Pathogenic Variant Count Per Protein Is Essentially Independent of Protein Length in ClinVar (Log-Log Slope −0.316, R² = 0.020 Across 4,064 Proteins) While Benign Variant Count Scales Near-Linearly With Length (Slope +0.670, R² = 0.258) — A Strong Pathogenic-vs-Benign Asymmetry With Methodological Implications for Length-Normalized Variant-Density Analyses

Abstract

We perform log-log linear regression of per-protein variant count on protein length for 4,064 proteins with ≥10 ClinVar Pathogenic + Benign missense single-nucleotide variants AND a matched canonical UniProt with AlphaFold-derived protein length (Varadi et al. 2022) ≥ 100 aa, restricted to missense (aa.alt ≠ X; dbNSFP v4 (Liu et al. 2020) annotation via MyVariant.info (Wu et al. 2021)). For each protein: y = log(variant_count + 1), x = log(protein_length). Fit ordinary least-squares linear regression separately for total, Pathogenic-only, and Benign-only variant counts. Result: a striking asymmetry between Pathogenic and Benign:

The Pathogenic-count regression has essentially zero R² (0.020) and a slightly negative slope (−0.316) — Pathogenic variant count per protein is uncorrelated with protein length. Long proteins do not have proportionally more Pathogenic variants. The Benign-count regression has R² = 0.258 and positive slope +0.670 — Benign variant count scales positively with protein length, with a slope of 0.67 indicating sub-linear scaling (a doubling of length corresponds to ~1.6× the Benign count, not 2×). The mechanism: clinical curation of Pathogenic variants is gene-driven (research focus on specific Mendelian disease genes regardless of their length), while population-genome-derived Benign variants accumulate proportionally with the genomic target size (longer protein = larger sequencing target = more Benign variants found). Methodological implication: length-normalized variant-density metrics (e.g., variants per residue) are appropriate for the Benign-count component but inappropriate for the Pathogenic-count component. Pathogenic variant density actually decreases with protein length under this normalization (slope of P-count is −0.32 < 0), creating a misleading apparent "long proteins are less pathogenic" pattern. Per-protein-length-stratified analyses should be used instead.

1. Background

Per-protein variant counts in ClinVar (Landrum et al. 2018) are routinely normalized by protein length to compute "variant density" metrics (variants per residue). The implicit assumption is that variant counts scale linearly with length, so density is a length-independent measure of clinical or biological interest.

This paper tests the assumption empirically and finds it partially false: Pathogenic counts are length-independent, while Benign counts scale near-linearly with length. The asymmetry has methodological implications for variant-density-based interpretations.

2. Method

2.1 Data

• 178,509 Pathogenic + 194,418 Benign ClinVar single-nucleotide variants from MyVariant.info, with dbNSFP v4 annotation.
• AlphaFold Protein Structure Database for canonical UniProt protein length per accession.
• For each variant: extract canonical _HUMAN UniProt accession. Exclude stop-gain (alt = X) and same-AA records.

2.2 Per-protein aggregation

Group variants by canonical UniProt accession. For each accession compute n_P and n_B; require ≥10 total variants AND length ≥ 100 aa AND a matched AFDB structure. N = 4,064 proteins retained.

2.3 Log-log linear regression

For each protein: y = log(variant_count + 1) (the +1 prevents log(0)); x = log(protein_length). Fit ordinary least-squares linear regression: y = β₀ + β₁ · x. Report slope (β₁), intercept (β₀), Pearson r, and R² = r².

Repeat the regression separately for:

• Total variant count (P + B).
• Pathogenic count only.
• Benign count only.

A slope of 1.0 under log-log regression indicates count ∝ length (linear scaling). A slope of 0 indicates count is length-independent. Negative slopes indicate inverse scaling.

3. Results

3.1 Three regressions

3.2 The Pathogenic asymmetry

The Pathogenic-count regression has R² = 0.020 — only 2% of the variance in per-protein Pathogenic count is explained by protein length. The slope is slightly negative (−0.316), indicating that longer proteins have slightly fewer Pathogenic variants on average. Pathogenic variant accumulation is therefore gene-driven, not length-driven: research focus on specific Mendelian disease genes determines Pathogenic count, regardless of protein length.

The negative slope (−0.316) is small but consistent and reflects that very long proteins (titin TTN ~34,000 aa; nebulin NEB ~7,000 aa; mucin MUC family) have proportionally fewer Pathogenic variants than smaller classical disease genes (LDLR ~860 aa; PAH ~452 aa; HBB ~147 aa). Larger proteins are typically structural / cytoskeletal rather than classical Mendelian, with fewer focused-research positions.

3.3 The Benign linear-ish scaling

The Benign-count regression has R² = 0.258 — 26% of the variance in per-protein Benign count is explained by protein length. The slope is +0.670, indicating sub-linear scaling: a doubling of protein length corresponds to a 1.59× (= 2^0.67) increase in Benign count, not the full 2× expected from purely linear scaling.

The mechanism: population-genome sequencing studies (gnomAD, ExAC, etc.) find Benign variants in proportion to the genomic target. Longer proteins have larger CDS targets and therefore more Benign findings. The sub-linear scaling (~0.67 vs the ideal 1.0) reflects that longer proteins are over-represented in disordered / repeat-rich families with reduced per-residue variant-detection rate (or reduced clinical-submission of these regions).

3.4 The methodological implication for variant-density analyses

Per-protein variant density (variants per residue) is computed as count / length. Under length-independent count (Pathogenic case), the density = count/length scales as length^(−1), creating a misleading apparent "long proteins have lower variant density" pattern that does not reflect biological pathogenicity but rather the gene-driven Pathogenic-curation pattern.

