Neuronal wiring of sensory systems

Synaptic connectivity between neurons enables the propagation of signals—including sensory information—throughout the nervous system. The configuration of these connections—the connectome’s topology—thus plays a central role in shaping information flow [45]. To investigate how network structure contributes to sensory integration, we first examine the wiring among N_sensory = 16,349 annotated sensory neurons. These neurons span several modalities: gustation, hygrosensation, mechanosensation, olfaction, thermosensation, vision (both optic lobe and ocellar), and a category labeled “unknown.”

We extracted the subgraph comprising all synaptic connections between sensory neurons (Fig 2a). This subgraph was notably sparse, with a binary connection density of —approximately six times lower than the full connectome’s density (). Moreover, it was significantly sparser than randomly sampled subgraphs of the same size (p < 10⁻³; 1000 random samples; see S4 Fig).

The sensory subgraph also exhibited strong modularity. Of the 54,302 synapses, 54,134 (99.7%) connected neurons within the same modality (Fig 2b). This high degree of within-modality wiring highlights a parallel, segregated architecture with minimal direct cross-talk between modalities.

Taken together, these results indicate that direct sensory-sensory interactions are both rare and strongly modality-specific. This organization suggests that multimodal integration likely occurs through polysynaptic pathways and that the secondary steps along these pathways involve non-sensory neurons.

To explore this possibility, we used a stochastic cascade model to simulate how activation might spread from sensory neurons across the full connectome (see Fig 1). This abstract model is broadly applicable to networked systems [46], and provides a tractable framework for studying the spatiotemporal dynamics of signal propagation.

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Fig 1. Schematic illustration of cascade model.

Neurons can take on three states; active, inactive, or refractory. Inactive neurons are activated probabilistically by their pre-synaptic partners. Once a neuron has been activated, it enters a refractory period, wherein it cannot be activated at any subsequent time point. We consider three variations of this model. (a) Unimodal sensory cascades: wherein the initial population of active neurons (the seed population) are all of the same sensory modality. The model proceeds until either all neurons have been activated or there exists a time point wherein no neurons are currently active. (b) Cooperative sensory cascades: we consider two populations of sensory neurons, each of which represents a different sensory modality. Nonetheless, in their active states, these neurons carry identical information (the same state value), and therefore generally improve (reduce) activation times such that neuron i will tend to be activated earlier in the cooperative condition than in the unimodal condition. (c) Competitive sensory cascades: we, again, consider two populations of sensory neurons, but force them to carry different information and therefore “compete” for territory. Under the competitive model, it is possible for a neuron to be activated at the same time step by multiple neurons from both sensory cascades (green and red, in this panel). If this occurs, we count the number of green and red neurons. The neuron is assigned the color of the winning cascade. If there is an exact tie, then the winner is selected randomly.

https://doi.org/10.1371/journal.pcsy.0000091.g001

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Fig 2. Synaptic connectivity within and between primary sensory neurons.

(a) Complete sub-network of sensory-to-sensory connections. Gray lines delineate systems (modalities) from one another. (b) Synapse count between pairs of systems. (c) Binary density of connections between pairs of systems (and remaining neurons, labeled “others”). Note that in c the color and labels are on a logarithmic scale. (d) Anatomical depiction of sensory neurons.

https://doi.org/10.1371/journal.pcsy.0000091.g002

In the model, each neuron can be in one of three states: active, inactive, or refractory. At time t = 0, a small set of N_seed “seed” neurons is initialized as active—all others begin inactive. At time t = 1, the seed neurons can activate their post-synaptic partners. The Drosophila connectome is polyadic, meaning that the same pair of neurons can be connected by multiple synapses (at different locations along their processes). For pairs of neurons connected by more than one synapse, we assume that any of the synapses can activate the post-synaptic neuron. We treat each synapse as a Bernoulli trial where the probability of a “success” (activation of post-synaptic neuron) is equal to p_transmission. Following activation, neurons turn off the next step (entering a “refractory” state), where they cannot activate their post-synaptic partners nor can they be activated by their pre-synaptic inputs at any point during the rest of the cascade. The cascade continues until no neurons are active. See S1 Fig for example cascades and for details on the influence of model parameters. In the main text we fix parameter values to p_transmission = 0.01 and N_seed = 16. These particular values were selected practically; they are both large enough to ensure that the majority of cascades propagate to the entire network but still small enough to ensure that the cascades evolve over a long enough timescale to allow for meaningful analysis. We note, however, that alternative parameter values tend to stretch or contract activation timing, generally preserving rank order of activation (see S1 Fig d-f and S2 Fig).

