial begins with bringing the animals to the next start location from the platform. All starting locations for a total of 16 trials were counterbalanced, and escape latency, path length, and trajectory were all acquired for offline analyses (HVS IMAGE, UK). In an open-field (OF) task, used as an analysis control, animals were left to freely explore a square (73 × 73 × 51 cm) box for 6 min.

Data Processing—General

WM data were segmented into distinct behavioral epochs for further processing based on behavioral markers generated by the HVS program. Fixed-length epochs were: (1) 2 s immediately before placing the animals in the pool; (2) 2 s immediately before the animals climbed up onto the platform; and (3) the subsequent 2 s while the animals were on the platform. In addition, recordings from the variable-length swimming period from each individual trial were separately segmented. Behavioral markers used to segment the WM data were inserted randomly into the OF recordings, and the same segmentation method was applied to generate equal-length data for WM:OF comparisons—using the randomized OF records as a statistical control. Segments of raw data with the DC component removed were exported from Spike2 (CED, UK) for further analysis in MATLAB (Mathworks, Natick, MA).

Custom-made code involving the multitaper spectral analysis (Mitra and Pesaran, 1999) and DTF (Kaminski and Blinowska, 1991; Young and Eggermont, 2009) are based on the respective cited references. Hilbert transform of zero-phase digitally filtered data (4–12 Hz) were used to calculate instantaneous phase and frequency. Raw data and examples of various analyses in time–frequency representations are shown in Figure 1.

Data Processing—Spectral Analysis

Multitaper spectral analysis was used to gauge the frequency and coherence spectra of the data. The multitaper method was used for its ability to reduce spectral estimate biases while dealing with short-length data. Three tapers with a bandwidth product of 3 were used as parameters for both coherence and frequency spectra. (Bandwidth product is the ratio of the bandwidth in cycles per second to the data length in seconds.) In the time–frequency analyses, a 0.9 s window with 90% overlap was used. The frequency spectra were calculated with the periodogram method, whereas the coherence was calculated by normalizing the squared cross spectra from the HPC and SuM by individual spectra, to yield a value between 0 and 1—where 1 denotes perfect phase and amplitude correlation. Theta-band coherence was determined by averaging across coherence values from 4 to 10 Hz. Theta frequency was extracted as the peak HPC frequency in the spectra in the 4–10 Hz band.

Data Processing—Directed Transfer Function

To determine how each signal's past might reliably predict the future of the other signal, a DTF was applied using methods described previously (Kaminski and Blinowska, 1991; Young and Eggermont, 2009). Multivariate autoregressive modeling was used to model the HPC and SuM LFPs, where x is the signal being modeled (x₁ = HPC; x₂ = SuM), ϵ is the error variance (noise), and p is the model order.

A model order of 10 was used as a compromise between computational efficiency and model accuracy for investigating the frequencies of interest. The autoregressive model was then transformed into the frequency domain. The normalized form of DTF (nDTF) was used to reduce between-subjects variation derived from electrode placement. That is, the directed coherence estimates in a particular row of the matrix were divided by the sum of all estimates in the same row of the matrix. The time–frequency representation of nDTF was also carried out with 0.9 s, 90% overlapping windows. Finally, the putative direction of control was determined by subtracting the SuM nDTF values from the HPC values to form an index for theta propagation (nDTF_(HPC-SuM)), where a positive value suggests HPC LFP is predictive of SuM LFP and vice versa for a negative value.

Data Processing—Instantaneous Phase and Frequency

Angle values from the Hilbert transformed data were obtained as the instantaneous phase. The instantaneous frequency (h(f)_inst) is obtained by taking the absolute value of the complex phase derivative times the sampling frequency.

Both the instantaneous frequency and phase were averaged in 0.9 s windows.

Statistical Analysis

All statistical analyses were computed in SPSS15 (SPSS, Chicago, IL). Pearson's linear correlation coefficients and the corresponding two-tailed significance tests were calculated to determine if two variables were interdependent. One-way ANOVAs with polynomial contrasts were used to examine how measured variables changed as a function of learning. The z transform (z(x) = 0.5(log₁₀((1 + x)/(1 − x))) was applied to the coherence and DTF values to normalize the error variance. All variables submitted to parametric tests, such as ANOVA, had approximately normal error distributions.

Hippocampo-Supramammillary Theta Interactions During WM Learning

To explore the relationship between the theta variables and WM acquisition, we pooled variable-length swimming epochs from all trials into four-trial blocks and spatially by pooling data obtained from a particular quadrant in the maze (Fig. 2).

The key global observations are that theta coherence between SuM and HPC is not particularly high overall, and DTF values are generally positive (indicating a potential driving of SuM by HPC rather than the reverse). The bulk of the phase differences are also more consistent with an HPC to SuM direction of propagation. There is, therefore, no evidence for any strong control of HPC by SuM and, except possibly in the later stages of training, little evidence consistent with even modest control.

Because of the large differences in numbers of data points across trials and quadrants, we performed one-way ANOVAs with polynomial contrasts to examine which polynomial fit accounted for the greatest variance (see Table 1) for each quadrant. In addition, correlations of the values from the SE quadrant (the target quadrant with the hidden platform) as a reference against the values for the rest of the quadrants were computed to assess how similar the changes across trials were across quadrants (see Table 2).

