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.

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.

Overview of data.

An overview of all analysed sessions from four animals performing either an alternation task or a switching task. For both tasks, the number of trials is indicated, and for the switching task the number of reward contingency switches is indicated between brackets. For both septal subregions LSD and LSI, the number of recorded cells and corresponding mean firing rate are listed.

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). The inset shows values for theta peak index, Monte-Carlo p-value a z-scored index relative to shuffle distribution.

(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.

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 (56.9%; yellow) cycle skipping occurs only on a single journey type. For another population of cells (20.9%; blue), cycle skipping occurs on outbound, inbound, left, or right journeys.

(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 representing cells with significant CSI value (corrected 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 values 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. The black line and shaded region represent the linear fit and 95% confidence interval (r=0.27, p=1.8×10−5). (C) The mean CSI value of cycle skipping cells is significantly higher in LSD as compared to LSI (mean±sem CSI, LSD 0.40±0.02, LSI 0.32±0.02; two-sided two-sample t-test, t(237)=2.82, p=0.0053). Thin lines represent the 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 (49.3%; yellow) cycle skipping occurs only on a single journey type. For another population of cells (28.0%; 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 (60.4%; yellow) cycle skipping occurs only on a single journey type. For another population of cells (17.7%; blue), cycle skipping occurs on outbound, inbound, left, or right journeys.

(A) Spatially resolved auto-correlation (top), corresponding cycle skipping index (CSI; middle), and spatial tuning (bottom) for four example cells during outbound journeys. 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. The first and third example were recorded in the alternation task, the other two examples in the switching task. (B) Same as (A) but for cells with significant cycle skipping on inbound journeys. The first and second example were recorded in the switching task, the other two examples in the alternation task.

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

(A) Spatially-resolved (overlapping 60 cm bins) cycle skipping index for all outbound (left) and inbound (right) cycle skipping cells (in both tasks) with a minimum of 50 spikes in at least one of the spatial bins. Left/right trajectories were analyzed separately. Spatial bins that do not meet the minimum number of spike requirement are not shown, exposing the background hatching pattern. Cell-trajectory pairs are sorted according to the location of their maximum CSI value. (B) Average CSI value as a function of location along outbound (left) and inbound (right) trajectories. Thick lines represent average across all analyzed cells-trajectory pairs to/from left and right goals. The shaded region represents 95% CI. (C) Same as (B) but for the percent of analyzed cells-trajectory pairs with significant cycle skipping.

(A) Left: lateral septum cells that exhibit theta cycle skipping on outbound trajectories increase their firing rate from stem to goal arm. The trajectory-specific (i.e., outbound left and outbound right) spatial tuning curves were mean-corrected for each cell. The solid line represents the average rate deviation for all cell-outbound trajectory pairs with significant theta cycle skipping. The shaded area represents the 95% CI. Right: No increase in firing rate was present for cell-outbound trajectory combinations without theta cycle skipping. (B) Quantification of the goal arm rate bias across all cell-outbound trajectory pairs with or without significant theta cycle skipping. Welch’s independent samples t-test: t(260.3)=3.63, p=0.00034. (C) The same analysis as in (A), but for inbound trajectories. (D) Quantification of the goal arm rate bias across all cell-inbound trajectory pairs with or without significant theta cycle skipping. Welch’s independent samples t-test: t(219.1)=2.36, p=0.019.

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). Examples in top row and right most example in bottom row are recorded in the alternation task, other examples are recorded in the switching task. (B) Distribution of outbound goal arm selectivity (left), inbound goal arm selectivity (middle), and directional selectivity (right) of all analyzed neurons in LSD and LSI. Light gray: full distribution of all cells. Black: highlighted part of the distribution that represent cells with significant selectivity (Monte-Carlo p-value < 0.01).

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 represents cells with significant spatial information (Monte-Carlo p-value < 0.01). Overall mean±sem of significant cell population, spatial information in bits/spike: LSD 0.42±0.02, LSI 0.21±0.01; spatial information in bits/second: LSD 0.69±0.05, LSI 0.37±0.02. Welch’s independent t-test comparing spatial information of significant cell populations in LSD and LSI, bits/spike: t(358.5)=8.17, p=5.3×10−15; bits/second: t(330.0)=6.38, p=6.0×10−10.

(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 in LSD (J) and LSI (K).

