1
Integration of optic flow into the sky compass
network in the brain of the desert locust
Frederick Zittrell 1,2, Kathrin Pabst 2,3, Elena Carlomagno 1,◦, Ronny Rosner 1,
Uta Pegel,1, Dominik M. Endres 2,3and Uwe Homberg 1,2,∗
1Department of Biology, Philipps-Universit¨
at Marburg, Marburg , Germany
2Center for Mind, Brain and Behavior (CMBB), Philipps-Universit¨
at Marburg and
Justus Liebig Universit¨
at Gießen
3Department of Psychology, Philipps-Universit¨
at Marburg, Marburg, Germany
Correspondence*:
Uwe Homberg
Philipps-Universit¨
at Marburg
Karl-von-Frisch Straße 8
35043 Marburg
Germany
homberg@staff.uni-marburg.de
◦Present Address: Department of Psychiatry, Philipps-Universit¨
at Marburg,
Marburg, Germany.
Words: (5496 excluding appendix) 6219 (including appendix), Figures: 9, Tables: 02
ABSTRACT3
Flexible orientation through any environment requires a sense of current relative heading that
4
is updated based on self-motion. Global external cues originating from the sky or the earth‘s
5
magnetic field and local cues provide a reference frame for the sense of direction. Locally, optic
6
flow may inform about turning maneuvers, travel speed and covered distance. The central complex
7
in the insect brain is associated with orientation behavior and largely acts as a navigation center.
8
Visual information from global celestial cues and local landmarks are integrated in the central
9
complex to form an internal representation of current heading. However, it is largely unclear which
10
neurons integrate optic flow in the central-complex network. We recorded intracellularly from
11
neurons in the locust central complex while presenting lateral grating patterns that simulated
12
translational and rotational motion to identify these sites of integration. Certain types of central-
13
complex neurons were sensitive to visual self-motion independent of the type and direction of
14
simulated motion. Columnar neurons innervating the noduli, paired central-complex substructures,
15
were tuned to the direction of simulated horizontal turns. Modelling the connectivity of these
16
neurons with a system of proposed compass neurons can account for rotation-direction specific
17
shifts in the activity profile in the central complex corresponding to turn direction. Our model
18
is similar but not identical to the mechanisms proposed for angular velocity integration in the
19
navigation compass of the fly Drosophila.20
Keywords: optic flow, sky compass, desert locust, orientation, computational model, central complex, head direction, intracellular
21
recordings22
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Zittrell et al. Sky-Compass Optic Flow Integration
1 INTRODUCTION
Animals navigate to feed, escape, migrate, and reproduce. Navigational tasks require a sense of current
23
travel direction, which must be anchored to external cues and updated by internal cues, generated by
24
ego-motion. Celestial cues are used as external cues by many insects, such as bees (von Frisch, 1946),
25
ants (Fent, 1986), butterflies (Perez et al., 1997), dung beetles (Byrne et al., 2003), fruit flies (Weir and
26
Dickinson, 2012), and caterpillars (Uemura et al., 2021). The sun and the skylight polarization pattern
27
provide a reliable reference for dead reckoning (Gould, 1998). Internal cues, such as proprioceptive
28
feedback (Wittlinger et al., 2006) and optic flow (Srinivasan, 2015; Stone et al., 2017), provide information
29
about traveling speed and covered distance and may update the inner sense of direction in the absence of
30
external cues. Only the flexible combination of information from external and internal cues enables robust
31
and efficient navigation behavior, such as path integration (Heinze et al., 2018).32
The central complex (CX), a midline spanning group of neuropils, houses the internal sense of direction
33
in the brain of insects. It consists of the protocerebral bridge (PB), the lower (CBL) and upper (CBU)
34
division of the central body, also termed ellipsoid- and fan-shaped body, and a pair of layered noduli (NO),
35
and is associated with learning, memory and, importantly, spatial orientation (Pfeiffer and Homberg, 2014).
36
The PB and the CBL are subdivided into series of 16 or 18 columns that are connected across the brain
37
midline in a precise topographic manner (Pfeiffer and Homberg, 2014; Hulse et al., 2021; Hensgen et al.,
38
2022).39
CX neurons in various insect species are tuned to celestial cues (Heinze, 2017; Honkanen et al., 2019)
40
and encode the solar azimuth in a compass-like manner in the locust (Pegel et al., 2019; Zittrell et al., 2020).
41
Silencing compass neurons in the CX impairs navigation behavior in the fruit fly (Giraldo et al., 2018),
42
showing the necessity of the CX for this behavior. Like mammalian head direction cells (Taube, 1998, 2007),
43
specific CX neuron populations are tuned to the animal’s current heading (Seelig and Jayaraman, 2015;
44
Hulse and Jayaraman, 2020). This internal heading estimate is multimodally tethered to environmental cues,
45
such as visual compass cues and wind direction (Okubo et al., 2020), but also operates without external
46
input, because internal cues from self motion are likewise integrated (Green et al., 2017; Turner-Evans
47
et al., 2017; Green and Maimon, 2018).48
Although the understanding of the CX network has made considerable progress, mainly owing to research
49
in the fruit fly, and plausible models explaining network computations for navigation have been proposed
50
(Stone et al., 2017), it is largely unclear at which network stages optic flow input is integrated in the
51
sky compass network. To investigate this, we recorded intracellularly from various CX neurons in the
52
desert locust (Schistocerca gregaria), a long-distance migratory insect, while stimulating laterally with
53
wide-field visual motion that simulated self-motion to the animal. We analyzed general motion sensitivity
54
for translational and rotational self-motion directions and tested whether the neural responses to opposing
55
motion directions were discriminated (direction selectivity).56
We implemented an algorithmic model (in the sense of Marr and Poggio (1979)) of the CX circuit which
57
integrates visual self-motion cues with head direction representation. Modeling was guided by data on two
58
types of columnar neurons with one being sensitive to the direction of simulated horizontal turns.59
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Zittrell et al. Sky-Compass Optic Flow Integration
2 METHODS
2.1 Animals and preparation60
Desert locusts (Schistocerca gregaria) were kept and dissected as described previously (Zittrell et al.,
61
2020). Animals were reared in large groups (gregarious state) at 28
◦
C with a 12 h / 12 h light / dark cycle;
62
adult locusts from either sex were used for experiments. Limbs and wings were cut off, the animals were
63
fixed on a metal holder with dental wax, and the head capsule was opened frontally, providing access to the
64
brain. The esophagus was cut inside the head, close to the mandibles, and the abdomen’s end was cut off to
65
take out the whole gut through this opening. The brain was freed of fat, trachea and muscle tissue and was
66
stabilized with a small metal platform that was fixed to the head capsule. Shortly before recording, the
67
brain sheath was removed at the target site with forceps, permitting penetration with sharp glass electrodes.
