Modelling the Insect Navigation Toolkit: How the Mushroom Bodies and Central Complex Coordinate Guidance Strategies

The robust navigation of insects arises from the coordinated action of concurrently functioning and interacting guidance systems. Computational models of specific brain regions can account for isolated behaviours such as path integration or route following but the neural mechanisms by which their outputs are coordinated remains unknown. Here we take a functional modelling approach to identify and model the elemental guidance subsystems required by homing insects before producing realistic adaptive behaviours by integrating their outputs in a biologically constrained unified model mapped onto identified neural circuits. Homing paths are quantitatively and qualitatively compared with real ant data in a series of simulation studies replicating key infield experiments. Our analysis reveals that insects require independent visual homing and route following capabilities which we show can be realised by encoding panoramic skylines in the frequency domain, using image processing circuits in the optic lobe and learning pathways through the Mushroom Bodies and Anterior Optic Tubercle respectively before converging in the Central Complex steering circuit. Further we demonstrate that a ring-attractor network inspired by firing patterns recorded in the Central Complex can optimally integrate the outputs of path integration and visual homing systems guiding simulated ants back to their familiar route, and a simple non-linear weighting function driven by the output of the Mushroom Bodies provides a context-dependent switch allowing route following strategies to dominate and the learned route retraced back to the nest when familiar terrain is encountered. The outcome is a biologically realistic neural model capable of reproducing an array of adaptive homing behaviours in realistic environments through the combined action of the Central Complex and the Mushroom Bodies neuropils forwarding the case for a distributed architecture of the insect navigational toolkit.


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isolated behaviours such as path integration or route following but the neural mechanisms by 13 which their outputs are coordinated remains unknown. Here we take a functional modelling 14 approach to identify and model the elemental guidance subsystems required by homing insects 15 before producing realistic adaptive behaviours by integrating their outputs in a biologically 16 constrained unified model mapped onto identified neural circuits. Homing paths are quantitatively 17 and qualitatively compared with real ant data in a series of simulation studies replicating key infield 18 experiments. Our analysis reveals that insects require independent visual homing and route 19 following capabilities which we show can be realised by encoding panoramic skylines in the 20 frequency domain, using image processing circuits in the optic lobe and learning pathways through 21 the Mushroom Bodies and Anterior Optic Tubercle respectively before converging in the Central 22 Complex steering circuit. Further we demonstrate that a ring-attractor network inspired by firing 23 patterns recorded in the Central Complex can optimally integrate the outputs of path integration 24 and visual homing systems guiding simulated ants back to their familiar route, and a simple circuitry has yet to be developed. In this work we develop a unified neural navigation model that 51 extents the core guidance modules from two (PI and VM) to three (PI, RF, and VH) and by integrating 52 their outputs optimally using biologically realistic models of the CX produces realistic homing 53 behaviours. 54 The foremost challenge in realising this goal is to ensure that the core guidance subsystems with the optimal integration of PI and VH when Off-Route (b) switch from Off-Route (PI and VH) to 85 On-Route (RF) strategies when familiar terrain is encountered. Mathematical models have been 86 developed that reproduce aspects of cue integration in specific scenarios (Cruse and Wehner, 2011; 87 Hoinville and Wehner, 2018), but to date no neurobiologically constrained network revealing how 88 insects might realise these capabilities has been developed. 89 To address these questions a functional modelling approach is followed that extends to the 90 2 of 22 All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. . https://doi.org/10.1101/856153 doi: bioRxiv preprint Manuscript submitted to eLife current base model described by (Webb, 2019) (Narendra, 2007). Biological realism is enforced by constraining models to the known anatomy of 99 specific brain areas, but where no data exists we take an exploratory approach to investigate the 100 mechanisms that insects may exploit. Figure 1 depicts the adaptive behaviours observed in animals 101 that we wish to replicate and an overview of our unified model of insect navigation.  Optimally Integrating Visual Homing and Path Integration 136 We have demonstrated how ants could use visual cues to return to the route in the absence of capabilities produced by the model replicate the adaptive homing behaviour of insects with path integration and visual homing combined optimally to drive the animal back to familiar surroundings (banded red and green path segment) before the route is recognised and retraced home (blue path segment). (B) The proposed conceptual model of the insect navigation toolkit from sensory input to motor output. Three elemental guidance system are all modelled in this paper: path integration , visual homing (VH) and route following (RF) . Their outputs must then be coordinated in an optimal manner appropriate to the context as in insects. (C) The unified navigation model maps the elemental guidance systems to distinct processing pathways: RF: optic lobe -> AuTo -> CX; VH: optic lobe -> MB -> SMP -> CX; PI: optic lobe -> CX. The outputs are then optimally integrated in the ring attractor networks of the FB in CX to generate a single motor steering command. Images of the brain regions are adapted from the insect brain database https://www.insectbraindb.org.
vector readout offering an alternative, and often conflicting, guidance cue to that provided by visual 139 homing. In such scenarios desert ants strike a comprise by integrating their PI and VH outputs in a 140 manner consistent with optimal integration theory by weighting VH relative to the familiarity of the The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. . https://doi.org/10.1101/856153 doi: bioRxiv preprint For every time step from − 2 to , the sensory data of visual novelty will drive the agent's motor to descent the visual novelty gradient. How this left turn is generated neurally is showni n A, where the desired heading is shifted 90 degrees from the current heading, leading to increased activity on in the turn left ring of the steering circuit. (C) Resultant visual homing behaviours as in (Wystrach et al., 2012). The grey curve shows the habitual route along which ants were trained. RP indicated the release point from which simulated and real ants were tested. The firing rate of the MBON sampled across locations at random orientation is depicted by the heat-map showing a clear gradient leading back to the route directly. The ability of the MB->SMP->CX model to generate realistic homing data in this scenario is shown by the initial paths of simulated ants which closely match those of real ants (see inserted polar plot), and also the extended homing path shown. Note that once the agent get the vicinity of the route, it will wandering around because of the flat of visual novelty gradient.

