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.
‡Present Address: Institute of Developmental Biology and Neurobiology,
Johannes-Gutenberg University Mainz, Mainz, Germany.
Words: (9692 excluding appendix) 11004 (including appendix), Figures: 10, 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 less clear how optic
10
flow is integrated into the central-complex network. We recorded intracellularly from neurons in the
11
locust central complex while presenting lateral grating patterns that simulated translational and
12
rotational motion to identify these sites of integration. Certain types of central-complex neurons
13
were sensitive to optic-flow stimulation independent of the type and direction of simulated motion.
14
Columnar neurons innervating the noduli, paired central-complex substructures, were tuned to
15
the direction of simulated horizontal turns. Modelling the connectivity of these neurons with a
16
system of proposed compass neurons can account for rotation-direction specific shifts in the
17
activity profile in the central complex corresponding to turn direction. Our model is similar but not
18
identical to the mechanisms proposed for angular velocity integration in the navigation compass
19
of the fly Drosophila.20
Keywords: optic flow, sky compass, desert locust, orientation, computational model, central complex, head direction, intracellular
21
recordings. This is a preprint of an article accepted for publication in Frontiers in Neural Circuits22
1
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 that monitor self-motion, such
28
as proprioceptive feedback (Wittlinger et al., 2006), and optic flow (Srinivasan, 2015; Stone et al., 2017)
29
provide information about traveling speed and covered distance and may update the inner sense of direction
30
in the absence of external cues. Only the flexible combination of information from external and internal
31
cues enables robust 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 sense of direction in the
33
brain of insects. It consists of the protocerebral bridge (PB), the lower (CBL) and upper (CBU) division of
34
the central body, also termed ellipsoid body (EB) and fan-shaped body (FB), and a pair of layered noduli
35
(NO), and is associated with behavioral decisions related to spatial orientation (Pfeiffer and Homberg,
36
2014). The PB and the CBL are subdivided into series of 16 or 18 columns that are connected across the
37
brain midline in a precise topographic manner (Pfeiffer and Homberg, 2014; Hulse et al., 2021; Homberg
38
et al., 2022).39
CX neurons in various insect species are tuned to celestial cues (Heinze and Homberg, 2007; Heinze,
40
2017; Honkanen et al., 2019). Evidence from the fly Drosophila (Hardcastle et al., 2021) and the desert
41
locust (Pegel et al., 2019; Zittrell et al., 2020) suggest that solar azimuth is encoded in the CX in a
42
compass-like manner. Silencing compass neurons in the CX impairs menotactic navigation behavior in
43
the fruit fly (Giraldo et al., 2018), showing the necessity of the CX for this behavior. Like mammalian
44
head direction cells (Taube, 1998, 2007), specific CX neuron populations are tuned to the animal’s current
45
heading (Seelig and Jayaraman, 2015; Hulse and Jayaraman, 2020). This internal heading estimate is
46
multimodally tethered to environmental cues, such as visual compass cues and wind direction (Okubo
47
et al., 2020), but also operates without external input, because internal cues from self motion are likewise
48
integrated (Green et al., 2017; Turner-Evans et al., 2017; Green and Maimon, 2018).49
The cellular understanding of the CX navigation network has made considerable progress, largely owing
50
to research in the fruit fly (Seelig and Jayaraman, 2015; Turner-Evans et al., 2017; Okubo et al., 2020;
51
Hulse et al., 2021; Lu et al., 2022; Lyu et al., 2022), desert locust (Homberg et al., 2011, 2022), dung
52
beetles (Dacke and el Jundi, 2018; el Jundi et al., 2019), monarch butterflies (Heinze and Reppert, 2011;
53
Nguyen et al., 2021), and bees (Stone et al., 2017; Sayre et al., 2021). Based on these data, plausible models
54
explaining network computations for navigation have been proposed (Stone et al., 2017; Le Mo
¨
el et al.,
55
2019; Sun et al., 2020, 2021). In the desert locust (Schistocerca gregaria), a long range migratory insect, sky
56
compass signals enter the CX through tangential neurons targeting the CBL, termed TL2 and TL3 neurons
57
(Figure 1A,D) that correspond to certain ER neurons in the fly (Homberg et al., 2022). Their postsynaptic
58
partners, CL1a columnar neurons (E-PG neurons in the fly), connect the CBL to single columns in the PB
59
(Figure 1B,E) and establish a 360
◦
representation of space related to solar azimuth in the PB. Tangential
60
neurons, termed TB1 and TB2 in the locust and
∆
7 in the fly, distribute the compass signal across the
61
columns of the PB (Figure 1A,D). They provide input to columnar CPU1 and CPU2 neurons (PFL neurons
62
in flies) connecting single columns of the PB to wide areas in the lateral accessory lobes (Figure 1C,D),
63
where navigation-related signals are conveyed to descending channels (Homberg et al., 2022; Rayshubskiy
64
et al., 2020). Compass representations in the CX of the fly and the locust differ in several aspects. In
65
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Zittrell et al. Sky-Compass Optic Flow Integration
Drosophila calcium imaging of E-PG neurons showed a flexible representation of 360
◦
of space in the EB
66
leading to a twofold representation of 360
◦
across the PB (Seelig and Jayaraman, 2015; Hardcastle et al.,
67
2021). In contrast in locusts, single-cell intracellular recordings from various types of PB neurons suggest a
68
single 360
◦
representation of space across the PB which is assumed to be fixed across the locust population
69
(Heinze and Homberg, 2007; Zittrell et al., 2020). Whether these differences are related to differences
70
in circuit architecture such as the EB in the fly being a closed toroidal structure, and the locust CBL, an
71
open kidney-like neuropil (Pisokas et al., 2020), or differences in the analyzed cell types representing the72
compass remains to be seen. Research in flies and bees suggests that optic flow input is integrated in the
C
POTU
PB
CBU
CBL
NO
LX
CPU2
CPU5
CPU1
POTU
PB
CBU
CBL
NO
LX
CL1a
CL2
CP2 CP1 PoU
POTU
PB
CBU
CBL
NO
LX
TB1
TL2
TL3
TU
AB
D
TL3
TB1
CPU1 CL1a
IN
OUT
INPUT
TL3, TL2
CL1a
TB1
CPU1, CPU2
OUTPUT
E
Information flow sun compass Hypothetic optic flow pathways
TRANSLATION
CPU5
PoU
ROTATION
CL2
CL1a
ROT TRANS
PoU
CPU5 CL2
CL1a
Figure 1. 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). (D) Information flow through core neuronal elements of the sun compass
circuit in the locust central complex, based on Heinze and Homberg (2007) and Heinze et al. (2009). For
reasons of simplicity TL2 and CPU2 neurons are not included in the diagram. (E) Hypothetic neuronal cell
types shown in A-C and their putative connectivity, that might be involved in optic flow signaling. Data are
based on corresponding cell types in the fly Drosophila (Green et al., 2017; Turner-Evans et al., 2017; Lu
et al., 2022) and the sweat bee Megalopta genalis (Stone et al., 2017).
