Gene-Phenotype Tests (N ≥ 25)
67,022
Median VIF = 1.019 (17,410 genes)
M1: LoF Only (1 df)
13 (12)
p < 3.4e-7
M2: AM Only (1 df)
10 (8)
p < 3.4e-7
M4: LoF + Constraint (2 df)
21 (19)
p < 3.4e-7
M5: AM + LoF (2 df)
22 (19)
p < 3.4e-7
M7: AM + LoF + Con (3 df)
26 (22)
p < 3.4e-7

1. Collinearity-Free Stepwise Progression (M1 → M7)

Exome-wide significant associations (p < 3.4×10−7) without missense_ind or GERP_RS across DEE, GGE, EPI, and NAFE.

2. Unified Meta-Regression vs. Epi25 Exome Browser Burden

Click any gene point to inspect its stepwise trajectory and orthogonal partial R² breakdown below.

3. Interactive Gene Trajectory & Orthogonal 3-Moderator Partial R² Inspector

Select any gene from the dropdown or click a row in the table below.

4. Deep Biological Pathway Architecture — Ultra-Rare Coding Variants (AF ≤ 0.0001)

Unbiased pathway, clinical phenotype, and functional module enrichment is computed across all 21,568 pre-defined gene sets across 9 libraries (DisGeNET Disease, HPO Clinical Phenotype, 8 Highlighted Functional Biological Modules, GO Biological Process, GO Molecular Function, GO Cellular Component, Reactome, KEGG, and WikiPathways) strictly within the exact tested Epi25 exome universe, with exact Poisson-Binomial gene-length & variant-count adjustment (plen-adj, ORlen-adj) separately for All Combined (ALL), DEE (Encephalopathies), GGE (Genetic Generalized), NAFE (Focal), and EPI (All Epilepsies Meta).

Epilepsy Syndrome Cohort:

Unbiased Exact-Universe & Length-Adjusted Ontology Enrichment (All Protein Lengths — Cohort: ALL)

