Protein folding scoping for srmech — 2026-05-09 cross-domain absorption round

Round: Protein folding (NMA / GNM / ANM / contact-map / coevolution / AlphaFold-era) Date: 2026-05-09 Method: Dual-agent research pattern (feedback_dual_agent_research_pattern.md)

Headline findings

1. GNM / ANM / NMA on the residue-interaction network is graph-Laplacian eigendecomposition. Literally the same primitive ephemerides-spectral uses on the 52-body resonance graph (§13 gateway-graph Fiedler partition; Matthews φ = +0.336, Spearman ρ = +0.743 vs empirical Δv). Same math, different graph. Not analogy — identity. Strongest cross-domain validation evidence to date that srmech's manifold-parameterised Laplace-Beltrami framing (§3.5) is load-bearing rather than aesthetic.
2. Helmholtz wave on residue interaction network = NMA harmonic time evolution. g(λ_k) = cos(c·t·√λ_k) where √λ_k = ω_k (vibrational frequency from Hessian eigenvalues). The §4.1 "Helmholtz wave" row from the absorption brief is the harmonic time evolution of vibrational modes on a protein. Same equation; not metaphor.
3. Protein contact / distance map = 2D image. Heat-kernel blur, Perona-Malik bilateral, DoG, Varadhan SDF, anisotropic-tensor, power-spectrum noise — all graphics primitives port verbatim. Perona-Malik on contact map preserves α-helix and β-sheet diagonal-band structure precisely because Perona-Malik preserves edges (state-dependent diffusion); biologically meaningful primitive.
4. Ramachandran (φ, ψ) torus T² = §3.5 torus row instantiated. First non-graphics use of the flat torus row. Same λ_{m,n} = m² + n² Fourier eigenvalues.
5. Protein surface = §3.5 sphere S² and triangle-mesh rows. Globular proteins approximate genus-0 sphere → spherical harmonics with λ = l(l+1) (3D Zernike, ZAFCM shape descriptors). Solvent-accessible-surface mesh → cotangent Laplacian; heat-kernel signature (Sun-Ovsjanikov-Guibas) is direct port of Varadhan SDF framework.
6. Foldseek 3Di alphabet = SkPhase9BIP structural cousin. 20-letter learned structural alphabet (VQ-VAE on protein structure). Cyclic-group-amenable; drop-in HDC binding analogue. The strongest non-text discrete-alphabet HDC fit outside chess + ephemerides.
7. Sheaf-Laplacian on RIN ↔ doom-spectral §3 sheaf-Laplacian raycasting. Each residue's local frame (rotamer state, local environment) is a stalk; RIN edges are restriction maps. Sheaf cohomology over RIN is a real research direction. Cross-pollination with doom-spectral, not just graphics.
8. AMSC binary_archive scaling forcing function. AlphaFold DB ~25 TB; ESM Atlas ~100 TB (via ~600M predicted structures). 4000–20000× larger than JPL DE441 (~5 GB). Forces binary_archive adapter to mature: streaming-download, partial fetch, content-addressed deduplication. Forcing function for AMSC design beyond ephemerides scope.
9. Config-vs-substrate ratio inverts to ~20/80. Closed-form menu (NMA / GNM / contact-map smoothing / Ramachandran T² priors / surface heat-kernel signatures / coevolution Potts) is meaningful but the actual computational work is substrate-dominated: molecular dynamics, AlphaFold / ESMFold / RoseTTAFold, Rosetta abinitio, Monte Carlo, replica-exchange, ligand docking. Calibration update for §4.2 — config/substrate ratio is domain-dependent, not a fixed 80/20.
10. EMDR-project connection: none direct. Protein folding is a cross-domain stretch test for srmech's universality, not a productisation target. Honest framing.

