The DOI matches its Crossref record; 67 of the 67 references it cites were found in a registry or an index; 24 of the 46 sources its claims cite were checked for support.
An open quantum systems approach to proton tunnelling in DNA
Open accessAbstract
One of the most important topics in molecular biology is the genetic stability of DNA. One threat to this stability is proton transfer along the hydrogen bonds of DNA that could lead to tautomerisation, hence creating point mutations. We present a theoretical analysis of the hydrogen bonds between the Guanine-Cytosine (G-C) nucleotide, which includes an accurate model of the structure of the base pairs, the quantum dynamics of the hydrogen bond proton, and the influence of the decoherent and dissipative cellular environment. We determine that the quantum tunnelling contribution to the proton transfer rate is several orders of magnitude larger than the classical over-the-barrier hopping. Due to the significance of the quantum tunnelling even at biological temperatures, we find that the canonical and tautomeric forms of G-C inter-convert over timescales far shorter than biological ones and hence thermal equilibrium is rapidly reached. Furthermore, we find a large tautomeric occupation probability of 1.73 × 10 −4 , suggesting that such proton transfer may well play a far more important role in DNA mutation than has hitherto been suggested. Our results could have far-reaching consequences for current models of genetic mutations.
Overview
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Written from the paper’s full text.
TL;DR
The paper models proton transfer in the Guanine–Cytosine hydrogen bonds using an open quantum systems approach with a Caldeira–Leggett thermal bath. It finds that quantum tunnelling dominates over classical over-the-barrier hopping, giving rapid canonical–tautomeric interconversion and a tautomeric occupation probability of \(1.73 \times 10^{-4}\) at 300 K.
Key findings
- The quantum tunnelling contribution is much larger than classical hopping: the tunnelling factor \(\kappa\) is \(\sim 10^5\), with quantum forward/reverse rates \(k_f = 7.61 \times 10^5\ \mathrm{s^{-1}}\) and \(k_r = 1.69 \times 10^{13}\ \mathrm{s^{-1}}\), versus classical rates \(k_f = 7.596\ \mathrm{s^{-1}}\) and \(k_r = 1.692 \times 10^8\ \mathrm{s^{-1}}\).
- The tautomeric occupation probability at 300 K is \(1.73 \times 10^{-4}\), more than four orders of magnitude larger than classical/semiclassical predictions; the classical thermal equilibrium constant from \(\Delta E = 0.435\ \mathrm{eV}\) is \(K_{\mathrm{eq}} = 5.4 \times 10^{-8}\).
- The canonical and tautomeric forms interconvert on timescales far shorter than biological ones, so thermal equilibrium is rapidly reached; quantum half-lives are \(9.11 \times 10^{-7}\ \mathrm{s}\) for the reactant and \(4.09 \times 10^{-14}\ \mathrm{s}\) for the product.
- The kinetic isotope effect at biological temperatures is \(\mathrm{KIE} = 30\), and the model uses a forward barrier of \(0.705\ \mathrm{eV}\), reverse barrier of \(0.270\ \mathrm{eV}\), and first eigenstate energy \(E_0 = 0.049\ \mathrm{eV}\).
Methods
- The proton is treated as a quantum system in an asymmetric double-well potential derived from an ab initio potential energy surface for G–C tautomerisation, represented by a back-to-back double Morse potential.
- Dynamics use the Caldeira–Leggett quantum Brownian motion model, with the proton coupled to an Ohmic thermal bath of harmonic oscillators; the Wigner–Moyal–Caldeira–Leggett equation is solved numerically with a low-temperature correction replacing \(k_B T\) by \(E_\omega = \frac{\hbar\omega}{2}\coth(\frac{\hbar\omega}{2k_B T})\).
- Numerical integration uses the method of lines, finite differences, and VCABM5 in Julia, with proton mass \(1836\ \mathrm{a.u.}\), bath temperature \(298.15\ \mathrm{K}\), and friction \(\gamma = 3900\ \mathrm{cm^{-1}}\); rates are obtained from probability flux, and the KIE is computed by doubling the mass.
Limitations
- The paper states that the master equation is rigorously valid only in the weak-coupling and high-temperature limits; at biological temperatures the high-temperature limit is invalid, so a low-temperature correction is applied.
- The model drops third-order potential terms, assumes a single effective reaction coordinate with a single proton mass at the transition state, and neglects collective classical rearrangement of the remaining base atoms.
- The paper notes that experimental tautomerisation rates for G–C double proton transfer are not available, that KIE measurements in biological assays are problematic, and that the KIE calculation neglects isotopic changes to the energy landscape; it also suggests added dimensions could introduce corner-cutting effects.