68
The brain was kept moist with locust saline (Clements and May, 1974) throughout the experiment.69
2.2 Intracellular recording and histology70
Sharp microelectrodes were drawn with a Flaming/Brown filament puller (P-97; Sutter Instrument), their
71
tips filled with Neurobiotin tracer (Vector Laboratories; 4 % in 1 mol
·
l
−1
KCl) and their shanks filled
72
with 1 mol
·
l
−1
KCl. Intracellular recordings were amplified with a custom-built amplifier and digitized
73
with a 1401plus (Cambridge Electronic Device, CED) analog-digital converter (ADC) or amplified with a
74
BA-01X (npi electronic GmbH) and digitized with a Micro mkII with an ADC12 expansion unit (CED).
75
Signals were monitored with a custom-built audio monitor and recorded with Spike2 (CED). Neurons were
76
traced by electrically injecting Neurobiotin (
∼
1 nA positive current for several minutes). Each neuron
77
presented in this study originates from a different specimen. Brains were dissected and immersed in fixative
78
(4 % paraformaldehyde, 0.25 % glutaraldehyde and 0.2 % saturated picric acid, diluted in 0.1 mol
·
l
−1
79
phosphate buffered saline [PBS]) over night, followed by optional storage at 4
◦
C in sodium phosphate
80
buffer until further processing. Brains were rinsed in PBS (4 × 15 min) and incubated with Cy3-conjugated
81
streptavidin (Dianova; 1:1,000 in PBS with 0.3 % Triton X-100 [PBT]) for 3 d at 4
◦
C. After rinsing in
82
PBT (2 × 30 min) and PBS (3 × 30 min), they were dehydrated in an ascending ethanol series (30 %, 50
83
%, 70 %, 90 %, 95 %, and 2 × 100 %, 15 min each) and cleared in a 1:1 solution of ethanol (100 %) and
84
methyl salicylate for 20 min and in pure methyl salicylate for 35 min, to finally mount them in Permount
85
(Fisher Scientific) between two coverslips. For anatomical analysis, brains were scanned with a confocal
86
laser-scanning microscope (Leica TCS SP5; Leica Microsystems). Cy3 fluorescence was elicited with a
87
diode pumped solid-state laser at 561 nm wavelength. The resulting image stacks were processed with
88
Amira 6.5 (ThermoFisher Scientific, Waltham, MA) and Affinity Photo (Serif, Nottingham, UK). The
89
chirality of some neurons could not be determined because multiple neurons of the same neuron class but
90
on both brain sides were stained in these cases.91
2.3 Experimental Design92
We used two monitors (FT10TMB, 10“, 1024x768 px at 60 Hz, Faytech, Shenzhen, China) that were
93
placed 12.7 cm apart on the left and right side of the animal. They were mounted vertically to present
94
sinusoidal grayscale grating patterns (Figure 1A). The displays were covered with diffuser sheets to
95
eliminate light polarization inherent to LCD monitors. The patterns were drawn on the inner center-square
96
(15.35 cm edge length) of the displays, covering
62.3◦
of the visual field on each side. The monitor
97
brightness amounted to 1.12
·1011
photons cm
−2·
s
−1
when displaying a black area and 7.09
·1013 ·98
cm
−2·
s
−1
when displaying a white area. Monitor brightness was measured using a digital spectrometer
99
(USB2000; Ocean Optics) placed at the position of the locust head.100
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Zittrell et al. Sky-Compass Optic Flow Integration
The grating patterns were animated to simulate self-motion to the animal. We tested translational (forward
101
and backward) motion, yaw rotation (left and right turning), lift (upward and downward), and roll (counter
102
clockwise and clockwise). Throughout this study, these direction labels refer to simulated self-motion
103
directions and not absolute motion of the displayed patterns. Thus, “forward motion” means that both
104
monitors displayed a grating pattern with horizontal bands (perpendicular to the locust’s body axis, cf.
105
Figure 1A) that continuously moved from top to bottom. For the sake of readability, we use “visual motion”
106
for this wide-field visual motion stimulation, although this term includes diverse visual stimulation types,
107
such as looming objects, small moving targets or full-panoramic optic flow, neither of which we presented
108
to the animals.109
Each motion direction was tested in a series of trials; each trial consisted of two phases, a motion phase
110
and an immediately following stationary phase (Figure 1B,B’). All phases in the same recording lasted for
111
five or six seconds. Each series consisted of two to five trials; each trial was immediately followed by the
112
next one, unless it was the last of the series. Neurons typically responded strongly to the pattern display
113
switch between series. Therefore, each series of a given motion direction was preceded by an adaptation
114
phase which was discarded; this phase was a single stationary phase of the same pattern used during the
115
upcoming series, immediately followed by the first motion phase of the series. If the same motion direction
116
was tested in more than one series, all trials were treated as if they belonged to the same series. Not all
117
neurons could be tested for all motion directions due to recording instability.118
A separate PC running MATLAB (R2019, MathWorks) with the Psychophysics toolbox (Brainard, 1997)
119
was used to generate the grating patterns (Figure 1A). The sine gratings had a spatial resolution of 0.005
120
cycles
·
px
−1
(one sine cycle spanned 200 px) and were shifted with 2 cycles
·
s
−1
during the motion
121
phases. This PC was USB-connected to an Arduino Uno (Arduino) via which TTL pulses were sent to
122
the ADC, recorded at 500 Hz. These pulses indicated grating pattern animation and onset of stimulation
123
phases. Two squares with 30 px edge length in the top left corner of each display were used to indicate
124
the presented motion type by flashing them white: Each motion type was assigned a distinct number of
125
flashes (20 ms duration) that were generated at the end of the adaptation phase of each series. Each square
126
was covered by a photo diode that picked up the white flashes and whose signal was recorded by the
127
ADC at 200 Hz. This allowed for encoding the motion type of each stimulation series in the data file. The
128
generation of each rectangle flash was also recorded via the Arduino as a TTL rectangle pulse of the same
129
duration, which allowed for measuring the precise timing of stimulus display by cross correlating diode
130
signal and TTL signal.131
2.4 Statistical Analysis132
Spikes were detected by median filtering (500 ms window width) the voltage signal and applying a
133
manually chosen threshold. Spikes and non-spikes (gaps) within 2 ms time bins were counted during the
134
whole 5 s long interval of each trial of stimulation condition. We chose 2 ms time bins for this analysis
135
because this is the approximate length of the refractory period of the neurons.136
2.4.1 Motion Sensitivity137
We define motion sensitivity as a neuron’s property to have different firing rates during motion and
138
stationary phases. We analyzed motion sensitivity for each tested neuron and motion direction by comparing
139
the neuron’s firing rate during the motion phase with that during the previous stationary phase. Firing
140
probabilities were computed by integrating prior knowledge about compass neuron activity in general and
141
the condition-specific data from each neuron via Bayesian inference. For each neuron
n
, we computed
142
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Zittrell et al. Sky-Compass Optic Flow Integration
a posterior over three different hypotheses: First, that the firing probability in 2 ms time bins during the
143
motion phase
rm
is lower than the firing probability
rs
during the stationary phase,
H(rm< rs)
, second,
144
that the firing probabilities are equal
H(rm== rs)
, or third, that
rm
exceeds
rs
,
H(rm> rs)
. A high
145
posterior for the first or third hypothesis would indicate motion sensitivity, while a high posterior for the
146
second hypothesis would indicate that the neuron does not respond to the motion stimulation.147
