Quantum tunnelling in DNA
Tunnelling is a quantum phenomenon in which a particle is able to access a classically forbidden region. This often manifests as a “hopping” motion in which it appears that a particle has overcome an energy barrier which is greater than its kinetic energy. Studying quantum systems allows us to determine tunnelling rates and decide whether it is likely to happen.
In 1964, it was proposed by Per-Olov Löwdin  that quantum tunnelling can occur within the hydrogen bonds joining Watson-Crick nucleotide pairs. Since then, quantum tunneling has been explored as a mechanism at work in enzyme catalysis , olfaction , and other biological processes. Here at the Leverhulme Quantum Biology Doctoral Training Centre we use open quantum systems and density functional theory amongst other theoretical tools to make predictions about tunneling rates, and have experiments running in parallel to try and detect tunneling in the lab.
Mutations are a cause of cancer and genetic disease as well as being the driver of drug-resistance in cancer and infectious disease. Watson and Crick proposed that these spontaneous mutations arise through tautomerization of DNA bases, involving the tunnelling of protons. However, despite a great deal of theoretical support for their model, experimental evidence is scanty, mostly because of difficulties in mapping proton position in the DNA double helix.
This project will bring together expertise in quantum biology and chemistry available at the University of Surrey with neutron crystallographic methods at the Institut Laue-Langevin (ILL) in Grenoble. The aim of this highly innovate, cutting-edge project will be to directly determine the protonation states in each of three major forms of DNA, A, B and Z, and to model these in the context of hydration-driven stereochemical pathways that are known to occur between them.
Particular attention will be focused on changes in protonation in these different forms and possible implication of tunnelling in mediating such shifts that may be a cause of mutation. This project will generate new data that will inform ongoing QB-DTC projects investigating tunnelling in DNA.
Modelling tunnelling in DNA base pairs
The 1964 work by Löwdin  proposes that there is a non-zero probability that the protons in hydrogen bonds holding together the two strands of DNA in the Watson-Crick model  can tunnel from one nucleotide to the other, dramatically altering the bond length. This spontaneous position shift transforms a base pair form the canonical to the tautomeric form. This causes an error in the genetic code, and accumulated errors of this kind could be responsible for mutation, ageing, and - in extreme cases - tumour formation. The work at the Leverhulme Centre builds on previous work carried out at Surrey .
In order to model this system, an open quantum systems  approach which uses the Caldeira-Leggett master equation  to describe the interaction of the proton in the hydrogen bond, the backbone of the DNA structure, and the surrounding cellular aqueous environment. Density functional theory is used to calculate the shape of the potential due to the DNA backbone. After solving the master equation, we explore the sensitivity of tunnelling rates due to the form of the environmental interaction, the asymmetry of the backbone potential, and the "memory" retained by the environment.
Although working closely together, Sapphire will focus on the mathematical behaviour described by the Caldeira-Leggett master equation and Louie will focus on the chemical properties of the DNA structure.
I am looking at tunnelling in open quantum systems with a particular focus on modelling a realistic cellular environment: noisy, dissipative, and with non-Markovian “memory" effects. This approach uses the Caldeira-Leggett model of path integrals. We hope to eventually make a statement about the relevance of proton tunnelling in DNA base pairs as a method for tautomerisation.
This project has scope to expand into related disciplines and I hope to look into quantum information theory, entanglement, and quantum thermodynamics. When I am not in the office, I can often be found arguing about the Copenhagen interpretation, de Broglie-Bohm theory, and the many worlds interpretation, as well as trying to convince my colleagues that the passage of time is not physical.
My PhD project focuses on how mismatches between DNA base pairs can be caused by quantum tunnelling. All within the framework of a noisy open quantum system. I have future aspirations to extend the model to other applications such as enzyme catalysis.
Experimental detection of tunnelling via mutation
Inspired by the experiments that demonstrated the importance of proton tunnelling in enzyme catalysis , Antonio and Virginia are currently investigating whether a similar kinetic isotope effect can alter the spontaneous mutation rate. If quantum tunnelling is involved in the transition of a DNA base from the common to its rare tautomeric form, then replacing a hydrogen nucleus (a single proton) with a deuterium nucleus (consisting of a proton and a neutron) should slow the transition rate since quantum tunnelling will be highly sensitive to doubling the mass of the particle trying to tunnel. By using deuterated water (D2O) as solvent rather than H2O and employing advanced experimental techniques from molecular biology, they aim to explore a potential relation between proton tunnelling and mutations.
Professor Jim Al-Khalili
Distinguished Chair, Professor of Physics, Professor of Public Engagement in Science, Centre Director
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