Neural recording in the lateral septum.

(A) Left: coronal brain slice showing part of the Neuropixels probe trajectory (white arrow) in the lateral septum (animal LS-k-7). Right: the number of recorded cells along the probe shank for one recording session in the same animal. Depth is measured relative to the white matter above the lateral septum. Vertical line at the right indicates the span of the recorded electrodes on the probe. (B) A schematic overview of the probe tracks in all animals, projected onto a single coronal slice at 0.36 mm anterior to Bregma. (C) Left: example tracked position from a session in which the animal performed the alternation task on the Y-maze. Right: definition of outbound and inbound trajectories. (D) Left: the percentage of correct visits for all alternation task sessions. Gray dots represent individual sessions, black dot represents median and 95% confidence interval across sessions. Right: the mean percentage of correct visits for 15 trials after a reward switch for all switching task sessions. (E) Log-distribution of mean firing rates for LSD (top) and LSI (bottom) cells in all analyzed sessions. Overall mean±sem firing rate: LSD 2.52±0.18 Hz, LSI 5.21±0.24 Hz. (F) Example behavior and spiking activity in a single session during one outbound journey. Top: running speed. Gray region marks the outbound journey. Bottom: spike raster plot of all cells recorded in LSD and LSI.

Overview of data.

An overview of all analysed sessions from four animals performing either an alternation task or a switching task, with the number of recorded cells and corresponding mean firing rate for septal subregions LSD and LSI.

Theta rhythmicity and theta cycle skipping in lateral septum cells.

(A) Spiking auto-correlograms of four example cells in LSD and LSI that show clear rhythmicity at theta frequency. (B) Power spectra of (binned) spike trains for the same cells as in panel A. Gray traces represent spectra of locally shuffled spike trains. Theta peak index is computed as the normalized difference between theta peak power (dark orange) and theta base power (light orange). Inset shows values for theta peak index, Monte-Carlo p-value an z-scored index relative to shuffle distribution.

Theta cycle skipping is trajectory specific.

(A) Local shuffling procedure to compute significance of cycle skipping effect in single cells. Each spike is randomly shifted by a multiple of the theta cycle (fixed to 125 ms) according to a normal distribution (shown on the left). (B) Left: example spiking auto-correlogram of original spike train (black line) and shuffled spike trains (gray). A cycle skipping index (CSI) is computed as the normalized difference between the first and second theta-related peaks. Right: distribution of CSI values for 250 shuffled spike trains (gray) and CSI value of the original spike train (black line). (C) Spiking auto-correlograms of four example cells in LSD and LSI separately for each of the four kinds of journeys (top: outbound journeys, bottom: inbound journeys). Legend at the top of each plot indicates for each journey type the CSI value (printed in bold for significant CSI values). The symbol × means that a cycle skipping index could not be computed because of low number of spikes. From left to right, the first and fourth cell show significant cycle skipping only for a single trajectory type (respectively, inbound left and outbound left). The second cell shows significant cycle skipping for three trajectory types, and the third cell for both outbound trajectories. (D) Venn diagram showing overlap of cell populations with significant theta rhythmicity and theta cycle skipping. (E) Histogram of the number of cells with a significant cycle skipping index for all possible journey combinations. Note that for most cells (55.4%; yellow) cycle skipping occurs only on a single journey type. For another population of cells (22.0%; blue), cycle skipping occurs on outbound, inbound, left, or right journeys.

Examples of theta cycle skipping during single journeys.

(A) Spike raster plots (bottom) of selected lateral septum cells (animal LS-k-7) during four outbound journeys to the left goal. Top: position of the animal represented as the distance between home and goal. Middle: local field potential in the LSD filtered in the theta band (6-10 Hz). Vertical grey lines indicate times of peaks in theta oscillation. Bottom: for each cell, spike times (black lines) and an instantaneous estimate of cycle skipping (CSIi, red indicates relative excess of spike intervals in range 0.2- seconds). (B) Same as in for selected cells (animal LS-k-8) during four inbound journeys starting from the left goal.

Theta cycle skipping occurs on approach to the choice point and in the goal arms.

(A) Average CSI value as a function of location along outbound (left) and inbound (right) trajectories. Thick lines represent average across all analyzed cells and trajectories to/from left and right goals. Thin lines represent average for individual animals. (B) Same as (A) but for the percent of analyzed cells and trajectories with significant cycle skipping.

Spatial coding in the lateral septum.

