Network statistics of the whole-brain connectome of Drosophila
Lin, A., Yang, R., Dorkenwald, S. et al. Network statistics of the whole-brain connectome of Drosophila. Nature 634, 153–165 (2024). https://doi.org/10.1038/s41586-024-07968-y
Core Content
This paper presents a comprehensive network statistical analysis of the first complete adult brain connectome of Drosophila melanogaster. This is the first complete adult fly brain connectome containing over 130,000 neurons and millions of synaptic connections, offering an opportunity to analyze the statistical properties and topological features of a complete brain. The study computed the prevalence of two- and three-node motifs, examined their strengths, related this information to neurotransmitter composition and cell type annotations, and compared these metrics with wiring diagrams of other animals. The research found that the fly brain network displays rich-club organization, with a large population (30% of the connectome) of highly connected neurons, and identified subsets of rich-club neurons that may serve as integrators or broadcasters of signals.
Background and Dataset
Dataset Overview
This study analyzed the whole-brain, synapse-resolution connectome generated by the FlyWire Consortium (v630 snapshot), the first complete wiring diagram of an adult brain, that of a female D. melanogaster. The dataset contains 127,978 neurons and 2,613,129 connections, with connections defined as at least 5 synapses between two neurons. The connection weight for each pair is defined by the total number of synapses between two neurons, which is considered a proxy for connection strength. Although the fly brain has far more neurons than C. elegans (302-364 neurons), the connection probability is only 0.000161, much lower than that of C. elegans (0.026-0.036), making it a very sparse network matrix.
Basic Properties of the Connectome
The connectome also contains synapse-level neurotransmitter predictions. The classifier discriminates between six neurotransmitters: the fast-acting classical neurotransmitters acetylcholine (ach), GABA and glutamate (glut), and the monoamines dopamine (da), octopamine (oct) and serotonin (ser). In Drosophila, ach is excitatory and GABA is inhibitory. Glutamate can be either excitatory or inhibitory, but within the brain of the fly, it has largely been observed to be inhibitory. A neuron's in-degree is defined as the number of presynaptic partners, and the out-degree is defined as the number of postsynaptic partners. The average in/out-degree of an intrinsic neuron in the brain is 20.5, but in-degree and out-degree are not highly correlated (Pearson R = 0.76, P < 0.001). The average connection consists of 12.6 synapses, and the connection probability is highest among neurons with nearby arbours. Only 3% of neuron pairs have arbours within 50 μm of each other, but such pairs make 71% of all connections.
Network Connectivity Analysis
Strongly and Weakly Connected Components
Despite its sparsity, the brain forms a highly connected network. 93.3% of neurons are contained in a single strongly connected component (SCC), while 98.8% of neurons are contained in a single weakly connected component (WCC). These giant connected components, which contain the majority of neurons, persist when either the strongest or weakest connections are pruned and are robust to threshold choice, indicating that connectivity is robust: many paths connect neuron pairs. Within the giant SCC, the average shortest directed path length between neuron pairs is 4.42 hops, with every neuron reachable within 13 hops. In the giant WCC, the average shortest undirected path length between neuron pairs is 3.91 hops, with every neuron reachable within 11 hops. These short path lengths show that the fly brain is relatively shallow compared with artificial networks. The similarities in size and path length distribution between the giant SCC and WCC highlight the prevalence of recurrent connections in the brain.
Survival Curve Analysis
Robust network connectivity does not depend on a small number of highly connected neurons. To assess whether high interconnectivity is a consequence of a relatively large number of interconnected neurons, or a small number of very highly connected neurons, survival curves were constructed, observing whether large connected components persist when neurons are removed. Removing neurons from the directed network, starting with those of largest total degree, the first SCC persists until a total degree of 50, at which point the network splits into two SCCs of roughly equal size. These two SCCs correspond to the left and right hemispheres, and do not split into separate networks until about 60% of neurons are removed. Removing neurons from the network by smallest total degree does not result in division of the first SCC. These results highlight the brain's robust interconnectivity—it is not dependent on a small population of neurons.
Rich-Club Organization
Discovery of Rich-Club
The fly brain exhibits rich-club organization, containing approximately 30% of neurons. Many networks exhibit the rich-club property, in which well-connected nodes are preferentially connected to other well-connected nodes. Comparing the observed network to a degree-preserving configuration (CFG) random model, there exists a rich-club regime in the fly brain, with a cut-off of total degree = 37. This regime contains 40,218 neurons, approximately 30% of neurons in the brain, roughly 10 times larger than the rich club in C. elegans (11 neurons, 4%). The connection probability within the rich club is 0.000870, 5.4 times that of the overall connection probability. When considering in-degree alone, a rich-club regime is found with an in-degree threshold of 10, while no rich club is observed when considering out-degree alone, as the subnetwork always remains sparser than random.
