CRT Protein Folding Proxy

CRT approach to protein contact prediction over Z/214,414,200. CC0.

Protein structure prediction is dominated by neural networks with billions of parameters (AlphaFold, ESMFold). CRT approach: encode each amino acid's 7 physical properties into 7 CRT channels of Z/214,414,200. Contact prediction = channel coupling. Fold classification from channel averages. No training data. No GPU. No neural network. Just ring arithmetic on 20 amino acids.

How It Works

CRT Protein Contact Theorem
Each of the 20 amino acids maps to an element of Z/214,414,200 encoding 7 physical properties in 7 CRT channels: mod 8 = hydrophobicity, mod 9 = charge, mod 25 = size, mod 49 = H-bond capacity, mod 11 = aromaticity, mod 13 = backbone flexibility, mod 17 = secondary structure propensity. Contact between residues i and j is predicted by channel coupling: high hydrophobicity in both (mod-8 channel), opposite charges (mod-9 channel), or mutual aromaticity (mod-11 channel). 3+4 split: data channels (mod 8, 25, 49) = fold drivers. Parity channels (mod 9, 11, 13, 17) = fold validators.
20 amino acids
Ring elements
Each AA = one number in Z/214,414,200. Physical properties split across 7 channels.
7 interaction types
7 CRT channels
Hydrophobic, charge, size, H-bond, aromatic, flexibility, SS propensity. Independent.
Contact prediction
Channel coupling
High coupling in mod-8 + mod-11 channels = predicted contact. No neural network.
Fold classification
Channel averages
Channel averages determine structural class. mod-8 + mod-11 dominate.

Analyze Protein

Example (0-3):

Select example protein. CRT decomposes each residue into 7 channels, predicts contacts, classifies fold type.

All 20 Amino Acids

All 20 standard amino acids decomposed into 7 CRT channels. Physical properties are the channel values.

CRT vs Neural Network Folding

ParametersAlphaFold: 93M parameters, trained on 170K structuresCRT: 20 ring values. Zero training.ComputeGPU cluster, hours per predictionRing arithmetic, microsecondsChannelsAttention heads (opaque learned features)7 CRT channels = 7 named physical propertiesInterpretabilityBlack box: cannot explain WHY residues contactTransparent: mod 8=hydrophobic, mod 9=charge, mod 11=aromaticError detectionSeparate confidence scoresmod-11 channel gives free integrity checkPatent statusDeepMind/Google (AlphaFold), Meta (ESMFold)CC0. Public domain. Forever.

Source code · Public domain (CC0)

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