(A) Spatial tuning curves for 10 example neurons in LSD and LSI for the four different trajectories. (top: trajectory-specific neurons firing differentially on the left/right goal arms, bottom: direction-specific neurons firing differentially on the outbound versus inbound journeys). (B,C) Distribution of outbound (B) and inbound (C) goal arm selectivity of all analyzed neurons in LSD and LSI. Light orange: full distribution of all cells. Dark orange: highlighted part of the distribution that represent cells with significant goal arm selectivity (Monte-Carlo p-value < 0.01). (D,E) Values of outbound (D) and inbound (E) goal arm selectivity index increases for cells located closer to the white matter. Dots represent individual cells with significant goal arm selectivity index from all sessions and animals. Black line and shaded region represent linear fit and 95% confidence interval. (F,G) Mean value of outbound (F) and inbound (G) goal arm selectivity index is significantly higher in LSD as compare to LSI (mean±sem goal arm selectivity, outbound: LSD 0.75±0.02, LSI 0.49±0.02, two-sided two-sample t-test, t(434)=9.40, p=3.1×10-19; inbound: LSD 0.61±0.03, LSI 0.44±0.02, two-sided two-sample t-test, t(237)=4.65, p=5.6×10-6).

Position and direction coding in the lateral septum cell population.

(A) Example result of decoding run direction (top) and position (bottom) for a single dataset (animal LS-k-7). For both direction and position, the marginal posterior probability is shown in grey scale. Position on the track is “linearized” and the horizontal black lines indicate the extent of the three maze sections: stem (bottom), left goal arm (middle) and right goal arm (top). Note that the home platform and goal platforms are excluded from the encoding model, and no decoding is performed for the time that the animal spent at the platforms. A sequence of ten outbound/inbound journeys is shown (separated by vertical lines). Red dots indicate the true position of the animal on the track. (A) Confusion matrix of the decoding result for the same session as in (A). Each dot represents a single maximum a posteriori position estimate in a 200 ms time bin during run periods (speed > 10 cm/s) in outbound/inbound journeys. The diagonal structure indicates good correspondence between estimated and true positions. The color map in the background shows the confusion matrix for decoding the three maze sections. For this session, median position error is 12.0 cm and 94.7% of direction estimates are correct. (C) Spatial and direction decoding performance for all sessions using all LSD and LSI cells combined or using only cells in LSD or LSI. Vertical and horizontal lines indicate mean performance across sessions.

Neural decoding of theta-scale dynamics in lateral septum.

(A) Example result of decoding run direction (outbound or inbound; top) and position (middle) at fine time scale (20 ms) for a single dataset (animal LS-k-7). For both direction and position, the marginal posterior probability is shown in grey scale (black represents probability of 1 for direction, and ≥0.25 for position). Position on the track is “linearized” and the horizontal black lines indicate the extent of the three maze sections: stem, left goal arm and right goal arm. Note that the home platform and goal platforms are excluded from the encoding model, and no decoding is performed for the time that the animal spent at the platforms. A sequence of one outbound and one inbound journey is shown (separated by vertical lines). Red dots indicate the true position of the animal on the track. Bottom: time courses of the summed posterior probability in the three maze sections.

Alternation of spatial representations on approach to choice point.

(A) Auto- and cross-correlation of posterior probability time courses for the three maze sections when the animal is running along the stem in the outbound direction towards the choice point. Correlations are computed as the Pearson correlation coefficient at varying time lags. For each plot, drawings at the left show the animal’s behavior (black arrow) and the maze sections for which correlations are computed (color indicates whether the highlighted maze section is local (blue) or non-local (orange) relative to the animal’s position on the track). Top: auto-correlation of local representations in the stem. Second from top: auto-correlations of non-local representations in the two goal arms. Third from top: cross-correlations between local and non-local representations. Bottom: cross-correlation between non-local representations in the two goal arms. (B) Same as (A), but for times when the animal is running along one of the goal arms in the inbound direction towards the choice point. Equivalent correlations for the two goal arms are computed jointly.

Alternation of spatial representation is task dependent.