73
sky compass network through the PB and/or NO (Stone et al., 2017; Turner-Evans et al., 2017; Green et al.,
74
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Zittrell et al. Sky-Compass Optic Flow Integration
2017; Lu et al., 2022). In bees, inputs to the NO, termed TN neurons, provide optic-flow based speed
75
information allowing for computation of path integration in the CX (Stone et al., 2017). In Drosophila,
76
columnar neurons receiving input via the NO (from TN-type neurons) and the PB (via SpsP neurons) signal
77
translational velocity and, by convergence on internal h
∆
B neurons of the FB, lead to a representation of
78
translational velocity in world-centric space (Lu et al., 2022; Lyu et al., 2022). Whereas circuits involved in
79
translational velocity coding involve the upper units of the NO and the CBU/FB, Turner-Evans et al. (2017)
80
and Green et al. (2017) showed in flies, that columnar neurons innervating the lower units of the NO (P-EN
81
neurons) are involved in angular velocity signaling and, through interaction with E-PG neurons, are suited
82
to shift compass activity in the PB corresponding with turns of the fly during walking. Although neurons
83
apparently homologous to optic-flow encoding neurons in bees and flies are known morphologically in
84
locusts, such as TB7 (SpsP in flies), TN-type neurons, pontine PoU neurons (h
∆
in flies), CL2 columnar
85
neurons (P-EN in flies), CPU4 and 5 neurons (PFNd in flies; Figure 1E; Heinze and Homberg (2008); von
86
Hadeln et al. (2020)), only a single study has so far addressed the sensitivity of CX neurons of the locust
87
to translational optic flow (Rosner et al., 2019). That study showed that neurons at all levels of the sky
88
compass network were sensitive to translational forward motion, but often responses could not be separated
89
from the effects of concurrently occurring leg movements that were elicited by the optic flow stimulus.90
To investigate optic flow sensitivity in the CX of the locust more systematically, we recorded intracellularly
91
from various types of CX neurons while stimulating laterally with wide-field gratings that simulated self-
92
motion to the animal. We analyzed general motion sensitivity for translational and rotational motion
93
directions and tested whether the neural responses to opposing motion directions were discriminated
94
(direction selectivity).95
We implemented an algorithmic model (in the sense of Marr and Poggio (1979)) of the CX circuit which
96
integrates visual self-motion cues with head direction representation. Modeling was guided by data on two
97
types of columnar neurons with one being sensitive to the direction of simulated horizontal turns.98
2 METHODS
2.1 Animals and preparation99
Desert locusts (Schistocerca gregaria) were kept and dissected as described previously (Zittrell et al.,
100
2020). Animals were reared in large groups (gregarious state) at 28
◦
C with a 12 h / 12 h light / dark cycle;
101
adult locusts from either sex were used for experiments. Limbs and wings were cut off, the animals were
102
fixed on a metal holder with dental wax, and the head capsule was opened frontally, providing access to the
103
brain. The esophagus was cut inside the head, close to the mandibles, and the abdomen’s end was cut off to
104
take out the whole gut through this opening. The brain was freed of fat, trachea and muscle tissue and was
105
stabilized with a small metal platform that was fixed to the head capsule. A chlorinated silver wire, inserted
106
into the hemolymph surrounding the brain, served as the indifferent electrode. Shortly before recording, the
107
brain sheath was removed at the target site with forceps, permitting penetration with sharp glass electrodes.
108
The brain was kept moist with locust saline (Clements and May, 1974) throughout the experiment.109
All animal procedures were performed according to the guidelines of the European Union (Directive
110
2010/63/EU) and the German Animal Welfare Act.111
2.2 Intracellular recording and histology112
Sharp microelectrodes were drawn with a Flaming/Brown filament puller (P-97; Sutter Instrument), their
113
tips filled with Neurobiotin tracer (Vector Laboratories; 4 % in 1 mol
·
l
−1
KCl) and their shanks filled
114
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Zittrell et al. Sky-Compass Optic Flow Integration
with 1 mol
·
l
−1
KCl. Intracellular recordings were amplified with a custom-built amplifier and digitized
115
with a 1401plus (Cambridge Electronic Device, CED) analog-digital converter (ADC) or amplified with a
116
BA-01X (npi electronic GmbH) and digitized with a Micro mkII with an ADC12 expansion unit (CED).
117
Signals were monitored with a custom-built audio monitor and recorded with Spike2 (CED). Neurons were
118
traced by electrically injecting Neurobiotin (
∼
1 nA positive current for several minutes). Each neuron
119
presented in this study originates from a different specimen. Brains were dissected and immersed in fixative
120
(4 % paraformaldehyde, 0.25 % glutaraldehyde and 0.2 % saturated picric acid, diluted in 0.1 mol
·
l
−1
121
phosphate buffered saline [PBS]) over night, followed by optional storage at 4
◦
C in sodium phosphate
122
buffer until further processing. Brains were rinsed in PBS (4 × 15 min) and incubated with Cy3-conjugated
123
streptavidin (Dianova; 1:1,000 in PBS with 0.3 % Triton X-100 [PBT]) for 3 d at 4
◦
C. After rinsing in
124
PBT (2 × 30 min) and PBS (3 × 30 min), they were dehydrated in an ascending ethanol series (30 %, 50
125
%, 70 %, 90 %, 95 %, and 2 × 100 %, 15 min each) and cleared in a 1:1 solution of ethanol (100 %) and
126
methyl salicylate for 20 min and in pure methyl salicylate for 35 min, to finally mount them in Permount
127
(Fisher Scientific) between two coverslips. For anatomical analysis, brains were scanned with a confocal
128
laser-scanning microscope (Leica TCS SP5; Leica Microsystems). Cy3 fluorescence was elicited with a
129
diode pumped solid-state laser at 561 nm wavelength. The resulting image stacks were processed with
130
Amira 6.5 (ThermoFisher Scientific, Waltham, MA) and Affinity Photo (Serif, Nottingham, UK). The
131
chirality of some neurons could not be determined because multiple neurons of the same neuron class but
132
on both brain sides were stained in these cases.133
2.3 Experimental Design134
We used two monitors (FT10TMB, 10“, 1024x768 px at 60 Hz, Faytech, Shenzhen, China) that were
135
placed 12.7 cm apart on the left and right side of the animal. They were mounted vertically to present
136
sinusoidal grayscale grating patterns (Figure 2A). The displays were covered with diffuser sheets to
137
eliminate light polarization inherent to LCD monitors. The patterns were drawn on the inner center-square
138
(15.35 cm edge length) of the displays, covering
62.3◦
of the visual field on each side. The monitor
139
brightness amounted to 1.12
·1011
photons cm
−2·
s
−1
when displaying a black area and 7.09
·1013
140
cm
−2·
s
−1
when displaying a white area. Monitor brightness was measured using a digital spectrometer
141
(USB2000; Ocean Optics) placed at the position of the locust head.142
The grating patterns were animated to simulate self-motion to the animal. We tested translational (forward
143
and backward) motion, yaw rotation (left and right turning), lift (upward and downward), and roll (counter
144
clockwise and clockwise). Throughout this study, these direction labels refer to simulated self-motion
145
directions and not absolute motion of the displayed patterns. Thus, “forward motion” means that both
146
monitors displayed a grating pattern with horizontal bands (perpendicular to the locust’s body axis, cf.
