Network Statistics of the Whole-Brain Connectome of Drosophila

Abstract

Brains comprise complex networks of neurons and connections. Network analysis applied to the wiring diagrams of brains can offer insights into how brains support computations and regulate information flow. The completion of the first whole-brain connectome of an adult Drosophila, the largest connectome to date, containing 130,000 neurons and millions of connections, offers an unprecedented opportunity to analyze its network properties and topological features. To gain insights into local connectivity, we computed the prevalence of two- and three-node network motifs, examined their strengths and neurotransmitter compositions, and compared these topological metrics with wiring diagrams of other animals. We discovered that the network of the fly brain displays rich club organization, with a large population (30% percent of the connectome) of highly connected neurons. We identified subsets of rich club neurons that may serve as integrators or broadcasters of signals. Finally, we examined subnetworks based on 78 anatomically defined brain regions or neuropils. These data products are shared within the FlyWire Codex and will serve as a foundation for models and experiments exploring the relationship between neural activity and anatomical structure.

Keywords: Drosophila melanogaster; brainwide network analysis; connectomics.

Figure 1.. Whole-brain network properties.

(a) The FlyWire dataset (27, 28, 30) is an EM reconstruction of the complete brain of an adult female Drosophila melanogaster, with both hemispheres of the brain and both optic lobes. The volume contains 127,978 neurons and 32 million synapses with a threshold of 5 synapses/connection applied (subsample of synapse locations shown in the inset). (b) The distribution of the number of synapses per connected neuron pair. (c) The in-degree (number of presynaptic partners) plotted against the out-degree (number of post-synaptic partners), with log-scale x and y-axes. (d) Strongly connected components (SCCs) consist of a subset of nodes in a network which are mutually reachable via directed edges. In the fly brain there exists one giant SCC containing 93.3% of all neurons after thresholding at 5 synapses per connection. The distribution of shortest path lengths between neuron pairs within this SCC is plotted. (e) Weakly connected components (WCCs) consist of a subset of nodes in a network which are mutually reachable, regardless of edge direction. In the fly brain there exists one giant WCC containing 98.8% of all neurons. The distribution of path lengths between neuron pairs within this WCC is plotted. (f) We examine the role high-degree neurons play in connecting the brain by plotting the sizes of the first two strongly connected components (SCCs) as nodes are removed by total degree (2500 neurons per step). Removal of neurons starting with those with largest degree results in the brain splitting into two SCCs when neurons of approximately degree 50 start to be removed, a deviation from when neurons are removed in a random order (dotted lines). The largest surviving total degree as a function of the number of remaining nodes is plotted in gray. (g) Removal of neurons starting with those with smallest degree results in a single giant SCC until all neurons are removed (2500 neurons per step). The smallest surviving total degree as a function of the number of remaining nodes is plotted in gray. (h) The relative rich club coefficient as a function of total degree, computed relative to CFG null models. The range over which the relative rich club coefficient is greater than 1.01 is 37 to 93. We take all neurons with total degree > 37 to be within the rich club regime.

Figure 2.. Characterizing reciprocal connections in the brain.

(a) Edges that are part of reciprocal connections (reciprocal edges) are stronger on average than unidirectional connections. (b) Breakdown of unidirectional and reciprocal edges by neurotransmitter. Unidirectional connections are most likely to be cholinergic. Reciprocal connections are more likely than unidirectional connections to contain a GABAergic neuron. (c) The frequency of neurotransmitter pairs forming reciprocal connections, compared to the expected frequency of neurotransmitter pairs under the assumption of independent neurotransmitter choice (red). A majority of reciprocal connections are formed by acetylcholine-GABA pairs. The next most common reciprocal connection type is acetylcholine-glutamate, with acetylcholine-acetylcholine pairs under-represented. (d) Heatmaps of the relative strengths (synapse counts) of the two connections forming acetylcholine-GABA reciprocal pairs (left), acetylcholine-glutamate reciprocal pairs (center), and acetylcholine-acetylcholine reciprocal pairs (right). The strengths of the edges of reciprocal pairs are uncorrelated. Excitatory-inhibitory pairs (acetylcholine-GABA and acetylcholine-glutamate) have higher average strengths than excitatory-excitatory (acetylcholine-acetylcholine) pairs. (e) Distributions of reciprocal degree (the number of reciprocal connections a given neuron makes) for cholinergic neurons (left), GABAergic neurons (middle), and glutamatergic neurons (right). GABAergic neurons are more likely to make large numbers of reciprocal connections, while cholingeric neurons are more likely to have smaller numbers of reciprocal connections. (f) Scatterplot of 2 times the reciprocal degree of neurons versus their total degree (in-degree + out-degree). Dotted lines indicate a factor of 2 around the x = y line. Large neurons for which reciprocal connections form the majority of their total connections are most likely to be GABAergic. (g) Visualizations of exemplar reciprocal neuron pairs. Cell labels are listed where available.

