Fig 1.
Overall model anatomical diagram.
(A) Inputs to the CX from different other brain regions. We consider these inputs as three types. Sensory Compasses Insects are sensitive to various cues that give information about their allocentric orientation. Sensory compass pathways converge to the ellipsoid body (EB) where they connect with the EPGs, mostly through Ring Neurons (ER). Movement perception The CX receives information about self motion at the level of the Noduli (NO), mostly from visual (optic flow) and/or mechanosensory (proprioception) origin. Higher level neuropils The CX receives a large number of inputs from higher level regions that process multisensory information. Mushroom Bodies (MB) and Lateral Horns (LH), for example, mostly connect to the CX at the level of the fan-shaped body (FB) through FB tangential (FBt) neurons. (B) CX neuropils and the different modeled neuron type connectivity. The whole circuitry can roughly be segmented in three different functional parts, (1) the inner compass circuit (Fig D in S1 Text), represented on the top right by 4 cell types, EPG, PEG, PEN and Δ7, and projecting in-between the EB to the protocerebral bridge (PB), (2) the steering circuit (Fig 3), represented on the top left, is located between the PB, the FB and the lateral accessory lobes (LAL), including mainly 3 cell types, PFN, hΔ and PFL, and (3) a long-term vector memory circuit (Fig 4), represented by the parallel neural types FBt and DAN (Dopaminergic neurons) presenting a tangential projection pattern across the whole FB functional columns.
Fig 2.
Functional principle of the CX steering circuit.
A-C Different model abstraction levels. (A) Vector operations underlying the transformation of the current and desired headings into a steering output signal. (C) Neurons population activity through the different CX neuropils involved in the steering circuit. (B) Mathematical principles of the transformation of the neuron population activities into a steering output signal. I-IV Steps of the transformation from a heading and desired heading to the steering output signal. (I) Compass level. The neuron activity has a bump at the level of the ellipsoid body that follows the allocentric orientation of the agent. This bump, as well as the bump representing the goal orientation, take the form of a sinusoid in the model, where the peak position and amplitude can be interpreted as respectively the direction and length of a vector. (II) Compass signal copy. At the level of the protocerebral bridge the compass signal is copied into 2 corresponding hemispheric signals. This allows idiothetic rotation cues to move the compass (see Fig D in S1 Text) and, downstream, a comparison of the compass with the goal direction signals. (III) Compass and goal direction comparison. At the level of the fan-shaped body, the two copies of the compass signal are compared with rightward and leftward shifted copies of the desired heading. This allows the identification of the required direction of rotation to align with the desired orientation. (IV) Left and right hemisphere comparison. The summation of resulting population activity in each hemisphere, at the level of the lateral accessory lobes, results in a differential signal (left-right) that can be used to generate the appropriate turn toward the desired orientation. Clipart(s) in the figure have been modified from https://openclipart.org/.
Table 1.
Interspecies central complex neuropil and neuron names correspondence.
Originally from Sayre et al., 2021 [36].
Fig 3.
(A) Circuit diagram incorporating the direct PFN − to − PFL and the indirect PFN − to − hΔ − to − PFL pathways. The activity rate of hΔ is updated continuously based on the PFN inputs to retain the PI memory. (B) Detailed connectivity diagram of the PI circuit, from the compass circuit output (Δ7) to the steering generator (Comparison of summed outputs of the PFL from both hemispheres). (C) Vectors encoded by the PI circuit over the path of the agent. The direct PFN − PFL pathway encodes a vector of constant length and with the immediate orientation of the agent. Note that, because we did not use a purely theoretical sinusoidal signal to represent the inner compass, the PFN population signal inherit some variability, in amplitude and shape, that can modify the length of this vector in a relative small magnitude. The indirect PFN − hΔ-PFL pathway encodes the integrated homing vector that points to the starting location of the path (nest/home). Clipart(s) in the figure have been modified from https://openclipart.org/.
Fig 4.
(A) PI circuit with the addition of vector memory. The FBt pathways receive control from contextual/motivational signals based on the inner state (e.g. hunger). The DANs pathway receives inputs from reward signal(s) that define when a condition (dependent also on the context/task) is fulfilled and trigger a modulation of the FBt − PFN or FBt − hΔ synaptic strength at the level of PFN and/or hΔ axons to PFL. (B) Proposed mechanism for vector memory by synaptic modulation within the FBt − DAN − PFN/hΔ trios. Whenever a DAN is activated, any active FBt has its synaptic strength in every column modified proportionally to the activity rate of the corresponding PFN or the hΔ. The modulation of the synaptic weight could happen at the level of either the presynaptic partner (FBt), the postsynaptic level (PFN/hΔ), or both. An activity rate of PFN/hΔ greater than 0.5 (more active than inactive) induces an increase of the strength of the inhibitory FBt synapse; and an activity rate of PFN/hΔ lower than 0.5 (more inactive than active) induces a decrease of the synaptic strength. (C) Applied to all the functional columns, this mechanism stores a copy of the PFN and hΔ activity rates, at the time of reward via DANs, in the form of altered FBt synaptic strengths. The amplitude of the “copy” depends on the learning rate parameters, βPFN and βhΔ. Clipart(s) in the figure have been modified from https://openclipart.org/.