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The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. . https://doi.org/10.1101/856153 doi: bioRxiv preprint network is added to the CX model (see Figure 3A) that takes as input the desired headings from  Figure 4A). 186 The route following model accurately replicates the initial paths of real ants in Wystrach et al. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. . https://doi.org/10.1101/856153 doi: bioRxiv preprint  The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. . https://doi.org/10.1101/856153 doi: bioRxiv preprint  Figure 2C). Also the fact 204 that off-route strategies (PI and VH) compute their turning angles with reference to the celestial 205 compass whereas the on-route strategy is driven with reference to a terrestrial compass provides a 206 means to modulate their impact on the steering circuit independently. This is realised through a 207 non-linear weighting of the on-route and off-route strategies which we propose acts through the 208 same SMP pathway as the VH model (see the SN1 and SN2 neuron in Figure 5A). 209 Figure 5B shows example paths of simulated ants when released sidewards of their habitual 210 route with and without access to their PI system, i.e., the full vector and zero vector agent. Zero-211 vector agents apply VH to approach the route directly as in Figure 5B (Ardin et al., 2016; Müller et al., 2018), but rather the spatially varying (but rotationally-invariant) 238 sensory valence more suited to gradient descent strategies such as visual homing (Zeil et al., 2003) 239 and other taxis behaviours (Wystrach et al., 2016). This is inline with the hypothesis forwarded by 240 Collett and Collett (2018) that suggest that the MBs output "whether" the current sensory stimulus 241 is positive or negative and the CX then adapts the animal heading, the "whither", accordingly. 242 Conceptually this flexible mechanism has the potential to play a key role realising other navigation 243 9 of 22 All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. . https://doi.org/10.1101/856153 doi: bioRxiv preprint The coordination are modelled as three neurons in SMP: switching neuron 1 (SN1) and switching neuron 2 (SN2) has mutual exclusive firing state so they work together to switch on/off the output from the on-route RF or off-route PI+VH integrated cue and the celestial/terrestrial current heading to the steering neurons depending on the visual novelty from the MB; The tuning neuron (TN) is the same in Figure 3. The activation functions of these neurons are shown in the left side of SMP box. (B): Reproduce the desired homing behaviours of the insect navigation in Figure 1A, dashed curve depicts the non-linear weighting of on and off-route strategies (i.e., VH and RF) for zero vector (ZV) agent and solid curve shows the optimal weighting of the off-route strategies (i.e., PI and VH) and then successfully retrace the habitual route and do RF for the full vector (FV) agents.  All rights reserved. No reuse allowed without permission.
The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. . https://doi.org/10.1101/856153 doi: bioRxiv preprint and tussocks based on triangular patches. Therefore, the data of this simulated world is stored in a 298 matrix with the size of × 3 × 3, defining the three dimensional coordinates of the three vertices 299 of (number of patches) patches. A test area with size 20 × 20 was selected specifically to meet 300 the condition that there is no obstacles, so the agent can freely explore in that area (see Figure 6A).
Where ∈ + is the order and is the repetition meeting the condition: ∈ , | | ≤ and − | | 312 is even to get the rotational invariant property. ( ) is the radial polynomial defined as: For a continuous image function ( , ), the ZM coefficient can be calculated by: For a digital image, summations can replace the integrals to get the ZM: From which we can see that the magnitude of ZM coefficient is keeping the same while the phase of 321 ZM carries the information of rotation (see Figure 6B). This property is the cornerstone of the visual 322 navigation model where the magnitudes (amplitudes) encode the features of the view (see the heat 323 map of Figure 6C) while the phase defines the terrestrial compass (see the quiver plot of Figure 6C). 324 For the inputs of the VH model, as the ZM with different orders encode the information of The relationship between the Δ and the is shown as following: Where is the scale factor. 406 Therefore, the 1 and 2 for this ring attractor network can be calculated by:  switching neurons (SN1 and SN2) in the SMP (Figure 3A). These two switch neurons is modelled in a 445 binary way with the step function defined activation function. SN1 will always fire unless SN2 fires 446 while SN2 will keep silent unless the excitation injection from MBON exceeds activation threshold 447 ℎ 2 (see Figure 5). 448