Ontology Pre-Defined Pathway / Ontology Term Hits / Tested (Expunadj → Explen) Length-Adjusted OR (plen-adj) Exact Fisher OR (pFisher) Comp. Z (pcomp) Med Hit R² Active Significant Epilepsy Genes (with Protein Length)
Figure 7: Ultra-Rare Pathway Enrichment and Functional Architecture of Epilepsy
Figure 7. Ultra-Rare (AF ≤ 0.0001) Multi-Database Pathway Enrichment (DisGeNET / GO / WikiPathways / Reactome / HPO) and Functional Module Breakdown Across DEE, NAFE, GGE, and Combined Epilepsy. 🔍 Open 300-DPI PNG
Module 1: Neuronal Chromatin Remodeling and Activity-Dependent Transcription
Module 1 Illustration (OR = 31.6×, p = 1.41×10−10). Neuronal Chromatin Remodeling & Activity-Dependent Transcriptional Architecture in Epilepsy: CHD2, H1-6, SETD1B (H3K4me3), KANSL1 (H4K16ac), TBL1XR1 (R² = 53.4%), ANKRD11, NR2F1 (R² = 64.0%), SP4 (R² = 20.4%), and DYRK1A. 🔍 Open High-Res PNG
Module 2: Axon Initial Segment and Presynaptic Voltage-Gated Ion Channels
Module 2 Illustration (OR = 39.7×, p = 3.46×10−8). Axon Initial Segment (AIS) & Presynaptic Voltage-Gated Na+, K+ & Ca2+ Channelopathies: SCN1A (NaV1.1, p = 3.2×10−25, R² = 29.0%), KCNQ2 (KV7.2, R² = 26.3%), KCNB1 (KV2.1, R² = 29.1%), CACNA1A (CaV2.1), CACNA1B (CaV2.2), RYR2, SCN8A, and ATP2B2. 🔍 Open High-Res PNG
Module 3: Lysosomal GATOR1 Complex and mTORC1 Nutrient-Sensing Brake
Module 3 Illustration (OR = 45.9×, p = 6.21×10−5). Lysosomal GATOR1 Complex & mTORC1 Nutrient-Sensing Brake in Non-Acquired Focal Epilepsy (NAFE): DEPDC5 (p = 9.9×10−16, R² = 16.7%), NPRL3 (p = 2.2×10−7, R² = 18.4%), NPRL2, and EGF. 🔍 Open High-Res PNG
Module 4: GABAergic Synaptic Inhibition, SNARE Vesicle Exocytosis and Postsynaptic Ras-GAP
Module 4 Illustration (OR = 19.8×, p = 8.47×10−5). GABAergic Synaptic Inhibition, SNARE Vesicle Exocytosis & Postsynaptic Ras-GAP Architecture: STXBP1/Munc18-1 (p = 5.3×10−15, R² = 63.6%), SLC6A1/GAT-1 (p = 1.2×10−11, R² = 60.8%), GABRB3, GABRA1, LGI1, SYNGAP1 (R² = 28.4%), and TANC2. 🔍 Open High-Res PNG
Module 5: Blood-Brain Barrier GLUT1/OCT1 Transport, Mitochondrial Shuttle and ER Lipid Homeostasis
Module 5 Illustration (OR = 14.5×, p = 2.68×10−4). Blood–Brain Barrier GLUT1/OCT1 Transport, Mitochondrial Malate–Aspartate Shuttle & ER Lipid Homeostasis: SLC2A1/GLUT1 (R² = 20.9%), SLC22A1/OCT1 (R² = 20.7%), SLC25A11 (R² = 50.0%, Constraint R² = 40.1%), and ARV1 (R² = 54.8%). 🔍 Open High-Res PNG
Module 6: Neuronal Autophagy, Nuclear LINC Cytoskeleton, Microtubule Motors and Neurovascular ECM
Module 6 Illustration (OR = 8.8×, p = 1.14×10−2). Neuronal Autophagy, Nuclear LINC Cytoskeleton, Microtubule Motors & Neurovascular ECM Scaffolds: MAP1LC3A/LC3A (p = 4.3×10−9, R² = 79.9%), SYNE1 (Nesprin-1), KIF26B, HABP2 (R² = 20.2%), and HMCN1. 🔍 Open High-Res PNG
Nano Banana Biological Illustration: Cortical Excitatory-Inhibitory Synapse and Ion Channels
Biological Pathway Illustration 1 (Nano Banana). Cortical Excitatory–Inhibitory Synapse, Axon Initial Segment Voltage-Gated Ion Channels (SCN1A, SCN8A, KCNQ2, KCNB1, CACNA1A/B/H), SNARE Vesicle Exocytosis (STXBP1, ITSN2), Synaptic Cleft GABA Reuptake (SLC6A1/GAT-1) & LGI1 Bridge, and Postsynaptic GABAA (GABRB3, GABRA1) & NMDA/Ras-GAP Signaling (GRIN2D, SYNGAP1, TANC2) (32.3× Enriched in Epi25 Exome). 🔍 Open High-Res PNG
Figure 8: Quantitative Cortical Synapse and Ion Channel Schematic
Figure 8. Quantitative Molecular Architecture & Discovery Gain Across Axon Initial Segment Cation Channels, Presynaptic SNARE Exocytosis, GABAergic Inhibition, and Postsynaptic Density Scaffolds Across DEE, NAFE, GGE, and EPI. 🔍 Open 300-DPI PNG
Nano Banana Biological Illustration: GATOR1-mTORC1, Chromatin Remodeling, and Neurovascular Architecture
Biological Pathway Illustration 2 (Nano Banana). Lysosomal GATOR1 Complex & mTORC1 Restraint in Focal Epilepsy (DEPDC5, NPRL3), Neuronal Chromatin Remodeling (CHD2, ANKRD11, SETD1B, KANSL1, NCOR1, TBL1XR1, KDM4A/5B, SP4), Blood–Brain Barrier Solute Transport (SLC2A1/GLUT1, SLC4A5, SLC25A11, ARV1), and Neuro-Immune Alarmin, Perineuronal ECM & Nuclear LINC Cytoskeletal Architecture (AGER/RAGE, SERPINI2, TRIO, VPS13B, MACF1, SYNE1/2, HSPG2, HMCN1, FRAS1). 🔍 Open High-Res PNG
Figure 9: GATOR1-mTORC1, Chromatin Remodeling, and Neurovascular Architecture Map
Figure 9. Quantitative Pathway Map of Lysosomal GATOR1–mTORC1 Nutrient Sensing, Neuronal Chromatin Remodeling, Blood–Brain Barrier Transport, and Neuro-Immune/Cytoskeletal Loci Across Epilepsy Syndromes. 🔍 Open 300-DPI PNG