Fig 5.
(A) Navigation using PI and vector memory, replicating [20]. a. The steering circuit in this simulation is only composed of the hΔ pathway, supporting path integration. When the agent is lacking food (food = 0) it promotes the exploration behaviour through the excitation of a specific FBt. When food is found, the DAN circuit triggers memory formation. The motivation then switches to the return state (food = 1) where the FBt is inhibited, leading to homing behaviour. b. Sequence of behaviour implemented: (1) the agent leaves the nest to explore (pre-determined zig-zag pattern). (2) When the agent reach 200l.u. from the nest, it is provided with a food reward, triggering the formation of the memory while simultaneously switching the motivation to the return mode. (3) Homing behaviour to the nest (catchment area of 20l.u. diameter) c. Reset of the motivation to the exploration mode (food=0). This time, the behaviour of the agent is left under the control of the steering circuit which should bring it back to the memorised location. See results in Fig 6. (B) Navigation using visual guidance and vector memory, replicating and extending [26]. a. For visual navigation without PI the steering circuit is only composed of the PFN to PFL pathway. The DAN reward circuit receives inputs from the sum of the target-detection ommatidia activity (see B.b), so the circuit forms a vector memory of its direction when facing the target. See results in Fig 7. b. Visual circuit used to control the recognition of a green object in the central visual field (Fig B in S1 Text). c. For visual navigation with PI, the circuit includes both PFN and hΔ pathways to the PFL. The agent thus forms a memory of both the direction of the visual target and the location from which it was seen, further improving its ability to locate the target. See results in Fig 8. Clipart(s) in the figure have been modified from https://openclipart.org/.
Fig 6.
PI and vector memory of a food location.
(A) PI during the outbound journey (black path) and inbound journey (green path). The activity rate of the hΔ neurons is indicated for different location of both journeys; it encodes the home vector as a sine wave with amplitude corresponding to length and phase corresponding to angle. The agent is rewarded (finds food) when it reaches a set distance from the nest (200 l.u.) and triggers the creation of the synaptic long-term memory at the level of the FBt − to − hΔ axonal connections. (B) Retrieval outbound journey. The long-term FBt memory induces the steering circuit to drive the agent towards the location where the memory and PI cancel, i.e., the rewarded location. The distance between the search peak and target is used as a measure of precision in C. (C) Effect of varying the learning parameter βhΔ on the precision of retrieval journey: this modulates the vector length stored in memory. Each point represents one simulation with a fixed βhΔ randomly chosen in the [0 4] range. Note that because we modulated the motivational input to the FBt with a factor IFBt = 0.5, we corrected the value of βhΔ to verify that the best retrieval was achieve with a perfect memory (βhΔxIFBt ≈ 1).
Fig 7.
(A) Examples of trajectories from the nest to the target. (B) Left panel Example of reward input activity over time steps. Right panel Boxplot of the reward activity rate across all simulations. (C) Success rate and time to reach the target. Time is between first sighting the target and reaching it, normalised by the distance to the target at the first sighting. (D) Success to reach the target as a function of the learning parameter βPFN. (E) Time to reach the target as a function of the learning parameter βPFN. Clipart(s) in the figure have been modified from https://openclipart.org/.
Fig 8.
Visually guided navigation including PI memory.
(A) Examples of trajectories from the nest to the target. (B) Left panel Example of a simulation reward input activity over time steps. Right panel Boxplot of the reward activity rate during the simulations (n = 200). (C) Success rate and time to reach the target. (D) Success to reach the target as a function of the learning parameter βPFN. Dots indicate individual simulation outcome. (E) Time to reach the target as a function of the learning parameter βPFN. (F) Conceptual comparison of the models with and without the hΔ/PI pathway for visual guidance. a. Without hΔ/PI pathway, the agent tries to correct its heading to be the same as the heading when the target was last sighted. b. With hΔ/PI pathway, the agent is steered towards the vector sum of the location where the target was last sighted, and the heading in which it was sighted, preventing overshoot. Clipart(s) in the figure have been modified from https://openclipart.org/.
Fig 9.
Navigating when a target disappears.