147
Figure 2A) that continuously moved from top to bottom.148
Each motion direction was tested in a series of trials in pre-defined order, starting with translational
149
motion and yaw rotation followed by lift and roll; each trial consisted of two phases, a motion phase and an
150
immediately following stationary phase (Figure 2B,B’). All phases in the same recording lasted for five or
151
six seconds. Each series consisted of two to five trials; each trial was immediately followed by the next
152
one, unless it was the last of the series. Neurons typically responded strongly to the pattern display switch
153
between series. Therefore, each series of a given motion direction was preceded by an adaptation phase
154
of five to six seconds which was discarded; this phase was a single stationary phase of the same pattern
155
used during the upcoming series, immediately followed by the first motion phase of the series. If the same
156
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Zittrell et al. Sky-Compass Optic Flow Integration
A B
B’
C’
C’’ C’’’
CMot. Stat.
Mot. Stat.
Mot. Stat.
Mot. Stat.
Figure 2. 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. An asterisk indicates ‘strong evidence’ in favor of the hypothesis that the firing rates differ
between the motion and stationary phases (i.e., it indicates a Bayes factor
≥
10 according to the conventions
established by Kass and Raftery (1995)).
motion direction was tested in more than one series, all trials were treated as if they belonged to the same
157
series. Not all neurons could be tested for all motion directions due to recording instability.158
A separate PC running MATLAB (R2019, MathWorks) with the Psychophysics toolbox (Brainard, 1997)
159
was used to generate the grating patterns (Figure 2A). The sine gratings had a spatial resolution of 0.005
160
cycles
·
px
−1
(one sine cycle spanned 200 px) and were shifted with 2 cycles
·
s
−1
during the motion
161
phases corresponding to a velocity of 32.5
◦
s
−1
in the center of the screen. These parameters are well
162
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Zittrell et al. Sky-Compass Optic Flow Integration
within the range of motion stimuli eliciting optomotor responses in tethered flying locusts (Thorson, 1964;
163
Preiss and Spork, 1995). The PC was USB-connected to an Arduino Uno (Arduino) via which TTL pulses
164
were sent to the ADC, recorded at 500 Hz. These pulses indicated grating pattern animation and onset of
165
stimulation phases. Two squares with 30 px edge length in the top left corner of each display were used
166
to indicate the presented motion type by flashing them white: Each motion type was assigned a distinct
167
number of flashes (20 ms duration) that were generated at the end of the adaptation phase of each series.
168
Each square was covered by a photo diode that picked up the white flashes and whose signal was recorded
169
by the ADC at 200 Hz. This allowed for encoding the motion type of each stimulation series in the data file.
170
The generation of each rectangle flash was also recorded via the Arduino as a TTL rectangle pulse of the
171
same duration, which allowed for measuring the precise timing of stimulus display by cross correlating
172
diode signal and TTL signal.173
2.4 Statistical Analysis174
Spikes were detected by median filtering (500 ms window width) the voltage signal and applying a
175
manually chosen threshold. Spikes and non-spikes (gaps) within 2 ms time bins were counted during the
176
whole 5 s long interval of each trial of stimulation condition. We chose 2 ms time bins for this analysis
177
because this is the approximate length of the refractory period of the neurons.178
In the following, we describe our design of a Bayesian analysis of motion sensitivity and direction
179
selectivity. This analysis allows us to compute statistics on the quantities of interest directly, rather than
180
testing against a distributional assumption that has no clear relationship to the data generating process, such
181
as a t-statistic. Furthermore, the Bayesian approach guarantees internal consistency when multiple statistics
182
on the same data are computed. These epistemic advantages are empirically backed by the observation
183
that standard t-test statistics yielded very noisy and correspondingly uninterpretable results on our data.
184
Lastly, Bayesian approaches will yield results on small samples, albeit at the cost of increased uncertainty
185
in the conclusions. All computations were performed with the Python programming language (version
186
3.10.8) and the PyTorch (version 1.13.0) and Pandas (version 1.5.2) libraries . Plots were created with the
187
Matplotlib library (version 3.6.2).188
2.4.1 Motion Sensitivity189
We define motion sensitivity as a neuron’s property to have different firing rates during motion and
190
stationary phases. We analyzed motion sensitivity for each tested neuron and motion direction by comparing
191
the neuron’s firing rate during the motion phase with that during the following stationary phase. Firing
192
probabilities were computed by integrating prior knowledge about compass neuron activity in general and
193
the condition-specific data from each neuron via Bayesian inference. For each neuron
n
, we computed
194
a posterior over three different hypotheses: First, that the firing probability in 2 ms time bins during the
195
motion phase
rm
is lower than the firing probability
rs
during the stationary phase,
H(rm< rs)
, second,
196
that the firing probabilities are equal
H(rm== rs)
, or third, that
rm
exceeds
rs
,
H(rm> rs)
. A high
197
posterior for the first or third hypothesis would indicate motion sensitivity, while a high posterior for the
198
second hypothesis would indicate that the neuron does not respond to the motion stimulation.199
Using Bayes’ rule, we computed the posterior distribution
P(H|D)
over the three hypotheses
200
H∈ {H(rm< rs), H(rm== rs), H(rm> rs)}
given the experimental data
D
, assuming an uniform
201
hypothesis prior, a Bernoulli observation model and a joint Beta prior for the firing probabilities. This joint
202
prior was restricted by the firing probability constraints expressed in each hypothesis, e.g. for
H(rm< rs)
,
203
the probability P(rm≥rs)=0etc. For details, see appendix 5.1.204
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To summarize the information embedded in this posterior and to simplify comparison across multiple
205
neurons, we computed two scores: First, the Bayes factor BF=in favor of rm=rs:206
BF==P(H(rm< rs)|D) + P(H(rm> rs)|D)
P(H(rm== rs)|D).(1)
We plotted an asterisk in Figure 2 and Figure 4 whenever
BF=≥10
which indicates ’strong evidence’
207
in favor of unequal firing rates (Kass and Raftery, 1995). Second, we evaluated a single motion sensitivity
208
score (MSS) per neuron and motion direction (dir):209
MSSdir =
H(rm> rs) : 1
H(rm== rs) : 0
H(rm< rs) : −1
(2)
We weight this score with the corresponding hypothesis posterior probability and sum across all neurons
210
of one type. The maximal value for one firing probability hypothesis is therefore equal to the number of
211
neurons of a given type.212
Further, we computed absolute motion sensitivity scores (AMSS) for four motion categories (cat),
213
each comprised of two opposing motion directions
A
and
B
: translational motion (forward or backward
214
direction), yaw rotation (left or right turning), lift (upward or downward), and roll (counterclockwise or
215
clockwise):216
AMSScat = 1 −[P(H(rm,A == rs,A)|D)∗P(H(rm,B == rs,B)|D)] (3)
where
rm,A
and
rm,B
are firing probabilities during stimulation with opposing motion directions in the
217
respective motion category. In other words, this score will be close to one if at least one motion direction
218
of a category elicits a strong deviation from the stationary firing probability. We sum this score across all
219
neurons of a given type.220
2.4.2 Direction Selectivity221
We define direction selectivity as a neuron’s property to respond contrarily to two opposing motion