Edge contributions to cascades

The cascade model allows us to track how activity spreads not only across neurons, but also across individual synapses. This feature enables the identification of dynamic sensory pathways—sequences of synaptic contacts—that support the propagation of activation from sensory neurons into the broader brain. We can then ask: which types of neurons participate in these cascades? Do these pathways align with structural features of the connectome? And are the most active synapses associated with classical hub neurons?

To address these questions, we performed 1000 simulations of the cascade model in which N_seed = 16 sensory neurons were randomly drawn across all modalities and activated with p_transmission = 0.01. At each time step, we calculated across all simulations three quantities: the total number of active synapses, the number of unique synapses used, and their ratio (unique/total). Here, we consider a synapse to be active at time t if its post-synaptic neuron was inactive at t–1 but activated at time t. We measured three quantities: the total number of active synapses, the number of unique synapses used, and their ratio (unique/total). A high ratio would indicate consistent usage of the same synapses across simulations; a low ratio would suggest variable, diverse pathways. Note that while the seed neurons are drawn from all sensory modalities, we view this model as a special case of the unimodal model. The rationale for doing so is that, whereas the cooperative and competitive models explicitly test for synergistic effects of multi-sensory seeding and yield estimates of sensory “boundaries”, respectively, the summary statistics we would derive for this model–drawing seeds randomly from among all sensory modalities–are identical to the statistics used to summarize the unimodal model.

Early in the cascade, we observed a pronounced “bottlenecking” effect—specific synapses were repeatedly and consistently used to relay activity from the sensory seeds to other, secondary neurons (Fig 3c). We show the most frequently used neurons and their connections at each of the first four steps in Fig 3a and the average over all steps in Fig 3b. This consistency declined at later stages, as the cascade diversified into multiple alternative routes (Fig 3c). These findings suggest that a small set of high-traffic synapses mediates the initial wave of integration, while later dynamics engage a broader array of pathways.

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Fig 3. Edge sequencing.

(a) Top 1000 edges (by usage) over first four time steps. (b) We constructed a weighted connectivity matrix by averaging edge usage across all time points, where at each time point an edge is present if it activates a postsynaptic neuron. We then calculate the out-degree of each node to highlight influential spreaders. (c) Across 1000 simulations, we count the total number of active synapses at each time point along with the unique number of active synapses. If the same synapses were active across all runs, then these numbers would coincide; however, due to the stochasticity of the cascade model and variation in the set of seeded neurons, different synapses appear at different time points. (d) Correlation of the instantaneous out-degree with basic structural properties of the network. (e) Active synapses (edges) grouped by annotation data. Circumference and color circle are proportional to the logarithm of their usage (count normalized by the number of synapses between pairs of annotations).

https://doi.org/10.1371/journal.pcsy.0000091.g003

To examine whether synapse usage could be predicted from static network features, we computed the outdegree of each neuron based on edge usage (dynamic centrality) and compared this to their degree and strength in the underlying connectome (structural centrality). Early in the cascade, correlations between dynamic and structural centrality were weak (maximum r = 0.15), indicating that highly connected neurons in the static network did not dominate the initial spread (Fig 3d). However, as activity progressed beyond t = 6, correlations rose sharply, exceeding r > 0.9 by t = 7, consistent with a transition toward greater reliance on structural hubs for sustaining propagation.

To better understand the cellular and anatomical substrates of these dynamics, we aggregated the × edge usage matrix at each time point by hierarchical annotation categories—“Flow”, “Super-class”, “Class”, and “Sub-class” (see Materials and Methods). Early cascade stages primarily involved synapses between afferent and intrinsic neurons, many of which were sensory (Fig 3e, top panels). At intermediate time steps, uni- and multiglomerular projection neurons became prominent, including reciprocal interactions among these cell types and with tangential neurons—suggesting the involvement of antennal lobe circuits and early olfactory integration (Fig 3e, middle).

From t = 2 onward, activation increasingly involved downstream targets such as the mushroom body—particularly Kenyon cells—and neurons of the central complex. These populations serve as known convergence zones for multi-modal integration in Drosophila [47–49], and they relay activity to neurons in the optic lobes at later stages (Fig 3e, bottom). These dynamics suggest a structured flow from afferent sensory neurons through intermediate integration zones toward broader, distributed activation of the brain.

Overlapping and distinct spatiotemporal profiles of unimodal sensory cascades

In the previous section, we examined cascade dynamics following simultaneous activation of neurons from all sensory systems. Here, we restrict seeding to individual modalities, allowing us to isolate features that are shared across, or unique to, specific sensory systems.

To illustrate modality-specific dynamics, we compare cascades seeded from gustatory and hygrosensory neurons by visualizing their activation probability maps from t = 2 to t = 6 (Fig 4a). Early-stage activity patterns are largely uncorrelated, consistent with non-overlapping sensory pathways. However, over time, cascades converge, with activation maps becoming increasingly similar. These observations suggest that the dynamics most specific to each sensory modality occur early on and over the first several steps (see S1 Fig). Note that these activation probability maps, which were estimated by simulating the cascade model 1000 times, represent probability that a single neuron is active at time step t.