(A) Average CSI value as a function of location along outbound (left) and inbound (right) trajectories, separately for alternation and switching tasks. Shaded region represents 95% CI. (B) Same as (A) but for the percent of analyzed cells and trajectories with significant cycle skipping. (B) Auto- and cross-correlations of non-local spatial representations in the two goal arms as animals run outbound in the stem towards the choice point, computed separately for alternation and switching tasks. See Figure 9 for details. (C) Same as (C), but for times when the animal is running along one of the goal arms in the inbound direction towards

Left: coronal brain slice showing part of the Neuropixels probe trajectory (white arrow) in the lateral septum (animal, A: LS-k-8, B: LS-k-11, C: LS-k-14). Right: the number of recorded cells along the probe shank for one recording session in the same animal. Depth is measured relative to the white matter above the lateral septum. Vertical line at the right indicates the span of the recorded electrodes on the probe.

(A) Distribution of theta modulation index of all analyzed neurons in LSD and LSI. Light orange: full distribution of all cells. Dark orange: highlighted part of the distribution that represent cells with significant theta modulation index (Monte-Carlo p-value < 0.01). (B) Mean firing rate of theta rhythmic (dark orange) and non-rhythmic (light orange) cells differ significantly in both lateral septum subregions. Two-sided two-sample t-test, LSD: t(337)=11.18, p=6.9×10-25, LSI: t(881)=14.45, p=1.2×10-42. (C) Values of theta peak index for theta rhythmic cells increases for cells located closer to the white matter. Dots represent individual cells with significant theta peak index from all sessions and animals. Black line and shaded region represent linear fit and 95% confidence interval (r=0.18, p=2.1×10-6). (D) Mean value of theta peak index is significantly higher in LSD as compared to LSI (mean±sem theta peak index, LSD 0.17±0.005, LSI 0.13 ± 0.003; two-sided two-sample t-test, t(714)=5.33, p=1.4×10-7). Thin lines represent mean theta peak index for individual sessions, with the line color indicating the animal.

(A) Distribution of CSI values for all analyzed neurons in LSD and LSI. For each cell, the CSI value is taken from the trajectory with the highest z-scored CSI value relative to the shuffle distribution. Light orange: full distribution of all cells. Dark orange: highlighted part of the distribution that represent cells with significant CSI value (Monte-Carlo p-value < 0.05). (B) CSI values increase for cells located closer to the white matter. Dots represent individual cells with significant CSI value from all sessions and animals. For each cell, the CSI value is taken from the journey with the highest z-scored CSI value relative to the shuffle distribution. Black line and shaded region represent linear fit and 95% confidence interval (r=0.23, p=1.5×10-5). (C) Mean CSI value is significantly higher in LSD as compared to LSI (mean±sem CSI, LSD 0.36±0.02, LSI 0.29±0.01; two-sided two-sample t-test, t(352)=2.70, p=0.0074). Thin lines represent mean CSI value for individual sessions, with the line color indicating the animal.

(A) Venn diagram showing overlap of cell populations with significant theta rhythmicity and theta cycle skipping in LSD (B) Histogram of the number of cells in LSD with a significant cycle skipping index for all possible journey combinations. Note that for most cells (52.3%; yellow) cycle skipping occurs only on a single journey type. For another population of cells (23.4%; blue), cycle skipping occurs on outbound, inbound, left, or right journeys. (C) Venn diagram showing overlap of cell populations with significant theta rhythmicity and theta cycle skipping in LSI (D) Histogram of the number of cells in LSI with a significant cycle skipping index for all possible journey combinations. Note that for most cells (56.7%; yellow) cycle skipping occurs only on a single journey type. For another population of cells (21.5%; blue), cycle skipping occurs on outbound, inbound, left, or right journeys.

Spatially resolved auto-correlation (top), corresponding cycle skipping index (CSI; middle) and spatial tuning (bottom) for four example cells during outbound left journeys (animal LS-k-7). The same cells as in Figure 4A are shown). Auto-correlation and cycle skipping index were computed for overlapping 60 cm long sections along the trajectory to the goal. In the middle plot, colored points indicate significant cycle skipping (p<0.05), light grey crosses indicate that too few spikes (<50) were available and no cycle skipping index was computed. Black vertical lines indicate the choice point separating the stem and goal arms.

Spatially resolved auto-correlation (top), corresponding cycle skipping index (CSI; middle) and spatial tuning (bottom) for four example cells during inbound left journeys (animal LS-k-8). The same cells as in Figure 4B are shown. Auto-correlation and cycle skipping index were computed for overlapping 60 cm long sections along the trajectory to the goal. In the middle plot, colored points indicate significant cycle skipping (p<0.05), light grey crosses indicate that too few spikes (<50) were available and no cycle skipping index was computed. Black vertical lines indicate the choice point separating the stem and goal arms.