(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 representing 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 representing cells with significant retrospective coding (Monte-Carlo p-value < 0.01). (C) Binary classification of left/right outbound trajectory as a function location on the maze. Thin lines: individual sessions; thick line: mean across sessions; shaded region: 95% CI. (D) Binary classification of left/right inbound trajectory as a function location on the maze. Thin lines: individual sessions; thick line: mean across sessions; shaded region: 95% CI. (E) Binary classification of run direction (outbound or inbound) as a function of location on the maze. Thin lines: individual sessions; thick line” mean across sessions; shaded region: 95% CI.

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. (B) 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. Vertical and horizontal lines indicate mean performance across sessions.

Spatial coding is stronger is LSD than LSI.

(A,B) Dependency of decoding performance for position (A) and direction (B) on the number of cells included in the decoding model. 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 cells are required. (C) Comparison of decoding performance between LSD and LSI for a fixed cell population (n=20 cells). Each connected pair of dots represents a single session. Horizontal and vertical lines represent the population mean. Wilcoxon signed rank test, position: statistic=0.0, p=0.00098; direction: statistic=5.0, p=0.0098.

Neural decoding of theta-scale dynamics in lateral septum.

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 ≥0.5 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 (left) and one inbound journey (right) is shown. 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.

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.

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.

(A) Cycle skipping index computed from the auto-correlations of local and non-local spatial representations, separately for outbound and inbound trajectories. Two-way ANOVA for the effects of locality and run direction on cycle skipping index: no significant interaction between locality and run direction, F(1,44)=0.30, p=0.59; a significant main effect for locality, F(1,44)=20.77, p=4.1×10−5; no significant main effect for run direction, F(1,44)=7.7×10−5, p=0.99). (B) Peak cross-correlation between the two non-local spatial representations for outbound and inbound trajectories. Paired samples t-test: t(11)=2.83, p=0.016.

(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.

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. (C) 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 10 for details. (D) Same as (C), but for times when the animal is running along one of the goal arms in the inbound direction towards the choice point. (E) Quantification of the cycle skipping index computed from the auto-correlation of the local and non-local spatial representations for both run directions and separated by task. The results of a three-way ANOVA to evaluate the effects of task, locality, and run direction on the cycle skipping index are presented in Figure 11 – table supplement 1. (F) Quantification of the peak cross-correlation of the non-local spatial representations for both run-directions and separated by task. The results of a two-way ANOVA for the effects of run direction and task on peak correlation are presented in Figure 11 – table supplement 3. Corresponding post-hoc comparisons are listed in Figure 11 – table supplement 4.

(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 (corrected Monte-Carlo p-value < 0.05). Right: mean CSI value is significantly higher in LSD as compared to LSI (mean±sem CSI, LSD 0.40±0.03, LSI 0.29±0.02; two-sided two-sample t-test, t(152)=3.38, p=0.00093). 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 0.41±0.04, LSI 0.36±0.03; two-sided two-sample t-test, t(83)=0.79, p=0.43).

(A) Auto– and cross-correlations of the non-local spatial representations in the first five outbound trajectories in the alternation task (left) and switching task (right). (B) Task comparison of the cycle skipping index computed from the auto-correlation of non-local spatial representations in the first five outbound trajectories of each session. Independent samples t-test: t(10)=1.12, p=0.29. (C) Task comparison of the peak cross-correlation of non-local spatial representations in the first five outbound trajectories of each session. Independent samples t-test: t(10)=2.54, p=0.029.

(A) Auto– and cross-correlations of the non-local spatial representations in the five trials before (left) and after (right) the change in reward contingency in switching task sessions. Only outbound trajectories are included in the analysis. (B) Pre– vs post-switch comparison of the cycle skipping index computed from the auto-correlation of non-local spatial representations in outbound trajectories. Paired samples t-test: t(5)=1.57, p=0.018. (C) Pre– vs post-switch comparison of the peak cross-correlation of non-local spatial representations in outbound trajectories. Paired samples t-test: t(5)=1.64, p=0.016.

Three-way ANOVA for the effect of locality, direction, and task on the cycle skipping index of decoded spatial representations.

Post-hoc comparisons for three-way ANOVA in Figure 11 – table supplement 1.

Two-way ANOVA for the effect of direction and task on the peak cross-correlation of non-local spatial representations.

Post-hoc comparisons for two-way ANOVA in Figure 11 – table supplement 3.