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Claims the paper makes
29 Own interpretation · 25 Own result · 15 No basis given · 10 No full text of the sources · 7 Supported · 7 Partly supported · 2 Supported so far · 2 Sources not found · accuracy not yet measured
Every source the paper cites for this claim was checked and supports it.
In the paper
“The phenomenological rate law applies only after a characteristic time τ c in which this transient phase has ended.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
What the sources say
- Supportedcites [35] Hänggi, P., Talkner, P. & Borkovec, M. Reaction-rate theory: fifty years after kramers. Rev. Mod. Phys. 62, 251 (1990). source
In Section II, “Method of reactive flux” (Fig. 4; page unavailable), the paper describes transient recrossings at early times and says the rate appears as a plateau at later times. Its discussion of time-scale separation identifies a characteristic local relaxation time. Together, these support applying the phenomenological rate law after the transient phase has ended. (LLM, conf=0.89)
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In the paper
“However, it is well known that crucial quantum effects such as decoherence and dissipation are not treated correctly in adiabatic, thermally uncoupled models of tunnelling 6,18 .”
§ An open quantum systems approach to proton tunnelling in DNA > Abstract
What the sources say
- Partly supportedcites [6] Godbeer, A., Al-Khalili, J. & Stevenson, P. Modelling proton tunnelling in the adenine–thymine base pair. Phys. Chem. Chem. Phys. 17, 13034–13044 (2015). sourceExperimental — accuracy not yet measured
Section 4 (page not provided) adds an environment-coupled Lindblad term to model dissipation, and Section 5 says that without it, a proton initially in the ground state would not tunnel. This supports the importance of dissipative coupling in this model, but our copy does not establish the broader claim that adiabatic, thermally uncoupled models treat both decoherence and dissipation incorrectly. (LLM, conf=0.79)
- Not checked — no full text of the sourcecites [18] Liu, Y., Yan, Y., Xing, T. & Shi, Q. Understanding the large kinetic isotope effect of hydrogen tunneling in condensed phases by using double-well model systems. J. Phys. Chem. B 125, 5959–5970 (2021). source
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In the paper
“Based on previous evaluations 4 of tunnelling in this system, we expect that the tautomeric population of the monomeric forms are unlikely to see any meaningful change while in transit from the helicase until it matches another base pair.”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
What the sources say
- Supportedcites [4] Slocombe, L., Al-Khalili, J. & Sacchi, M. Quantum and classical effects in dna point mutations: Watson–Crick tautomerism in at and gc base pairs. Phys. Chem. Chem. Phys. 23, 4141–4150 (2021). source
Section 4.3 states that monomeric tautomers are significantly more stable than paired tautomers and could persist long enough to lead to a point mutation if they survive dissociation. Its tunnelling-rate discussion also finds that formation of tautomers in the single-stranded configuration is relatively unlikely. These findings support the citing authors’ hedged expectation about little change during transit, rather than a direct measurement of that interval. (LLM, conf=0.85)
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In the paper
“Alternatively, the linearised entropy is a computationally convenient but accurate approach to measure coherence 58,59 .”
§ An open quantum systems approach to proton tunnelling in DNA > The low-temperature limit
What the sources say
- Partly supportedcites [58] Zurek, W. H., Habib, S. & Paz, J. P. Coherent states via decoherence. Phys. Rev. Lett. 70, 1187 (1993). sourceExperimental — accuracy not yet measured
The opening passage (p. 1187) says the rate of increase in linear entropy can quantify stability during decoherence, supporting its use as a measure of coherence loss in the harmonic-oscillator model. It does not say linear entropy is computationally convenient or establish its accuracy as a general measure; the nearby statement about mathematical convenience refers to coherent states, not entropy. (LLM, conf=0.82)
- Not checked — no full text of the sourcecites [59] Włodarz, J. J. Entropy and wigner distribution functions revisited. Int. J. Theor. Phys. 42, 1075–1084 (2003). source
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In the paper
“More recently, tautomerisation in DNA has been experimentally observed using NMR relaxation dispersion.Here, hairpin DNA duplex structures were observed to interchange between a wobble G-T and a Watson-Crick-like structure via tautomerisation (neutral) or ionisation (charged) 9,51 .”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
What the sources say
- Supportedcites [9] Kimsey, I. J. et al. Dynamic basis for dg⋅ dt misincorporation via tautomerization and ionization. Nature 554, 195–201 (2018). source
Split into 2 atoms — 2 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
- Supportedcites [51] Kimsey, I. J., Petzold, K., Sathyamoorthy, B., Stein, Z. W. & Al-Hashimi, H. M. Visualizing transient Watson–Crick-like mispairs in dna and rna duplexes. Nature 519, 315–320 (2015). source
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plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Furthermore, in a proton transfer reaction catalysed by enzyme soybean lipoxygenase, in the wild type, a high KIE of ~80 41 has been experimentally observed and verified using theory 42 .”