Distribution of spatial information in bits/spike (A) and bits/second (B) of all analyzed neurons in LSD (top) and LSI (bottom). Light orange: full distribution of all cells. Dark orange: highlighted part of the distribution that represent cells with significant spatial information (Monte-Carlo p-value < 0.01). Overall mean±sem spatial information in bits/spike: LSD 0.42±0.02, LSI 0.21±0.01.

(A,B,C) Distribution of outbound goal arm (A), inbound goal arm (B) and directional (C) selectivity of all analyzed neurons in LSD and LSI. Light orange: full distribution of all cells. Dark orange: highlighted part of the distribution that represent cells with significant selectivity (Monte-Carlo p-value < 0.01). (D,E,F) Values of outbound goal arm (D), inbound goal arm (E) and directional (F) selectivity index increases for cells located closer to the white matter. Dots represent individual cells with significant selectivity index from all sessions and animals. Black line and shaded region represent linear fit and 95% confidence interval. (G,H,I) Mean value of outbound goal arm (G), inbound goal arm (H) and directional (I) selectivity index is significantly higher in LSD as compared to LSI (mean±sem selectivity, outbound goal arm: LSD 0.75±0.02, LSI 0.49±0.02, two-sided two-sample t-test, t(434)=9.40, p=3.1×10-19; inbound goal arm: LSD 0.61±0.03, LSI 0.44±0.02, two-sided two-sample t-test, t(237)=4.65, p=5.6×10-6; directional: LSD 0.48±0.02, LSI 0.29±0.01, two-sided two-sample t-test, t(416)=9.14, p=2.7×10-18). (J,K) Overlap between goal arm and directional selectivity for cells

(A) Distribution of prospective coding of all analyzed neurons in LSD and LSI. Light orange: full distribution of all cells. Dark orange: highlighted part of the distribution that represent cells with significant prospective coding (Monte-Carlo p-value < 0.01). (B) Distribution of retrospective coding of all analyzed neurons in LSD and LSI. Light orange: full distribution of all cells. Dark orange: highlighted part of the distribution that represent cells with significant retrospective coding (Monte-Carlo p-value < 0.01).

Dependency of decoding performance for position (top) and direction (bottom) on the number cells included in the analysis. Left: all LSD and LSI combined; right: separately for LSD and LSI cells. The result for each session is plotted separately. Dots: the decoding performance for each session when including all available cells. Lines: the decoding performance for each session when subsampling the cells. Note that for a similar decoding performance, fewer LSD cells than LSI are required.

Average posterior probability following theta time scale decoding that is assigned to non-local maze arms (i.e., the arms where the animal is not currently located). Data for the goal arms is combined and position is expressed as distance to home. Vertical line indicates the choice point. Thin lines represent data for individual sessions; thick lines represent average across sessions.

(A) Auto- and cross-correlation of posterior probability time courses for the three maze sections when the animal is running along the stem in the inbound direction towards home. Correlations are computed as the Pearson correlation coefficient at varying time lags. For each plot, drawings at the left show the animal’s behavior (black arrow) and the maze sections for which correlations are computed (color indicates whether the highlighted maze section is local (blue) or non-local (orange) relative to the animal’s position on the track). Top: auto-correlation of local representations in the stem. Second from top: auto-correlations of non-local representations in the two goal arms. Third from top: cross-correlations between local and non-local representations. Bottom: cross-correlation between non-local representations in the two goal arms. (B) Same as (A), but for times when the animal is running along one of the goal arms in the outbound direction towards the reward platform. Equivalent correlations for the two goal arms are computed jointly.

(A) Left: distribution of CSI values for LSD (top) and LSI (bottom) neurons in sessions in which rats performed the alternation task. For each cell, the CSI value is taken from the trajectory with the highest z-scored CSI value relative to the shuffle distribution. Light orange: full distribution of all cells. Dark orange: highlighted part of the distribution that represent cells with significant CSI value (Monte-Carlo p-value < 0.05). Right: mean CSI value is significantly higher in LSD as compared to LSI (mean±sem CSI, LSD 0.37±0.03, LSI 0.28±0.02; two-sided two-sample t-test, t(211)=2.90, p=0.0041). Thin lines represent mean CSI value for individual sessions, with the line color indicating the animal. (B) Same as (A), but for sessions in which animals performed the switching task. Mean CSI value (right) is not different between LSD and LSI (mean±sem CSI, LSD 0.32±0.03, LSI 0.29±0.02; two-sided two-sample t-test, t(139)=0.69, p=0.49).