4B. Relationship Between Ultra-Rare Unified M7 −log10(p-value), Explained Variance (R²), and Gene Size (Amino Acids, LAA) at AF ≤ 0.0001

Across 67,022 ultra-rare gene–phenotype tests at AF ≤ 0.0001, canonical protein length LAA correlates linearly with ultra-rare coding variant count Mg (r = +0.908, ≈0.239 variants/AA), while exhibiting virtually zero correlation with −log10(pM7) (Pearson r(log10AA) = +0.0915, Spearman ρ = +0.0707) and an inverse critical variance law R²crit(LAA) ≈ 31.8 / (0.239 LAA + 27.8) where compact synaptic and channel genes (≤800 AA) achieve massive variance explained (R² = 20–64%).

Figure 10: M7 -log10(p) vs Gene Size in Amino Acids at AF <= 0.0001
Figure 10 (Ultra-Rare AF ≤ 0.0001). 4-Panel Analysis of Unified Model M7 Significance (−log10 pM7), Explained Variance (R²), and Canonical Protein Length in Amino Acids (LAA, GENCODE v44). 🔍 Open 300-DPI PNG

4C. Unbiased Size-Restricted Pathway Enrichment of Compact Proteins (LAA < 2,000 AA) & Add-Back Comparison — AF ≤ 0.0001

Strictly unbiased over-representation and competitive enrichment across all 9,953 pre-defined ontology gene sets (GO, Reactome, KEGG, WikiPathways) restricted to the exact tested universe of proteins with LAA < 2,000 amino acids (17,130 / 17,572 = 97.48% of tested genes), with exact Poisson-Binomial adjustment for gene length log10(LAA) and variant count log10(Mg), plus head-to-head comparison when adding back LAA ≥ 2,000 AA (which unlocks SCN1A [2,009 AA], CACNA1A [2,506 AA], CACNA1B [2,339 AA], and RYR2 [4,967 AA]). Switch between ALL, DEE, GGE, NAFE, and EPI below.

Epilepsy Syndrome Cohort:
Exact Tested Universe (< 2,000 AA)
17,130 / 17,572 (97.48%)
Exact tested protein-coding universe (zero external genome-background bias)
Significant Genes (< 2,000 AA — ALL)
44 / 55 (80.0%)
Median protein length = 735 AA (< 2,000 AA) vs. 3,144 AA (≥ 2,000 AA)
Explained Variance R² (< 2,000 AA vs ≥ 2,000 AA)
26.55% vs. 4.61% (5.76×)
Compact < 2,000 AA significant genes explain 5.8× more variance per gene
Top Unbiased Length-Adjusted Pathway
Inorganic Anion Transport (20.6×)
Exact Poisson-Binomial length-adjusted p = 6.24e-5 (SLC6A1, GABRB3, GABRA1, SLC25A11)

Unbiased Exact-Universe & Length-Adjusted Ontology Enrichment (LAA < 2,000 AA — Cohort: ALL)

Ontology Pre-Defined Pathway / Ontology Term Hits / Tested (Expunadj → Explen) Length-Adjusted OR (plen-adj) Exact Fisher OR (pFisher) Comp. Z (pcomp) Med Hit R² Active Significant Epilepsy Genes (with Canonical AA Length)

Head-to-Head Comparison: What Happens When We Add Back Genes with LAA ≥ 2,000 AA? (< 2,000 AA vs. All Protein Lengths)

In Epilepsy, pore-forming voltage-gated Na+ and Ca2+ channel α1-subunits lie just above 2,000 AA (SCN1A [2,009 AA], SCN5A [2,015 AA], CACNA1B [2,339 AA], CACNA1A [2,506 AA], RYR2 [4,967 AA]), so adding back LAA ≥ 2,000 AA strongly amplifies Regime I (Calcium & Sodium Channel, GABAergic Synapse & Dravet Pathways) even after strict Poisson-Binomial length control, while Regime III (GATOR1–mTORC1 in NAFE, Compact GABAA & Chromatin Modules) is 100% invariant.