222
directions
A
and
B
. We analyzed direction selectivity in the four motion categories outlined above:
223
translation, yaw rotation, lift, and roll. In the following, the hypothesis
H(rm,A ≥rs,A) = H(rm,A >224
rs,A)∨H(rm,A == rs,A)where ∨indicates a logical ’or’, and ∧is a logical ’and’.225
We compute a direction selectivity score as226
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
(4)
For example,
DSStranslation
is +1(-1) if the firing probability does not decrease during forward(backward)
227
motion and decreases during backward(forward) motion, or if it increases during forward(backward) motion
228
and does not change during backward (forward) motion. It is 0 if the firing probability changes in the same
229
direction for both motion directions. We weight this score with the corresponding hypothesis posterior
230
probability and sum across all neurons of one type. The maximal value for one firing probability hypothesis
231
is therefore equal to the number of neurons of a given type, similar to MSSdir.232
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Zittrell et al. Sky-Compass Optic Flow Integration
As an indicator for the total number of neurons with any direction sensitivity at all, we computed the
233
expected absolute direction sensitivity score (ADSS):234
⟨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)(5)
This score can take values between 0 and 1, with values close to zero indicating no direction selectivity
235
and values close to one indicating direction selectivity, disregarding which motion direction elicits greater
236
firing rates. We sum this score across all neurons of a given type.237
The appendix 5.1 comprises a power analysis for the analyses of motion sensitivity and direction
238
selectivity outlined above, indicating which difference in the recorded firing rates is considered evidence
239
for the hypothesis that a neuron fires more in one of the two conditions.240
2.5 Computational Model241
All computations were performed with the Python programming language (version 3.10.8) and the
242
PyTorch (version 1.13.0) library. Plots were created with the Matplotlib library (version 3.6.2).243
Our model comprises CL1a and CL2 neurons, adopting the projection schemes proposed by Heinze and
244
Homberg (2008).245
In contrast to a previous model of the CL1a-CL2 circuit (Pabst et al., 2022), the model described here
246
also accounts for the reported arborization widths: No arborizations broader than one column were found
247
in the PB. In the CBL, CL2 neurons innervate single columns. Ramifications of CL1a neurons, especially
248
in the upper layers of the CBL, span up to five columns (Heinze and Homberg, 2008). These ramifications
249
lead to an effective CL2 - CL1a connectivity in the CBL extending over up to five columns in the model.
250
We assume that, as shown for E-PG and P-EN neurons in the fly (Turner-Evans et al., 2017), CL1a neurons
251
provide synaptic inputs to CL2 neurons in the PB, which in turn provide synaptic inputs to CL1a neurons in
252
the CBL. We further assume a combination of excitation and inhibition within the CL1a-CL2 connectivity
253
instead of excitatory loops paired with global inhibition, as has been proposed for Drosophila (Turner-
254
Evans et al., 2017). We refer to the model outlined thus far as the default model
Modeld
and introduce
255
another version where all CL2 neurons from the same hemisphere are interconnected. This model is termed
256
ModelNO
as synapses giving rise to such a connectivity could occur in the lower units of the two NO (cf.
257
Figure 5), which appears to be the case in Drosophila (Hulse et al., 2021). Since data on the excitatory
258
and inhibitory nature of (proposed) synapses in the circuits modeled here are missing, all synaptic weights
259
were determined via optimization with the objective of either maintaining or shifting compass activity.
260
Initial weights are uniform for all excitatory and inhibitory connections, 0.5 and -0.5, respectively. They
261
are set such that CL1a neurons excite CL2 neurons, which in turn inhibit CL1a neurons. Reversing this
262
relation led to identical results after weight optimization. The firing rate neurons and synaptic connections
263
in our model are linearized around their operating point, thus approximating their non-linear dynamics.
264
We represent the CL1a-CL2 connectivity with matrices
Md
and
MNO
for the two versions of the model,
265
Modeld
and
ModelNO
, respectively. For all neurons, the connectivity features additional self-recurrent
266
connections and synapses onto neurons of the same type arborizing in adjacent PB columns to enable the267
maintenance of a baseline activity. The network’s activity is characterized by deviations from a baseline
268
firing rate, represented by a vector
xt
with components
xt,1:16
and
xt,17:32
covering the CL1a and CL2
269
neurons, respectively. Vector components for each neuron type are ordered from left to right according
270
to their PB column, which we label
L8, . . . , L1, R1, . . . , R8
. The network is recurrent and iterated across
271
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time steps such that the activity at the next time point,
t+ 1
, can be computed from the activity at the
272
current time point, t:273
xt+1 =Mxt(6)
2.5.1 Maintenance of a Stable Head Direction Signal274
In the framework outlined above, maintenance of the head direction representation or CL1a activity
275
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,
276
t+ 1:277
xt,1:16 =xt+1,1:16 (7)
According to Equation 6, this is given if
Mxt=xt
. We refer to such
xt
as stable states. We defined
278
sinusoidal CL1a and CL2 activity targets
ˆxt,1:16 = ˆxt,17:32
matching the tuning observed across the PB
279
(Pegel et al., 2019; Zittrell et al., 2020). Each target had an activity maximum (’compass bump’) in one
280
PB column. We used as many targets as there are PB columns in our model. For more details, see Pabst
281
et al. (2022). We employed the L-BFGS algorithm (Liu and Nocedal, 1989) to optimize synaptic weights
282
of
Md
and
MNO
by minimizing the mean-squared deviation between these targets and the network outputs
283
over two time steps subject to the aforementioned arborization width constraints. Furthermore, we apply a
284
weak quadratic synaptic weight regularization to push all non-essential connectivity to zero. Our results are
285
robust against changes of the relative weight of the regularization, as long as it is ≈0.1−0.2.286
2.5.2 Rotation-induced Shifts of the Head Direction Signal287
We tested two possible computational mechanisms that would produce a phasic shift from
xt
to
xt+1
,
288
representing the influence of rotational flow inputs on the compass system, putatively conveyed by TN or289
TB7 neurons: A purely feed-forward input exciting and/or inhibiting the CL1a and/or CL2 neurons and a
290
modulatory input modifying the connectivity. We used the targets described above as initial network states.
291
For both left and right turns, we defined targets
ˆxt+1,1:16 = ˆxt+1,17:32
and
ˆxt+2,1:16 = ˆxt+2,17:32
shifted
292
in the direction opposing turn direction, such that the activity maximum or compass bump transitioned
293
from one PB column to an adjacent one in each time step. For more details, see Pabst et al. (2022).Both
294
feed-forward and modulatory inputs were optimized to minimize the mean-squared deviation between
295
these shifted targets and the network outputs over two time steps using the L-BFGS algorithm subject to
296
the aforementioned arborization width constraints and the weight regularization.297
2.5.3 Simulation298
To test whether the learnt network parameters render a stable compass that can integrate an initial head
299
direction signal with rotation inputs over a series of time points, we implemented an agent simulation. We
300
simulated forward motion interrupted by a turn to the right followed by a turn to the left of equal magnitude.
