Protein Folding
Protein folding is the τ-categorical morphism that promotes a 1D τ¹-resident sequence (the τ¹ × T² mRNA→protein readout) into a 3D T² spatial structure. It is the information→structure bridge: the canonical map by which decoded code commits itself to a fiber-localized functional defect.
τ-Definition
Protein folding is the τ-categorical morphism that promotes a 1D τ¹-resident sequence (the τ¹ × T² mRNA→protein readout) into a 3D T² spatial structure. It is the information→structure bridge: the canonical map by which decoded code commits itself to a fiber-localized functional defect.
Categorical invariant. The τ-categorical promotion morphism (1D sequence on τ¹ × T²) → (3D conformation on T²); the dimensional lift in the central-dogma factorization (VI.P15) that turns codon output into spatial expression.
Primary registry anchor:
VI.D40
τ-Derivation Chain
Empirical Correlate
Biomarker: Native 3D structure (secondary: α-helix, β-sheet; tertiary: domain fold; quaternary: subunit assembly); free-energy minimum at native state; cooperative folding transition; chaperone-assisted folding for ~30% of proteome.
Measurable range: Folding times: ~µs (small fast folders, e.g. villin headpiece) to seconds (large multidomain proteins); native-state stability ΔG ≈ 5-15 kcal/mol; AlphaFold2 / AlphaFold3 structural prediction accuracy ≈ 1-2 Å RMSD on most CASP targets.
Observation method: X-ray crystallography (sub-Å resolution); cryo-EM (now < 2 Å for stable complexes); NMR (solution dynamics); AlphaFold/RoseTTAFold structure prediction; H/D exchange mass spectrometry (folding kinetics); single-molecule force spectroscopy.
Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel
Anchor chain:
- VI.L18 chirality channel
- L-amino acid α-carbon chirality (fixed by K_χ)
- right-handed α-helix as the only stable propeller given L-residues
- fold geometry as chirality-locked information→structure bridge
Manuscript reference: manuscript-sources/book-06/part04/ch27-genetic-code.tex
Lean Coverage
Status: Planned