Ontology Pathway Term Add-Back Regime Hits: <2k → All AA (+≥2k) Length-Adj OR (plen): <2k → All AA Unadj Fisher OR (pFish): <2k → All AA Comp. Z: <2k → All Added ≥ 2,000 AA Genes (Rose) & Retained < 2,000 AA Genes (Blue)

Top Exome-Wide Significant Compact Genes (LAA < 2,000 AA) in Selected Epilepsy Cohort — Click Any Row to Inspect

Gene Cohort Length Unified pM7 R² (M7) Partial R² Decomposition (AlphaMissense / pLoF / Constraint)

Functional System Classification Breakdown: Compact (< 2,000 AA) vs. Large (≥ 2,000 AA) Loci in Selected Cohort (Click Any Card to Filter Gene Table)

5. Variant-Level WLS Meta-Regression Profile Viewer

Inspect individual rare coding variants (sized by inverse-variance weight wi = 1/SEi²), showing how Firth 2×2 penalized-likelihood log-odds ratios covary with AlphaMissense pathogenicity, pLoF status, and WES HMM mutational constraint.

6. Interactive Gene-Level Results Table (Omnibus P, Length-Invariant R², Moderator Slopes β & Benchmark Δlog-OR)

Click any column header or use the Ranking Strategy selector below to rank genes by Omnibus p-value, Gene-Length-Invariant Explained Variance (R²M7), Empirical Bayes Shrunk Moderator Slopes (β̂kEB) / 95% Lower Confidence Bounds (β̂kLCB), or Composite Benchmark Pathogenic Variant Effect (Δlog-ORbench). Selecting an effect-size ranking automatically applies the Stage-1 Exome-Wide Significance Gate (p < 3.0×10−7).

Gene ↕ Group ↕ Length (AA) ↕ Nvar ↕ pLoF / Mis M5: AM+LoF ↕ M7: AM+LoF+Con ↕ R² (M7) ↕ Δlog-ORbench (OR) ↕ β̂AMEB (Raw) ↕ pAM (R²AM) ↕ β̂LoFEB (Raw) ↕ pLoF (R²LoF) ↕ β̂ConEB (Raw) ↕ pCon (R²Con) ↕ Browser min p ↕

7. Publication-Quality Figures (300 DPI — Click Any Figure to Open Full-Resolution PNG)

All 12 figures from the collinearity-free Epi25 meta-regression and biological pathway analysis are embedded in the PDF manuscript and displayed below.

