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Mutation in DNA: A quantum mechanical non-adiabatic model

Hossien Hossieni

TL;DR

This work tackles the problem of quantifying DNA mutation probability arising from proton-transfer tautomerization in the Adenine–Thymine base pair using quantum mechanics. It builds an analytical Adenine–Thymine potential with an asymmetric double-well and solves the 1D Schrödinger equation to obtain proton eigenstates, then introduces a nonadiabatic barrier-collapse scenario to estimate right-well occupation probabilities. The key findings show ground-state mutation probabilities of about $1.56\times10^{-6}$ and excited-state probabilities of about $5.34\times10^{-4}$, aligning with experimental mutation ranges and supporting a nonadiabatic mechanism for tautomerization-driven mutations. The approach links tautomerization, ultrafast nonadiabatic dynamics, and observed mutation rates, offering a tractable analytical framework with implications for IR-triggered proton transfer in DNA.

Abstract

We propose a new analytical potential function to model proton transfer in the adenine-thymine base pair and develop a non-adiabatic quantum mechanical framework to calculate genetic mutation probabilities. This potential has been used to calculate the probability of mutation in a non-adiabatic process. The results of the new model have been shown to be consistent with the findings of other researchers.

Mutation in DNA: A quantum mechanical non-adiabatic model

TL;DR

This work tackles the problem of quantifying DNA mutation probability arising from proton-transfer tautomerization in the Adenine–Thymine base pair using quantum mechanics. It builds an analytical Adenine–Thymine potential with an asymmetric double-well and solves the 1D Schrödinger equation to obtain proton eigenstates, then introduces a nonadiabatic barrier-collapse scenario to estimate right-well occupation probabilities. The key findings show ground-state mutation probabilities of about and excited-state probabilities of about , aligning with experimental mutation ranges and supporting a nonadiabatic mechanism for tautomerization-driven mutations. The approach links tautomerization, ultrafast nonadiabatic dynamics, and observed mutation rates, offering a tractable analytical framework with implications for IR-triggered proton transfer in DNA.

Abstract

We propose a new analytical potential function to model proton transfer in the adenine-thymine base pair and develop a non-adiabatic quantum mechanical framework to calculate genetic mutation probabilities. This potential has been used to calculate the probability of mutation in a non-adiabatic process. The results of the new model have been shown to be consistent with the findings of other researchers.
Paper Structure (4 sections, 13 equations, 9 figures)

This paper contains 4 sections, 13 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Adenine-Thymine Potential
  3. A Non-Adiabatic Quantum Mechanical Model for DNA Mutation
  4. Conclusion

Figures (9)

  • Figure 1: The Adenine-Thymine potential curve from Eq.\ref{['ch3eq4']} shows an asymmetric double-well potential, indicating the energy difference between A--T and its tautomer $A^{*} - T^{*}$. At the bottom of the wells, the proton is stable but at different energy levels. The central barrier is slightly shifted from $\zeta = 0$, reflecting the inequality in energy levels. The curve is scaled from $eV$ to cm$^{-1}$ using a factor of 8065.73. Reused from Godbeer2015. Licensed under a CC-BY-3.0 License.
  • Figure 2: Variation of the adenine–thymine potential obtained analytically Sitnitsky2017 and by fitting Godbeer2015. The symbol of the horizontal axis represents both $\zeta$ and $x$ in Eqs. \ref{['ch3eq4']}and \ref{['ch3eq5']}, respectively. We set the values of the parameters in Eq.\ref{['ch3eq5']}$h = 70$, $a = 300$, $b = 850$ and $c=\sqrt{h}$.
  • Figure 3: The first thirty eigenstates of the analytical potential in Eq.\ref{['ch3eq5']} are shown, along with their corresponding energies $E_i \ (i=0,1,2...29)$ in cm$^{-1}$. The double-well potential is included to illustrate the spatial distribution of these states. These eigenstates are directly related to proton transfer, which is a key step in tautomeric mutations.
  • Figure 4: Comparison of the non-adiabatic potential (\ref{['ch3eq9']}) with the analytic double-well potential (Eq. \ref{['ch3eq4']}).
  • Figure 5: The first thirty eigenstates for the non-adiabatic process along with their energies $E_i (i=0,1,2,...29)$ in $cm^{-1}$. The non-adiabatic potential is also shown.
  • ...and 4 more figures