Using Bayes’ rule, we computed the posterior distribution
P(H|D)
over the three hypotheses
148
H∈ {H(rm< rs), H(rm== rs), H(rm> rs)}
given the experimental data
D
, assuming an uniform
149
hypothesis prior, a Bernoulli observation model and a joint Beta prior for the firing probabilities. This joint
150
prior was restricted by the firing probability constraints expressed in each hypothesis, e.g. for
H(rm< rs)
,
151
the probability P(rm≥rs)=0etc. For details, see appendix 5.1.152
To summarize the information embedded in this posterior and to simplify comparison across multiple
153
neurons, we computed a single motion sensitivity score (MSS) per neuron and motion direction (dir):154
MSSdir =
H(rm> rs) : 1
H(rm== rs) : 0
H(rm< rs) : −1
(1)
We weight this score with the corresponding hypothesis posterior probability and sum across all neurons
155
of one type. The maximal value for one firing probability hypothesis is therefore equal to the number of
156
neurons of a given type.157
Further, we computed absolute motion sensitivity scores (AMSS) for four motion categories (cat),
158
each comprised of two opposing motion directions
A
and
B
: translational motion (forward or backward
159
direction), yaw rotation (left or right turning), lift (upward or downward), and roll (counterclockwise or
160
clockwise):161
AMSScat = 1 −[P(H(rm,A == rs,A)|D)∗P(H(rm,B == rs,B)|D)] (2)
where
rm,A
and
rm,B
are firing probabilities during stimulation with opposing motion directions in the
162
respective motion category. In other words, this score will be close to one if at least one motion direction
163
of a category elicits a strong deviation from the stationary firing probability. We sum this score across all
164
neurons of a given type.165
2.4.2 Direction Selectivity166
We define direction selectivity as a neuron’s property to respond contrarily to two opposing motion
167
directions
A
and
B
. We analyzed direction selectivity in the four motion categories outlined above:
168
translation, yaw rotation, lift, and roll. In the following, the hypothesis
H(rm,A ≥rs,A) = H(rm,A >169
rs,A)∨H(rm,A == rs,A)where ∨indicates a logical or, and ∧is a logical and.170
We compute a direction sensitivity score as171
DSScat =
[H(rm,A ≥rs,A)∧H(rm,B < rs,B)] ∨[H(rm,A > rs,A)∧H(rm,B == rs,B)] : 1
[H(rm,A < rs,A)∧H(rm,B ≥rs,B)] ∨[H(rm,A == rs,A)∧H(rm,B > rs,B)] : −1
otherwise : 0
(3)
For example,
DSStranslation
is +1(-1) if the firing probability does not decrease during forward(backward)
172
motion and decreases during backward(forward) motion, or if it increases during forward(backward) motion
173
and does not change during backward (forward) motion. It is 0 if the firing probability changes in the same
174
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Zittrell et al. Sky-Compass Optic Flow Integration
direction for both motion directions. We weight this score with the corresponding hypothesis posterior
175
probability and sum across all neurons of one type. The maximal value for one firing probability hypothesis
176
is therefore equal to the number of neurons of a given type, similar to MSSdir.177
As an indicator for the total number of neurons with any direction sensitivity at all, we computed the
178
expected absolute direction sensitivity score (ADSS):179
⟨ADSScat⟩=P(H(rm,A > rs,A)|D)∗P(H(rm,B < rs,B)|D)
+P(H(rm,A < rs,A)|D)∗P(H(rm,B > rs,B)|D)(4)
This score can take values between 0 and 1, with values close to zero indicating no direction selectivity
180
and values close to one indicating direction selectivity, disregarding which motion direction elicits greater
181
firing rates. We sum this score across all neurons of a given type.182
The appendix 5.1 comprises a power analysis for the analyses of motion sensitivity and direction
183
selectivity outlined above, indicating which difference in the recorded firing rates is considered evidence
184
for the hypothesis that a neuron fires more in one of the two conditions.185
2.5 Computational Model186
All computations were performed with the Python programming language (version 3.10.8) and the
187
Pandas (version 1.5.1) and PyTorch (version 1.13.0) libraries. Plots were created with the Matplotlib library
188
(version 3.5.3).189
Our model comprises CL1a and CL2 neurons, adopting the projection schemes proposed by Heinze and
190
Homberg (2008). We assume that, as shown for E-PG and P-EN neurons in the fly (Turner-Evans et al.,
191
2017), CL1a neurons provide synaptic inputs to CL2 neurons in the PB, which in turn provide synaptic
192
inputs to CL1a neurons in the CBL. We further assume a combination of excitation and inhibition within
193
the CL1a-CL2 connectivity instead of excitatory loops paired with global inhibition, as has been proposed
194
for Drosophila (Turner-Evans et al., 2017). The firing rate neurons and synaptic connections in our model
195
are linearized around their operating point, thus approximating their non-linear dynamics. We previously
196
implemented this circuit with CL1a neurons exciting the CL2 neurons and CL2 neurons inhibiting the CL1a
197
neurons (Pabst et al., 2022), referred to as Model A. In the present work we implemented an additional
198
version of the model, referred to as Model B, where this relation is reversed because both versions are
199
equally likely given the available data.200
We represent the CL1a-CL2 connectivity with a matrix
M
-
MA
and
MB
for Model A and Model
201
B, respectively. The matrix features additional self-recurrent connections at all neurons to enable the
202
maintenance of a baseline activity. Weights are uniform for all excitatory and inhibitory connections,
203
0.5 and -0.5, respectively. The network’s activity is characterized by deviations from a baseline firing
204
rate, represented by a vector
xt
with components
xt,1:16
and
xt,17:32
covering the CL1a and CL2 neurons,
205
respectively. The network is recurrent and iterated across time steps such that the activity at the next time206
step can be computed from the current activity:207
xt+1 =Mxt(5)
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Zittrell et al. Sky-Compass Optic Flow Integration
2.5.1 Maintenance of a Stable Head Direction Encoding208
In the framework outlined above, maintenance of the head direction representation or CL1a activity
209
pattern
x1:16
translates to an equality of
xt,1:16
at time point
t
and
xt+1,1:16
at the following time point,
210
t+ 1:211
xt,1:16 =xt+1,1:16 (6)
According to Equation 5, this is given if
Mxt=xt
. We refer to such
xt
as stable states. We defined CL1a
212
activity targets
ˆxt
matching the tuning observed across the PB (Pegel et al., 2019; Zittrell et al., 2020) and
213
employed an optimization algorithm to find stable states containing these targets. For more details, see
214
Pabst et al. (2022).215
2.5.2 Rotation-induced Shifts of Compass Activity216
We have previously described a possible computational mechanism that would produce a phasic shift
217
from
xt
to
xt+1
with Model A (Pabst et al., 2022), representing the influence of rotational flow inputs on
218
the compass system, putatively conveyed by TN or TB7 neurons. In the present work we adjusted the
219
modulatory effect to allow for broad arborizations in the CBL, in addition to the PB, and optimized the
220
synaptic weights to produce compass bump shifts with Models A and B. Furthermore, we applied additional
221
constraints to both models for better alignment with physiological data: In Model A we found that purely222
feed-forward input to the CL1a and/or CL2 neurons cannot account for the observed shift behavior (Pabst
223
et al., 2022). Instead, we found a modulatory mechanism that successfully shifts the compass bump. In our
224
previous study we relaxed the original connectivity matrix
MA
to allow for arborizations into adjacent PB
225
columns and optimized the weights in this relaxed matrix
MAr
to achieve shifts to either direction, adding
226
inhibitory or excitatory connections in up to two further PB columns on each side of all existing synapses.