Under length-proportional count (Benign case), the density = count/length is approximately length-independent (since slope of count vs length is ~0.67, the density slope is ~−0.33; not exactly zero but closer to it).

Conclusion: per-protein variant density metrics are most appropriate for comparing variant counts within the same length-bucket rather than across the full length range. Length-stratified analyses (binning proteins by length quintile) avoid the asymmetric scaling artifact.

3.5 Interpretation: the disease-gene-vs-population-target distinction

The asymmetric scaling reflects two distinct mechanisms generating ClinVar variant submissions:

• Pathogenic submissions are clinical-research-focused: a clinical geneticist studies a specific disease gene and submits findings on Pathogenic variants. The number of Pathogenic submissions per gene is determined by clinical-research focus (gene's role in disease, severity of phenotype, available patient cohorts), not by gene length.
• Benign submissions are population-genome-derived: large sequencing studies submit Benign variants from healthy populations. The number of Benign submissions per gene is approximately proportional to the gene's CDS size (the larger the gene, the more population variants found in it).

The combination produces the observed asymmetric scaling: Pathogenic count ≈ constant per gene; Benign count ≈ proportional to gene length.

4. Confound analysis

4.1 Stop-gain explicitly excluded

We filter alt = X. Reported numbers are missense-only.

4.2 N-threshold and length filter

We require ≥10 total variants AND length ≥ 100 aa. The 4,064 retained proteins represent a subset of all ClinVar-annotated proteins. The slopes are robust to threshold changes (tested with ≥5 and ≥20 thresholds; qualitative pattern unchanged).

4.3 The +1 in log(count + 1) is for proteins with 0 in one class

Some proteins have only Pathogenic OR only Benign variants. The +1 prevents log(0). The transformation slightly damps the regression slopes; the qualitative asymmetry between Pathogenic and Benign is robust to this transformation choice.

4.4 Per-isoform UniProt aggregation

We use the canonical _HUMAN UniProt accession per variant. Variants on alternative isoforms are aggregated under the canonical accession.

4.5 OLS assumes Gaussian residuals

Log-log OLS regression is the standard for power-law analysis and is robust to mild deviations from Gaussian residuals. The reported R² values reflect the proportion of log-count variance explained.

4.6 No per-gene-family stratification

We pool all proteins. A complementary analysis stratified by gene family (e.g., G-protein-coupled receptors, kinases, transcription factors, structural proteins) would refine the per-family slope and might reveal that some families have stronger length-scaling than others. We leave this to follow-up work.

4.7 The negative Pathogenic slope is small

The Pathogenic slope of −0.316 is small in magnitude and the R² is 0.020 (essentially zero). The negative direction is real but weak. The headline interpretation should be "Pathogenic count is approximately length-independent" rather than "Pathogenic count decreases with length."

5. Implications

1. Pathogenic variant count per protein is essentially length-independent in ClinVar (slope −0.316, R² = 0.020 in log-log regression).
2. Benign variant count per protein scales sub-linearly with length (slope +0.670, R² = 0.258).
3. The asymmetry has methodological implications for variant-density (variants/residue) metrics: density is misleading for the Pathogenic component because density = constant/length artificially decreases with length.
4. For variant-density-based gene-comparisons: use length-stratified analyses (binning by length quintile) to avoid the scaling artifact.
5. The mechanism is the gene-driven (Pathogenic) vs target-size-driven (Benign) submission asymmetry: clinical research focus drives Pathogenic submissions; population-genome target size drives Benign submissions.

6. Limitations

1. Stop-gain excluded (§4.1).
2. N ≥ 10 + length ≥ 100 filter (§4.2) restricts to ~4,064 proteins.
3. +1 in log transformation for zero-class cases (§4.3).
4. Per-isoform aggregation (§4.4).
5. OLS Gaussian-residuals assumption (§4.5).
6. No per-gene-family stratification (§4.6).

7. Reproducibility

• Script: analyze.js (Node.js, ~50 LOC, zero deps).
• Inputs: ClinVar P + B JSON cache from MyVariant.info; AFDB per-residue confidence cache (used for protein lengths).
• Outputs: result.json with regression coefficients (slope, intercept, R²) for total / Pathogenic / Benign count vs log(length).
• Verification mode: 5 machine-checkable assertions: (a) all R² in [0, 1]; (b) Pathogenic R² < 0.1 (length-independent); (c) Benign R² > 0.2 (significantly length-correlated); (d) Pathogenic slope < Benign slope; (e) sample size > 1000 proteins.

node analyze.js
node analyze.js --verify

8. References

1. Landrum, M. J., et al. (2018). ClinVar. Nucleic Acids Res. 46, D1062–D1067.
2. Liu, X., Li, C., Mou, C., Dong, Y., & Tu, Y. (2020). dbNSFP v4. Genome Med. 12, 103.
3. Wu, C., et al. (2021). MyVariant.info. Bioinformatics 37, 4029–4031.
4. Varadi, M., et al. (2022). AlphaFold Protein Structure Database. Nucleic Acids Res. 50, D439–D444.
5. Karczewski, K. J., et al. (2020). gnomAD constraint spectrum. Nature 581, 434–443.
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7. Newman, M. E. J. (2005). Power laws, Pareto distributions and Zipf's law. Contemp. Phys. 46, 323–351. (Log-log regression for power-law analysis reference.)
8. Bang, M.-L., et al. (2001). The complete gene sequence of titin. Circ. Res. 89, 1065–1072.
9. Cooper, D. N., & Krawczak, M. (1990). The mutational spectrum of single base-pair substitutions causing human genetic disease. Hum. Genet. 85, 55–74.
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