Adapting multiscale EDN representation into sequence-specific node embeddings for De Bruijn graph learning

Graph neural networks (GNNs) have emerged as an effective framework for biological sequence classification using De Bruijn graphs, yet node representations have received comparatively less attention. Although multiscale Expected Density of Nucleotide (EDN) provides informative sequence-level representations, it cannot be directly incorporated into graph-based sequence learning because De Bruijn graphs require node-level representations. To address this challenge, we propose Contextual Multiscale Expected Density of Nucleotide (cMSEDN), a lightweight, deterministic framework that adapts multiscale EDN sequence representations into sequence-specific node embeddings for De Bruijn graph learning while preserving k-mer identity and incorporating occurrence-level context. Unlike static k-mer encodings, cMSEDN aggregates occurrence-level contextual features so that identical k-mers can receive distinct sequence-specific representations across different biological sequences. We evaluated the proposed framework on seven biological sequence classification datasets spanning transcription factor binding prediction, promoter recognition, and RNA subcellular localization across multiple species, and encompassing both DNA and RNA sequence analysis tasks using GCN and GIN architectures. Compared with conventional context-independent node representations, off-the-shelf foundation models serving as static node-feature extractors, and a static EDN-based baseline, cMSEDN consistently achieved improved classification performance across the benchmark suite for De Bruijn Graph Neural Networks while using compact deterministic embeddings. These results indicate that our sequence-specific k -mer encoding is an effective, computationally lightweight bio-sequence graph representation for sequence classification, requiring no modifications to the underlying GNN architecture.