227
We constrained these shift-matrices
MAr,c
and
MBr,c
to better account for available physiological data:
228
For the neurons modeled here, no arborizations broader than one column were found in the PB, while
229
arborizations, in the CBL, especially in the upper layers, do in fact span three to five columns (Heinze and
230
Homberg, 2008). We refer to these models as ‘relaxed and constrained models’.231
3 RESULTS
We surveyed CX neurons at different integration stages for sensitivity to visually simulated self-motion
232
(Figures 1,2). In total 62 morphologically identified neurons with arborizations in the CX were studied
233
(Figure 2). These included 4 tangential input neurons (TL) to the CBL comprising the subtypes TL2 and
234
TL3 (Figure 2A), 21 CL1a columnar neurons connecting the CBL to the PB, two CL2 columnar neurons
235
connecting the PB, CBL and NO, five TB1 tangential neurons of the PB, three CPU1, seven CPU2 and one
236
CPU5 neurons connecting distinct columns of the PB and CBU to the lateral complex (CPU1, CPU2) or a
237
nodulus (CPU5), one CP1 and two CP2 neurons connecting the PB to distinct areas of the lateral complex
238
(Figure 2B), eight PoU pontine neurons (Figure 2B), and various TU-type tangential neurons of the CBU239
(Figure 2A). We found sensitivity to visual self-motion in some neural classes while others did not respond
240
to the stimulation.241
3.1 Visual Self-motion Sensitivity and Direction selectivity in the Central Complex242
Neurons in most of the examined morphological classes shown in Figures 2A-C were not sensitive
243
to the moving gratings. Some of the tested TL-, CL1a-, and CPU2 neurons, however, were sensitive to
244
grating patterns moving in at least one motion direction (motion sensitivity; Figures 3A,3B). Response
245
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Zittrell et al. Sky-Compass Optic Flow Integration
scores, indicating the sign of the firing rate change due to visual self-motion perception, were likewise
246
inconsistently distributed within these neuron classes. Overall, within a given neuron class, individual
247
neurons responded with excitation, inhibition or not at all to the same stimulus, independent of their
248
brain side of origin (Figures 3A,3B). Two CL2 neurons, however, were not only motion sensitive but
249
also responded differently to opposing motion directions (direction selectivity, Figures 3A,3B,4, and
250
Supplementary Figure 2).251
3.2 Yaw-rotation is processed by CL2 neurons252
We recorded from two mirror-symmetric CL2 neurons. One neuron had smooth, presumably postsynaptic
253
arborizations in the left NO and in column R4 of the right half of the PB, and beaded processes in layers
254
1-3 of column L2 in the left half of the CBL (Figure 4B). The second CL2 neuron had ramifications in
255
the right NO, column L4 in left half of the PB, and column R2 in the right half of the CBL (Figure 4D).
256
Both neurons were directionally selective for visual motion that simulated yaw rotation, but with opposite
257
polarity (Figures 4A,A’,C,C’ and Supplementary Figure 2). The CL2 neuron with arborizations in the right
258
half of the PB and in the left NO (unit 801
R
, Supplementary Figures 1 and 2) responded to right turns
259
with an increase and to left turns with a decrease in firing rate, compared to baseline. The neuron was also
260
weakly inhibited by forward motion. The CL2 neuron arborizing in the left half of the PB and the right
261
NO (unit 800
L
in Supplementary Figures 1 and 2) on on the other hand responded to left turns with an
262
increase and to right turns with a decrease in firing rate. Responses to translational motion stimuli were
263
not tested. CL2 neurons are part of the internal compass system in the locust CX (Pegel et al., 2018) and
264
likely homologous neurons in Drosophila (P-EN) apparently signal rotational self-motion, updating the
265
internal heading representation when the animal turns. Our data support the idea that the locust internal
266
compass signal is also shifted during turns via asymmetric excitation and inhibition of CL2 neurons (Figure
267
5B’). The site of this interaction may either be the NO (via TN neurons) or the PB (via TB7 neurons).
268
Both cell types are, like their equivalents in Drosophila, the GLNO neurons and the SpsP neurons (Hulse269
et al., 2021) morphologically suited to provide asymmetric input to the CL2 population. Like in Drosophila
270
P-EN neurons, the projections of locust CL2 neurons in the CBL are shifted by one column relative to the
271
projections of CL1 neurons (Figures 5A,5B). A notable difference between compass representation in the
272
locust and the Drosophila compass system is that the E-PG population activity peak in the EB results in
273
two activity peaks with a fixed offset along the PB, while available data in the locust suggest a single peak
274
along the PB that results from azimuthal tuning to celestial cues ((Pegel et al., 2019; Zittrell et al., 2020)).
275
If so, locust CL2 neurons might have inhibitory connections to CL1a neurons (Figure 5B). However, these
276
connections and their polarity are hypothetical as there are no data on functional connectivity in the locust
277
CX. Alternatively, the observed tuning could be a consequence of the projection and connectivity patterns
278
of CL1a and CL2 neurons.279
3.3 Computational Model280
3.3.1 Maintenance of a Stable Head Direction Encoding281
Model A and B maintain an initial CL1a activity pattern with an activity maximum or compass bump
282
representing head direction relative to a global cue, such as the sun, when no yaw rotation is simulated.