Figure 1: Stepwise Model Progression
Figure 1. Collinearity-Free Stepwise Discovery Progression Across Models M1–M7. 🔍 Open 300-DPI PNG
Figure 2: Unified vs Browser AF 0.0001
Figure 2. Ultra-Rare Variant Meta-Regression (AF ≤ 0.0001, 100% Firth 2×2 Rescue) vs. Epi25 Browser Burden Masks. 🔍 Open 300-DPI PNG
Figure 3: Moderator Trajectories
Figure 3. Stepwise Moderator Trajectories Across Collinearity-Free Models (M1 → M7) for Flagship Epilepsy Genes. 🔍 Open 300-DPI PNG
Figure 4: Orthogonal Partial R2 Decomposition
Figure 4. Ultra-Rare Concordance and True Orthogonal Moderator Partial R² Decomposition. 🔍 Open 300-DPI PNG
Figure 5: SCN1A, KCNQ2, STXBP1, and DEPDC5 Variant Profiles
Figure 5. Variant-Level WLS Meta-Regression Profiles for SCN1A, KCNQ2, STXBP1, and DEPDC5 Across Epilepsy Syndromes. 🔍 Open 300-DPI PNG
Figure 6: Ultra-Rare Pathway Enrichment Network
Figure 6. Ultra-Rare (AF ≤ 0.0001) Multi-Database Pathway Enrichment (DisGeNET / GO / WikiPathways / Reactome / HPO) and Functional Module Breakdown Across DEE, NAFE, GGE, and EPI. 🔍 Open 300-DPI PNG
Figure 7: Quantitative Cortical Synapse and Ion Channel Schematic
Figure 7. Quantitative Molecular Schematic of Axon Initial Segment Cation Channels, SNARE Vesicle Fusion, GABAergic Inhibition, and Postsynaptic Density Scaffolds. 🔍 Open 300-DPI PNG
Figure 8: GATOR1-mTORC1, Chromatin Remodeling, and Neurovascular Architecture Map
Figure 8. Lysosomal GATOR1–mTORC1 Focal Epilepsy Architecture, Neuronal Chromatin Remodeling, Blood–Brain Barrier Transport, and Neuro-Immune/Cytoskeletal Loci. 🔍 Open 300-DPI PNG
Figure 9: M7 -log10(p) vs Gene Size in Amino Acids at AF <= 0.0001
Figure 9. Ultra-Rare (AF ≤ 0.0001) Relationship Between Unified Meta-Regression Significance (−log10 pM7), Explained Variance (R²), and Canonical Protein Length in Amino Acids (LAA). 🔍 Open 300-DPI PNG
Figure 11: Nano Banana Cortical Synapse and Ion Channels
Figure 11 (Nano Banana Biological Illustration). Cortical Excitatory–Inhibitory Synapse, Axon Initial Segment Voltage-Gated Ion Channels, SNARE Vesicle Fusion, and GABA/NMDA Receptor Architecture in Epilepsy. 🔍 Open High-Res PNG
Figure 12: Nano Banana GATOR1, Chromatin & Neuro-Immune Architecture
Figure 12 (Nano Banana Biological Illustration). GATOR1–mTORC1 Nutrient Sensing, Neuronal Chromatin Remodeling, Blood–Brain Barrier Solute Transport, and Neuro-Immune/Cytoskeletal Architecture in Epilepsy (Epi25). 🔍 Open High-Res PNG

8. Acknowledgements & Data Resources

Author: Manuel A. Rivas (Department of Biomedical Data Science, Stanford University, Stanford, CA, USA 94305).

Epi25 Exome Sequencing Browser (https://epi25.broadinstitute.org) & Epi25 Collaborative: In accordance with the citation and acknowledgement requirements of epi25.broadinstitute.org, we cite the consortium's primary publication, “Exome sequencing of 20,979 individuals with various epilepsies reveals 26 risk genes” (Epi25 Collaborative / Chen et al., Nature Neuroscience 27, 1864–1879, 2024; doi:10.1038/s41593-024-01747-8), and provide a link to the browser (https://epi25.broadinstitute.org; public data download Epi25_variant_results.tsv.bgz).

“The authors would like to thank the Epi25 Collaborative and the individual study teams that contributed to this resource. A full list of Epi25 collaborators can be found at epi-25.org.”

The Epi25 Collaborative is a global collaboration committed to sequencing and deep-phenotyping patients with epilepsy to advance gene discovery across Developmental and Epileptic Encephalopathies (DEE), Genetic Generalized Epilepsy (GGE), and Non-Acquired Focal Epilepsy (NAFE), supported by the National Human Genome Research Institute (NHGRI) Centers for Common Disease Genomics (CCDG) program (grant UM1 HG008895) and the Stanley Center for Psychiatric Research at the Broad Institute of MIT and Harvard.

Functional Annotation, Constraint & Meta-Regression Framework: We thank Google DeepMind (Cheng et al., Science 2023) for proteome-wide AlphaMissense pathogenicity predictions, Aguilar, Rivas & Rivas (medRxiv 2025; wgs-constraint-llm; 10.1101/2024.06.27.24309590) and Lauer & Rivas (bioRxiv 2025; 10.1101/2025.01.23.634522; PMID: 39896616) for base-pair resolution WES hidden Markov model mutational constraint probabilities and the unified rare-variant meta-regression methodology, and the GENCODE Consortium (Frankish et al., Nucleic Acids Research 2021) for human reference gene annotations.