Building an allocentric travelling direction signal via vector computation
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Abstract
Many behavioural tasks require the manipulation of mathematical vectors, but, outside of computational models 1-7, it is not known how brains perform vector operations. Here we show how the Drosophila central complex, a region implicated in goal-directed navigation 7-10, performs vector arithmetic. First, we describe a neural signal in the fan-shaped body that explicitly tracks the allocentric travelling angle of a fly, that is, the travelling angle in reference to external cues. Past work has identified neurons in Drosophila 8,11-13 and mammals 14 that track the heading angle of an animal referenced to external cues (for example, head direction cells), but this new signal illuminates how the sense of space is properly updated when travelling and heading angles differ (for example, when walking sideways). We then characterize a neuronal circuit that performs an egocentric-to-allocentric (that is, body-centred to world-centred) coordinate transformation and vector addition to compute the allocentric travelling direction. This circuit operates by mapping two-dimensional vectors onto sinusoidal patterns of activity across distinct neuronal populations, with the amplitude of the sinusoid representing the length of the vector and its phase representing the angle of the vector. The principles of this circuit may generalize to other brains and to domains beyond navigation where vector operations or reference-frame transformations are required.
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Central complex hDelta cell types (not in ground truth) are a set of 190 neurons whose morphologies are very similar, and which segment the fan-shaped body.
“Central complex hDelta cell types77,90,127,183 (not in our ground truth) are a set of 190 neurons whose morphologies are very similar, and which segment the fan-shaped body of the fly.”
From Neurotransmitter classification from electron microscopy images at synaptic sites in Drosophila melanogaster (2024) · cites this paper as [183]
The 'Beyond heading in the central complex' section describes hΔB cells as a columnar class with arbors in fan-shaped-body columns, supporting the anatomical part of the claim. The Methods cell-type list gives 19 neurons for hΔB, but the paper does not establish the claimed total of 190 across hDelta cell types or say their morphologies are very similar. No page numbers are available in our copy. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe insect central complex has the necessary circuit properties to support vector computations by representing vectors as sinusoid curves in activity across a neural array.
“This idea has been bolstered by direct evidence that the insect central complex has the necessary circuit properties to support vector computations by representing vectors as sinusoid curves (vector phasor representation) in activity across a neural array [10].”
From A model of cue integration as vector summation in the insect brain (2023) · cites this paper as [10]
Both speed and direction parameters are under feedback control, as sensory reafference continuously informs the brain about the body's instantaneous forward velocity and heading.
“Both parameters are also under feedback control, as sensory reafference continuously informs the brain about the body’s instantaneous forward velocity76–78 and heading79”
From Fine-grained descending control of steering in walking Drosophila (2024) · cites this paper as [77]
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“Phase shifts in the CX are determined based on propagating a potential activity bump from the compass neurons to their downstream partners in the PB and the FB [29, 60].”
BackgroundMethodFine-grained descending control of steering in walking <i>Drosophila</i>
Yang, H. H., Brezovec, L. E., Serratosa Capdevila, L., Vanderbeck, Q. X., Adachi, A., Mann, R. S., & Wilson, R. I. (2023) · doi:10.1101/2023.10.15.562426 · Cited by 55 · see citing works
A model of cue integration as vector summation in the insect brain
Mitchell, R., Shaverdian, S., Dacke, M., & Webb, B. (2023) · Proceedings of the Royal Society B: Biological Sciences · doi:10.1098/rspb.2023.0767 · Cited by 13 · see citing works
“This idea has been bolstered by direct evidence that the insect central complex has the necessary circuit properties to support vector computations by representing vectors as sinusoid curves (vector phasor representation) in activity across a neural array [10].”
BackgroundConverting an allocentric goal into an egocentric steering signal
Pires, P. M., Abbott, L. F., & Maimon, G. (2022) · doi:10.1101/2022.11.10.516026 · Cited by 110 · see citing works
Self-citationZhao, A., Nern, A., Koskela, S., Dreher, M., Erginkaya, M., Laughland, C. W., Ludwigh, H., Thomson, A., Hoeller, J., Parekh, R., et al. (2023) · doi:10.1101/2023.10.16.562634 · Cited by 15 · see citing works
Transforming a head direction signal into a goal-oriented steering command
Westeinde, E. A., Kellogg, E., Dawson, P. M., Lu, J., Hamburg, L., Midler, B., Druckmann, S., & Wilson, R. I. (2022) · doi:10.1101/2022.11.10.516039 · Cited by 85 · see citing works
- Authors
- Lyu, C., Abbott, L. F., & Maimon, G.
- Affiliations
- Howard Hughes Medical Institute (US)
- Mortimer B. Zuckerman Mind Brain Behavior Institute (US)
- Corresponding author
- Maimon, Gaby
- Venue
- Nature
- Published
- 2021-12-15
- Volume
- 601
- Issue
- 7891
- Pages
- 92-97
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- PMC
- PMC11104186
- OpenAlex
- W4200478016
- Semantic Scholar
- b1d78d88db14026af61529469b24d2b7ad1f6fee
- Cited by
- 215
- References
- 77
- Citations by year
- 2026: 34 · 2025: 37 · 2024: 51 · 2023: 42 · 2022: 34 · 2021: 16 · 2020: 1
- FWCI
- 16.40
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Locations
- Nature (publishedVersion)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- National Science Foundation (1707398, P40OD018537, NIH P40OD018537)
- Howard Hughes Medical Institute
- National Institutes of Health (1707398, NIH P40OD018537, P40OD018537)
- National Institute of Neurological Disorders and Stroke (R01NS104934)
- Topics
- Life Sciences › Neuroscience › Cellular and Molecular Neuroscience › Neurobiology and Insect Physiology Research
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory and Neural Mechanisms
- Physical Sciences › Engineering › Automotive Engineering › Spatial Cognition and Navigation
- Keywords
- fan-shaped body, vector addition, coordinate transformation, heading angle, reference frame transformation, spatial navigation, neural circuits, vector computation
- MeSH terms
- Animals, Brain, Cues, Drosophila melanogaster, Female, Flight, Animal, Goals, Head, Mathematics, Models, Neurological, Neurons, Space Perception, Walking, Spatial Memory, Spatial Navigation
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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