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Fig 4. Modal specificity and similarity of cascades.

Here, we consider cascades in which neurons associated with different sensory modalities are treated as seeds. From these seeds we simulate cascades and compare the spatiotemporal trajectories between sensory modalities. (a) Schematic for comparing cascades. For two sensory modalities (gustation and hygrosensation, in this case) we calculated the similarity between spatial maps at each time step as a correlation. (b) We extended this comparison to all pairs of sensory modalities as well as the “all” category (pan-sensory cascade), wherein sensory neurons from all modalities are treated as seeds, and show the similarity between all pairs at each time step, from t = 1 to t = 12. (c) We also concatenated the activation probability maps across time steps for a given sensory modality and computed the similarity between these omnibus maps, yielding a single time-invariant similarity score for pairs of sensory modalities. (d) We calculated dominance maps, where each neuron is assigned the label of the sensory modality corresponding to the greatest activation probability at a given time step. (e) We also calculated an “overlap index” for neurons as the number of sensory modalities with activation probability exceeding some threshold (here, 25%) at a given time step. (f) Composition of dominant modality as a function of time. (g) Pairwise overlap between pairs of sensory modalities. That is, how often did two sensory modalities simultaneously exceed the activation probability threshold together. (h) Frequency of overlap motifs, ranging from size 2 to size 7. (i) Enrichment statistics for overlap index across annotations as a function of time.

https://doi.org/10.1371/journal.pcsy.0000091.g004

This convergence is a general feature of unimodal cascades. At early time points, each modality follows a distinct trajectory, but progressively merges into larger, more overlapping clusters (Fig 4b). For instance, thermosensory, hygrosensory, and olfactory cascades form a cluster beginning at t = 2 that persists until around t = 5, echoing known anatomical and functional coupling between these systems [50]. Gustatory and “unknown” modalities form a smaller cluster at , later joined by mechanosensory inputs at t = 4. In contrast, ocellar and visual cascades remain distinct from all other modalities through at least t = 6, forming their own cluster around t = 7 and maintaining separation until t = 12.

To quantify overall relationships between modalities, we computed an “omnibus” similarity matrix. For each modality, we constructed a single vector by stacking the whole-brain activation probability vectors from time steps t = 1 to t = 12 (each vector was one-dimensional and had length N × 12) and calculated pairwise correlations between modalities–i.e. between the stacked vectors (Fig 4c). These relationships recapitulate known connectivity patterns—modalities with similar anatomical wiring also produce more similar cascade profiles (S3 Fig).

We further analyzed the progression of cascade overlap using two complementary statistics. First, for each neuron i, we identified the dominant sensory modality at each time step—i.e., the modality with the highest activation probability (Fig 4d). Second, we calculated an “overlap index,” defined as the number of unimodal cascades exceeding a 25% activation threshold for a given neuron and time step (Fig 4e).

Notably, dominant modalities shift over time. From t = 2 to t = 6, thermosensory cascades dominate large fractions of the network, peaking at t = 4 and then declining as other modalities—especially hygrosensory, olfactory, gustatory, and mechanosensory—gain influence. Visual cascades, by contrast, remain inactive until around t = 7, by which time other modalities are already declining.

We summarized convergence patterns by computing an overlap matrix. For each pair of modalities, we identified neurons with supra-threshold activation for both modalities at the same time step and tallied across time and space (Fig 4g). As expected, the overlap matrix mirrors the cascade similarity matrix: visual cascades rarely co-activate with others, while thermosensory + hygrosensory and gustatory + unknown modalities frequently do. Mechanosensory and olfactory cascades exhibit less consistent clustering, suggesting more selective or delayed engagement with broader network dynamics.

To characterize multi-modal overlap more finely, we tabulated the most frequent combinations of 2 to 7 modalities co-activating a neuron. These groups consistently include thermosensory, hygrosensory, gustatory, olfactory, and mechanosensory inputs (Fig 4h). Visual modalities appear only in the final stages, and no neurons were activated by all eight modalities under these parameters.

Finally, we performed a time-resolved enrichment analysis on overlap scores. At each time t, we computed mean overlap index for each annotation category, standardized against a null distribution obtained by permuting labels (Fig 4i). As expected, early overlap of cascades is enriched among afferent, thermosensory, and sensory neurons (step t = 1). At t = 2, enrichment shifts to antennal lobe and glomerular neurons, consistent with their role in propagating activity. At later stages, overlapping cascades are enriched in intrinsic and efferent neurons (steps t = 3 − 5), tangential and columnar neurons (steps t = 6−7), and specific populations such as Kenyon cells, lateral horn, and central complex neurons.