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basic speed of the agent and is the total time for outbound phase determining the length of 482 the outbound route. As for the simulated homing route, we duplicate the outbound route when 483 = 700 but with a inverted heading direction. And then the visual navigation network was trained 484 with images sampled along a simulated route (grey curve in Figure 3B). 485 Tuning PI uncertainty 486 The agent in this simulation was allowed to forage to different distances of 0.1m, 1m, 3m or 7m 487 from the nest to accrue different PI states and directional certainties before being translated to a 488 never-before-experienced test site 1.5m from the nest. (RP1 in Figure 3B). For each trial, we release behaviour is very close to that observed in real ants and can account for the optimal integration of 502 navigational cues Figure 3B. 503 Tuning visual uncertainty 504 The agent in this simulation was allowed to forage to the distances of 1m from the nest to accrue 505 different PI states and directional certainties before being translated to two different release points 506 (RP2 and RP3 in Figure 3B). From RP1 to RP3, the distance from nest is creasing so does the 507 visual uncertainty. For each trial, we release 12 agents with different initial headings that is evenly 508 distributed in [−180, 180). The headings of each agent at the position that is 0.3m from the start 509 point is taken as the initial headings.

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Simulation of the whole model 511 The first simulation (results in Figure 5B) to show the zero-vector agent homing from the sideway 512 release points to the familiar route and then switch to RF use the same habitual route in subsection . 513 So does the learning process. 514 The second simulation showing the full-vector agent integrating PI and VH to the familiar sites 515 and then switch to RF uses the large arc-shaped route generated by: The extended homing paths of 20 agents released at RP2 and RP3 in Figure 3B. 681 All rights reserved. No reuse allowed without permission.