Operator counts

• Manifolds: 22 (main) / 22 (sub) — backbone dihedral T² / side-chain rotamer T^k / RIN graph / contact map 2D / distance map / Cα polymer 1D / 3D Cartesian / internal coords / energy landscape / folding funnel / sequence space / MSA latent / AlphaFold pair-rep / PPI graph / surface mesh / spherical projection / topology graph / ensemble config space / fragment library / DSSP alphabet / β-sheet topology / allosteric network
• Transforms: ~18 — graph-Laplacian on RIN (GNM), Hessian (ANM, full atomistic NMA), 2D Fourier on T², spherical harmonics, mesh Laplacian, PCA / tICA / diffusion maps on ensemble, DCA / mfDCA / plmDCA / GREMLIN / EVcouplings on coevolution, wavelets on Cα, fragment-library projection, DCT-II/III on contact map, Plate-style HRR, sheaf-Laplacian, KLT on aligned ensemble
• Closed-form g(λ) operators: 50+ (main) / 43 (sub-agent numbered) across thematic groups: NMA / mode-propagation family (B-factor prediction, slow-mode reconstruction, mean-square fluctuation, cross-correlation matrix, allosteric perturbation response, domain decomposition / Fiedler partition, hinge-residue identifier, vibrational entropy, mode-coupling, Einstein heat-capacity); contact-map smoothing family (heat-kernel blur, sharpen, DoG, Varadhan SDF, anisotropic, Helmholtz wave, power-spectrum noise, log-normal); Ramachandran T² family (density smoothing, log-prior, band-pass, Kramers' transition rates, harmonic basis fit); coevolution / DCA family (contact prediction, spectral DCA denoising, APC); PCA / ensemble family (essential dynamics, tICA, RMSIP, quasi-harmonic free energy, diffusion-map embedding); Cα-polymer family (smoothing, high-pass, curvature spectrum); surface family (3D Zernike, HKS, WKS, SES smoothing); coarse-graining family (MARTINI-style spectral, RG block-spin, mixed-resolution NMA)
• Substrate primitives: 25+ — MD (Amber / GROMACS / NAMD / OpenMM / CHARMM), Langevin, Brownian, REMD / T-REMD / H-REMD, metadynamics, umbrella sampling, MSM, MC (Metropolis / Wang-Landau), Rosetta abinitio + relax, AlphaFold⅔, ESMFold / OmegaFold / RoseTTAFold / RoseTTAFold-AllAtom, SCWRL4 / OPUS-Rota, MODELLER, loop modeling (KIC), AutoDock Vina / Glide / DiffDock, HADDOCK / pyDock / AlphaFold-Multimer, FEP / TI, polarisable force fields (AMOEBA), implicit solvent (GB/SA), steered MD, NMR structure determination (CYANA / ARIA), cryo-EM reconstruction (RELION / cryoSPARC), reaction-diffusion fold prediction (legacy 1980s), Cahn-Hilliard fold-domain separation, QM/MM
• HDC cyclic groups: Z₂₀ amino-acid alphabet (caveat: bag with metric structure, not pure cyclic — bind via random projection), Z_64 codon table (degeneracy mapping to Z_20 as sheaf projection), backbone (φ, ψ) on T² (genuine cyclic), side-chain χ-tuples on T^d, secondary-structure 3-letter / 8-letter (DSSP) alphabets, Foldseek 3Di alphabet (20-letter structural — strongest non-text fit), Plate-style HRR for sequence binding, k-mer / window binding, structural-fragment binding (Rosetta 9-mer / 3-mer)

Cross-pollination with already-absorbed srmech primitives

§3.5 cross-manifold table extends — protein instantiation column:

Manifold	Protein instantiation
Euclidean grid + Neumann BC	Distance map; contact map
Sphere S²	Globular protein surface (genus-0 topology)
Flat torus T²	Ramachandran (φ, ψ) backbone dihedrals
Triangle mesh	Solvent-accessible surface mesh
General graph	Residue-interaction network — primary protein structure manifold; GNM / ANM / NMA live here

Direct primitive ports (graphics → contact map):

• Heat-kernel blur on contact map → smooth predicted contact maps from coevolution; clean noisy AlphaFold pair logits
• Perona-Malik on contact map → preserves α-helix (long stretches of i, i+3, i+4 contacts) and β-sheet (long off-diagonal stretches) while smoothing intra-domain noise
• DoG on contact map → fold boundary detection (where contact density transitions intra-domain → inter-domain)
• Sharpen / band-pass on contact map → emphasises secondary-structure boundaries
• Anisotropic-tensor on contact map → smooth along sequence direction differently from off-diagonal long-range contacts; preserves diagonal-band α-helix structure
• Helmholtz wave on RIN → allosteric perturbation propagation as standing waves (NMA in time domain — same equation)
• Power-spectrum noise on RIN → log-normal-distributed per-residue properties (B-factor, conservation, accessibility)
• Varadhan SDF analogue → reverberation-time-from-RIR-to-distance-to-reverb-tail-onset structurally identical to heat-kernel-decay-to-distance for graphics SDF

