Assembly Gap Enrichment in Human Chromosomes Detected via Windowed Thermodynamic Approximation (WTA)

Abstract

Assembly Gap Enrichment in Human Chromosomes Detected via Windowed Thermodynamic Approximation (WTA) Abstract Background. Assembly gaps — runs of undetermined nucleotides ('N') in genomic reference assemblies — are conventionally interpreted as technical sequencing artifacts. We hypothesized that regions of elevated thermodynamic divergence, as detected by the Windowed Thermodynamic Approximation (WTA) method, may show statistically significant co-localisation with assembly gap positions in human chromosomes. Methods. We applied TSA (WTA engine, W=200 nt, step=50 nt, threshold=Mean+3.5σ) to chromosome 19 (GRCh38.p14, 58.6 Mb) and chromosome 21 (GRCh38.p14, 46.7 Mb). Structural peaks (SCZ) were identified and tested for proximity intersection (±50 bp) with 'N' positions using a one-proportion Z-test under the null hypothesis of random co-localisation. Results. Chr21: 104/451 SCZ peaks intersect with N-gaps (Hit rate 23.06% vs baseline 14.18%; Z=+5.41, p<0.0001; enrichment 1.63×). Chr19: 14/900 peaks intersect with N-gaps (Hit rate 1.56% vs baseline 0.30%; Z=+6.86, p≈3×10⁻⁷; enrichment 5.20×). Both chromosomes show statistically significant enrichment independent of the absolute N-count. Interpretation. The non-linear relationship between N-content and enrichment ratio (Chr21: 14.18% N → 1.63× enrichment; Chr19: 0.30% N → 5.20× enrichment) suggests that WTA-detected structural conflict zones are not proportionally driven by N-abundance, but reflect specific structural features of assembly gap boundaries. This supports the operational hypothesis that WTA structural peaks co-localise with genomic regions of elevated structural complexity. Data Availability. Method: DOI 10.5281/zenodo.21476786. Validation dataset: DOI 10.5281/zenodo.21203626. Audit scripts and CSV outputs available on request. Keywords: WTA, Windowed Thermodynamic Approximation, assembly gaps, N-gaps, human chromosomes, structural conflict zones, TSA, Tengri Structural Audit 1. Introduction Reference genome assemblies inevitably contain regions where sequence resolution is incomplete. These positions are encoded as the IUPAC ambiguity character 'N' (Any nucleotide) and account for a variable fraction of the total assembly depending on sequencing technology and assembly algorithm. In the GRCh38 assembly of the human genome, N-positions are concentrated in centromeric regions, subtelomeric repeats, segmental duplications, and satellite sequences — areas of inherently complex DNA topology. The conventional interpretation is that N-positions represent sequencing failures: insufficient coverage, collapsed repeats, or algorithmic inability to resolve ambiguous signal. We propose a complementary perspective: that N-positions may also mark the boundaries of structurally complex DNA domains whose thermodynamic properties create measurable signals in sliding-window energy analysis — independent of any prior knowledge of the annotation. This hypothesis was formulated after observing that the WTA engine [1], when applied to clean (N-free) genomic sequences of bacteria and viruses [2], consistently produces SCZ (Structural Conflict Zone) peaks at functionally meaningful positions. The question then arises: if the same engine is applied to eukaryotic chromosomes containing N-blocks, do the WTA peaks preferentially co-localise with those N-positions? We report here empirical tests on two human chromosomes that demonstrate statistically significant enrichment of WTA structural peaks at assembly gap boundaries. 2. Materials and Methods 2.1 WTA Method The Windowed Thermodynamic Approximation (WTA) was applied as described in [1]. Briefly, each nucleotide is assigned an energy weight: G=C=1.0, A=T=0.5, N=0.0. A bidirectional sliding window of width W computes forward and backward local means: Sf(i) = mean(E[i : i+W]) Sb(i) = mean(E[i−W : i]) D(i) = |Sf(i) − Sb(i)| ← Divergence Index Parameters: W=200 nt, step=50 nt, threshold=Mean+3.5σ. Structural Conflict Zones (SCZ) are clusters of consecutive windows exceeding the threshold. 2.2 Genomic Data Chromosome 19 GRCh38.p14 · 58,617,616 bp · 176,858 N-positions (0.30%) Chromosome 21 GRCh38.p14 · 46,709,983 bp · 6,621,361 N-positions (14.18%) Source NCBI RefSeq GRCh38.p14 (downloaded July 2026) 2.3 Intersection Test For each SCZ peak (Critical Node position), a proximity window of ±50 bp was applied. A peak was counted as intersecting an N-region if any nucleotide within the ±50 bp window carried the 'N' designation. The empirical hit rate was compared to the baseline expected rate (fraction of N-positions in the chromosome) using a one-proportion Z-test: Z = (p̂ − p₀) / √(p₀(1−p₀)/n) where p̂ = empirical hit rate, p₀ = baseline N-fraction, n = number of SCZ peaks All computations were performed using the audit.py script (Python 3.11, Windows 11). Audit outputs were validated by manual spot-checking of ten randomly selected peak positions against the FASTA source. 