Parameter‑Free DNA Mechanics and Transcription Kinetics from a Single 0.090 eV Quantum
Recognition Physics Institute, Austin, Texas, USA
Summary
A minimal recognition principle fixes a golden‑ratio cascade $r_n=L_{P}\,\varphi^{n}$ and a single coherence quantum $E_{\mathrm{coh}}=0.090$ eV. With no tuned energetic parameters, this constant alone predicts B‑DNA geometry and elasticity and the kinetics of RNA polymerases, including invariant pause lifetimes and force–velocity behavior.
Abstract
The cascade selects the canonical minor‑groove width (13.6 Å) and helical pitch (34.6 Å). A quadratic fluctuation expansion yields bending and twist persistence lengths ($A\approx56$ nm, $C\approx72$ nm at physiological salt) after standard electrostatic corrections. Polymerase translocation follows an integer‑quantum gate: multi‑subunit RNAPs use $n^\star=3$ and T7 uses $n^\star=2$, fixing activation energies and the Arrhenius slope. A drag‑limited law sets a ceiling near 50 bp s$^{-1}$ and reproduces stall forces (∼14 pN multi‑subunit; 25–30 pN T7) without altering $E_{\mathrm{coh}}$. Pausing emerges from fixed escape barriers $2E_{\mathrm{coh}}$ and $\tfrac{5}{2}E_{\mathrm{coh}}$, giving invariant lifetimes of ∼1 s and ∼10 s across enzymes; sequence modulates entry via nascent‑RNA hairpin $\Delta G$.
Key Results
- Golden‑ratio cascade: $r_n=L_{P}\,\varphi^{n}$ → minor groove 13.6 Å; pitch 34.6 Å
- Elasticity: $A\approx56$ nm; $C\approx72$ nm (with salt correction); predicts $1/T$ scaling at fixed ionic strength
- Integer‑quantum gating: $n^\star=3$ (multi‑subunit), $n^\star=2$ (T7); activation energies 0.27 eV / 0.18 eV
- Force–velocity: drag‑limited law; ceiling ∼50 bp s$^{-1}$; stalls ∼14 pN (multi‑subunit), 25–30 pN (T7)
- Pauses: invariant lifetimes 1 s / 10 s from fixed escape barriers; sequence controls entry via hairpin $\Delta G$
Implications
DNARP collapses historically empirical DNA/transcription phenomenology to a deterministic core: one universal quantum, integer gates, and benign per‑enzyme drag/prefactor fits. It makes crisp predictions: cross‑enzyme force–velocity collapse in reduced units, $1/T$ scaling of $A$ and $C$, and a pump–probe sideband at $3E_{\mathrm{coh}}$.