§ An open quantum systems approach to proton tunnelling in DNA > Results
What the sources say
- Not checked — no full text of the sourcecites [41] Glickman, M. H., Wiseman, J. S. & Klinman, J. P. Extremely large isotope effects in the soybean lipoxygenase-linoleic acid reaction. J. Am. Chem. Soc. 116, 793–794 (1994). source
- Partly supportedcites [42] Li, P., Soudackov, A. V. & Hammes-Schiffer, S. Impact of mutations on the binding pocket of soybean lipoxygenase: implications for proton-coupled electron transfer. J. Phys. Chem. Lett. 9, 6444–6449 (2018). sourceExperimental — accuracy not yet measured
The passage on wild-type SLO (section labelled Abstract; page unavailable) reports an experimentally observed KIE of approximately 80 at room temperature. The paper uses molecular-dynamics simulations and PCET theory to interpret experimental KIE trends, but does not report a theoretical verification of the specific value of 80. (LLM, conf=0.83)
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In the paper
“A strong dependence of the reaction rate on the reduced mass of the system can indicate tunnelling.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
What the sources say
- Supportedcites [37] Johannissen, L. O., Hay, S. & Scrutton, N. S. Nuclear quantum tunnelling in enzymatic reactions – an enzymologist’s perspective. Phys. Chem. Chem. Phys. 17, 30775–30782 (2015). source
Section 2 (page unavailable) identifies the magnitude of the primary kinetic isotope effect—a change in reaction rate upon isotope substitution—as a reasonable first approximation of tunnelling. Its tunnelling-probability equation also depends on mass. Together, these support the qualified claim that a strong mass dependence can indicate tunnelling. (LLM, conf=0.87)
- Could not verifycites [38] Johannissen, L. O., Iorgu, A. I., Scrutton, N. S. & Hay, S. What are the signatures of tunnelling in enzyme-catalysed reactions? Faraday Discuss. 221, 367–378 (2020). sourceExperimental — accuracy not yet measured
The only passage returned from our copy is the paper’s title and author metadata (no section or page). Searches for reduced mass, reaction rate, and isotope-related mass dependence found no substantive passage, so the claim cannot be verified from our copy. (LLM, conf=0.75)
- Supportedcites [39] Klinman, J. P. & Offenbacher, A. R. Understanding biological hydrogen transfer through the lens of temperature dependent kinetic isotope effects. Acc. Chem. Res. 51, 1966–1974 (2018). source
The Introduction (page unavailable) links the greater mass of deuterium to differences in hydrogen-transfer kinetics and explains how isotope-dependent measurements inform tunneling models. The paper cautions that the magnitude of a kinetic isotope effect alone does not establish tunneling, but that is consistent with the claim’s qualified wording, “can indicate.” (LLM, conf=0.84)
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In the paper
“On the other hand, computational studies suggest that the monomeric form of the tautomers are stable and extremely longlived due to their prohibitively large reaction barriers 4,13,48,49 .”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
What the sources say
- Supportedcites [4] Slocombe, L., Al-Khalili, J. & Sacchi, M. Quantum and classical effects in dna point mutations: Watson–Crick tautomerism in at and gc base pairs. Phys. Chem. Chem. Phys. 23, 4141–4150 (2021). source
The Abstract says the calculations indicate remarkably long lifetimes for tautomeric bases in monomeric form. Section 4.3 (page not available) reports that tautomers formed by intramolecular proton transfer have lifetimes averaging 10⁹ times those of the corresponding tautomeric base pairs, while section 4.2 reports substantial barriers for intra-base transfer. This supports the claim about monomers, not the short-lived A–T and G–C tautomeric pairs. (LLM, conf=0.91)
- Partly supportedcites [13] Soler-Polo, D., Mendieta-Moreno, J. I., Trabada, D. G., Mendieta, J. & Ortega, J. Proton transfer in Guanine-Cytosine base pairs in b-dna. J. Chem. Theory Comput. 15, 6984–6991 (2019). sourceExperimental — accuracy not yet measured
The discussion of Figure 6 (indexed under Abstract; page unavailable) reports a very large, approximately 48 kcal/mol barrier between isolated guanine and its rare tautomer, consistent with a long-lived monomeric guanine tautomer. It does not establish that monomeric tautomers generally are extremely long-lived; the paper also reports a much smaller reverse barrier for the gas-phase G*C* base pair. (LLM, conf=0.85)
- Not checked — no full text of the sourcecites [48] Gorb, L., Podolyan, Y. & Leszczynski, J. A theoretical investigation of tautomeric equilibria and proton transfer in isolated and monohydrated cytosine and isocytosine molecules. J. Mol. Struct. 487, 47–55 (1999). source
