DNA Proton Tunneling | mysimulator.uk

Base Pair

H-bond Potential

Barrier height V₀ 1.30

Tautomer asymmetry Δ 0.00

Isotope (proton mass)

Live State

Canonical 100%Rare tautomer 0%

Sim time τ

0.00

Tunneling period T

measuring…

⟨x⟩ proton position (well units, −1=canonical / +1=rare)

−1.00

How it works

A hydrogen bond N–H···N/O in a DNA base pair can be modelled as a single light proton moving in a double-well potential along the bond axis — one minimum at the normal ("canonical") position bonded to its usual partner, one minimum at the rare tautomeric position (an enol/imino shift) bonded the other way:

iħ ∂ψ/∂t = [ −ħ²/2m ∂²ψ/∂x² + V(x)ψ ]
V(x) = V₀·[(x/a)² − 1]² − Δ·x

The proton's ground state is not confined to one well: quantum mechanically it has a small overlap through the barrier, so a wavepacket started in the canonical well periodically tunnels into the rare-tautomer well and back — this is exactly the double-well tunneling-splitting effect. Löwdin (1963) proposed that if DNA replication happens to copy a base while its proton sits in the tautomeric well, the base mispairs with the wrong partner (e.g. a tautomeric G pairs with T instead of C), producing a point mutation at the next replication round. It remains a real, actively studied hypothesis — thought to be a small but genuine contributor to the spontaneous mutation rate, not the dominant one.

This simulator integrates the time-dependent Schrödinger equation exactly with the split-step Fourier method on a 256-point grid:

ψ ← e^(−iVΔt/2ħ) ψ
ψ̃ ← FFT(ψ);  ψ̃ ← e^(−iħk²Δt/2m) ψ̃;  ψ ← IFFT(ψ̃)
ψ ← e^(−iVΔt/2ħ) ψ

Base pair — sets the well separation and default barrier: G–C has 3 H-bonds and a shorter, stiffer bond (higher barrier) than A–T's 2 H-bonds.
Barrier height V₀ — how strongly the bond resists the proton crossing; a higher barrier exponentially lengthens the tunneling period.
Asymmetry Δ — the energy mismatch between the canonical and rare-tautomer wells; a larger mismatch generally suppresses how completely probability transfers across.
Isotope — swapping ¹H for ²H (deuterium) roughly doubles the tunneling mass, exponentially suppressing the rate. This kinetic isotope effect is exactly what D₂O-growth experiments use to test the tunneling-mutation hypothesis in real organisms.

All quantities use natural simulation units (ħ = 1); the physics — a real double-well Schrödinger equation solved exactly — is what matters, not a literal femtosecond scale.

Canonical well (base A) Rare-tautomer well (base B) Proton |ψ(x)|² density

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