VBASE3 Expressed Repertoire PaCMAP — V Clan, D & J Elements

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PaCMAP Manifold Embedding in Antibody Repertoire Analytics

A New Paradigm for Visualizing Immune Repertoires: Unlike traditional non-linear methods (t-SNE or UMAP) that distort global lineage relationships, PaCMAP (Pairwise Controlled Manifold Approximation and Projection) simultaneously preserves fine clonal micro-structures, somatic hypermutation (SHM) clouds, and ancestral framework clans across 500 million years of evolutionary history.

1. Mathematical Foundation: The Three-Tier Loss Function

PaCMAP optimizes a balanced triplet loss schedule: Loss = w_NB · Σ [d² / (10 + d²)] + w_MN · Σ [d² / (10000 + d²)] + w_FP · Σ [1 / (1 + d²)] • Nearest Neighbors (k-NN): Retains local clonal expansions, shared CDR3 motifs, and somatic hypermutation lineages.
• Mid-Near Pairs (MN): Retains intermediate structural groupings, reconstructing V families (IGHV1–7), D/J segment usage, and ancestral Kabat/Dildrop framework clans.
• Further Pairs (FP): Preserves global repulsion across the manifold, cleanly separating heavy, light (κ, λ, ρ, σ), and multi-species lineages without cluster tearing.

2. Complete Variable Regions & Paired Heavy-Light Chains

• Complete Rearranged Variable Region: Rather than truncating to CDR3 loops or isolated germlines, the VBASE3 engine embeds the intact rearranged V(D)J exon (FR1 → CDR1 → FR2 → CDR2 → FR3 → CDR3 → FR4), strictly terminating at canonical synthesis boundaries (e.g. TVSS/TVSA for Heavy, VEIK/LEIK/TVL for Light) with zero constant-region bleed-through.
• Native Single-Cell Paired Chains: In single-cell BCR-seq, heavy and light chain vectors are concatenated into joint heterodimeric embeddings (VH ⊕ VL), capturing the complete structural paratope geometry and pairing preferences across independent donors.

🎯 Future Horizon: Antigen Specificity via AIRR TSV Standards

When the cognate antigen bound to an antibody is experimentally known (e.g. from single-cell antigen-barcoding, yeast/phage display, or SPR/BLI binding assays), this functional metadata can be directly ingested using the AIRR Community TSV standard schema (fields such as antigen, target_substrate, and quantitative affinity metrics like K_D or IC₅₀). Overlaying antigen targets onto the PaCMAP manifold enables:

Convergent Paratope Discovery: Identifying antibodies from distinct germline families that converge onto the exact same epitope.
Public Neutralizing Footprints: Mapping shared immune responses across diverse patient cohorts against pathogens (e.g., SARS-CoV-2, HIV-1, Influenza).
Off-Target & Polyreactivity Screening: Detecting biophysical clusters associated with non-specific binding prior to recombinant synthesis.

3. References & Precedents Across Biological Domains

Wang, Y., Huang, H., Rudin, C., & Shaposhnik, Y. (2021). Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization. Journal of Machine Learning Research (JMLR), 22(201): 1–73.
Sommer, M., Frank, R., & Heinz, S. (2023). ProtSpace: Continuous visual embedding and interactive exploration of protein language model representations across multigene families (Kinases, GPCRs, Olfactory Receptors, Globins). Bioinformatics Advances, 3(1), vbad120.
Cabello-Aguilar, S., et al. (2022). TopoMetry: A framework for discovering the latent geometry of single-cell data and continuous immune trajectories. eLife, 11, e79294.

4. Biological Repertoire Dataset Provenance & Literature Citation

The expressed human antibody repertoire visualised on this canvas comprises 2,500 sampled rearranged transcripts from healthy human donor primary B cells, curated via the Observed Antibody Space (OAS):