- Supportedcites [49] Podolyan, Y., Gorb, L. & Leszczynski, J. Ab initio study of the prototropic tautomerism of cytosine and guanine and their contribution to spontaneous point mutations. Int. J. Mol. Sci. 4, 410–421 (2003). source
The Results and Discussion report that proton transfer is very slow for isolated cytosine and guanine because their tautomerization barriers are much higher without water. Table 2 also gives low reverse-reaction rates for the isolated bases, supporting the description of their rare tautomers as long-lived. The paper's calculations concern these two bases, not monomeric tautomers generally. (LLM, conf=0.88)
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In the paper
“The authors reported a KIE as the rate of exchange between the two conformations of the mismatch was ~3-fold slower in D 2 O than in H 2 O.”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
What the sources say
- Supportedcites [52] Rangadurai, A., Szymanski, E. S., Kimsey, I., Shi, H. & Al-Hashimi, H. M. Probing conformational transitions towards mutagenic Watson–Crick-like g⋅ t mismatches using off-resonance sugar carbon r 1ρ relaxation dispersion. J. Biomol. NMR 74, 457–471 (2020). source
The Results and discussion report that the G·T mismatch exchange rate measured in D2O was approximately 3.5-fold slower than in H2O. The same section describes the reduction as a kinetic isotope effect, supporting the citing sentence’s approximate threefold figure. (LLM, conf=0.94)
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In the paper
“In our case, at the transition state, the motion of a single proton dominates 4 .”
§ An open quantum systems approach to proton tunnelling in DNA > Methods
What the sources say
- Supportedcites [4] Slocombe, L., Al-Khalili, J. & Sacchi, M. Quantum and classical effects in dna point mutations: Watson–Crick tautomerism in at and gc base pairs. Phys. Chem. Chem. Phys. 23, 4141–4150 (2021). source
Section 3 (page unavailable) says that, in the paper’s tunnelling model, the rate-determining step is one proton crossing the barrier while the other transfers afterward. This supports the cited point that a single proton’s motion dominates at the barrier, although the paper presents the asynchronous transfer as a model assumption. (LLM, conf=0.87)
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- Probably not a substantial claim. 11
- It may state two separate claims as one. 27
The sources with a verdict support this claim; the rest weren’t checked yet, have no full text we could read, or their verdicts aren’t rated yet.
In the paper
“The argument is that in the standard Watson-Crick configuration, the formation of the single proton transfer is either unstable or energetically unfavourable 5,7,11,12 .”
§ An open quantum systems approach to proton tunnelling in DNA > Abstract
What the sources say
- Not checked — no full text of the sourcecites [5] Brovarets’, O. O. & Hovorun, D. M. Atomistic mechanisms of the double proton transfer in the h-bonded nucleobase pairs: Qm/qtaim computational lessons. J. Biomol. Struct. Dyn. 37, 1880–1907 (2019). source
- Supportedcites [7] Gheorghiu, A., Coveney, P. & Arabi, A. The influence of base pair tautomerism on single point mutations in aqueous dna. Interface Focus 10, 20190120 (2020). source
The A:T tautomerism section reports that the single-proton-transfer product is energetically unstable and rapidly reverts. The Conclusion likewise describes the A+:T− product as kinetically and thermodynamically unstable. This supports the claim, although the paper also finds single proton transfer more favourable than double proton transfer in A:T. (LLM, conf=0.88)
- Not checked — no full text of the sourcecites [11] Brovarets’, O. O. & Hovorun, D. M. Why the tautomerization of the g ⋅ c Watson-Crick base pair via the dpt does not cause point mutations during dna replication? qm and qtaim comprehensive analysis. J. Biomol. Struct. Dyn. 32, 1474–1499 (2014). source
- Not checked — no full text of the sourcecites [12] Brovarets, O. O. & Hovorun, D. M. Can tautomerization of the a ⋅ t Watson-Crick base pair via double proton transfer provoke point mutations during dna replication? a comprehensive qm and qtaim analysis. J. Biomol. Struct. Dyn. 32, 127–154 (2014). source
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
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In the paper
“Our decision to study G-C rather than A-T is because the tautomeric state, A*-T*, is extremely unstable, with a fleetingly short lifetime, and therefore not as likely to play a role in mutagenesis 4,5,7,13 .”