(A-C) Simulation paradigm diagram. (A) The first phase corresponds to the previous simulation using visual-driven processing. (B) However, when the agent reach 50l.u. from the target, it disappears. (C) This agent is then left navigating without any new visual information modifying the FBt − PFN/hΔ guidance system in the CX. (D-G) Model without PI. (D) Example of a simulation path (black line). The location of the first sight of the target is indicated by the cyan dot and the last sight by a red dot. The target location is shown as a green plain circle and the origin location by a blue star. (E) Success rate (%) to reach the target location. (F) Success and failed attempts as a function of the βPFN learning parameter value. Success rate are calculated for every 0.25 section. (G) Mean distance to the target (blue dots) and the last sight (red dots) locations after the last sight event occurrence as a function of the βPFN learning parameter value. The lines show a 2nd degree polynomial fit for both location distances (blue for the target, red for the last sight). (H-K) Model with PI. Respectively identical to (D-G). Clipart(s) in the figure have been modified from https://openclipart.org/.
Fig 10.
Navigating using the MB long-term visual memory.
(A) Mushroom body model. Visual input is based on the blue channel of an insect-inspired eye model (see Fig B in S1 Text), with lateral inhibition to encode edges in the layer of visual projection neurons (vPN) that provide input to the MB. (B) Left panel Diagram of the initiation of the MB “snapshot” memory following a straight route. Right panel Boxplot of the MB model performance index for the 2 versions of the model (see details in Fig H in S1 Text). (C) Simulation without PI. Left panel Path of 15 route following attempts for 1 single route learned. The red arrow indicates the learned route. Right panel Heatmap of 8 pooled simulations, realigned on the learned route direction (red arrow). (D) Simulation with PI, similar to (C) panels. (E) Boxplots of, from left to right, the average distance to the route (on the whole path and on the path detected on the route, see Fig G in S1 Text), the percentage of route traveled and the minimal distance to the end route. All the data have been filtered based on the MB performance index (B). (F) Success rate measured at different portions of the route for the model with (blue stars) or without (red triangles) PI. Individual simulations (1 single route learning and 15 route following attempts) are indicated in thin lines while pooled data are indicated in thick lines. Clipart(s) in the figure have been modified from https://openclipart.org/.
Fig 11.
Route following using the MB visual long-term memory.
(A) Left panel Simulation example of a single route learning paradigm (red zigzag arrow) and route following trials (black lines, n = 15). The MB learning, only during the walk (with constant speed) along this route, is continuous and modulated by a learning rate of 0.1. All route following attempts are initiated at a random location situated around the starting point of the route (±20l.u.). Right panel Individual trial of route following. The route is shown as a black line and the route following attempt in blue. The red dots indicate the position at which the route has been considered lost (see Fig G in S1 Text for calculation details). (B) Estimation of the MB model performance scores for 15 attempts to follow a single learned route Left panel Probability density function of the MBON reward inactivity (on-route views) in relation to the orientation relative to the nearest route orientation. Right panel Boxplot of the MB evaluation scores (see Fig H in S1 Text for calculation details). (C) Left panel Boxplots of the MB performance score for the two different versions of the model (no PI: red, PI: blue) before (outside large boxplots) and after (inside small boxplots) the elimination of low MB performance score (see Fig H in S1 Text). Right panel Boxplot of the average distance to the route with both versions of the model calculated on the whole path or only before the route was considered lost (see Fig G in S1 Text). (D) From top to bottom, boxplots (red: without PI, blue: with PI) of the minimum distance from the route end, the percentage of route traveled and the average distance to the route in relationship with the MB performance score. Each boxplot is based on the pooled data of simulations with MB performance index value within a 0.1 range (grey and white bands). (E) Success rate of the model to reach different portion of the route. Data have been selected based on the MB performance score threshold. Clipart(s) in the figure have been modified from https://openclipart.org/.
Fig 12.
Simulations using a “settler” or “nomadic” CX to harvest multiple food sources.
(A) Settler brain The CX model used in this simulation is similar to Fig 5B.c. Both sensory stimulations from the green visual pathway and food discovery are used as reward to the FBt − DAN circuit. The agent is placed at the nest and left to find food located at different location randomly assigned in a quadrant of 90° and at a distance of 100–400 l.u.. When a food source is found, it is fully consumed and disappears. Simultaneously, a memory is formed on the FBthΔ and the motivation is switched to trigger homing behaviour. When the agent reaches the nest, the motivation is switched again to promote further exploration. The simulation is stopped when the agent spends more than 5000 t.u. without finding a new food source or the nest and is considered lost. (B) Nomad brain The CX model used in this simulation is modified to replace any DAN stimulation by a re-zeroing of the hΔ activity, i.e. of the PI. The rest of the simulation is similar to (A). Clipart(s) in the figure have been modified from https://openclipart.org/.