283
The CL2 population’s activity is constrained by the polarity of synapses: We have previously shown that
284
with CL1a neurons exciting CL2 neurons in the PB and CL2 neurons inhibiting CL1a neurons in the CBL
285
in Model A, each CL2 neuron must have the same activity as the CL1a neuron associated with the same
286
PB column to maintain a stable CL1a activity pattern (Pabst et al., 2022). In contrast, in Model B, where
287
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Zittrell et al. Sky-Compass Optic Flow Integration
CL1a neurons inhibit CL2 neurons and CL2 neurons excite CL1a neurons instead, the CL2 activity pattern
288
across the PB must be the inverse of the CL1a pattern for CL1a activity maintenance.289
3.3.2 Rotation-induced Shifts of Compass Activity290
Feed-forward input to the CL1a/CL2 neurons can induce compass bump shifts neither in Model A nor in
291
Model B. However, the weights in relaxed versions of the connectivity matrices
MAr
and
MBr
(Figures
292
6B,B’) could be optimized to induce compass bump shifts in both versions of the model. Optimizations
293
for both Model A and Model B resulted in a connectivity with excitatory synapses from CL1a onto CL2
294
neurons in the PB, a characteristic of Model A during compass bump maintenance (Figures 6B,B’). In the
295
‘relaxed and constrained models’, we allowed the optimizer to broaden arborizations of CL2 neurons in the
296
CBL to more than one column and reduced arborizations of CL1a neurons in the PB to single columns
297
(Heinze and Homberg, 2008). Compared to the results obtained with the ‘unconstrained relaxed models’,
298
optimization converged at a solution where the weights for self-recurrent connections had greater absolute
299
values (Figures 6C,C’). Lastly, we enabled the addition of connections among CL2 neurons of the same
300
hemisphere during the optimization process. Projection patterns suggest that all CL2 neurons of the same
301
hemisphere branch in the lower unit of the contralateral NO, like P-EN neurons in Drosophila (Wolff
302
et al., 2015) and the bumblebee (Sayre et al., 2021). Optimization converged at a solution with excitatory
303
and inhibitory connections among CL2 neurons branching in the same nodulus. With these additional
304
connections, synapses from CL2 onto CL1a neurons are weaker than in the other model versions (Figures
305
6D,D’).306
4 DISCUSSION
We analyzed the sensitivity to visually simulated self-motion in different neuron classes in the locust CX
307
network, from input-providing neurons (TL, TU neurons) to intermediate stage neurons (CL1a, CL2, POU,
308
and TB1) and output neurons (CPU1, CPU2, CPU5, CP1, and CP2). Neurons in most of the investigated
309
classes were not sensitive to visual self-motion. We hardly encountered consistent responses within the
310
same neuron class, suggesting that single cells flexibly switch their cue sensitivity based on the internal state
311
of the animal and environmental conditions. Exceptions were CL2 neurons, which mirror-symmetrically
312
encoded yaw rotation direction, depending on the brain hemisphere in which they arborized, suggesting a
313
role in keeping the internal compass system up to date during turning. A large fraction of cell types studied
314
here (TL, CL1a, CL2, TB1, CPU1, CPU2, CP1, CP2) are elements of the sky compass system in the CX of
315
the locust (Vitzthum et al., 2002; Heinze et al., 2009; Bockhorst and Homberg, 2015; Pegel et al., 2018;
316
Zittrell et al., 2020). These neurons are sensitive to the azimuth of an unpolarized light spot (simulated sun)
317
as well as to the polarization pattern above the animal (simulated sky) matching the position of the sun
318
(Zittrell et al., 2020). The preference angles for solar azimuth in columnar neurons of the PB showed that
319
solar azimuth is represented topographically across the columns of the PB as illustrated in Figure 5. The
320
lack of responses to large-field motion stimuli in most of these neurons is in contrast to data from Rosner
321
et al. (2019), who showed that a majority of sky compass neurons in the locust CX (types TL, CL1, TB1,
322
CPU1, CPU2) were sensitive to progressive motion simulated through moving gratings. The reason for
323
these different results most likely lies in different preparations of the animals. While in this study, legs
324
and wings were removed, animals in the study of Rosner et al. (2019) had their legs attached and could
325
perform walking motion on a slippery surface. Therefore, while the responses to sky compass signals may
326
be affected only mildly, differences in behavioral context and internal state apparently play a major role
327
for the sensitivity of sky compass neurons to visually simulated self-motion. Neurons of the CBU (PoU,
328
TU, CPU5) that are not directly involved in sky compass signaling, were, likewise, unresponsive to visual
329
9
Zittrell et al. Sky-Compass Optic Flow Integration
self-motion. This coincides with studies on Drosophila that found that responsiveness of neurons of the
330
fan-shaped body (corresponding to the locust CBU) to motion stimuli highly depended on whether the
331
animals were actively engaged in flight (Weir and Dickinson, 2015; Shiozaki et al., 2020). It is therefore
332
likely, as for neurons of the sky compass system, that neurons at this integration stage are silent in locusts
333
under the constrained conditions of our experiments. H
∆
b neurons in Drosophila (corresponding to PoU
334
neurons in the locust) integrate external and internal self-motion cues to transform egocentric directions into
335
world-centric coordinates (Lu et al., 2022; Lyu et al., 2022). The lack of mechanosensory feedback under
336
our experimental conditions likely explains why PoU neurons did not respond to purely visual self-motion
337
cues. Under such conditions, PoU neurons, instead, strongly respond to looming objects (Rosner and
338
Homberg, 2013), thus they might rather be involved in escape reactions when quiescence is signaled by
339
the body. In general, physiological activity of locust CX neurons is considerably affected by active leg
340
movement (Rosner et al., 2019). In our study, the legs were cut off, eliminating any proprioceptive sensory
341
feedback.342
In contrast to the lack of responsiveness in most cell types, two mirror-symmetric CL2 neurons showed343
robust responses to simulated yaw rotation with opposite directional preference. Inspired by the proposed
344
role of P-EN neurons in Drosophila (corresponding to CL2 neurons in the locust) in updating and shifting
345
the activity peak across the columns of the PB, we developed a computational model testing the likely
346
function of CL2 neurons in the locust. The computational model of the CL1a-CL2 network resembles the
347
recurrent loop connectivity between E-PG and P-EN neurons accounting for angular velocity integration in
348
the Drosophila CX (Turner-Evans et al., 2017, 2020; Hulse et al., 2021). However, distinct differences exist,
349
based on the 360
◦
angular representation in the locust PB (Pegel et al., 2019; Zittrell et al., 2020) compared
350
to the 2 × 360
◦
representation of space in the Drosophila PB. While in Drosophila E-PG neurons form a
351
360
◦
representation of space in the ellipsoid body, two opposite 180
◦
representations of space would be
352
topographically intercalated in the CBL of the locust (Figure 5A). In Drosophila P-EN and E-PG neurons
353
are connected by recurrent excitatory loops with additional global inhibition (Turner-Evans et al., 2017). In
354
the locust, instead, both inhibitory and excitatory connections between CL1a and CL2 neurons are required.