Figure 3.. Examining 3-node motifs.

(a) The distribution of three-node motifs across the whole brain. Absolute counts of each motif are on the left, and the frequency of each motif relative to that in an ER null model is plotted to the right, together with the average motif frequencies of 100 CFG models (gray violin plots). When we compare the whole-brain network to both ER and CFG null models, we observe an under-representation of simple motifs (#1-3) and an over-representation of other motifs, particularly highly recurrent motifs (#10, 12, 13). (b) The average strength of edges that are part of the 3-node motifs. The dotted line is the average connection strength in the brain. (c) Breakdown by neurotransmitter of edges participating in two motifs: feed-forward loops (motif #4) and 3-unicycles (motif #7). Edges in feed-forward loops are more likely to be cholinergic. (d) Further examining the neurotransmitter composition of these motifs, we find that feed-forward loops (motif #4) are most likely to be acetylcholine-acetylcholine-acetylcholine, (e) while 3-unicycles (motif #7) tend to contain at least one inhibitory edge (glutamate or GABA). (f) Visualizations of exemplar 3-node motifs. Cell labels are listed where available.

Figure 4.. Large-scale neuron connectivity in the brain.

(a) Using the in-degree vs. out-degree scatterplot, we can divide the intrinsic rich club neurons into three distinct categories: broadcasters, integrators, and large balanced neurons. Comparing the prevalence of (b) neurotransmitters and (c) intrinsic superclasses (optic lobe intrinsic, visual projection, visual centrifugal, and central brain intrinsic) of all intrinsic neurons, rich club neurons, integrators, and broadcasters. (d) Examples of rich club neurons in these three categories. (e) Applying the information flow model from Schlegel et al. 2021 (28, 48), we determined the percentile rank distributions of rich club, integrator, and broadcaster neuron populations from all inputs to the brain (above), as well as to specific modalities (Figure S4d). (f) Average percentile rank of rich club, integrator, and broadcaster neurons for different modalities. Across all modalities, rich club neurons are closer than average to sensory inputs.

Figure 5.. Neuropil-specific differences in connectivity.

(a) An exploded view of the brain showing the brain regions, or neuropils, that the FlyWire dataset is divided into. Each synapse is assigned to a neuropil based on synapse location. (b) A schematic showing how neuropil subnetworks are identified for motif analyses. With the standard threshold of 5 synapses per edge applied, all connections composed of synapses within the neuropil of interest (Neuropil A) are treated as edges of the Neuropil A subnetwork. All neurons reached by this set of edges are included in the subnetwork. However connections composed of synapses outside of Neuropil A are not included, even if those connections involve neurons included in the subnetwork. (c) The reciprocity within each neuropil subnetwork. Differences in the percentage of (d) cholinergic and (e) GABAergic edges between reciprocal and unidirectional connections, across different neuropils. Refer to Figure S6 for the absolute percentages. (f) Heatmaps showing the relationship between excitatory and inhibitory connection strengths in reciprocal connections in different brain regions. (g) Assessing the number of large (rich club), highly reciprocal neurons which span specific neuropils: making most of their incoming and outgoing connections within a single neuropil and also having a high reciprocal degree. Examples of neurons which meet these criteria are shown. (h) Map of the total number of reciprocal pairs between different neuropils. Examples of such pairs are shown in Figure S7e.

Figure 6.. Differences in three-node motifs across neuropils.

(a) Three-node motif distributions for three example neuropils: the EB, AL(R), and MB-ML(R). The frequency of each motif relative to that in an ER null model is plotted to the right, together with the average motif frequencies of 100 CFG models (gray violin plots). Further examples of other neuropils available in Figure S8a. (b) Motif frequencies for the 3-node motifs across all 78 neuropil subnetworks, normalized by their respective CFG null models. (c) Average strengths of edges participating in 3-node motifs in the different neuropil subnetworks relative to the average 3-node motif strength in each subnetwork. Refer to Figure S8b for average strengths relative to average neuropil subnetwork edge strength.