Together, these results suggest that sensory cascades initially activate distinct and largely non-overlapping subnetworks, before converging on common populations of intrinsic neurons. Visual modalities remain the most distinct, engaging late and following unique trajectories through the network. These patterns reflect and reinforce known principles of modularity and sensory integration in the Drosophila brain.

Cooperative sensory cascades

At the end of the previous section, we defined a measure—the overlap index—to relate the spatiotemporal trajectories of multiple sensory cascades. However, this measure was based on non-interacting cascades. A more realistic extension of the model allows cascades to interact—either cooperatively or competitively. In this sub-section, we examine a cooperative model. In this model, we seed cascades in different sensory modalities–e.g. setting N_seed hygrosensory neurons and N_seed thermosensory neurons active at time t = 0. Postsynaptic neurons can be activated by either modality, generally leading to earlier activation. Conceptually, this reflects polysensory integration, where multimodal sensory events (e.g., a change in temperature and visual input) occur simultaneously, boosting signal propagation speed through the nervous system. This type of early multisensory convergence has been observed in vivo in the Drosophila brain, particularly in thermosensory and olfactory circuits [50], and is consistent with integration within higher-order centers like the mushroom body and lateral horn [40,41].

To characterize this phenomenon, we simulated cooperative cascades in which seed neurons were drawn from pairs of sensory modalities. After 1000 simulations per pair, we computed each neuron’s mean activation time and compared it to the same neuron’s activation time in unimodal simulations. We highlight these distinctions by calculating the difference between the cooperative and unimodal activation probability for each sensory modality. This yielded a measure of relative speed-up—i.e., the reduction in activation time due to cooperation.

We found that, in general, cooperative stimulation resulted in modest speed-ups. Across all system pairs, the average activation time reduction was −0.11 ± 0.05 steps. Pairs that yielded the greatest reductions included gustatory+unknown (–0.18), olfactory+unknown (–0.18), visual (retinal + ocellar) systems (–0.18), and gustatory+olfactory (–0.17) (Fig 5a).

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Fig 5. Cooperative cascade statistics.

Here, we consider cascades in which neurons associated with different sensory modalities are treated as seeds. In contrast with the competitive cascade model, where postsynaptic neurons are activated by one sensory modality or the other, neurons here can be activated by either sensory modality. In principle, then, the cooperative cascade leads to reductions in activation time for “synergistic” sensory modalities. That is, pairs that target distinct neuronal populations or sufficiently enhance the probability of activating a single neuronal population. (a) Average reduction in activation time for all pairs of sensory modalities. Note that the colormap is inverted, so that the greatest reductions are depicted in bright colors. (b) We also compared unimodal cascade activation times against the scenario where seed neurons are selected randomly from all sensory modalities. Here, we show the mean reduction in activation time for such a scenario. (c) The same information at single-cell resolution and in anatomical space. (d) Enrichment statistics for speed-ups. (e) The distribution of speed-ups was heavy-tailed. Here, we highlight the tail of this distribution (the top 1% of neurons by average reduction in activation time), showing their composition across annotation categories.

https://doi.org/10.1371/journal.pcsy.0000091.g005

To explore a more extreme case of cooperation, we simulated pan-sensory cascades where all eight sensory modalities were simultaneously seeded. This condition led to significantly faster propagation: compared to unimodal cascades originating in visual neurons, the pan-modality cascade reduced activation time by nearly 2 steps (Fig 5b). For completeness, we visualized the reduction in activation time for each neuron in anatomical space (averaged over all eight unimodal conditions; Fig 5c).

We also used annotation-based enrichment analyses to examine the neurons most affected by multisensory cooperation (Fig 5d). Because activation time reductions were heavy-tailed—a small number of neurons showed large effects—we focused on the top 1% of neurons (ranked by activation time reduction). Fig 5e summarizes the raw annotation counts for this subset, highlighting that cooperation disproportionately benefits certain neuron classes.

Together, these results suggest that visual cascades, which follow distinctive trajectories compared to other modalities, benefit most from multisensory stimulation. Nevertheless, the modest mean reductions indicate that even unimodal cascades can leverage connectome architecture to propagate efficiently through the brain.