Cross-pollination with non-graphics srmech projects:

• GNM/ANM Fiedler partition ↔ ephemerides §13 gateway-graph Fiedler partition. Identical math; same architectural slot. Quantitative ephemerides results (Matthews φ = +0.336; Spearman ρ = +0.743 vs Δv) suggest the protein-domain Fiedler analysis would yield comparable predictive power for dynamic-domain identification.
• Sheaf-Laplacian on RIN ↔ doom-spectral §3 sheaf-Laplacian raycasting. Stalk = local residue frame; restriction maps = RIN edges.
• HDC sequence binding ↔ chess BIP / ephemerides BIP / SkPhase9BIP. Foldseek 3Di alphabet is the closest structural cousin.

AMSC ingestion paths

literature_curated

Ramachandran 1963 + revisions (Lovell 2003 top-8000), DSSP secondary-structure dictionary (Kabsch-Sander 1983), STRIDE secondary structure (Frishman-Argos), rotamer libraries (Dunbrack 2011, SCWRL4), force-field parameters (AMBER ff14SB / ff19SB, CHARMM36m, GROMOS 54A7, OPLS-AA / OPLS-AA/M), BLOSUM matrices (45 / 50 / 62 / 80 / 90), PAM matrices (Dayhoff series), substitution matrices (JTT / WAG / LG), Chou-Fasman propensities, hydrophobicity scales (Kyte-Doolittle, Hopp-Woods, Eisenberg, Wimley-White), disorder predictor tables, CATH / SCOP / SCOPe / ECOD fold classifications, Pfam / InterPro family definitions, EC enzyme classification, GO annotations, OPM membrane orientations, Atchley factors (5D PCA), genetic-code table, Foldseek 3Di alphabet centroids, BLOSUM / PAM matrices.

binary_archive

Source	Scale	Format
Protein Data Bank (PDB)	~220K experimental structures, ~50 GB compressed / ~500 GB uncompressed	PDBx / mmCIF
AlphaFold Database	~214M predicted structures, ~25 TB	mmCIF + pLDDT
ESM Atlas / MGnify3D	~617M predicted structures, ~100 TB	structure + confidence
UniProt (TrEMBL + Swiss-Prot)	~250M sequences, ~250 GB	FASTA
MGnify metagenomic	~2.5B sequences, ~2.5 TB	FASTA
BFD (Big Fantastic Database)	~2.5B clustered MSAs, ~270 GB	FASTA
MSA databases per UniRef cluster	precomputed alignments	various
CASP archives (CASP7–CASP16)	targets + models + evaluations, ~10 GB	various
SCOP / SCOPe / CATH	domain-classification trees, ~500 MB	versioned
Pfam / InterPro	family HMMs + signatures, ~3 / 30 GB	HMMER
Foldseek / MMseqs2 indices	precomputed alignment indices, ~50–500 GB	binary
Rosetta fragment libraries	per-target ~10 MB	text
EMDB cryo-EM density maps	~30K maps	MRC
Crystallographic structure factors	per-PDB diffraction data	various
MD trajectory databases	Folding@home, GPCRmd, MoDEL, MemProtMD	various
Mutation effect databases	ProTherm, HumSavar, ClinVar	various
Drug-target interaction databases	ChEMBL, BindingDB, PDBbind	various

csv_bulk / json_api

UniProt API (REST + SPARQL), Ensembl / NCBI Gene / KEGG, PDBe API, AlphaFold REST, ESM Atlas API.

Scale comment: AlphaFold DB at 25 TB and ESM Atlas at 100 TB are the largest binary archives the project would touch. Per-structure lazy retrieval via REST is probably right; don't pre-mirror at this scale. Per-protein hypervector precompute (Path D pattern: spectral index over heavy store) is structurally preferable for similarity search.

Honest project-mission assessment

Direct EMDR-pulser connection: none. Protein folding has zero overlap with bilateral haptic therapy. Don't force a connection.

What this round genuinely earns srmech:

1. Validates the cross-manifold framing empirically. Protein NMA literally is the ephemerides Fiedler-partition primitive on a different graph. Universal-claim survives the most demanding stretch test.
2. Forces AMSC binary_archive maturation. 25 TB / 100 TB scales force streaming-download, partial fetch, content-addressed dedup design earlier than ephemerides DE441 alone would.
3. Calibration update for §4.2. 80/20 is graphics+audio; 20/80 is proteins. Architectural framing must accommodate both ratios.
4. Path D pattern more relevant than Path C in substrate-dominated domains. Spectral index over heavy store > full unification of computation.
5. HDC sister application. Foldseek 3Di alphabet → Phase3DiBIP similarity-search service is a clean Path D demo (separate from EMDR device).

