An Allele-Centric Pan-Graph-Matrix Representation for Scalable Pangenome Analysis

TL;DR

The paper addresses scalable pangenome analysis by introducing an allele-centric pan-graph-matrix (H1) that encodes exact haplotype membership per allele with adaptive dense or sparse encodings, allowing population structure to drive compression. It additionally presents H2, a path-centric dual representation that recovers ordered haplotype paths while remaining information-equivalent to H1, enabling analyses that depend on haplotype topology. The authors demonstrate substantial structure-aware compression, especially for structural variants, via a first-order Markov model with context-dependent Huffman coding, achieving near-entropy-optimal performance (e.g., $L_{global}-H_{global} \ll 1$) and real-world compression ratios such as $\bar{L}_{real} \approx 1.0218$ bits/symbol and $\approx 31.3\times$ on-disk savings. The framework provides a unified, scalable foundation for population-aware pangenome analysis, supporting rare-variant interpretation, cohort stratification, and privacy-friendly data sharing, with concrete visualizations and implementations that separate population incidence from haplotype ordering for flexible downstream use.

Abstract

Population-scale pangenome analysis increasingly requires representations that unify single-nucleotide and structural variation while remaining scalable across large cohorts. Existing formats are typically sequence-centric, path-centric, or sample-centric, and often obscure population structure or fail to exploit carrier sparsity. We introduce the H1 pan-graph-matrix, an allele-centric representation that encodes exact haplotype membership using adaptive per-allele compression. By treating alleles as first-class objects and selecting optimal encodings based on carrier distribution, H1 achieves near-optimal storage across both common and rare variants. We further introduce H2, a path-centric dual representation derived from the same underlying allele-haplotype incidence information that restores explicit haplotype ordering while remaining exactly equivalent in information content. Using real human genome data, we show that this representation yields substantial compression gains, particularly for structural variants, while remaining equivalent in information content to pangenome graphs. H1 provides a unified, population-aware foundation for scalable pangenome analysis and downstream applications such as rare-variant interpretation and drug discovery.

Figures (3)

• Figure 1: Schematic correspondence between three information-equivalent pangenome representations. (Left) A pangenome graph encodes structural alternatives as bubbles and haplotypes as implicit paths. (Center) The H2 path-centric representation makes haplotype paths explicit as ordered sequences of reference and alternative segments. (Right) The pan-graph-matrix (H1) encodes allele--haplotype incidence, with rows corresponding to alleles and columns to haplotypes, stored using adaptive sparse or dense encodings based on carrier distribution. Together, the graph, H2, and H1 representations encode the same underlying genomic variation while emphasizing complementary dimensions: structural topology, haplotype ordering, and population incidence.
• Figure 2: SV-backbone pangenome graph for a 2 Mb region on chromosome 1 derived from the H1 pan-graph-matrix. The reference backbone is segmented exclusively at structural-variant breakpoints, resulting in 91 reference segments across the region. Forty-five true structural variants are represented as alternative paths (bubbles) connecting backbone segments. Single-nucleotide variants are not used to split the backbone and are instead retained as annotations associated with the corresponding reference segments. This representation yields a compact, largely linear graph in which each bubble corresponds to a true structural rearrangement, making the large-scale genomic structure easy to interpret.
• Figure 3: Coarse pangenome graph for the same 2 Mb region on chromosome 1 incorporating both single-nucleotide variants and structural variants. The reference backbone is segmented using 1 kb intervals in addition to structural-variant boundaries, producing 2,090 reference segments. Structural variants are represented as alternative paths between segments, while approximately 25,000 single-nucleotide variants are attached as short alternative nodes without splitting the backbone at single-base resolution. The resulting graph is substantially denser and visually crowded, faithfully reflecting the full spectrum of genomic variation in the region. Meaningful inspection therefore requires selective filtering or sampling, for example by focusing on structural variants or a subset of single-nucleotide variants.