Competitive sensory cascades

An alternative scenario for exploring interacting cascades is the so-called competitive cascade, wherein the signal propagated from two sensory modalities retains modal specificity. That is, neurons activated by either of these two modalities inherit the “label” of their respective sensory activator, maintaining the distinct identity of each signal. For instance, we could set N_seed hygrosensory and N_seed thermosensory neurons active at time t = 0. The hygrosensory and thermosensory seeds are active with labels “1” and “2”, respectively. At the next time step, t = 1, post-synaptic neurons activated by hygrosensory neurons inherit the label “1” while those activated by thermosensory neurons inherit the label “2”. Neurons can only have one of these two labels; never both. As with the cooperative cascade, the competitive cascade model can be interpreted in terms of multisensory stimulation. However, unlike the cooperative case, where multiple sensory modalities amplify a signal, in the competitive scenario, the more “salient” of the two modalities can dominate, effectively muting responses from the other modality. This dynamic may resemble behavioral scenarios in which conflicting sensory cues must be resolved by suppressing one modality to favor another [41,50]. In this section, we report results under this competitive scenario.

As an illustrative example, we show distinctions between unimodal and competitive cascades originating in gustatory and hygrosensory neurons. In Fig 6a (top+bottom), we show probabilistic activation maps corresponding to unimodal gustatory and hygrosensory cascades—i.e., without any competitive interaction. However, when we allow the cascades to evolve simultaneously and compete for territory, we find distinct spatiotemporal trajectories (Fig 6a, middle). We highlight these distinctions by calculating the difference in activation probability (competitive minus unimodal).

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Fig 6. Competitive cascade statistics.

(a) Comparison between unimodal gustatory and hygrosensory cascades (top and bottom) with competitive cascade (middle). (b) Entropy map for the gustatory and hygrosensory competitive cascade. High entropy neurons have “diverse” neighborhoods, i.e. their neighbors are activated by both gustatory and hygrosensory neurons. The inset with smaller brain maps depicts entropy maps of other competitive cascades involving the gustatory sensory modality at t = 4. (c) For every pair of neurons and at each time step, we calculated the relative dominance of one sensory modality over the other. That is, when we consider all active neurons, is one sensory modality over-expressed? Here, we plot this balance as a difference in proportion for all pairs of systems from time steps t = 2 to t = 6.

https://doi.org/10.1371/journal.pcsy.0000091.g006

One of the useful statistics that arises from competitive cascades is the so-called “neighborhood entropy”—a summary measure of how balanced a neuron’s neighbors are in terms of their assigned labels. A neuron whose neighbors all have only one label will have low entropy, whereas if the labels are distributed uniformly, the entropy is high. In Fig 6b, we depict neighborhood entropy in anatomical space for the gustatory versus hygrosensory competitive cascade. Neurons with high entropy—indicated by bright colors—sit at the boundaries of competing cascades. Thus, entropy serves as a complementary metric for identifying locations where multiple signals converge onto shared targets, potentially supporting multisensory integration.

We estimated the “winning” sensory modality at each time step by calculating the imbalance in the number of neurons assigned to each label. Specifically, we calculate the difference in the number of neurons activated by sensory modality, r, compared to the other, s (we express this number as a fraction of all N neurons). In Fig 6c, we show the balance metric as a function of time step. Each entry in this matrix corresponds to the difference in territory occupied by sensory system r versus s. For example, at t = 6, two cascade pairs show strong imbalances (red). In one case, thermosensory neurons outcompete visual neurons; in another, unknown sensory neurons dominate ocellar inputs. We also show a more balanced case (hygrosensory vs. mechanosensory), where territorial differences are minimal at t = 6.

This competitive cascade model helps us better understand how multisensory signals might resolve within a weighted and directed connectome. For instance, we can use neighborhood entropy to track the formation of “fronts” or boundaries between competing sensory signals. Neurons with high entropy are structurally poised for integration—they receive input from, or project to, neurons with differing sensory identities. Because the Drosophila connectome is directed, we defined three forms of entropy: based on presynaptic partners, postsynaptic partners, and their union. In a pan-sensory competitive cascade model, where all sensory systems were seeded equally, these three measures were highly correlated (mean pairwise similarity across time points r = 0.81 ± 0.21). Nonetheless, subtle differences were evident, likely due to the strong—but not perfect—correlation between in- and out-degree (r = 0.82) [40].

We further found that a neuron’s degree was strongly predictive of its time-averaged entropy (r = 0.91; Fig 7b). In general, high entropy neurons tended to be structural hubs, consistent with their broad connections across sensory domains. This was true for both binary and weighted degrees (Fig 7c). However, a neuron’s role in sensory integration is not static: entropy varied across time. Mean entropy increased rapidly to a peak at step 5 before decreasing (Fig 7d). Entropy maps showed low similarity across time—maps from early and late steps were even anti-correlated (Fig 7e), suggesting a complex temporal dynamic shaped by cascade propagation and network topology.

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Fig 7. Additional competitive cascade statistics.

