GGaaaahhhhh i have set myself a harder task than i expected. I will say now I am not familiar with most of the open quantum systems stuff they discuss but I'm not sure the precise details matter too much. The paper is looking at the phyiscal mechanisms underlying DNA mutations- many sources of mutation are already known, like exposure to radioactivity and oxidative damage. Rather than concerning these, this paper looks at the causes of spontaneuous mutation. It is thought that proton transfer (tautomerisation, though this term can also include electron transfer) contributes to this, and there is evidence that it also confounds the proofreading that cells do when they copy DNA.
When you are considering single particles, then you have to take quantum mechanics into account. But, if you are considering 'hot' (above absolute 0) particles not in a vacuum, like in a cell, you need to take into account trhe environment, even temperature constitutes an environment to a quantum mechanical system. So we are in the realm of open quantum systems, basically shit hard maths and a fuckton of approximations, this is what 'density functional theory,' Lindblad terms, etc etc is being used for. It is important to note that open quantum systems are complicated as fuck and results may not be robust, trying a different computational approach to the same problem may yield contradictory results, as mentioned in the paper. So, there is no consensus in this area (rol of quantum tunneling in this type of DNA mutation), but experimental and theoretical evidence is mounting.
In physics, energy is king. If something is energetically favourable, it will happen. Particles are modelled as travelling through 'energy landscapes'- with valleys that are easy to get into and hills that you need some extra energy to get up. Quantum mechanics muddies this by allowing particles to sometimes 'tunnel' through energy barriers, a bit like you having some finite probability of being able to just walk through a wall you can't climb over. So in general, if something is 'hindered by a substantial energy barrier' a system would generally need to get a lot of energy from elsewhere to be expected to overcome this barrier, but quantum mechanics allows tunnelling through this barrier as an alternative, but very infrequently taken, route.
These guys modelled the energy landscape basically as DNA floating in water, then analysed the expected proton transfer, specifically calculating the probability of tunnelling in this system. I think, and I haven't been through the maths/modelling in detail and am rusty at this, that they are modelling the proton as a Gaussian wave packet, solving the Schrodinger equation (time evolution of a quantum system), and calculating the probability of the wave packet overcoming the energy barrier. They then analyse how stable the system would be in the state where the energy barrier is overcome.
Having obtained all this, they finally compare the probabilities of proton tunnelling-transfer induced mutation for different single or double stranded DNA bases and find that quantum effects may have a significant role in G-C tautomerisation and thus spontaneous point mutations.
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i hope that makes sense
@jrws ask any questions if you want. as i say, i am rusty and this is hard so take any detail with a pinch of salt.
i hope you are able to start doing something more interesting than crack and meth soon, they get boring as fuck after a while! glad you have a decent career to fall back on, must be so hard for people who don't have that when they get into recovery.