301
This trajectory was chosen to facilitate an intuitive understanding of the compass bump’s traversal along the
302
PB, including the ’wrapping around’ at its lateral ends. Note that we only distinguish between movement303
directions at this point, assuming a uniform absolute angular velocity for all turns, which is not entirely
304
biologically plausible. The starting compass bump position was set to an arbitrary PB column.305
3 RESULTS
We surveyed CX neurons at different integration stages for sensitivity to the moving gratings (Figures 1
306
and 2). In total 62 morphologically identified neurons with arborizations in the CX were studied (Figure 1).
307
These included 4 tangential input neurons (TL) to the CBL comprising the subtypes TL2 and TL3 (Figure
308
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1A), 21 CL1a columnar neurons connecting the CBL to the PB, two CL2 columnar neurons connecting
309
the PB, CBL and NO, five TB1 tangential neurons of the PB, three CPU1, seven CPU2 and one CPU5
310
neurons connecting distinct columns of the PB and CBU to the lateral complex (CPU1, CPU2) or a nodulus
311
(CPU5), one CP1 and two CP2 neurons connecting the PB to distinct areas of the lateral complex (Figure
312
1B), eight PoU pontine neurons (Figure 1B), and various TU-type tangential neurons of the CBU (Figure
313
1A). We found sensitivity to the optic flow stimuli in some neural classes while others did not respond to
314
the stimulation.315
3.1 Sensitivity to Translational and Rotational Optic Flow in the Central Complex316
Neurons in most of the examined morphological classes shown in Figures 1A-C were not sensitive
317
to the moving gratings. Some of the tested TL-, CL1a-, and CPU2 neurons, however, were sensitive to
318
grating patterns moving in at least one motion direction (motion sensitivity; Figures 3A,B). Response
319
scores, indicating the sign of the firing rate change due to visual self-motion perception, were likewise
320
inconsistently distributed within these neuron classes. Overall, within a given neuron class, individual
321
neurons responded with excitation, inhibition or not at all to the same stimulus, independent of their
322
brain side of origin (Figures 3A,B). Two CL2 neurons, however, were not only motion sensitive but
323
also responded differently to opposing motion directions (direction selectivity, Figures 3A,B, 4, and
324
Supplementary Figure 2).325
3.2 Yaw-rotation is processed by CL2 neurons326
We recorded from two mirror-symmetric CL2 neurons. One neuron had smooth, presumably postsynaptic
327
arborizations in the left NO and in column R4 of the right half of the PB, and beaded processes in layers
328
1-3 of column L2 in the left half of the CBL (Figure 4B). The second CL2 neuron had ramifications in
329
the right NO, column L4 in left half of the PB, and column R2 in the right half of the CBL (Figure 4D).
330
Both neurons were directionally selective for visual motion that simulated yaw rotation, but with opposite
331
polarity (Figures 4A,A’,C,C’ and Supplementary Figure 2). The CL2 neuron with arborizations in the right
332
half of the PB and in the left NO (unit 801
R
, Supplementary Figures 1 and 2) responded to right turns
333
with an increase and to left turns with a decrease in firing rate, compared to baseline. The neuron was also
334
weakly inhibited by forward motion. The CL2 neuron arborizing in the left half of the PB and the right NO
335
(unit 800
L
in Supplementary Figures 1 and 2), on the other hand, responded to left turns with an increase
336
and to right turns with a decrease in firing rate. Responses to translational motion stimuli were not tested.
337
Neurons apparently homologous to CL2 in Drosophila (P-EN) signal rotational self-motion, updating the
338
internal heading representation when the animal turns (Turner-Evans et al., 2017; Green et al., 2017).339
Although the physiological data on CL2 neurons are limited to only two recordings, which moreover
340
could not be tested for responses to backward motion, lift and roll, the striking similarity in projection
341
pattern between CL1/CL2 neurons in the locust and E-PG/P-EN neurons in the fly opens the possibility
342
that the locust internal compass signal may, like in the fly, be shifted during turns via asymmetric excitation
343
and inhibition of CL2 neurons (Figure 5B’). This idea is consistent with our simulation of compass shifts,
344
as described below. The site of this interaction may either be the NO (via TN neurons) or the PB (via
345
TB7 neurons). Both cell types are, like their equivalents in Drosophila, the GLNO neurons and the SpsP
346
neurons (Hulse et al., 2021) morphologically suited to provide asymmetric input to the CL2 population.
347
Like in Drosophila P-EN neurons, the projections of locust CL2 neurons in the CBL are shifted by one
348
column relative to the projections of CL1 neurons (Figures 5A,B). A notable difference between compass
349
representation in the locust and the Drosophila compass system is that the E-PG population activity peak
350
in the EB results in two activity peaks with a fixed offset along the PB, while available data in the locust
351
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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.
suggest a single peak along the PB that results from azimuthal tuning to celestial cues ((Pegel et al.,
352
2019; Zittrell et al., 2020)). We refer to this single peak as the ’compass bump’. If there is indeed a
353
(single) compass bump, locust CL2 neurons might have inhibitory connections to CL1a neurons (Figure
354
5B). However, these connections and their polarity are hypothetical as there are no data on functional
355
connectivity in the locust CX. Alternatively, the observed tuning could be a consequence of the projection
356
and connectivity patterns of CL1a and CL2 neurons.357
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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. An asterisk indicates ‘strong evidence’ in favor of the
hypothesis that the firing rates differ between the motion and stationary phases (i.e., it indicates a Bayes
factor
≥
10 according to the conventions established by Kass and Raftery (1995)). (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’). Like in A, an asterisk indicates ’strong evidence’ for a firing rate difference between the motion
and stationary phases. (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.
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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).
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3.3 Computational Model358
3.3.1 Maintenance of a Stable Head Direction Encoding359
Modeld
and
ModelNO
connectivities are based on the projection patterns described by Heinze and
360
Homberg (2008), assuming synapses between CL1a and CL2 neurons arborizing at the same location.
361
ModelNO
further accounts for possible synapses within the two CL2 neuron subsets arborizing in the
362
same nodulus, respectively. The proposed CL2-CL2 synapses are functionally equivalent to connections in
363
Drosophila (Hulse et al., 2021). Both models can maintain an initial network activity pattern with the CL1a
364
activity maximum or compass bump representing head direction relative to a global cue, such as the sun,
365
when no yaw rotation is simulated.366
For both model versions, optimization rendered all synapses from CL1a neurons onto CL2 neurons in the
367
PB excitatory (cf. the lower right quadrants in Figure 6A,B respectively). In both model versions, CL2
368
neurons inhibit CL1a neurons projecting into the opposite hemisphere of the PB via connections in the CBL
369
(cf. the two secondary diagonals in the upper left quadrants of Figure 6A,B, respectively) and excite CL1a
370
neurons branching in the same PB hemisphere (cf. the main diagonals in the upper left quadrants of Figures
371
6A,B, respectively). CL1a-CL1a connectivities are similar in both models: In addition to the excitatory
372
self-recurrent connection, CL1a neurons in adjacent PB columns are excited (cf. lower left quadrants in
373
Figure 6A,B). In
Modeld
, the CL2-CL2 connectivity resembles the CL1a-CL1a connectivity (cf. the upper
374
right quadrant of Figure 6A). In
ModelNO
, all CL2 neurons arborizing in the same PB hemisphere are
375
potentially interconnected in the contralateral NO (cf. Figure 5B). Furthermore, inhibitory synapses exist
376
in the noduli between CL2 neurons arborizing in opposite ends of each PB hemisphere (cf. the upper right
377
quadrant of Figure 6B).378
3.3.2 Rotation-induced Shifts of Compass Activity379
Feed-forward input to the CL1a/CL2 neurons could not be optimized to induce compass bump shifts in
380
Modeld
or
ModelNO
. However, the modulatory inputs were able to shift the bump (cf. Figures 6A’,B’
381
for modulated connectivities shifting the network activity to the right during left turns). The compass
382
bump is shifted by modulations of the network connectivity at multiple sites: In both models, CL2 neurons
383
asymmetrically excite or inhibit CL1a neurons branching in the same hemisphere of the PB (cf. the main
384
diagonal in the upper left quadrants of Figures 6A’,B’). In both models, CL1a neurons asymmetrically
385
excite and inhibit neurons of the same type arborizing in adjacent PB columns. During left turns, neighbors
386
to the left are excited and neighbors to the right are inhibited (cf. the lower left quadrants of Figure 6A’,B’),
387
and the opposite holds during right turns (not depicted). In
Modeld
, the same applies to CL2 neurons (cf.
