Fig 1.
How do axonal GJs help to efficiently encode the axis of ego rotation, θ, in the VS network of the fly?
(A) Schematic depiction of the visual stimuli used in the simulation. Six natural images (five are shown here except the frontal one) were randomly selected from the Van Hateren and Schilstra dataset [51]; each image was patched on a different face of a cube. Assuming that the fly is located in the center of this cube, we obtain the optic flow pattern of the fly’s ego rotation around θ (thick blue arrow) by rotating this cube around θ. (B) The fly visual system is composed of a retina, lamina, medulla, lobula and lobula plate. The retina, lamina and medulla are organized retinotopically. The vertical system (VS) network in the lobula plate integrates output from the upstream LMD units and sends global motion-sensitive signals downstream. (C) The VS model used in the present study; in this figure, the 10 VS cells of the right visual system are shown. In this model, the complex dendritic branches of the VS cells are reduced to a single compartment (gDe); this dendritic compartment is connected via an axial resistance to the axonal compartment (gAx-De). The VS cells are connected to each other sequentially via axonal GJs; each VS has a preferred dendritic receptive field (RF) center (e.g., 10° for VS1, 26° for VS2 and 154° for VS10, as indicated). The computed dendritic input following visual input are shown in red and purple for VS1 and VS10, respectively. The corresponding axonal voltages (VAx) are also shown. In this work, we only used the first 10 ms of the dendritic input and the axonal output.
Table 1.
The centers of dendritic RF for VS1-10 (right eye).
Fig 2.
GJs reduce the variability and enhance the clustering of the combined axonal responses to different axes of rotation.
(A) Response of VS5 to stimuli embedded with natural scenes as a function of the rotation axis when GJs are absent from the VS network. The continuous line shows the mean voltage response; the pink shaded area represents one standard deviation from that mean. (B) As in A but when the VS cells are all connected with GJs = 1 μS (see the circuit in Fig 1C). (C) Joint axonal voltage response of VS5 versus VS6 in the absence of GJs. A total of 1000 samples for both θ = 0° (green) and for θ = 60° (red) in response to natural stimuli are shown (see Materials and Methods). Their 95% confidence ellipses are shown in black. (D) As in C but with GJs = 1 μS. (E) Joint axonal voltages for VS5-6-7 of the left compound eye without GJs and (F) with GJs = 1 μS for six different axes of rotation (indicated by respective colors). Note the greatly improved separability of the axes of rotation in the presence of GJs.
Fig 3.
Near-optimal motion representation with GJs.
(A) Near optimal motion representation for natural stimuli due to GJs by both triplets of VS cells (blue cross) and by the whole VS network (blue dot). The efficiency of the representation for a subpopulation is denoted by a single point in the IDe−Ax − Iθ−Ax plane, which shows how much information (in bits) corresponds to the neural cost and how much information is provided at this cost to represent the axis of rotation. This plane shows the feasible (blue region) and infeasible (white region) separated by the bound , dark blue line (see Materials and Methods) for all axes of rotation of natural stimuli. The error bars depicting encoding efficiencies for triplets with/without GJs (blue vs. orange, respectively). Single cells with/without GJs appear in green/yellow squares, respectively (all 20 individual VS cells behaved very similarly to each other). The encoding efficiency of the whole VS network with/without GJs is shown in blue/orange circles. (B) The scatterplot of efficiencies for representations of all 120 triplets (all possible triplets out of the 10 VS cells; the same triplets were used in both sides of the visual system), with/without GJs (blue/orange respectively). The arrows point to VS5-6-7, the triplet connecting downstream to the neck motor center. Note the considerable improvement in efficiency due to GJs for this triplet. (C) Similar to (A), but for checkerboard stimuli. (D) Similar to (B), but for checkerboard stimuli.
Fig 4.
With GJs, the near-optimality encoding by the VS 5-6-7 triplet is robust over a wide range of signal-to-noise ratios.
(A) The information curve and the encoding efficiency of the axis of rotation by the VS 5-6-7 triplet in the IDe−Ax − Iθ−Ax plane to varying contrast levels of natural stimuli (contrast is coded by colors as shown in inset). The cases with GJs are represented by triangles and without GJs by circles. The blue curve is the same as in Fig 3. Note that for the case represented by the orange triangle (60% contrast with GJs) more information Iθ−Ax is extracted about motion and is closer to the information curve as compared to the orange, cyan and purple circles (representing 60%, 80% and 100% contrast without GJs, respectively). (B) As in (A), but using checkerboard stimuli. (C) As in (B) but with different luminance levels.
Fig 5.
GJs are particularly important for the fly's survival when encoding is based on the VS 5-6-7 triplet.
(A) RMSE for estimating axes of rotation (1600 samples, each in 5° steps) based on the encoding by the VS 5-6-7 triplet with GJs (blue) and without GJs (orange). The RMSE using all VS 1–10 cells with GJs is shown in magenta. (B) The variability of the estimated axis of rotation for the case of θ = 45° with (blue, with radius 1) and without (orange, with radius 1.5) GJs. Note that with GJs, the error falls within the same quadrant whereas without GJs the error is almost 180°. This means that without GJs, the fly cannot encode pitch axis correctly. Since the VS 5-6-7 triplet is connected downstream to the fly motor system, GJs are essential for the fly’s behavior, e.g., avoiding swats (see text). (C) Similar to (B), but for the θ = 180° stimulus.