3. Results 3.1 Summary Statistics Chromosome Length (bp) N-positions Baseline SCZ Peaks Hits Hit Rate Z p-value Enrichment Chromosome Length (bp) N-positions Baseline SCZ Peaks Hits Hit Rate Z p-value Enrichment Chr 21 (GRCh38) 46,709,983 6,621,361 14.18% 451 104 23.06% +5.41 <0.0001 1.63× Chr 19 (GRCh38) 58,617,616 176,858 0.30% 900 14 1.56% +6.86 ≈3×10⁻⁷ 5.20× 3.2 Key Observation — Non-Linear Relationship Critical finding: Chr21 has ~37× more N-positions than Chr19 in absolute terms (6.6M vs 177k). Yet Chr19 shows a higher enrichment ratio (5.20× vs 1.63×). This inverse relationship between N-abundance and enrichment specificity indicates that WTA structural peaks are not simply co-localising with N-regions by statistical inevitability (which would produce higher enrichment where N is more abundant). Instead, Chr19 demonstrates that even when N-positions are rare (0.30% of the sequence), WTA peaks preferentially find them at 5.2× the random expectation. This is consistent with the hypothesis that N-positions in Chr19 mark genuine structural boundaries (e.g., centromeric core, segmental duplications at chromosome arms) where thermodynamic complexity is concentrated, rather than large undifferentiated blocks of satellite sequence as in Chr21. 3.3 Statistical Verification Manual verification of the Z-score formula for Chr19: n = 900 peaks p̂ = 14/900 = 0.015556 p₀ = 176,858 / 58,617,616 = 0.003017 SE = √(0.003017 × 0.996983 / 900) = 0.001826 Z = (0.015556 − 0.003017) / 0.001826 = +6.88 Script output: +6.86 (rounding in p₀ — within acceptable tolerance) p-value ≈ 3 × 10⁻⁷ For Chr21: n = 451 peaks p̂ = 104/451 = 0.230599 p₀ = 6,621,361 / 46,709,983 = 0.141757 SE = √(0.141757 × 0.858243 / 451) = 0.016372 Z = (0.230599 − 0.141757) / 0.016372 = +5.43 Script output: +5.41 (minor rounding) — p < 0.0001 4. Discussion 4.1 Biological Context of N-Regions In the GRCh38 assembly, N-positions are not uniformly distributed. Chr19 is relatively N-poor (0.30%) and its gaps are concentrated near the centromere and a small number of segmental duplication boundaries. Chr21 is substantially N-rich (14.18%) with a large pericentromeric N-block and multiple interstitial gaps. Our results suggest that WTA peaks show higher specificity (enrichment ratio) in the N-poor chromosome, consistent with the interpretation that N-gaps in Chr19 mark more focally concentrated structural boundaries. 4.2 Operational N-Hypothesis We propose the following operational hypothesis, strictly limited to what the data support: Operational N-Hypothesis: WTA-detected Structural Conflict Zones (SCZ) are statistically enriched at assembly gap positions in human chromosomes, with enrichment ratios that are inversely related to background N-content. This suggests that WTA thermodynamic profiling may detect structural features associated with regions of limited sequencing resolution, independently of annotation. Importantly: we do not claim that N-positions represent physical molecular 'hinges', 'quantum wave interference', or that assembly gaps have a specific biological function detectable by WTA. The data demonstrate statistical enrichment; the biological mechanism of this enrichment requires experimental validation (e.g., ATAC-seq, Hi-C contact maps at gap boundaries). 4.3 Comparison with Existing Literature The co-localisation of structurally complex regions with sequencing gaps has been noted in the context of T2T (Telomere-to-Telomere) sequencing projects [3], where regions previously encoded as N were found to contain active satellite sequences and functional centromeric elements. Our WTA-based detection approach is computationally orthogonal to the alignment-based methods used in T2T assembly: it operates directly on the one-dimensional nucleotide weight sequence without reference to read depth or alignment quality. 4.4 Limitations • Sample size: two chromosomes. Expansion to all 23 human chromosomes, and validation in other species, is required. • Proximity window ±50 bp is arbitrary. Sensitivity analysis with different proximity windows was not performed in this version. • GRCh38 assembly. T2T-CHM13 (2022) has substantially fewer N-positions. Replication on T2T would provide a natural control experiment. • Causal mechanism is unknown. Statistical enrichment does not imply that N-positions cause WTA peaks or vice versa. 5. Conclusion We demonstrate that WTA structural peaks (SCZ) are statistically enriched at assembly gap ('N') positions in two human chromosomes from GRCh38, with Z-scores of +5.41 (Chr21, p<0.0001) and +6.86 (Chr19, p≈3×10⁻⁷). The non-linear inverse relationship between N-content abundan