388
the upper right quadrant of Figure 6A’). In
ModelNO
instead, a part of the inhibitory synapses among
389
CL2 neurons is attenuated. During left turns,
CL2L8−L5
and
CL2R1−R3
less strongly inhibit
CL2L1−L3
390
and
CL2R8−R6
, respectively (cf. the upper right quadrant of Figure 6B’ compared to its counterpart in
391
B). During right turns, this order is reversed: Inhibitory synapses from
CL2L1−L3
and
CL2R8−R5
onto
392
CL2L8−L5and CL2R1−R3, respectively, are attenuated (not depicted).393
3.3.3 Simulation394
An example of
Modeld
in action is shown in Figure 7, where we simulate a heading trajectory and the
395
resulting compass states. Results look identical for
ModelNO
, see Supplementary Figure S3. The top panel
396
shows the simulated motion directions and the two bottom panels depict the network activity at each time
397
point. Activation of the CL1a and CL2 populations is equal at all time points, with one global activity
398
maximum or bump along the PB in each subset of neurons. When the agent turns, both activity patterns
399
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Zittrell et al. Sky-Compass Optic Flow Integration
Motion direction
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
CL1a CL2
Postsynaptic Neurons
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
Presynaptic Neurons
CL1a CL2
CBL
PB
A
Modeld
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
CL1a CL2
Postsynaptic Neurons
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
CBL NO
PB
B
ModelNO
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
CL1a CL2
Postsynaptic Neurons
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
Presynaptic Neurons
CL1a CL2
CBL
PB
A'
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
CL1a CL2
Postsynaptic Neurons
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
CBL NO
PB
B'
-0.700 0 0.700
Synaptic Weight
Figure 6. Computational model connectivities. (A-B) Connectivity matrices
Md
and
MNO
optimized for
compass state maintenance. (A’-B’) Modulated connectivity matrices
Md
and
MNO
optimized for compass
state shifts, depicted for left turns. For right turns, resulting modulated matrices are identical but with
each quadrant rotated by 180
◦
. Excitatory synapses are depicted in yellow, inhibitory synapses in blue.
Neurons are indexed via the PB column (L8-R8) in which they arborize. Values are clipped at
±0.7
for
better visibility.
are shifted in the direction opposing turning direction. The initial and final bump positions are identical,
400
showing that direction information is integrated correctly across time. The compass bump can transition
401
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Zittrell et al. Sky-Compass Optic Flow Integration
between the lateral ends of the PB: Between time points 13 and 14, the compass maximum moves from
402
column L8 to R8, and a transition in the opposite direction happens between time points 23 and 24.403
Left
Forward
Right
Movement Direction
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
CL1a
0 5 10 15 20 25 30 35
Time [time points]
L8
L7
L6
L5
L4
L3
L2
L1
R1
R2
R3
R4
R5
R6
R7
R8
CL2
0.25 0.00 0.25
Deviation from Baseline Firing Rate [A.U.]
Figure 7. The circuit successfully integrates direction information into the heading signal. The top plot
shows movement direction at discrete time points during a simulated walk. The two bottom plots show
the firing rates of all CL1a and CL2 neurons in
Modeld
, respectively. Neurons are indexed and arranged
by their corresponding columns of the PB, revealing one activity bump along the PB in each subset of
columnar neurons.
4 DISCUSSION
We analyzed the sensitivity to visually simulated self-motion in different neuron classes in the locust CX
404
network, from input-providing neurons (TL, TU neurons) to intermediate stage neurons (CL1a, CL2, POU,
405
and TB1) and output neurons (CPU1, CPU2, CPU5, CP1, and CP2). Neurons in most of the investigated
406
classes were not sensitive to visual self-motion. We hardly encountered consistent responses within the
407
same neuron class, suggesting that single cells flexibly switch their cue sensitivity based on the internal state
408
of the animal and environmental conditions (Shiozaki et al., 2020; Beetz et al., 2022; Fisher et al., 2022).
409
Exceptions were CL2 neurons, which mirror-symmetrically encoded yaw rotation direction, depending on
410
the brain hemisphere in which they arborized, suggesting a role in keeping the internal compass system up
411
to date during turning.412
A large fraction of cell types studied here (TL, CL1a, TB1, CPU1, CPU2, CP1, CP2) are elements of the
413
sky compass system in the CX of the locust (Vitzthum et al., 2002; Heinze et al., 2009; Bockhorst and
414
Homberg, 2015; Pegel et al., 2018; Zittrell et al., 2020). These neurons are sensitive to the azimuth of an
415
unpolarized light spot (simulated sun) as well as to the polarization pattern above the animal (simulated
416
sky) matching the position of the sun (Zittrell et al., 2020). The preference angles for solar azimuth in
417
columnar neurons of the PB showed that solar azimuth is represented topographically across the columns
418
of the PB as illustrated in Figure 5. The lack of responses to large-field motion stimuli in most of these
419
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Zittrell et al. Sky-Compass Optic Flow Integration
neurons is in contrast to data from Rosner et al. (2019), who showed that a majority of sky compass neurons
420
in the locust CX (types TL, CL1, TB1, CPU1, CPU2) were sensitive to progressive motion simulated
421
through moving gratings. The reason for these different results most likely lies in different preparations
422
of the animals. While in this study, legs and wings were removed, animals in the study of Rosner et al.