355
Our model assumes homogeneously inhibitory or excitatory synapses from one neuron population onto
356
the other. We implemented two versions of the same model, differing only in the polarity of CL1a-CL2
357
connections. Both versions proved suitable for compass state maintenance but required different activity
358
patterns in the CL2 population. The version of the model with CL1a neurons inhibited by and exciting
359
CL2 neurons requires the CL2 population activity to equal that of the CL1a population. The reversed
360
version of this model in turn requires the CL2 population activity to be the inverse of the CL1a activity
361
pattern. Physiological data revealing the relationship between the activities of these two populations would
362
aid model evaluation and refinement. Close to equal E-PG and P-EN bump positions have been found in
363
Drosophila moving at a low angular velocity, with an offset increasing with angular velocity (Turner-Evans
364
et al., 2017). Neither of our versions could perform a shift of compass activity with a feed-forward input
365
only, which might be due to the fact that our models do not include a closed loop from one end of the
366
PB/CBL to the other. The inclusion of further neuron types might in fact close this gap and is the prospect
367
of future work. CL1b-d neurons (Heinze and Homberg, 2008; Heinze et al., 2009) might, in addition,
368
further stabilize the compass representation during standstill or forward motion. Franconville et al. (2018)
369
reported that connections from E-PG onto P-EN neurons in the PB are mediated by
∆
7 neurons. As TB1
370
and TB2 neurons cross the midline of the locust PB, they are, in addition to contralateral processes observed
371
in some CL1 neurons innervating the innermost columns of the PB (Sayre et al., 2021), candidates for
372
mediating ring closure. An internal compass representation must adapt to a new heading direction when
373
the animal turns. In the CX, this is likely accomplished by integrating rotation cues of different modalities.
374
10
Zittrell et al. Sky-Compass Optic Flow Integration
Two entry sites into the CX network for information on rotational self-motion have been proposed so far,
375
based on work in the fruit fly: i) The PB, where neurons may receive asymmetric input excited depending
376
on turning direction, conveyed via IbSpsP neurons (TB7 neurons in the locust) (Hulse et al., 2021). These
377
neurons connect specifically to P-EN neurons (CL2 neurons in the locust). ii) The NO, where GLNO
378
neurons (TN neurons in the locust) that receive input in the lateral complex and innervating one NO might
379
be excited/inhibited depending on turning direction. P-EN neurons convey these asymmetric inputs to
380
E-PG neurons via synapses in the ellipsoid body, leading to a shift of the internal heading representation
381
according to turning (Green et al., 2017; Turner-Evans et al., 2017). We explored possible mechanisms
382
inducing the compass bump shift on an algorithmic level.383
Instead of an additive input, different modulations of the network connectivity can produce a shift of the
384
compass network activity pattern. We adjusted the previously published modulatory effect (Pabst et al.,
385
2022) to feature broader arborizations in both the PB and the CBL and repeated optimization with Models A
386
and B. Relaxed versions (with broader arborizations in the PB and CBL) of both models could be optimized
387
to shift the compass signal in both directions. Optimization of Model B converged at the same solution as
388
optimization of Model A, with excitatory synapses from CL1a onto CL2 neurons in the PB, suggesting that
389
Model A can better explain the behavior of the compass network. To obtain a better fit to physiological data,
390
we narrowed down the width of arborizations in the CBL to three columns and we limited the arborizations
391
in the PB to single columns. Again, optimization of Model A and B was successful and converged at
392
modulated matrices with excitation in the PB in both cases. We further explored the possibility of synapses
393
among CL2 neurons of the same hemisphere, which could occur in the lower units of the two NO and
394
appear to be also present in Drosophila (Hulse et al., 2021). This additional degree of freedom rendered
395
synapses from CL2 onto CL1a neurons mostly redundant for shifts. In contrast to the shift-inducing matrix
396
presented previously (Pabst et al., 2022), the shift-inducing connectivity matrices shown here render a
397
closed, ring-like architecture in the sky compass network. The linear model and discrete motion steps
398
employed here are still quite abstract representations of the neuronal and behavioral characteristics of the399
locust. So far, our model is not dynamic; it switches between stable states but does not make the dynamics
400
underlying the transitions explicit. We aim to increase the model’s biological plausibility by implementing
401
velocity dependence in future work but expect the general principles of maintaining and updating the
402
compass bump to hold independently of the level of analysis.403
CONFLICT OF INTEREST STATEMENT
The authors declare that the research was conducted in the absence of any commercial or financial
404
relationships that could be construed as a potential conflict of interest.405
AUTHOR CONTRIBUTIONS
FZ, RR, and UH designed the experiments, FZ, EC, UP and RR performed the experiments. FZ wrote
406
manuscript. KP and DME designed the computational model and statistical analysis. KP revised the
407
manuscript, analyzed the data and implemented the computational model with DME. DME and UH
408
conceived, designed, and directed research, and helped write the manuscript. All authors contributed to the
409
article and approved the submitted version.410
11
Zittrell et al. Sky-Compass Optic Flow Integration
FUNDING
This work was supported by Deutsche Forschungsgemeinschaft (HO 950/28-1 to U. H. and EN 1152/3-1 to
411
D. M. E.), and the cluster project “The Adaptive Mind”, funded by the Excellence Program of the Hessian
412
Ministry of Higher Education, Research, Science and the Arts.413
ACKNOWLEDGMENTS
We thank Stefanie Jahn for preparing Figure 4D and Martina Kern for maintaining locust cultures.414
DATA AVAILABILITY STATEMENT
The datasets analyzed and generated for this study along with the code written for analysis and modeling
415
can be found in the data UMR repository (http://dx.doi.org/10.17192/fdr/76).416
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5 APPENDIX
5.1 Statistical Model and Power Analysis of Motion Sensitivity533
We designed a Bayesian model for the evaluation of the experimental spiking data, to test the hypotheses
534
that the firing probability of a motion phase
rm
is smaller, equal or larger than the firing probability
rs
during
535
a stationary phase. We denote these hypotheses by
H∈ {H(rm< rs), H(rm== rs), H(rm> rs)}
.
536
Given the firing probabilities, we assume that the data
D= (sm, gm, ss, gs)
of one experiment, comprised
537
of spikes
sm, ss
during motion/stationary phases and corresponding non-spikes/gaps
gm, gs
, are generated
538
by a Bernoulli process with a refractory period of 2 ms, which is typical for the neurons we investigate.