Tenuous-but-honest stretches (don't force these):

• UTLP for distributed MD — distributed MD already has well-developed infrastructure; UTLP overkill for fs/ms timesteps.
• Drug-discovery cross-cut — possible long-term direction, irrelevant to EMDR therapy device.
• Therapeutic-monitoring / patient-genomic correlation — multi-year horizon if at all.

First-principles cautions (framework-edge)

• Hessian vs Laplacian: distinct operators on the same graph. GNM uses Kirchhoff matrix (1D scalar springs); ANM uses 3N×3N anisotropic Hessian (3D vector springs along contact directions); NMA uses full atomistic Hessian. They share the graph but differ in the operator — different λ_k, different eigenvector structure. The (Transform, λ_k, g) decomposition needs to track which operator is meant.
• Residue interaction graph definition is non-canonical. Cα-Cα cutoff (8 Å, 10 Å, 15 Å variants) gives different graphs.
• Coarse-graining levels. Per-atom, per-residue, per-domain graphs all valid; eigenvalue interpretations differ.
• Protein topology is not closed S² in general. Globular proteins approximate sphere; membrane proteins, fibrous, IDPs, complexes don't.
• 20-amino-acid alphabet is not cleanly cyclic. HDC binding via random projection rather than cyclic shift, unlike audio Z₁₂.
• AlphaFold confidence (pLDDT, PAE) is itself a substrate output. Treating as ground truth for downstream operations is iffy; catalogue should attest source.
• Ensemble vs single-structure semantics. PDB entry may be one X-ray structure or 20 NMR models; catalogue must specify.
• Time scales are enormous. Vibrational ps, side-chain ns, loop μs, domain ms, folding s-min, evolution 10⁶ years — different spectral analysis applies at each.
• Allostery is intrinsically state-dependent. Pure-spectral g(λ) cannot capture conformational coupling that depends on ligand binding; substrate-primitive territory.

Comparison: main-agent vs sub-agent

Dimension	Main-agent (with conversation context)	Sub-agent (independent fresh-read)
Manifold count	22	22 (very close convergence)
Closed-form ops	50+	43 (numbered explicitly 1–43)
Substrate ops	25	25 (numbered explicitly 1–25)
Citation specificity	Loose	Strong — Bahar-Atilgan-Erman 1997 (GNM B-factor), Holm-Sander 1996 (Fiedler), Sun-Ovsjanikov-Guibas (HKS), Kabsch-Sander 1983 (DSSP), Lovell 2003
Ephemerides §13 quantitative parallel	Vague	Specific — Matthews φ = +0.336, Spearman ρ = +0.743 vs Δv
Sheaf-Laplacian → doom-spectral cross-link	Missed	Caught
20/80 inversion as framework calibration update	Missed	Caught + framed as meta-level insight
Reaction-diffusion fold-prediction historical context (1980s pre-AlphaFold)	Missed	Caught
Helmholtz wave on RIN = NMA (sharp identity claim)	Caught ("literally the same equation, not metaphor")	Stated but less sharp
Cyclic-group purity caveat for amino acids	Caught ("Z_20 is bag with metric structure, not clean cyclic")	Glossed (treated Z_20 as cyclic-group binding)
First-principles cautions as structured section	§10	Distributed
Time-scale enumeration (ps / ns / μs / ms / s / 10⁶y)	Caught	Light treatment
AMSC binary_archive maturation forcing function	Caught	Sharper framing
Path D index-over-heavy-store relevance	Implicit	Named explicitly for protein similarity search

Convergent core (both reached independently): all 10 headline findings above. Highest convergence of the three rounds (graphics absorption / audio / protein).

Takeaways landed in master srmech notebook

• §3.5 cross-manifold table: protein instantiation column added; explicit identity claim "GNM/ANM/NMA on RIN = ephemerides 52-body Fiedler partition primitive — not analogy, identity"
• §4.2 calibration: 80/20 (graphics, audio) vs 20/80 (protein) ratio variation by domain
• §5.3 absorption-round subsection: headline findings + link to this file
• §1.5 future-notebook candidates: protein-spectral row added (status: scoped, strongest cross-domain validation evidence to date, no direct EMDR-project connection)