The entropy patterns vary depending upon how one defines a neuron’s “neighborhood”. For instance, one can define a neighborhood based on a neuron’s pre- or post-synaptic neighbors or the combined neighborhood. Here, we compare these three definitions in panel a. We also related entropy to conventional network statistics. (b) Scatterplot of time-averaged entropy against the logarithm of nodes’ total degrees. (c) Correlation of entropy with various other network statistics: in/out/total degree and strength. (d) Mean whole-brain entropy of different neighborhood definitions as a function of step. (e) Similarity of whole-brain combined-neighborhood entropy patterns between time steps t = 0 to t = 9. (f) Enrichment statistics for whole-brain combined-neighborhood entropy.

https://doi.org/10.1371/journal.pcsy.0000091.g007

Finally, we examined whether neighborhood entropy was enriched within specific cell types and brain regions. As in previous analyses of activation time and overlapping cascades, we found distinct temporal trajectories by annotation. Afferent sensory neurons peaked in entropy early (steps 1–2), followed by efferent and intrinsic neuron types—including columnar neurons, Kenyon cells, central complex neurons, ascending/descending neurons, and visual centrifugal neurons (Fig 7f). These trajectories reinforce earlier observations that central brain neurons serve as hubs for signal convergence [40,41], with their entropy dynamics reflecting their role in integrating competing signals over time.

These observations suggest that intrinsic neurons in the central brain are key loci of sensory integration. Positioned at the boundaries of competing cascades and exhibiting high neighborhood entropy, these neurons are structurally and functionally poised to arbitrate between conflicting or convergent sensory inputs. Although high-degree neurons tend to show high entropy, the temporal dynamics of the competitive model underscore that a neuron’s role as integrator depends on timing and network context, not just connectivity.

Data-driven clustering of neurons based on cascade properties

We previously introduced a set of summary statistics derived from the spatiotemporal evolution of sensory cascades. These included activation time, overlap, competitiveness (entropy), and cooperative speed-up. We used enrichment analyses to relate these features to neurobiological annotations. Here, instead of aligning with known labels, we clustered neurons based solely on cascade-derived features to identify data-driven functional groupings.

To do so, we aggregated the aforementioned statistics—overlap, entropy (from competitive cascades), reduction in activation time (from cooperative cascades), and activation timing—into an N × matrix. We standardized (z-scored) each feature and applied k-means clustering using a correlation-based distance metric (Fig 8a). We varied k from 1 to 50, performed 100 random restarts per k, and selected k = 6 based on the “elbow” of the within-cluster sum of squared errors curve (Fig 8b). Spatial projections of these six clusters are shown in Fig 8b.

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Fig 8. Clustering neurons based on their cascade properties.

(a) Neurons ordered by cluster assignment. Columns correspond to z-scored cascade metrics. (b) Cluster labels depicted in anatomical space. (c) Cluster centroids. (d) Enrichment of cluster labels across annotations. Note that at the far right of panel a, we show the activation probability for each neuron at time points 1-50. In panel c, we show cluster centroid time courses for steps 1-20. Note further that for the purposes of clustering, we do not use the full activation time courses. Rather, we summarize the neuron × time point matrix into a neuron × 1 vector whose entries denote the average time of activation for each neuron.

https://doi.org/10.1371/journal.pcsy.0000091.g008

Each cluster was associated with a distinct centroid—an archetypal profile across cascade features (Fig 8c). Cluster 1 (yellow), for example, exhibited the earliest activation times and early-onset entropy. This cluster was enriched for afferent, sensory, and ascending neurons, consistent with its role as a cascade initiator. Cluster 2 (pink) followed temporally, with peaks in overlap, entropy, and activation between steps t = 3 and t = 6. It was enriched for efferent neurons, multiglomerular/monoglomerular projection neurons, and central complex interneurons, including Kenyon cells.

Clusters 3 through 6 exhibited progressively later activation profiles and distinct enrichment patterns. All were composed largely of intrinsic neurons and converged on visual projection and centrifugal neurons in the optic lobes.

These findings suggest that sensory spreading dynamics constrained by the connectome can be used to derive functionally meaningful, temporally ordered groupings of neurons. These groups reflect similarity in cascade participation and their respective roles in competition, cooperation, and convergence across the network.

Additional analyses

We conducted several supplementary analyses to assess the robustness and generality of our results. First, we verified that our findings were not sensitive to weak synaptic connections: thresholding the connectome to retain only synapses with at least five connections had minimal effect on results. Summary statistics remained highly correlated with those from the unthresholded network (Spearman correlations: , , ; all estimated with and ).

Second, we showed that activation timing could not be predicted solely from shortest path length—a static graph measure derived from connectivity alone (S5 Fig; see also [51]). Third, we examined how cascades unfolded across neurotransmitter classes, revealing transmitter-specific activation time distributions (S6 Fig).

