Lab Notebook · Interactive

DNA Proton Tunneling Simulator

Double-proton tunneling in a G–C base pair, run as an open quantum system under environmental decoherence.

By KW Norton.

This page models the two-level asymmetric double well that holds a proton pair across the hydrogen bonds of a guanine–cytosine base pair, coupled to a Lindblad master equation for the surrounding cellular environment. The proton pair can transfer from the canonical form (G–C) to the mutagenic tautomeric form (G*–C*). The hydration shell and neighbouring nucleotides act as a thermal bath: they destroy coherent oscillation quickly and hold the populations at a quantum-thermal steady state.

Move the controls and the integration re-runs in the browser. Nothing is installed, nothing is sent anywhere.

Final tautomer population P*

2.261e-4

Simulated occupancy of the mutagenic G*–C* state at the end of the window.

Classical thermal limit

2.240e-4

What detailed balance alone would predict from the Boltzmann factor.

Excess over thermal limit

0.948%

Difference between the simulated steady state and the purely classical expectation.

Excitation rate γ_excite

2.24e-3 ps⁻¹

Upward rate fixed by detailed balance at the chosen temperature.

Time evolution of the proton states

On a linear axis the canonical state looks flat at 1. That is the point: the mutagenic state is rare. The second chart puts it on a logarithmic axis so the accumulation becomes visible.

Mutagenic accumulation, logarithmic scale

What the model rests on

  • Löwdin (1963). First proposal that spontaneous mutations can arise from double proton transfer across the hydrogen bonds joining base pairs, with the protons bypassing the classical barrier by tunneling.
  • Slocombe, Sacchi and Al-Khalili (2021, 2022). Open-quantum-system treatment in which canonical and tautomeric forms interconvert far faster than biological timescales and settle at a steady-state tautomer occupancy near 1.73 × 10⁻⁴.
  • Why the environment matters. An isolated two-level system would oscillate indefinitely. Strong coupling to the hydration shell suppresses coherence within roughly a picosecond and pins the populations to their equilibrium ratio.

Status: this is a teaching instrument, not a published calculation. The default parameter set reproduces the literature ballpark; the sliders let a reader see which parameter the result actually depends on. If moving a slider changes the conclusion, the conclusion was never load-bearing.