Phase precession depends on running direction in intrinsic models but not extrinsic models. (A) Simulated trajectories (duration 2 s) in a 2-D environment (80 × 80 cm) with speed 20 cm/s in left and right (left column), diagonal (middle), and up and down (right) directions. (B-D) Simulation results from the intrinsic model (with fixed asymmetrical connectivity inspired from Tsodyks et al. (1996) model). Place cells only project synapses to their right neighbors. Spike raster plots of place cells along the orange (left panel) and light green (right panel) trajectories (colors defined in A). Theta sequences flip order with reversed running direction. Phase-position relation for the spikes colored in a. Linear-circular regression (gray line) parameters are indicated on top. Positions of the animal at the first and last spike are normalized to 0 and 1, respectively. (D) Averaged cross-correlation of all cell pairs separated by 4cm along the trajectory. Reversal of running direction does not flip the sign of the peak lags. (E-G) Same as A-D, but for the extrinsic model (spike-based variant of Romani and Tsodyks (2015) model). Synaptic connections are symmetrical but short-term depression penalizes the recurrent synaptic drive of the place cells “behind” the animal. (E-F) Theta sequences and phase precession are present and remain invariant for different movement directions. (G) Cross-correlations flip sign of peak lags when trajectory is reversed.

Model parameters used in simulations according to Figure panels

Directional input gives rise to spikes at lower theta phase. (A) Directional input component of an example place cell. (B) Total sensory input as the sum of directional and positional drive of an example place cell for the animal running in the best (red dashed line, left) and the worst (blue dashed line, right) heading direction of the cell. The sensory input is modelled by oscillatory currents arriving with +70° phase shift relative to theta peaks (gray vertical lines). Place fields are defined by a 5cm rectangular envelope. Solid lines depict the input current including short-term synaptic facilitation. (C) Synaptic weights (Wij, color) from the place cell at the center (darkest dot) to its neighbors in the 2-D environment. Each dot is a place field center in 2-D space. Arrows depict their best directions. (D) Spike raster plot sorted by visiting order of the place fields along the trajectory. Spikes of the cells with best and worst direction are colored in red and blue, respectively. (E) Phase position plots for the cells with best and worst direction from d (labels as in Figure 1C). The mean phase is marked as horizontal gray bar. (F) Example place cell centers with best (< 30° different from the trajectory; red) and worst (> 150°; blue) directions relative to the rightward trajectory (gray line). Only centers of cells that fire more than 5 spikes are shown. (G) Slopes and onsets of phase precession of the population from (F). Marginal slope and onset distributions are plotted on top and right, respectively. Note higher phase onset in the blue population with trajectory aligned to the worst directions. (H) Spike phase distributions. Higher directional inputs generate lower spike phases. Average spike correlation between all pairs with 4cm of horizontal distance difference when the animal runs rightwards and leftwards. Peak lags are flipped as expected from an extrinsic model.

DG-CA3 loop introduces directionality of theta sequences. (A) Illustration of synaptic connections from CA3 place cells to DG and vice versa. DG layer mirrors the place cell population in CA3 and redirects the CA3 inputs back to different locations. Here, DG cells project into CA3 place cells with fields 4 cm displaced to the right of the pre-synaptic CA3 cells. θDG denotes the angular difference between the DG projection direction and the animal’s movement direction. (B) Spike raster plots sorted by cell indices along the trajectory (2 s duration) from x=-20cm to x=20cm. Cells with best and worst angles are marked by red and blue colors, respectively. (C) Phase-position plots as is Figure 2E. (D) Distributions of precession slopes, onsets and spike phases as in Figure 2G-H. (E-H) Same as a-d, but with DG cells projecting opposite to the animal’s movement direction (θDG = 180°). (I) Average spike correlations for θDG = 0° and θDG = 180° for pairs separated by 4cm along the trajectory. Note that for θDG = 180°, there is a relative excess of spike-pairs with positive lags. (J) Left: Intrinsicity and extrinsicity (see Methods) for all pairs from the populations with best (red) and worst (blue) direction. Pairs above and below the identity line are classified as intrinsic and extrinsic pairs, respectively. Numbers are the ratios of extrinsic to intrinsic pairs. Note that the red best direction pairs are more extrinsic than the blue worst direction pairs due to higher sensory input. Middle: Ex/Intrinsicity of pairs with similar (< 30°) and dissimilar (> 150°) preferred angles. Pairs with similar preferred angle are more intrinsic due to stronger DG-CA3 recurrence. Right: Cumulative distribution of the differences between extrinsicity and intrinsicity. Dissimilar and best direction pairs have higher bias to extrinsicity than similar and worst direction pairs, respectively.

