Building an allocentric travelling direction signal via vector computation

Abstract

Many behavioral tasks require the manipulation of mathematical vectors, but, outside of computational models 1-8 , it is not known how brains perform vector operations. Here we show how the Drosophila central complex, a region implicated in goal-directed navigation 8-14 , performs vector arithmetic. First, we describe neural signals in the fan-shaped body that explicitly track a fly's allocentric traveling direction, that is, the traveling direction in reference to external cues. Past work has identified neurons in Drosophila 12,15-17 and mammals 18,19 that track allocentric heading (e.g., head-direction cells), but these new signals illuminate how the sense of space is properly updated when traveling and heading angles differ. We then characterize a neuronal circuit that rotates, scales, and adds four vectors related to the fly's egocentric traveling direction-the traveling angle referenced to the body axis--to compute the allocentric traveling direction. Each twodimensional vector is explicitly represented by a sinusoidal activity pattern across a distinct neuronal population, with the sinusoid's amplitude representing the vector's length and its phase representing the vector's angle. The principles of this circuit, which performs an egocentric-to-allocentric coordinate transformation, may generalize to other brains and to domains beyond navigation where vector operations or reference-frame transformations are required.

Behavioral signatures of structured feature detection during courtship in Drosophila

“…It is thus tempting to hypothesize that flies have in mind a model of the interacting conspecific that can be referred to when necessary to guide behavior, possibly using a vector-based mechanism. [95][96][97] Model-based object recognition approaches have been used in machine learning. 98 Article hierarchical networks, both biological and artificial, can be used for the recognition of complex objects by view integration, 1,99 possibly via learning.…”

“…110 It has been shown that dragonflies use internal models for prey interception. 111 Recent physiological and anatomical evidence point toward central complex circuits for egocentric and allocentric coordinate transformation in flies when heading and traveling directions differ, [95][96][97] a defining character of circling. Interestingly, we identified male circling via coordinate transformation with a female-centered reference frame (Figures 1, 2, and 3), raising the possibility of alternative, possibly othercentric, coordinates beyond egocentric and allocentric maps.…”

Neural dynamics and architecture of the heading direction circuit in a vertebrate brain

“…This link between function and structure exists in the insect central complex, where elegant studies have described networks that encode heading direction and constitute a neuronal implementation of a ring attractor network (Seelig and Jayaraman, 2015; Green et al, 2017; Kim et al, 2017; Fisher et al, 2019; Suver et al, 2019; Lyu et al, 2022). The level of detail being uncovered in these circuits allows for a mechanistic understanding of how a brain can integrate external and internal sensory cues, efference copies and carry out coordinate transformations that are important for behavior.…”

“…The activity in these head direction networks can be understood in terms of ring attractor networks, where local recurrent excitation is combined with long-range out-of-phase inhibition to create a stable localized bump of activity that encodes direction. This model has received remarkable empirical validation with the observation of heading direction representations in the insect central complex, where key components of a ring attractor network have been mapped onto its neuronal architecture (Seelig and Jayaraman, 2015; Green et al, 2017; Kim et al, 2017; Fisher et al, 2019; Suver et al, 2019; Lyu et al, 2022). However, such mechanistic understanding in vertebrates is still lacking.…”

Bumblebees navigate using path integration while walking

“…Over recent years, understanding of the neural basis of navigation behaviors in insects has increased substantially due to detailed functional studies and neuroanatomical descriptions of navigationally relevant brain regions. From these studies, the central complex, a conserved set of arthropod brain regions, has emerged as the likely navigational control center that both integrates navigationally relevant stimuli 35,[49][50][51][52][53][54][55] and directs steering movements during navigation 56 . By combining our behavioral arena with electrophysiological techniques used to record from either freely behaving animals 56 or by transferring our paradigm to a virtual reality setup for tethered behavior 41,51,[53][54][55]57 , hypotheses regarding the underlying neural mechanisms for path integration vector memory formation 35 can be directly tested.…”