Spatial Features of Rich-Club
To examine the extent to which long-distance connections contribute to the rich-club property observed in the fly brain, an extension of the CFG model was constructed in which the random network is constrained by enforcing the measured connection probabilities between the 78 neuropils. This neuropil connection (NPC) model implicitly contains mesoscale spatial information by fixing the number of connections between and within neuropils. The observed network is not more highly connected than the NPC model, indicating that interneuropil connections contribute to the rich-club effect. The extensive nature of this rich-club organization likely reflects the functional need for the brain to integrate information across regions.
Spectral Analysis and Attractor/Repeller Nodes
Random Walk Analysis
Brain topology shows unevenness in information flow. To better understand the brain's topology, a spectral analysis of a random walk in the giant SCC was performed, which converges to a stationary distribution over all neurons in which 3% of neurons were visited 61.2% of the time. These top-visited neurons are classified as attractor nodes. These attractors often make connections in the gnathal ganglia (GNG), a large midline neuropil that sends and receives information from the periphery and contains many connections to the ventral nerve cord (VNC). A reverse walk within the giant SCC was also performed, which converges to a stationary distribution in which 3% of neurons were visited 42.4% of the time. These neurons are repeller nodes, and include many with synapses in the antennal lobes (AL) and medullae (ME), brain regions that are close to the olfactory and visual periphery, respectively.
Two-Node Motifs: Reciprocal Connections
Prevalence of Reciprocal Connections
The fly brain has a high proportion of reciprocal connections, exceeding random expectations. Reciprocal connections refer to pairs where two neurons have bidirectional connections. The study found that connection reciprocity in the fly is 0.138, significantly larger than expected in Erdős–Rényi (ER), configuration (CFG), neuron-neuron distance (NND), or neuropil connection (NPC) models. In thresholded connections, 77,607 neurons participate in reciprocal connections, and 2,183 neurons are defined as highly reciprocal neurons. Reciprocal connections are not uniformly distributed spatially, with certain neuropils showing higher or lower reciprocity, indicating differences in information processing strategies across brain regions.
Neurotransmitters and Reciprocal Connections
Reciprocal connections of specific neurotransmitter combinations are enriched or depleted. Different neurotransmitter types show distinct patterns in reciprocal connections. For example, certain excitatory-inhibitory (ach-GABA) reciprocal connections are significantly enriched in certain brain regions, a pattern that may reflect regulatory mechanisms of local excitation-inhibition balance in the brain. The average strength of reciprocal connections (measured in synapse numbers) is also higher than unidirectional connections, further supporting the functional importance of reciprocal connections.
Three-Node Motif Analysis
Feedforward Loops and 3-Unicycles
Certain three-node motifs are significantly enriched, reflecting local computational properties of the network. The study systematically quantified the occurrence of distinct directed three-node motifs within the network. Feedforward loops, important motifs common in sensory processing and motor control, are significantly enriched in the fly brain. 3-Unicycles are also enriched in certain neuropils. The enrichment of these motifs suggests that brain networks utilize specific local connection patterns to implement computational functions. The study found 113,978 neurons participate in feedforward loops, and 66,835 neurons participate in 3-unicycles. Different neuropils show different motif frequency distributions, reflecting functional specialization of different brain regions.
Motif Strength Analysis
Connections participating in motifs have higher strength than non-motif connections. The study found that connections participating in three-node motifs have significantly higher average strength than the average connection strength in the network, indicating that these motifs are not only structurally important but also functionally stronger in signal transmission. This increase in strength may be a result of functional selection, where important computational modules require stronger connections to ensure reliable information transmission.
Broadcaster and Integrator Neurons
Functional Specialization
Rich-club neurons can be classified into broadcasters and integrators based on their connection patterns. The study identified 676 broadcaster neurons, which have an out-degree that is at least five times higher than their in-degree, primarily serving as signal broadcasters. Simultaneously, 638 integrator neurons were identified, which have an in-degree that is at least five times higher than their out-degree, primarily serving as signal integrators. Broadcaster neurons rank highly across multiple sensory modalities, particularly in visual and olfactory inputs, indicating their role in propagating sensory information to broader brain regions. Integrator neurons are more likely to rank highly in multimodal inputs, supporting their function of integrating information from multiple sources. This functional specialization reflects the diversity of information flow in the brain, with different neuronal subsets performing different information processing roles.
