Fig 1.
Organisation of head direction circuit in the Central Complex.
(A) Major central complex regions responsible for heading tracking: ring shaped ellipsoid body (EB; blue), bulb (BU; yellow) and protocerebral bridge (PB; green). Projection patterns of two example EPG cells (blue arrows) each from one EB wedge projecting to the equivalent glomeruli (left or right) of the PB; and PEN cells (green arrows) returning projections to one tile (made up of 2 wedges) clockwise or anticlockwise further around the ring. (B) Six populations of Leaky Integrate and Fire (LIF) neurons representing cell types of the central complex. Angular velocity information is provided to PEN neurons (green), positive and negative angular velocities are delivered to the right and left PEN neurons respectively. Visual scenes are provided via R2 and R4 ring neurons (yellow). Ring neuron activation is determined by each cell’s receptive field (two examples of averaged Drosophila ring neuron receptive fields [28] are shown, with excitatory (red) and inhibitory (blue) regions and the field of view indicated by the frame, which is 120 x 270 degrees). EPG cells (blue) send excitatory connections back onto themselves and to R (red), Δ7 (orange), and PEN cells. EPG cells receive excitatory input from PEN cells, and inhibitory connections from R, Δ7, R2 and R4 cells. (C) Effective circuit connections between each of 16 EPG (blue) and 16 PEN (green) cells split into right and left projecting cells. PEN cells return projections to both EPG cells one wedge further clockwise or anticlockwise around the ring. (D) Connections between all EPG cells and a single (out of 8) Δ7 cell. The connection pattern results in strongest inhibitory input to EPG cells opposite to the bump position. (E) Each ring neuron makes connections with every EPG cell in the ring. (F) Matrix showing all ring neuron to EPG cell connections, including strengthened weights between coactive ring and EPG cells.
Fig 2.
Specific cell to cell connections between populations.
(A) Matrix showing connections between EPG, PEN, Δ7 and R cells, following previously determined connectivity [22, 24, 25]. Blue and red indicate excitatory and inhibitory connections respectively. EPG → EPG (weight 0.02), EPG → PEN (weight 0.13), EPG → R (weight 0.01), EPG → Δ7 (weight 0.05), PEN → EPG (weight 0.14), R → EPG (weight -1.3), and Δ7 → EPG (weight -2.6). (B) R2 (top) and R4 (bottom) ring neuron receptive field centers arranged in hexagonal pattern over the visual scene. Cells are ordered such that their receptive fields are arranged from bottom left to the top right of the scene along rows. The cell at the end of each row is labeled. (C) Inhibitory connections between ring neurons. These connections decay with distance between field centers with random scaling to produce irregular inhibitory regions of the receptive fields (see S1 Fig). R4 → R4 (max weight 0.3) and R2 → R2 (max weight 0.3). Not shown R4 → EPG (initial random weight between 0 and -0.05), R2 → EPG (initial random weight between 0 and -0.05).
Table 1.
Connection weights between populations.
Fig 3.
Bump dynamics for vertical bar visual scenes.
(A) Raster plots of ring neuron and EPG cell spikes over 3 revolutions with a visual scene of a single bright vertical bar. For two revolutions both visual and angular velocity input are provided to the model. Only visual input is provided during the final revolution (green shaded region). The unwrapped ground truth heading and estimated heading (EPG cell at the center of the bump) are also shown. (B) Evolution of the synaptic weight matrix from random initial weights after 1 and 2 revolutions for the one bar visual scene. (C) Raster plots of ring neuron and EPG cell spikes over 9 revolutions. The initial 3 revolutions with a visual scene with a single bright vertical bar. For a further 3 revolutions an ambiguous visual scene with two identical bright vertical bars separated by 180 degrees (blue shaded region). For the final three revolutions the single bar visual scene was returned with the bar at one of the two offsets. A single bump of activity is maintained throughout by ring attractor dynamics. (D) Evolution of the synaptic weight matrix from random initial weights after each visual scene presentation. When two bars are presented, both positions are represented in the weight matrix. The final weight matrix can toggle between two states depending on the offset position of the final vertical bar (red box). Either maintaining the original mapping (3 revolutions vs 9 revolutions left) or remapping to the new bar position (3 revolutions vs 9 revolutions right). (E) Input current to PEN cells required to produce bump movement of different angular velocities. Below input current of 0.06 bump movement cannot be produced. (F) RMSE over the full 3 rotations when only input to PEN cells is provided for a range of angular velocities. Red star shows baseline RMSE for the angular velocity used in the 3 revolutions experiments. (G) RMSE during probe trial of the 3 revolutions experiment at a range of angular velocities. Hexagonal, Square Grid and Random symmetrical receptive field patterns all result in similar performance.
Fig 4.
Bump dynamics for revolutions in two natural visual scenes during rotation and translation.
(A,F) Single frame from each of the greyscale panoramic videos. Histogram equalisation is applied to each downsampled video (see Methods). A: Frame video with camera rotation only. F: Frame video with circular camera translation and rotation. (B,G) Correlation matrices showing correlation between each frame for three rotations. Strong correlation is seen between frames at the same rotation angle, but this correlation is not due to natural noise in the video. (C,H) Correlation matrices showing correlation between ring neuron activations at each frame for three rotations. Strong correlation is seen between activations for frames at the same rotation angle. (D,J) Raster plots of ring neuron and EPG cell spikes over 3 revolutions, and the unwrapped ground truth heading and estimated heading (EPG cell at the center of the bump). For two revolutions both visual and angular velocity input are provided to the model. Only visual input provided during the final revolution/probe trial (green shaded area). (E,K) Evolution of the synaptic weight matrix from random initial weights after 1 and 2 revolutions.
Fig 5.
Performance across different natural scenes during rotation and translation.
(A) Mean RMSE (degrees) between ground truth and estimated heading during the probe trial with only visual information available, over 20 simulated seeds and 16 shifts of the panorama initial angle ± bootstrapped standard error (top), and total number of failed simulations for each natural scene, where the bump of activity is lost (bottom). Scenes are separated into camera rotation only (left; 23 scenes), and circular translation and rotation (right; 10 scenes). (B-G) Comparisons of spiking and image properties between natural scenes with more than 1% failure rate, high or low variance. (B) Number of failures. (C) Mean ring neuron spikes. (D) Total number of ring neurons active. (E) Number of ring neurons with multi-directional receptive fields. (F) Mean over ring neuron activation correlation matrix. (G) Mean over video frame correlation matrix. (For all plots *** ANOVA p<0.001; ** ANOVA p<0.01; * ANOVA p<0.05).