For ΔDTF (Fig. 2A), there was a tendency for values to increase initially and then decrease later in training. However, a quadratic function accounted for the most variance (about four times that of the linear trend) in the SE (target) quadrant, which was also the case for NW (about 1.4 times the linear trend). For the SW and SE quadrants, there were decreases in ΔDTF between the start and the end of training resulting in significant linear trends (superimposed on the orthogonal quadratic trends). However, the overall trends (in terms of correlation between the mean values) were not found to be similar between SE (target) and the other quadrants, except perhaps for SW (r = 0.86, n = 4, P = 0.14). Consistent with previous findings, HPC theta frequency decreased across trials but did not show any quadrant-dependent changes (Fig. 2B), as indicated by all quadrants having the linear trend accounting for most of the variance. The means for all the other quadrants showed substantial linear correlations with SE (target), and, with the exception of SW (r = 0.92, n = 4, P = 0.08), these were significant (see Table 2). For SuM-HPC theta coherence (Fig. 2C), there was a tendency to higher coherence in the second-trial block relative to the third, giving rise to cubic trends—except in the SW quadrant. Also in the NE quadrant a quadratic trend accounted for greater variance than the cubic (Table 1). None of the nontarget quadrants demonstrated statistically significant linear correlations with SE (target) (Table 2). Finally, for HPC-SuM theta-phase differences (Fig. 2D), decreasing linear trends accounted for most of the variance on the north side of the maze, whereas quadratic trends describing an initial decrease followed by an increase in the last trial blocks were found to best account for the quadrants on the south side (Table 1). The only significant linear correlation between quadrants was found between the SE (target) and SW (r = 0.97, n = 4, P < 0.03; Table 2).

Hippocampo-Supramammillary Theta Propagation and Hippocampal Theta Frequency

A previous report (Kocsis and Kaminski, 2006) suggested that the direction of HPC-SuM theta propagation is dependent on HPC theta frequency. To explore this finding in the context of freely behaving animals, we correlated averaged instantaneous HPC theta frequency with the ΔDTF. No covariance across time can be seen between the two parameters (Fig. 3A). To further quantify this, 0.9 s bins of instantaneous HPC frequency and ΔDTF collected across all the animals tested in the WM were pooled, and an extremely weak linear relationship was found between the two (Fig. 3B, r = 0.001, n = 15163, P < 0.05), suggesting lower HPC frequency might very occasionally be associated with a HPC → SuM direction of theta propagation. To provide a degree of comparative control of this finding, we also performed the same analysis on equivalent data obtained in a separate OF test and found it to be statistically nonsignificant (r = 0.000001). There is a slight preference for higher ΔDTF values to be associated with lower HPC theta frequency during WM (Fig. 3C, left), corroborating the weak linear correlation coefficient reported in Figure 3B. There is no such trend in OF data relative to the WM, showing a skew of ΔDTF to higher values but without any HPC theta-frequency covariance (Fig. 3C, right). The ΔDTF and HPC theta-frequency distributions were further compared between the WM and OF conditions (Fig. 3D). There is an obvious skew of values to more positive values of ΔDTF in the WM compared with OF as the distributions between the conditions are statistically different (Mann-Whitney test, P < 0.001). In contrast, there appear to be more instances of higher HPC theta frequency in the OF condition compared with WM, as the distributions were also found to be statistically different (Mann-Whitney test, P < 0.001).

Experience-Dependent Modification of Theta Oscillation Dynamics Between the Hippocampus and Supramammillary Nucleus

To match the length of data analyzed for each animal across trials, we analyzed three 2-s epochs. The first (handling) was the 2 s immediately before placing animals into the pool; the second (swim) was the 2 s before arriving at the platform; and the third (platform) was the 2 s immediately after the arrival on the platform (Fig. 4A; see also methods). All animals decreased their path length as a function of experience (Fig. 4B). Correlations between path lengths and ΔDTF, HPC theta frequency, HPC-SuM coherence, and HPC-SuM phase differences were carried out for each of the 2 s behavioral epochs described above. These correlations are shown in Table 3. Individual data for the swim phase are shown in Figure 4. Consistent with the analysis of the quadrant data, there appears to be a modest positive relationship between ΔDTF and path length during WM swimming, suggesting a change in theta propagation in the direction of HPC → SuM toward SuM → HPC (r = −0.56, n = 16, P < 0.05, uncorrected; Fig. 4C). There may have been a weak similar trend on the platform; but there was no sign of such changes with handling. There were no such trends in equal-length data obtained during OF exploration (Fig. 4G). Also consistent with the quadrant analysis, there were significant reductions in HPC theta frequency as a function of path length, in the handling and swim epochs with a trend to reduction in the platform epoch (r = 0.54, n = 16, P < 0.05, uncorrected; Fig. 4D). Again, no equivalent trend was seen between the same variables during OF exploration (Fig. 4H). There were indications of an experience-dependent reduction in HPC-SuM phase differences only in the “platform” epoch (Fig. 4e; see Table 3). The lack of change in handling and swim is likely to be the result of cancellation between the effects seen in the northern quadrants and those in the southern (the “handling” period involves the holding of the animal predominantly in positions that are an extension, outside the pool, of a single quadrant within the pool). Theta coherence in the swim epoch between the SuM and HPC increased as animals reduced distance traveled to the hidden platform (r = −0.57, n = 16, P< 0.05; Fig. 4F). Once again, no significant trend was seen in the OF data (Fig. 4J). There was no sign of such a change in either the handling or platform epochs.