DG lesion reduces temporal correlations in theta sequences. DG recurrence is turned off to simulate the lesion condition. (A) Positional sensory inputs into a place cell in lesion (purple) and control (green) cases. The control case is identical to Fig 3. In the lesion case, DG input is compensated by increased sensory input with increased probability of synaptic release, hence reduced short-term synaptic facilitation. (B) Theta compression, i.e., correlation between peak correlation lag and distance of field centers in the control case. Each dot represents a field pair. Linear-circular regression line is indicated in black. Note that the sign of regression slope (a in radians per maximum pair distance) is determined by the directions of DG loop (negative in θDG = 180°). (C) same as b, but for the lesion case. Theta compression is reduced as compared to the control condition.

Extrinsic and intrinsic sequences are distinguishable through temporal properties in 2-D space. (A) Left: Schematic illustration of DG projection being tilted by 45° relative to the trajectory. Right: Distributions of phase precession onsets and slopes from the place cells along the trajectory as in Figure 2G. (B) Slopes (left), onsets (middle) and mean spike phases (right) of phase precession from the place cells as a function of field center. High spike phases and onsets occur along the DG-loop orientation where intrinsic spiking dominates. (C-D) Same as (A-B), but DG-loop projection is at 225° relative to trajectory. (D) For DG loops pointing opposite to the sensorimotor drive, prospective firing along the DG loop yields less steep precession slopes and lower onset. (E) Extrinsicity and intrinsicity of all pairs along the trajectory as in Figure 3J. Some pairs are totally extrinsic (Ex=1) because DG projection is absent at those parts of the trajectory. (F) Density of extrinsic/intrinsic pairs as a function of the orientation of field center difference vector relative to the x axis. Intrinsic fields peak at 45°. (G) Same as (A-D), but DG projections are perpendicular to the trajectory at 90° (top) and 270°. Prospective spikes from intrinsic sequences are initiated in the perpendicular directions. (G) Same as (E), but with higher Ex-In ratios. (I) Intrinsic pairs are at ±90°.

Intrinsic sequences provide a stable landmark for positional decoding using a tempotron. (A) Top: A tempotron is trained separately for place cells population within the top (with DG loop; blue) and bottom (no DG loop; red) squares, to recognize the presence of the corresponding sequence activities. DG-loop rightward projection is indicated by blue arrow and only exists in the blue square. Non-moving spatial inputs are applied to neurons with fields at two locations (marked by black crosses) to play out spike sequences. Bottom: Resulting spikes of place cells with centers from x=-10 to x=10 fixed at y=+20 (with-loop, top raster plot) and y=-20 (no-loop, bottom). Each theta cycle is one (+) training pattern, in which the tempotron is trained to classify by eliciting a spike. (B) Spikes of place cells from x=-10 to x=10 (in each rectangular row) fixed at different values of y. Only one theta cycle is shown as an example pattern. Each place cell delivers spikes to a dendrite of the tempotron, producing post-synaptic potentials (PSPs) at the soma (line plot at the bottom). Synaptic weights are adapted by the tempotron learning rule such that PSPs can cross the threshold (gray line) and fire for the detection of the sequence. After the tempotron has fired, the PSPs will be shunted. (C) Sequence detection is tested on trajectory directions (φ) from 0° to 360° with a 15° increment to detect the presence of sequence. (D) Detection accuracies (ACC) for with-loop (red line) and no-loop (blue) populations. Note that the tempotron cannot detect the no-loop sequences when tested on trajectories at various angles. (E) Detection of intrinsic sequence from a trajectory φ = 180° for the DG-loop population. Spike raster is shown for every two horizontal rows of place cells in the arena and color-coded by the synaptic weights (see color bar on the right). Tempotron soma potential is shown at the bottom for each pattern. (F) Same as (E), but for no-loop inputs. The tempotron remains silent.