423
(2019) had their legs attached and could perform walking motion on a slippery surface. Therefore, while
424
the responses to sky compass signals may be affected only mildly, differences in behavioral context and
425
internal state apparently play a major role for the sensitivity of sky compass neurons to visually simulated
426
self-motion. Neurons of the CBU (PoU, TU, CPU5) that are not directly involved in sky compass signaling,
427
were, likewise, unresponsive to visual self-motion. This coincides with studies on Drosophila that found
428
that responsiveness of neurons of the fan-shaped body (corresponding to the locust CBU) to motion stimuli
429
highly depended on whether the animals were actively engaged in flight (Weir and Dickinson, 2015;
430
Shiozaki et al., 2020). It is therefore likely, as for neurons of the sky compass system, that neurons at this431
integration stage are silent in locusts under the constrained conditions of our experiments. H
∆
b neurons in
432
Drosophila (corresponding to PoU neurons in the locust) integrate external and internal self-motion cues
433
to transform egocentric directions into world-centric coordinates (Lu et al., 2022; Lyu et al., 2022). The
434
lack of mechanosensory feedback under our experimental conditions likely explains why PoU neurons did
435
not respond to purely visual self-motion cues. Under such conditions, PoU neurons and others, instead,
436
strongly respond to looming objects (Rosner and Homberg, 2013), thus they might rather be involved in
437
escape reactions when quiescence is signaled by the body. In general, physiological activity of locust CX
438
neurons is considerably affected by active leg movement (Rosner et al., 2019). In our study, the legs were
439
cut off, eliminating any proprioceptive sensory feedback.440
In contrast to the lack of responsiveness in most cell types, two mirror-symmetric CL2 neurons showed441
robust responses to simulated yaw rotation with opposite directional preference. Inspired by the proposed
442
role of P-EN neurons in Drosophila (corresponding to CL2 neurons in the locust) in updating and shifting
443
the activity peak across the columns of the PB, we developed a computational model testing the likely
444
function of CL2 neurons in the locust. The model of the CL1a-CL2 network resembles the recurrent loop
445
connectivity between E-PG and P-EN neurons accounting for angular velocity integration in the Drosophila
446
CX (Turner-Evans et al., 2017, 2020; Hulse et al., 2021). However, distinct differences exist, based on
447
the 360
◦
angular representation in the locust PB (Pegel et al., 2019; Zittrell et al., 2020) compared to
448
the 2 × 360
◦
representation of space in the Drosophila PB. While in Drosophila E-PG neurons form a
449
360
◦
representation of space in the ellipsoid body, two opposite 180
◦
representations of space would be
450
topographically intercalated in the CBL of the locust (Figure 5A). In Drosophila P-EN and E-PG neurons
451
are connected by recurrent excitatory loops with additional global inhibition (Turner-Evans et al., 2017,
452
2020). In the locust, instead, both inhibitory and excitatory connections between CL1a and CL2 neurons
453
are required for compass state maintenance, see Figure 6.454
Physiological data revealing the relationship between the activities of these two populations would aid
455
model evaluation and refinement. Close to equal E-PG and P-EN bump positions have been found in
456
Drosophila moving at a low angular velocity, with an offset increasing with angular velocity (Turner-Evans
457
et al., 2017). Neither of our model versions could perform a shift of compass activity with a feed-forward
458
input only, which might be due to the fact that our models do not include a closed loop from one end
459
of the PB/CBL to the other. The inclusion of further neuron types might in fact close this gap and is the
460
prospect of future work. CL1b-d neurons (Heinze and Homberg, 2008; Heinze et al., 2009) might, in
461
addition, further stabilize the compass representation during standstill or forward motion. An internal
462
compass representation must adapt to a new heading direction when the animal turns. In the CX, this
463
is likely accomplished by integrating rotation cues of different modalities. Two entry sites into the CX
464
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Zittrell et al. Sky-Compass Optic Flow Integration
network for information on rotational self-motion have been proposed so far, based on work in the fruit fly:
465
i) The PB, where neurons may receive asymmetric input excited depending on turning direction, conveyed
466
via IbSpsP neurons (TB7 neurons in the locust) (Hulse et al., 2021). These neurons connect specifically to
467
P-EN neurons (CL2 neurons in the locust). ii) The NO, where GLNO neurons (TN neurons in the locust)
468
that receive input in the lateral complex and innervating one NO might be excited/inhibited depending
469
on turning direction. P-EN neurons convey these asymmetric inputs to E-PG neurons via synapses in
470
the ellipsoid body, leading to a shift of the internal heading representation according to turning (Green
471
et al., 2017; Turner-Evans et al., 2017). We explored two possible network connectivities and two possible
472
mechanisms inducing the compass bump shift on an algorithmic level.473
Based on the projection patterns of CL1a and CL2 neurons described by Heinze and Homberg (2008),
474
we assumed that an axon and dendrite are synaptically connected if they arborize at the same location. In
475
the default model
Modeld
, we did not assume CL2-CL2 connections within the two NO, but
ModelNO
476
allowed for such connections. They could occur in the lower units of the two NO, in Drosophila functionally
477
equivalent connections appear to be present (Hulse et al., 2021).478
Synaptic weights were initialized such that CL1a neurons excite CL2 neurons which in turn inhibit
479
CL1a neurons, and excitatory self-recurrent connections were added among both subpopulations. As data
480
supporting these assumptions are missing, all synaptic weights were optimized such that the models would
481
maintain a stable network activity in the absence of any inputs. Both models could be optimized to maintain
482
stable compass states.483
Modulations of the network connectivity could be optimized to bring about compass bump shifts in both
484
model versions: Shifts of the network activity are mediated by CL1a and CL2 neurons asymmetrically
485
exciting and inhibiting neurons of the same type arborizing in adjacent PB columns in a direction-dependent
486
manner. In
ModelNO
, shifts are additionally mediated by asymmetrically attenuating inhibitory synapses
487
between CL2 neurons arborizing at opposite ends of the same PB hemisphere. Note that the connectivity
488
among neurons of the same type implemented here is most likely an abstraction of the effective connectivity
489
which is likely mediated by neurons of other types not included in this model. Simulating an abstracted
490
heading trajectory, we demonstrated that both model versions can integrate motion direction-dependent
491
inputs to update a heading signal encoded in the network activity pattern. The networks can shift the
492
compass bump from one lateral end of the PB to the other, indicating compatibility with a ring-attractor
493
functionality also described in other species. Connectomics data would be necessary to evaluate which
494
model version to prefer over the other.495
In our models, the bump is not shifted by lateral transport of neuronal activation. Rather, during turns the
496
connections of CL1a/CL2 neurons to CL1a/CL2 neurons in neighboring columns are up- or down-regulated
497
depending on the turn direction. This leads to a corresponding change of the neuronal activation that yields
498
a compass bump shift. For example, during a left turn of the animal, the compass bump is shifted right
499
(see Figure 7, from 20-30 seconds). A right shift of the bump means that activities on the rising slope
500
of the bump, viewed from left to right, must decrease. Conversely, activities on the falling slope must
501
increase. This effect is brought about by computing the difference between activations in the neighboring
502
columns, i.e. a given CL1a neuron needs to receive inhibitory input from its right neighbor, and excitatory
503
input from its left neighbor (see Figure 6A’,B’). During right turns, the modulation is reversed. While
504
this mechanism does not require a ring closure in the network, such a closure would be necessary for a
505
lateral transport of neuronal activation. As mentioned above, it is conceivable that the consideration of
506
further neuron types in the future will render the compass network of the desert locust closed, and modeling
507
could be employed to explore possible mechanisms of activation transmission among the involved neuron
508
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Zittrell et al. Sky-Compass Optic Flow Integration
populations.