539
There might be additional dependencies between spikes that are not captured by a refractory Bernoulli
540
process, but these are not relevant for our hypotheses. The Bernoulli observation probability is given by541
P(D|rm, rs) = rsm
m(1 −rm)gm·rss
s(1 −rs)gs(7)
Since we are interested in hypotheses about firing probabilities relationships, we define a joint symmetric
542
Beta prior with parameters
α, β
on
rm
and
rs
, constrained by the hypothesis we wish to evaluate. We
543
choose a symmetric prior to avoid a-priori biases beyond H. For H(rm< rs), this prior is544
P(rm, rs|α, β, H(rm< rs)) ∝B(rm|α, β)B(rs|α, β)I(rm< rs)(8)
where
B(rm|α, β)
is a Beta density in
rm
and
I(rm< rs)
is an indicator function which is 1 if the condition
545
in the parentheses is true, and 0 otherwise. This indicator function ensures that only hypothesis-conforming
546
rm, rs
pairs have nonzero probability. The constant of proportionality can be obtained from the requirement
547
that the prior be normalized. Thus, this prior can be written as548
P(rm, rs|α, β, H(rm< rs)) = 2
B(α, β)2rα−1
m(1 −rm)β−1rα−1
s(1 −rs)β−1I(rm< rs)(9)
The prior resulting from
H(rm> rs)
can be obtained by inversion of the
<
in the indicator function,
549
whereas the prior for H(rm== rs)is simply one Beta prior for both (equal) firing probabilities.550
Since we are largely ignorant about the values of
α
and
β
, we chose these parameters by maximizing the
551
differential entropy subject to the condition that the average firing probability is
≈0.05
in a 2 ms time bin,
552
which is typical for our neurons. We found
α= 0.96
and
β= 18.28
, and used these values for the rest of
553
the analysis.554
To compute the hypothesis posterior555
P(H|D) = P(D|H)P(H)
PHP(D|H)P(H)(10)
via Bayes’ rule, we chose a uniform hypothesis prior
P(H) = 1
3
. We evaluated the probability
P(D|H)
by
556
marginalizing the firing probabilities using Equation 7 and Equation 9. For example, letting
H=H(rm<557
rs):558
15
Zittrell et al. Sky-Compass Optic Flow Integration
P(D|H(rm< rs)) = Z1
0
drsZ1
0
drmP(D, rm, rs|H(rm< rs))
=Z1
0
drsZ1
0
drmP(D|rm, rs)P(rm, rs|H(rm< rs))
=2
B(α, β)2Z1
0
drsZ1
0
drmrα+sm−1
m(1 −rm)β+gm−1rα+ss−1
s(1 −rs)β+gs−1I(rm< rs)
=2
B(α, β)2Z1
0
drsZrs
0
drmrα+sm−1
m(1 −rm)β+gm−1rα+ss−1
s(1 −rs)β+gs−1
=2B(α+sm, β +gm)
B(α, β)2Z1
0
drsrα+ss−1
s(1 −rs)β+gs−1IB(rs, α +sm, β +gm)(11)
where
IB(r, α, β)
is an incomplete beta function in
r
with parameters
α, β
. We solved the last integral by
559
Taylor-expanding
IB(rs, α+sm, β +gm)
to second order at
α+ss
α+ss+β+gs
, which yields a good approximation
560
as long as sm≈ssand gm≈gs. This is the case in our data.561
The probability
P(D|H(rm> rs))
can be evaluated by simply switching the roles of
rm
and
rs
in
562
the above derivation. For
P(D|H(rm== rs))
, where there is only one rate, the integrals can be solved
563
analytically to yield the well-known result564
P(D|H(rm== rs)) = B(α+sm+ss, β +gm+gs)
B(α, β).(12)
To facilitate interpretation of the values of the absolute motion sensitivity (AMSS, Equation 2) and the
565
motion hypothesis posterior, which we use to average the motion sensitivity scores (MSS, Equation 1),
566
we conducted a power analysis. We simulated 10,000 repetitions of a typical experiment in our study,
567
where an animal is stimulated for 5 s with either stationary or motion input. We generated spikes according
568
to the Bernoulli process assumption (Equation 7) with 2 ms time bins by drawing spike counts from a
569
binomial distribution. The firing rate of the stationary phase was set to 25 Hz, which corresponds to a firing
570
probability
rs= 0.05
and
N= 2500
Bernoulli trials during a single run of the experiment. An experiment
571
consisted of five simulated runs in the simulation. The firing probability during the motion phase was
572
assumed to be a multiple of
rs
in the range
1.15 . . . 1.30
. This range is covered by a strongly responding
573
neuron, see e.g. Figure 4A, right panel. To relate our motion sensitivity scores to standard measures used in
574
statistical contexts, we evaluated the Bayes factor in favor of a changed firing rate during motion:575
BF (rm=rs) = P(D|H(rm> rs)) + P(D|H(rm< rs))
P(D|H(rm== rs)) (13)
The simulation results are shown in Figure 7. The top panel shows the AMSS, the middle panel the
576
corresponding Bayes factors. The dotted lines show the boundaries for weak and strong evidence according
577
to Kass and Raftery (1995). For strong evidence, the firing rate ratio has to be greater than 1.25, which
578
implies an average AMSS
>0.65
. In the bottom panel, we plotted the hypothesis posterior, which we use
579
for averaging of the MSS. Strong evidence for an increased firing rate (MSS=+1 in Figure 3A) requires
580
MSS >0.65.581
16
Zittrell et al. Sky-Compass Optic Flow Integration
A B
B’
C’
C’’ C’’’
C
Figure 1
Mot. Stat.
Mot. Stat.
Mot. Stat.
Mot. Stat.
Figure 1. Experimental setup and visual-motion response of a CL1a neuron (neuron 550
L
in Supplementary
Figures 1 and 2). (A) Animals were mounted vertically and stimulated with motion of sinusoidal grating
patterns on two laterally placed monitors. (B) Response of a CL1a neuron to wide-field visual motion that
simulated horizontal left turning (left yaw). Raw data (top), detected spikes (middle) and smoothed firing
rate estimate (bottom). Vertical lines indicate onset of stimulation phases: Motion (Mot.) and stationary
phase (Stat.) were alternated, each pair constituting one stimulation trial. (B’) Same as B but for simulation
of horizontal right turn motion (right yaw). (C) Raster plot (left) of all left-turn trials. Vertical line at 5
s indicates onset of stationary phase. Diagram on the right shows differences in firing rate between the
motion (Mot) and stationary phase (Stat.) for each trial and mean firing rates for all trials. Error bars denote
standard deviation. (C’,C”,C”’) Same as C but for (C’) backward motion, (C”) left yaw and (C”’) right
yaw rotation.
17
Zittrell et al. Sky-Compass Optic Flow Integration
Figure 2. Morphology of neuron classes analyzed in this study. (A–C) Schematics of the locust central
complex and associated neuropils (CBL, lower division of the central body; CBU, upper division of the
central body; LX, lateral complex; NO, noduli; PB, protocerebral bridge; POTU, posterior optic tubercle)
with individual neurons from different classes superimposed. Large dots indicate somata, small dots
indicate axonal (presynaptic) arborizations, and fine lines indicate dendritic (postsynaptic) arborizations.
(A) Tangential neurons. We classified TU neurons as a group of diverse neurons that only have in common
that they have large presynaptic arborizations in the CBU and input regions outside the central complex.