Fourth, we compared sensory-driven cascades to cascades seeded from random non-sensory neurons. These exhibited systematically different spatiotemporal profiles, underscoring the distinctive topological embedding of sensory neurons (S7 Fig).

Fifth, we analyzed community structure in the connectome using a nested stochastic block model [52,53]. Cascade-derived statistics were highly enriched within and segregated between communities (S8 and S9 Figs). These findings support the idea that communities serve as mesoscale substrates for sensory integration and signal flow (see also [54–56]).

As a complementary continuous approach, we performed a principal components analysis on cascade features. The resulting components captured brain-wide gradients of variation and reflected global organizational motifs in cascade dynamics (S10 Fig).

Drosophila connectome dataset

All connectome data, including synaptic connectivity, three-dimensional coordinates, neuropil volumes, and annotations were obtained from https://codex.flywire.ai/. These derivatives represent the output of a process beginning with nanometer-resolution electron microscopy images of an adult female Drosophila [71]. The FlyWire project allowed citizen scientists to trace neurons [72] to reconstruct the connectome. Combined with automated approaches [73,74], the end result was a complete map of synaptic connections among approximately 139,000 neurons.

Neurons in Drosophila are polyadic, thus the same pair of neurons can synapse onto one another at multiple distinct sites. The https://codex.flywire.ai/ are shared in two versions: one in which pairs of neurons were connected if they were linked by, at minimum, five synapses and another in which even a single synapse was considered evidence that two neurons were connected (unthresholded). In the main text, we analyze the unthresholded connectome, but note that results are consistent with those obtained using the thresholded version.

Annotation data were obtained from at the same time as the connectome data. Annotations were grouped into four distinct categories [38]. The first two annotations are “dense,” in the sense that every neuron is assigned a label.

1. “Flow”: afferent, efferent, intrinsic.
2. “Super-class”: sensory (periphery to brain), motor (brain to periphery), endocrine (brain to corpora allata/cardiaca), ascending (ventral nerve cord (VNC) to brain), descending (brain to VNC), visual projection (optic lobes to central brain), visual centrifugal (central brain to optic lobes), or intrinsic to the optic lobes or the central brain

The other two categories are not dense–i.e. not all neurons are assigned a label. The “Class” and “Sub-class” annotations are nested hierarchically within the the parent “Super-class” and describe cell groups reported in the extant literature, e.g. neurons in the optic lobe [75].

Cascade model

Here we explore an abstract cascade model. In this model, each neuron exists in one of three states: active, inactive, or refractory. In our simulations, we set select sets of neurons to be active at time t = 0. These initially activated neurons are referred to as “seeds” and are selected from among sensory neurons alone. The seeds are intended to represent sensory stimuli.

In this model, neurons that are active at time t probabilistically activate their post-synaptic partners at t  +  1. Suppose neuron i makes a single synapse onto neuron j. Given that i is active at t, the probability that neuron i activates j at t + 1 is given by the transmission probability parameter, p_transmission. Conversely, the probability that i does not activate j is simply q = 1−p_transmission.

Oftentimes, neuron i makes multiple synapses onto j. We treat these as independent trials; only one successful trial is sufficient to activate neuron j. What is the probability that at least one event is successful? In the space of possible outcomes, there is exactly one outcome in which none of the synapses successfully activate j. Its probability is given by: − . All other possibly outcomes include at least one successful transmission event. Hence, the probability that j is activated by neuron i at time t + 1 is given by: .

For all unimodal, cooperative, and competitive cascades, 16 neurons from each sensory modality were selected randomly as seeds for the cascades.

At a high level, we view each cascade a single “sensory event” passing through the network. Previous studies have modeled this type of event using only “inactive” and “active” states (as in previous studies, e.g. [27,29]). That is, once a neuron is active, it stays active for the duration of the cascade and can activate its post-synaptic partners at every step after it becomes active. Here, we opt to introduce a third “refractory” state. Neurons enter this state immediately the step immediately following their activation.

The sequence “inactive→active→refractory” is consistent the simplest physiological spike cycle. The refractory state, which distinguishes our work from other related studies on cascade models, is appropriate for the timescales of sensory events, whereby channel inactivations following a spike prevent neurons from spiking again until recovery (which we assume takes much longer than the timescale of a sensory event). Moreover, this state sequence helps to create unidirectional waves of activation, which are consistent with observations of propagating calcium waves in Drosophila [76,77] and zebrafish [78].

