Receptive field structures for two celestial compass cues at the input stage of the central complex in the locust brain

ABSTRACT Successful navigation depends on an animal's ability to perceive its spatial orientation relative to visual surroundings. Heading direction in insects is represented in the central complex (CX), a navigation center in the brain, to generate steering commands. In insects that navigate relative to sky compass signals, CX neurons are tuned to celestial cues indicating the location of the sun. The desert locust CX contains a compass-like representation of two related celestial cues: the direction of unpolarized direct sunlight and the pattern of polarized light, which depends on the sun position. Whether congruent tuning to these two compass cues emerges within the CX network or is inherited from CX input neurons is unclear. To address this question, we intracellularly recorded from GABA-immunoreactive TL neurons, which are input elements to the locust CX (corresponding to R neurons in Drosophila), while applying visual stimuli simulating unpolarized sunlight and polarized light across the hemisphere above the animal. We show that TL neurons have large receptive fields for both types of stimuli. However, faithful integration of polarization angles across the dorsal hemisphere, or matched-filter ability to encode particular sun positions, was found in only two out of 22 recordings. Those two neurons also showed a good match in sun position coding through polarized and unpolarized light signaling, whereas 20 neurons showed substantial mismatch in signaling of the two compass cues. The data, therefore, suggest that considerable refinement of azimuth coding based on sky compass signals occurs at the synapses from TL neurons to postsynaptic CX compass neurons.

To judge AoP responses, we used the square value of the coefficient (rcl 2 ) because it follows a χ 2 distribution with two degrees of freedom (Berens, 2009).

Great-circle distance
Generally, for spherical coordinates of a given point α (azimuth α1, elevation α2) with 0° ≤ α1 < 360° and 0° ≤ α2 ≤ 90° (Fig. 1A,C), the position vector ⃗ is ⃗ = ( cos 1 • cos 2 cos 1 • sin 2 sin 1 ) The great-circle distance θ between the points α and β is calculated using vector products as follows; Single-scattering Rayleigh model We generated sky polarization patterns (angles and degrees of polarization) based on the single-scattering Rayleigh model (Strutt, 1871). The angle of polarization (AoP) at a given point of the sky is perpendicular to a great circle passing through the sun and the subject point. Thus, the vector of AoP is calculated as the cross vector product; where ⃗ and ⃗ are the position vectors of the sun and the subject point, respectively.
The degree of polarization (DoP), or percent polarization, varies between 0 (for unpolarized light) and 1 (for completely polarized light). In the single-scattering Rayleigh model, the DoP is calculated as a function of the great-circle distance between the sun and the subject point; where θ is the great-circle distance between ⃗ and ⃗. The DoP reaches its maximum (= 1) when the great-circle distance is 90°.
Spikes were counted per 1-s bins as background activity (BA) of the neurons (Fig. S1).
We used all bins during the absence of stimulation and current injection for the analysis, except during 5 s after the light was turned off to exclude rebound responses. We sometimes observed spike rate changes lasting after light stimuli were turned off. Such long-lasting aftereffects were more frequently observed in TL3 than in TL2 neurons.
However, as we did not have objective means to isolate these effects from spontaneous changes in BA, we used the whole recording fulfilling the criteria to avoid arbitrary omission of parts of the recording.
To evaluate BA characteristics of each cell type, we calculated the mean and Fano factor of spike counts per bin. Fano factor is the variance to mean ratio (variance/mean) of count data, commonly used to evaluate variability (Fano, 1947;Rajdl et al., 2020). That is because ideal count data follow a Poisson-distributed process where mean equals variance. When the Fano factor > 1 or < 1, BA is considered more fluctuating or more constant through the whole recording, respectively.
For statistical comparison of BA mean levels between cell types, we constructed a generalized linear model (GLM) of a gamma distribution by function "glm" in the "stats" package of R (R Core Team, 2021). The link function of GLM was "identity." Response variables were BA mean of individuals, and fixed effects were cell types. The statistical significance of a fixed effect was tested by Wald test of an estimated coefficient (Faraway, 2016). In this method, the test static z is obtained by dividing the coefficient value by its s.e.. The distribution of z is approximated by a normal distribution to calculate the p value under the null hypothesis that the coefficient = 0.  and TL2b neurons shared similar BA levels (A), with median group activities of 8.6 and 8.2 spikes/s, respectively, and a significant difference was not detected (Wald test,

Fig. S2. Receptive fields and AoP pattern fitting results (related to Figs. 4-6): TL2a neurons (ten out of 15 cells).
Each row shows the data from a single neuron. The information of cell type, ID, and brain hemisphere of its soma is indicated on the upper left corner of each row. All plots are top views on flattened sky hemispheres (see Fig. 1D for the coordinate system). Plots in column 1 indicate best matching sky polarization patterns and the corresponding sun positions, as shown in Fig. 5A. Plots in column 2 are related to the pattern matching analysis (Fig. 5), showing linearly interpolated pattern deviations between the AoP response pattern and sky polarization patterns generated by various solar coordinates.
Values at the bottom indicate the minimum pattern deviations (best match) yielded from the solar coordinates indicated by a crossed yellow circle. Plots of column 3 indicate polarization sensitivity as shown in Fig. 4A, and plots of columns 4 and 5 indicate the receptive field organizations to unpolarized green light as in Fig. 6C and unpolarized blue light, respectively. Blank spaces are properties that were not measured in the respective neurons.