Event Embedding of Protein Networks : Compositional Learning of Biological Function

Abstract

In this work, we study whether enforcing strict compositional structure in sequence embeddings yields meaningful geometric organization when applied to protein-protein interaction networks. Using Event2Vec, an additive sequence embedding model, we train 64-dimensional representations on random walks from the human STRING interactome, and compare against a DeepWalk baseline based on Word2Vec, trained on the same walks. We find that compositional structure substantially improves pathway coherence (30.2$\times$ vs 2.9$\times$ above random), functional analogy accuracy (mean similarity 0.966 vs 0.650), and hierarchical pathway organization, while geometric properties such as norm--degree anticorrelation are shared with or exceeded by the non-compositional baseline. These results indicate that enforced compositionality specifically benefits relational and compositional reasoning tasks in biological networks.

Figures (5)

• Figure 1: Pathway coherence comparison. Event2Vec (left) shows higher coherence and much lower random baseline than DeepWalk (right) across all 10 pathways.
• Figure 2: Protein arithmetic comparison. Event2Vec (left column) recovers biologically specific targets with high similarity. DeepWalk (right column) returns less specific predictions with lower similarity.
• Figure 3: Norm--degree anticorrelation. Both methods show that high-degree proteins (hubs) receive smaller embedding norms, but DeepWalk exhibits stronger anticorrelation ($r=-0.801$) than Event2Vec ($r=-0.627$). This suggests the pattern arises from skip-gram frequency effects rather than compositional structure. Red points highlight canonical hubs (TP53, MYC, AKT1, EGFR, SRC, JUN, BRCA1, TNF). Note the different norm scales: Event2Vec's additive constraint produces smaller, more tightly distributed norms.
• Figure 4: Hierarchical pathway organization. Cosine similarity between pathway centroids, reordered by Ward clustering. Event2Vec (left) reveals three biologically coherent super-clusters: housekeeping (Ribosome, OxPhos), nuclear/genome (DNA Repair, p53, Cell Cycle), and signaling (PI3K-AKT, MAPK/ERK, NF-$\kappa$B, Apoptosis). Negative correlations (blue) sharply delineate housekeeping pathways from signaling cascades. DeepWalk (right) shows uniformly positive similarities without clear cluster boundaries, indicating weaker functional discrimination.
• Figure 5: Embedding drift along signaling cascades. Cumulative sums of protein embeddings ($h_t = \sum_{i=1}^{t} e_i$) are computed along three canonical pathways (EGFR signaling, PI3K-AKT-mTOR, p53 DNA damage) and projected via PCA. Event2Vec (top row) produces smooth, directional trajectories where PC1 captures 96--98% of variance, indicating that sequential addition follows a coherent linear path. DeepWalk (bottom row) shows noisier trajectories with greater PC2 spread (PC1 explains only 89--94% of variance), reflecting the absence of an additive constraint. This directly validates Event2Vec's compositional structure: the embedding of a signaling history approximates the sum of its constituent proteins.