Synaptic activation in our cascade model is implemented as a Bernoulli process in which each structural synaptic contact provides an independent opportunity for postsynaptic activation. This formulation has a direct biological interpretation: real chemical synapses exhibit low and probabilistic vesicle-release rates, with measured release probabilities commonly ranging from 1–10% at many central synapses [79,80]. Moreover, individual synaptic contacts often behave as independent release sites, consistent with classical quantal models [81] and with ultrastructural reconstructions in Drosophila showing multiple discrete active zones per connection [82,83]. The effective probability that a presynaptic spike triggers a postsynaptic spike within a brief cascade timestep is further reduced by dendritic integration constraints [84], inhibitory shunting [85], short-term synaptic depression [86], and spike-threshold variability [87]. Thus, small transmission probabilities (1–5%) are biologically realistic when interpreted as the net probability that a single structural synapse produces a downstream spike during a transient propagation event.

In our model, cascade dynamics are initiated by activating a small number (N_seed) of seed neurons at t = 0, which reflects the fact that many neural events begin with sparse, localized activation rather than widespread population firing. Sensory pathways frequently exhibit highly selective and sparse initial responses, as seen in Drosophila olfaction where only a small subset of receptor neurons and projection neurons respond strongly to a given odor [88,89] and in vertebrate cortex where sparse coding is a dominant organizational principle [90]. Sparse initial activation is also characteristic of feature-selective neurons in early sensory systems [91] and of startle and escape circuits, where a very small number of command-like neurons seed fast recruitment [92]. Moreover, large-scale neural events such as cortical traveling waves or hippocampal sharp-wave ripple events typically originate from small focal clusters of neurons before propagating across the network [93,94]. Thus, seeding the cascade with a small set of neurons captures the biological reality that many propagating population events begin from a minimal, spatially or functionally localized trigger, consistent with both sensory-evoked activity and spontaneously initiated neural dynamics.

Community detection

Many studies have shown that biological neural networks at varying spatial scales can be meaningfully partitioned into clusters or communities [5,53,95–102]. In general, community structure is unknown ahead of time and must be estimated or inferred algorithmically. The procedure is referred to as community detection [103], and there exist many approaches for doing so [104–109], each of which makes specific assumptions about what constitutes a community.

One of the oldest approaches for community detection is the stochastic blockmodel [110–114]. Briefly, blockmodels imagine that every node in the network is assigned a label. The probability that any pair of nodes are connected and the weight of that connection depends only upon the communities to which they are assigned. In general, blockmodels estimate community labels and connection probability/weight distributions so as to maximize the likelihood that the model generated the observed network.

Recently, there has been renewed interest in the application of blockmodels to brain network data [20,101,115–122]. Here, we leverage a nested and weighted variant of the classical blockmodel to partition the Drosophila connectome into hierarchical communities [52]. Using this model, we obtained an estimate of the consensus hierarchical partition using a Markov Chain Monte Carlo procedure [123]. Briefly, this procedure entails allowing the Markov chain to equilibriate and sampling 10000 high-quality partitions. These partitions are aligned to one another to discover latent “modes” – partitions that share many characteristics with one another [124]. From these modes, we obtained for each neuron the community it was most likely assigned to. All analyses using communities were carried out on the resulting partition (S8 Fig and S9 Fig).

Clustering based on cascade properties

In the main text, we derived a series of statistics for neurons based on their activation times, overlap, neighborhood entropies, and speed-ups. We can use these data to partition neurons into clusters based not on their connectivity (information derived from the connectome) but these dynamic, cascade-based properties.

To do this, we constructed a [N × F] matrix, where N is the number of nodes and F = 27 is the total number of features. In this case, we considered the following features derived from omnibus sensory cascades–i.e. where all sensory modalities were seeded:

1. Activation probability: The [N × 1] vector of each neuron’s mean activation time.
2. Overlap index: The array of neurons’ overlap indices over the first 10 time steps.
3. Neighborhood entropy: The [N × 15] array of neurons’ neighborhood entropy (estimated using both pre-/post-synaptic partners).
4. Speed up: The [N × 1] vector of speed-ups (reductions in activation times) from single-modality unimodal cascades to the omnibus cascade.

To cluster these data, every column was standardized (z-scored). We then used k-means clustering to assign neurons to a unique cluster [125]. We selected the optimal number of clusters based on the inflection point in the summed square errors of cluster centroids relative to their constituents. Based on these analyses, we identified k = 6 as the optimal number of clusters.

Annotation enrichment analysis

Throughout this manuscript we describe an “enrichment” procedure for linking continuous data to categorical labels–e.g. annotations. The aim of this procedure, in more detail, was to determine if a particular variable was over-expressed (enriched) within a given annotation category. To do this, we calculated the variable of interest’s mean value within all neurons associated with a specific annotation. We then randomly permuted the annotation labels (keeping the total number constant) and calculated the new mean. We repeated this procedure 1000 times, generated a null distribution of mean values. The enrichment score for that variable within that annotation category is the original mean expressed as a z-score with respect to the null distribution.