Neuropil-Specific Analysis
Subnetworks of 78 Neuropils
Different neuropils exhibit unique network properties. The fly brain is divided into 78 distinct anatomical brain regions or neuropils. The study found significant differences among neuropils in connection probability, reciprocity, clustering coefficient, and motif frequencies. For example, certain sensory processing regions (such as antennal lobes and optic lobes) show higher connection density and reciprocity, while certain higher-order processing regions may show different patterns. These neuropil-specific network properties reflect the functional specialization requirements of each region.
Neuropil-Specific Highly Reciprocal Neurons
704 neuropil-specific highly reciprocal neurons (NSRNs) were identified. These neurons are intrinsic, meet rich-club criteria, with at least 50% of their incoming connections contained within the subnetwork of a single neuropil, and at least 50% of their outgoing connections also contained within the same neuropil. These neurons may serve as local processing hubs for specific brain regions, integrating and distributing information within limited spatial ranges. Their neurotransmitter composition also shows specific patterns, further supporting their functional specialization.
Clustering Coefficient and Small-World Properties
Network Clustering
The fly brain exhibits clustering higher than random expectations. The global clustering coefficient is 0.0463, significantly higher than the 0.0003 of the Erdős–Rényi model, and also higher than expected values in configuration models and neuropil connection models. This high clustering coefficient indicates that neurons tend to form locally densely connected clusters, a structure that may support local computation and signal processing. Small-world coefficient calculations show that the fly brain has a small-worldness of 141, indicating that it has both high clustering (similar to regular networks) and short path lengths (similar to random networks), a combination important for efficient information transmission and processing.
Data Products and Availability
Codex Platform
All data products and neuron lists are publicly available on the FlyWire Codex platform. The research team provides all computed network statistics and lists of identified neuronal populations on Codex (https://codex.flywire.ai), including neurons participating in two-node and three-node motifs, rich-club neurons, broadcaster and integrator neurons, and neuropil-specific neurons. These interactive neuron lists provide a foundation for future experimental and theoretical research, enabling researchers to explore the relationship between neural activity and anatomical structure. Connectome data are also available for download on Zenodo, and all analysis code is publicly available on GitHub.
Key Takeaways
The fly whole-brain connectome exhibits a highly connected sparse network structure. Despite an extremely low connection probability (0.000161), 93.3% of neurons are contained in a single strongly connected component, with an average path length of only about 4 hops, indicating that the brain has efficient information transmission capabilities. This connectivity is distributed, not dependent on a small number of highly connected neurons, but on a large number of moderately connected neurons.
Rich-club organization is a core feature of the fly brain network. Approximately 30% of neurons (40,218) belong to the rich club, a proportion far higher than other studied small connectomes (such as 4% in C. elegans). Rich-club neurons preferentially connect to each other, with a connection probability 5.4 times that of the overall network, an organization that may support information integration and propagation across brain regions. Rich-club neurons can be further classified into broadcaster (signal propagation) and integrator (signal integration) functional types.
Reciprocal connections are an important feature of the fly brain network. Connection reciprocity (0.138) is significantly higher than expected in various random models, with 77,607 neurons participating in reciprocal connections. The average strength of reciprocal connections is higher than unidirectional connections, and certain neurotransmitter combinations (such as excitatory-inhibitory pairs) are enriched in reciprocal connections, reflecting regulatory mechanisms of local excitation-inhibition balance.
Three-node motif analysis reveals the structural basis of local computation. Motifs such as feedforward loops and 3-unicycles are significantly enriched, and connections participating in these motifs have higher strength, indicating that they are not only structural features but also functionally important computational modules. Different neuropils show different motif frequencies, reflecting functional specialization.
Neuropil-specific analysis reveals the structural basis of functional specialization. The 78 neuropils show significant differences in connection density, reciprocity, and motif frequencies, with 704 neuropil-specific highly reciprocal neurons identified that may serve as local processing hubs. This regional specificity reflects differences in functional requirements across brain regions.
This study provides a comprehensive quantitative framework for understanding brain network organization. Through systematic analysis of the structural properties of the connectome, the research reveals multi-level network patterns from local motifs to global rich-club organization, establishing a solid foundation for future experimental and theoretical research, helping to understand how neural activity emerges from connection structure.