A minimal generative model for analyzing neurite growth and synaptogenesis in the C. elegans frontal ganglia connectome.
Zachary Laborde & Eduardo J. Izquierdo — Indiana University Bloomington
📄 ALIFE 2 Paper · 📧 zlaborde@iu.edu
Neurons coordinate to form efficient global structures using only local information (Pérez-Escudero et al., 2009), and these connections vary considerably across individuals (Witvliet et al., 2021). This project asks:
Can we create a minimal model to analyze the process of neurite growth and synaptogenesis?
C. elegans was chosen as the target organism because it is the only animal with a complete, multiply-recorded microconnectome (the C. elegans neuronal network, CENN). Neurons in its frontal ganglia have 1–2 neurites that act as both axons and dendrites, rarely branch, form mostly en passant synapses, and wrap around the pharynx — properties that lend themselves to geometric modeling.
SEEM generates a candidate connectome by simulating neurite geometry in 3D space:
- Draw Ray — Each neuron projects a ray toward its nearest neighbor on the opposite side of the nerve ring.
- Detect Intersections — Ray–ray intersection points (putative synaptic contact sites) are identified.
- Build Connection Network — Intersecting neurite pairs are recorded as potential connections.
- Sample Subnetworks — Directed subnetworks containing x edges are sampled from the full connection network.
A null-model variant of SEEM in which step 1 is replaced by random ray directions. REEM controls for structural bias introduced by the nerve-ring projection method while preserving the intersection-detection logic.
| Model | Description |
|---|---|
| RDDAM | Random Distance-Dependent Attachment Model (Itzhack & Louzoun, 2010) — connection probability decays as a power law of soma distance |
| ERN | Erdős–Rényi random network — uniform random edge assignment, matched edge count |
| Dataset | Source |
|---|---|
| 3D neuron positions | Skuhersky et al. (2022) |
| Adult connectome | Cook et al. (2019) |
| Developmental connectomes (L1–L5) | Witvliet et al. (2021) |
SEEM/
├── data/
│ ├── **/compiled/ # Processed graph objects
│ ├── **/original/ # Unmodified source graphs
│ ├── **/source/ # Raw source files
│ └── images/ # Generated plot images
├── lib/ # Shared library code
├── src/ # Core source modules
├── paper/ # Manuscript files
├── randNeur.py # Random neuron sampling utility
├── reemNeurites.sh # Shell script for running REEM
└── requirements.txt
| Step | Notebook | Description |
|---|---|---|
| 1 | convert.ipynb |
Parse source data files into graph objects |
| 2 | penpals.ipynb |
Find each neuron's nearest nerve-ring neighbor |
| 3 | edgeDistance.ipynb |
Compute Euclidean distance for each edge |
| 4 | SEEM.ipynb |
Run the SEEM algorithm |
| 5 | overlap.ipynb |
Compute edge overlap between graph pairs |
| Notebook | Description |
|---|---|
RDDAM.ipynb |
Generate RDDAM graphs |
random.ipynb |
Generate Erdős–Rényi random graphs |
modules.ipynb |
Community / module detection |
stats.ipynb |
Compute network statistics |
display.ipynb |
All plots and visualizations |
Models are evaluated against the CENN across four measures:
- Clustering Coefficient — How densely interconnected a node's neighbors are
- Edge Distance — Euclidean distance (μm) spanned by each edge
- Average Node Connectivity — Number of independent paths between node pairs
- Bidirectional Links — Count of reciprocal (A→B and B→A) connections
| Metric | Best model(s) | Notes |
|---|---|---|
| Clustering coefficient | SEEM, RDDAM | Proximity alone largely explains C. elegans clustering |
| Edge distance | SEEM, REEM | Neurite/soma spatial embedding accounts for most of this property; RDDAM systematically underestimates edge length |
| Average connectivity | None | CENN is far less redundant than all generative models — consistent with a metabolically efficient "rich club" architecture |
| Bidirectional links | RDDAM | May reflect gap-junction bias rather than a genuine structural match |
| Degree distribution | SEEM, RDDAM, REEM | C. elegans has more high-degree hub nodes than any model, indicating a "rich club" |
| Edge overlap with CENN | RDDAM (14.95%), SEEM (10.70%), REEM (10.32%), ERN (9.49%) | All models remain low, confirming they capture statistical properties but not specific wiring |
Key takeaway: Neurite geometry explains several statistical properties of the C. elegans frontal ganglia, but spatial embedding alone is insufficient. The CENN's metabolic efficiency and hub structure require additional biological mechanisms not captured by any purely geometric model.
- Connection feedback approach — Model how neurons locally "sense" that sufficient paths to a target already exist, suppressing redundant connections (addressing the average-connectivity gap).
- Axon budding model — Parameterize the complex, symmetric neurite trajectories observed in C. elegans to generate more anatomically realistic neurite paths.
git clone https://github.com/Zach-Attach/SEEM.git
cd SEEM
pip install -r requirements.txtThen open notebooks in the order listed above.
If you use this code, please cite:
Laborde, Z. & Izquierdo, E. J. (2023). Spatial Embedding of Edges in a
Synaptic Generative Model of C. elegans. ALIFE 2023.