Franconville et al. (2018)
reported that connections from E-PG onto P-EN neurons in the PB
509
are mediated by
∆
7 neurons. As TB1 and TB2 neurons cross the midline of the locust PB, they are, in
510
addition to contralateral processes observed in some CL1 neurons innervating the innermost columns of
511
the PB (Sayre et al., 2021), candidates for mediating ring closure.512
The linear model and discrete motion steps employed here are still quite abstract representations of the
513
neuronal and behavioral characteristics of the locust. So far, our model is not dynamic; it switches between
514
stable states but does not make the dynamics underlying the transitions explicit. We aim to increase the
515
model’s biological plausibility by implementing velocity dependence in future work but expect the general
516
principles of maintaining and updating the compass bump to hold independently of the level of analysis.517
CONFLICT OF INTEREST STATEMENT
The authors declare that the research was conducted in the absence of any commercial or financial
518
relationships that could be construed as a potential conflict of interest.519
AUTHOR CONTRIBUTIONS
FZ, RR, and UH designed the experiments, FZ, EC, UP and RR performed the experiments. FZ wrote
520
manuscript. KP and DME designed the computational model and statistical analysis. KP revised the
521
manuscript, analyzed the data and implemented the computational model with DME. DME and UH
522
conceived, designed, and directed research, and helped write the manuscript. All authors contributed to the
523
article and approved the submitted version.524
FUNDING
This work was supported by Deutsche Forschungsgemeinschaft (HO 950/28-1 to UH and EN 1152/3-1 to
525
DME), and the cluster project “The Adaptive Mind”, funded by the Excellence Program of the Hessian
526
Ministry of Higher Education, Research, Science and the Arts.527
ACKNOWLEDGMENTS
We thank Stefanie Jahn for preparing Figure 4D and Martina Kern for maintaining locust cultures.528
DATA AVAILABILITY STATEMENT
The datasets analyzed and generated for this study along with the code written for analysis and modeling
529
can be found in the data UMR repository (http://dx.doi.org/10.17192/fdr/76).530
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5 APPENDIX
5.1 Statistical Model and Power Analysis of Motion Sensitivity700
We designed a Bayesian model for the evaluation of the experimental spiking data, to test the hypotheses
701
that the firing probability of a motion phase
rm
is smaller, equal or larger than the firing probability
rs
during
702
a stationary phase. We denote these hypotheses by
H∈ {H(rm< rs), H(rm== rs), H(rm> rs)}
.
703
Given the firing probabilities, we assume that the data
D= (sm, gm, ss, gs)
of one experiment, comprised
704
of spikes
sm, ss
during motion/stationary phases and corresponding non-spikes/gaps
gm, gs
, are generated
705
by a Bernoulli process with a refractory period of 2 ms, which is typical for the neurons we investigate.
706
There might be additional dependencies between spikes that are not captured by a refractory Bernoulli
707
process, but these are not relevant for our hypotheses. The Bernoulli observation probability is given by708
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Zittrell et al. Sky-Compass Optic Flow Integration
P(D|rm, rs) = rsm
m(1 −rm)gm·rss
s(1 −rs)gs(8)
Since we are interested in hypotheses about firing probabilities relationships, we define a joint symmetric
709
Beta prior with parameters
α, β
on
rm
and
rs
, constrained by the hypothesis we wish to evaluate. We
710
choose a symmetric prior to avoid a-priori biases beyond H. For H(rm< rs), this prior is711
P(rm, rs|α, β, H(rm< rs)) ∝B(rm|α, β)B(rs|α, β)I(rm< rs)(9)
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
712
in the parentheses is true, and 0 otherwise. This indicator function ensures that only hypothesis-conforming
713
rm, rs
pairs have nonzero probability. The constant of proportionality can be obtained from the requirement
714
that the prior be normalized. Thus, this prior can be written as715
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)(10)
The prior resulting from
H(rm> rs)
can be obtained by inversion of the
<
in the indicator function,
716
whereas the prior for H(rm== rs)is simply one Beta prior for both (equal) firing probabilities.717
Since we are largely ignorant about the values of
α
and
β
, we chose these parameters by maximizing the
718
differential entropy subject to the condition that the average firing probability is
≈0.05
in a 2 ms time bin,
719
which is typical for our neurons. We found
α= 0.96
and
β= 18.28
, and used these values for the rest of
720
the analysis.721
To compute the hypothesis posterior722
P(H|D) = P(D|H)P(H)
PHP(D|H)P(H)(11)
via Bayes’ rule, we chose a uniform hypothesis prior
P(H) = 1
3
. We evaluated the probability
P(D|H)723
by marginalizing the firing probabilities using Equation 8 and Equation 10. For example, letting
H=724
H(rm< rs):725
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)(12)
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Zittrell et al. Sky-Compass Optic Flow Integration
where
IB(r, α, β)
is an incomplete beta function in
r
with parameters
α, β
. We solved the last integral by
726
Taylor-expanding
IB(rs, α+sm, β +gm)
to second order at
α+ss
α+ss+β+gs
, which yields a good approximation
727
as long as sm≈ssand gm≈gs. This is the case in our data.728
The probability
P(D|H(rm> rs))
can be evaluated by simply switching the roles of
rm
and
rs
in
729
the above derivation. For
P(D|H(rm== rs))
, where there is only one rate, the integrals can be solved
730
analytically to yield the well-known result731
P(D|H(rm== rs)) = B(α+sm+ss, β +gm+gs)
B(α, β).(13)
To facilitate interpretation of the values of the absolute motion sensitivity (AMSS, Equation 3) and the
732
motion hypothesis posterior, which we use to average the motion sensitivity scores (MSS, Equation 2),
733
we conducted a power analysis. We simulated 10,000 repetitions of a typical experiment in our study,
734
where an animal is stimulated for 5 s with either stationary or motion input. We generated spikes according
735
to the Bernoulli process assumption (Equation 8) with 2 ms time bins by drawing spike counts from a
736
binomial distribution. The firing rate of the stationary phase was set to 25 Hz, which corresponds to a firing
737
probability
rs= 0.05
and
N= 2500
Bernoulli trials during a single run of the experiment. An experiment
738
consisted of five simulated runs in the simulation. The firing probability during the motion phase was
739
assumed to be a multiple of
rs
in the range
1.15 . . . 1.30
. This range is covered by a strongly responding
740
neuron, see e.g. Figure 4A, right panel. To relate our motion sensitivity scores to standard measures used in
741
statistical contexts, we evaluated the Bayes factor in favor of a changed firing rate during motion:742
BF (rm=rs) = P(D|H(rm> rs)) + P(D|H(rm< rs))
P(D|H(rm== rs)) (14)
The simulation results are shown in Figure 8. The top panel shows the AMSS, the middle panel the
743
corresponding Bayes factors. The dotted lines show the boundaries for weak and strong evidence according
744
to Kass and Raftery (1995). For strong evidence, the firing rate ratio has to be greater than 1.25, which
745
implies an average AMSS
>0.65
. In the bottom panel, we plotted the hypothesis posterior, which we use
746
for averaging of the MSS. Strong evidence for an increased firing rate (MSS=+1 in Figure 3A) requires
747
MSS >0.65.748
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Zittrell et al. Sky-Compass Optic Flow Integration
Figure 8. 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 3. 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
2. 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.
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