Wiring schematics based on (von Hadeln et al., 2020). (B,C) Columnar neurons. Wiring schematics based
on (Heinze and Homberg, 2008).
18
Zittrell et al. Sky-Compass Optic Flow Integration
A
B
Figure 3. Overview of motion sensitivity and direction selectivity of all recorded neurons. (A) Absolute
motion sensitivity scores per motion direction (
AMSSdir
, left) and absolute direction selectivity scores per
motion direction category (ADSScat, right), summed over neuron cell types. Absolute motion sensitivity
scores take values between 0 and 1, with values close to 0 indicating no motion sensitivity and values close
to 1 indicating motion selectivity, disregarding whether the neuron responds with an increase or decrease in
activity. Absolute direction selectivity scores take values between 0 and 1, with values close to 0 indicating
no direction selectivity and values close to 1 indicating direction selectivity, disregarding which motion
direction elicits greater firing rates. Each cell holds the (rounded) sum of response scores over neuron
cell types. Numbers are given as sums of scores over the total number of tested neurons. The fractions of
summed scores and total possible scores are also indicated by the background color. The total number
of recorded neurons for each neuron class is indicated in parentheses. Empty cells mean that no neuron
was tested with the respective stimulus. (B) Distribution of motion sensitivity scores per motion direction
(
MSSdir
, left) and direction selectivity scores per direction category (
DSScat
, right), both per neuron
class. Cell shading codes for the fraction of summed scores and total possible scores.
19
Zittrell et al. Sky-Compass Optic Flow Integration
Figure 3
A
A’
C
C’
B
PB
NO
CBL
CBL
NO
PB
D
Mot. Stat.
Mot. Stat.
Mot. Stat.
Mot. Stat.
Figure 4. Physiological responses to yaw rotation and projections of CL2 neurons. (A,A’) Physiological
response (raster plots and mean firing rates) to left yaw rotation (A) and right yaw rotation (A’) of the CL2
neuron shown in B (unit 801
R
in Supplementary Figures 1 and 2). The neuron shows reduced firing rate
during simulated left yaw and increased firing activity during simulated right yaw. Vertical lines in the raster
plots indicate onset of the stationary phase. (B) Skeleton view of the CL2 neuron (view from posterior)
recorded in A and A’. The neurons arborized in column R4 of the right hemisphere of the protocerebral
bridge (PB), layers 1-3 of column L2 in the CBL, and in the lower unit of the left NO. Inset shows sagittal
view of ramifications in the lower division of the central body (CBL), and the left nodulus (NO). Scale
bar: 40 µm. (C,C’) Raster plots and changes in firing rate during simulated yaw in the second CL2 neuron,
shown in D (unit 800
L
in Supplementary Figures 1 and 2). The neuron increased its firing rate during
simulated left yaw (C) and decreased its firing rate during simulated right yaw (C’). (D) Two-dimensional
reconstruction of the neuron from confocal image stacks (view from posterior). It arborized in column L4
of the left hemisphere of the PB, column R2 in the CBL, and in the lower unit of the right NO. Inset shows
sagittal voltex view illustrating ramifications in the CBL and NO. Scale bar: 40 µm.
20
Zittrell et al. Sky-Compass Optic Flow Integration
Figure 4
A B
B’ B’’
Figure 5. Schematic wiring diagram of CL1a and CL2 columnar neurons in the central complex and
hypothetical shift mechanism of the internal heading signal in the PB. (A) Schematic wiring diagram of
the CX with a subset of the involved neuron types: CL1a and CL2 neurons are connected to one another
in the protocerebral bridge (PB) and lower division of the central body (CBL), while CL2 neurons also
have postsynaptic arborizations in the noduli (NO). CL1a neurons are topographically tuned to solar
azimuth along the PB (black arrows). (B-B”) Hypothetical shift mechanism of the internal heading signal
in the PB. (B) Full population of CL1a and CL2 neurons and initial activity state in the network: With an
environmental cue (sun) 90
◦
left of the locust (bottom), the CL1a population activity (top) has a distinct
maximum according to the neural tuning (highlighted arrows in PB and CBL). (B’) When the locust turns
right, CL2 neurons are excited or inhibited depending on their brain side. Neurons that innervate the left
(right) NO are excited (inhibited) by tangential neurons (TN) from the lateral complexes and relay onto
CL1a neurons from the left (right) half of the PB. This asymmetric input may analogously be conveyed
in the PB by tangential neurons (TB7) from the superior posterior slope. (B”) After turning, the CL1a
population activity maximum is shifted so that the neural heading estimate accordingly represents the
new heading relative to the external cue. Wiring schemes from (Heinze and Homberg, 2008), topographic
tuning in the PB and CBL based on (Zittrell et al., 2020).
21
Zittrell et al. Sky-Compass Optic Flow Integration
A A'
B'B
C C'
D D'
Figure 6. Computational Model. (A-A’) Connectivity matrices representing the projection and connectivity
schemes shown in Figure 5B, with additional self-recurrent excitatory connections. Excitatory synapses are
depicted in red, inhibitory synapses in blue. Neurons are indexed via the PB column (L8-R8) in which they
arborize. (A)
MA
, implying excitatory synapses from CL1a onto CL2 neurons in the PB and inhibitory
synapses from CL2 onto CL1a neurons in the CBL. (A’)
MB
implying a reversed polarity. (B-B’) Relaxed
versions
MAr
and
MBr
of the matrices shown in A-A’ optimized to produce shifts of the activity patterns
x
.(C-C’) Constrained versions
MAr,c
and
MBr,c
of
MAr
and
MBr
, representing broader arborizations in
the CBL but not the PB (compared to
MA
and
MB
). (D-D’)
MAr,c,NO
and
MBr,c,NO
; Same as C-C’ but
with added connections among CL2 neurons branching in the same hemisphere of the PB and the same
nodulus and optimized to shift activity patterns x.
22
Zittrell et al. Sky-Compass Optic Flow Integration
d
Figure 7. Power analysis of the Bayesian hypothesis comparison used for motion sensitivity analysis. The
circles and error bars are means and standard deviations computed across 10,000 repetitions of a simulated
experiment. The ratio of the motion phase firing rate
rm
and
rs
is shown along the abscissa. Top: absolute
motion sensitivity (AMSS), cf. Equation 2. Middle: Bayes factor in favor of the hypothesis that the firing
probabilities/rates are different during motion vs. equal rates, larger values represent stronger evidence.
The dotted lines show the boundaries for weak and strong evidence according to Kass and Raftery (1995).
Bottom: hypothesis posterior, used for the averaging of the motion sensitivity score (MSS), cf. Equation
1. The certainty of
H(rm> rs)
increases with an increasing
rm
rs
ratio.
rm
rs≈1.25
is sufficient for strong
evidence on average. For details, see text.
23