§ An open quantum systems approach to proton tunnelling in DNA > Abstract
What the sources say
- Supportedcites [4] Slocombe, L., Al-Khalili, J. & Sacchi, M. Quantum and classical effects in dna point mutations: Watson–Crick tautomerism in at and gc base pairs. Phys. Chem. Chem. Phys. 23, 4141–4150 (2021). source
Section 4.3 estimates the A*-T* lifetime at about 10⁻¹⁴ seconds and says hardly any formed through the Watson–Crick pathway would survive passage through the replication machinery. Section 5 concludes that the A-T tautomer is unstable and that this pathway is unlikely to be biologically relevant for spontaneous point mutations. (LLM, conf=0.94)
- Not checked — no full text of the sourcecites [5] Brovarets’, O. O. & Hovorun, D. M. Atomistic mechanisms of the double proton transfer in the h-bonded nucleobase pairs: Qm/qtaim computational lessons. J. Biomol. Struct. Dyn. 37, 1880–1907 (2019). source
- Partly supportedcites [7] Gheorghiu, A., Coveney, P. & Arabi, A. The influence of base pair tautomerism on single point mutations in aqueous dna. Interface Focus 10, 20190120 (2020). sourceExperimental — accuracy not yet measured
The Results and discussion describe A*:T* as highly unstable, and the Conclusion estimates its equilibrium abundance to be negligible, supporting a limited role in mutagenesis. But the paper does not establish a fleetingly short lifetime for A*:T*: the approximately 6 fs half-life reported in Results and discussion belongs to the distinct A+:T− zwitterion, while rate coefficients for A*:T* were not determined. Page numbers are unavailable in our copy. (LLM, conf=0.88)
- Partly supportedcites [13] Soler-Polo, D., Mendieta-Moreno, J. I., Trabada, D. G., Mendieta, J. & Ortega, J. Proton transfer in Guanine-Cytosine base pairs in b-dna. J. Chem. Theory Comput. 15, 6984–6991 (2019). sourceExperimental — accuracy not yet measured
The paper’s discussion of A*T* (indexed under Abstract; page not given) says gas-phase studies find no local minimum for it, or only a very shallow one, and concludes that double proton transfer does not contribute to A* or T* rare tautomers. That supports the instability and reduced mutagenic relevance attributed to the source, but the paper does not establish a fleetingly short A*T* lifetime or test its stability in B-DNA. (LLM, conf=0.83)
hedgeddirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Supported
The sources with a verdict support this claim; the rest weren’t checked yet, have no full text we could read, or their verdicts aren’t rated yet.
In the paper
“other spontaneous mutations will also take place in DNA aside from tautomerisation 54,55”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
What the sources say
- Not checked — no full text of the sourcecites [54] Kunkel, T. A. & Alexander, P. S. The base substitution fidelity of eucaryotic dna polymerases. mispairing frequencies, site preferences, insertion preferences, and base substitution by dislocation. J. Biol. Chem. 261, 160–166 (1986). source
- Supportedcites [55] Zahurancik, W. J., Klein, S. J. & Suo, Z. Significant contribution of the 3’ → 5’ exonuclease activity to the high fidelity of nucleotide incorporation catalyzed by human dna polymerase epsilon. Nucleic Acids Res. 42, 13853–13860 (2014). source
The Introduction (page not specified) describes DNA-copying errors from incorrect nucleotide incorporation, and the Discussion (page not specified) links impaired proofreading to increased mutations. These support the broad point that mutations can arise through processes other than tautomerisation, although the paper does not discuss tautomerisation itself. (LLM, conf=0.84)
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
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In the paper
“Since a definitive experimental hallmark of tunnelling is a temperature-independent rate at low temperature, the rate of classical over-the-barrier hopping becomes negligible at low temperatures, leaving only the quantum contribution 37,38 .”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
What the sources say
- Partly supportedcites [37] Johannissen, L. O., Hay, S. & Scrutton, N. S. Nuclear quantum tunnelling in enzymatic reactions – an enzymologist’s perspective. Phys. Chem. Chem. Phys. 17, 30775–30782 (2015). sourceExperimental — accuracy not yet measured
Section 2 models the classical over-barrier rate as temperature-dependent and the observed rate as a sum of classical and tunnelling contributions, supporting the distinction between the two pathways. But it does not identify a temperature-independent rate at low temperature as a definitive experimental hallmark, or establish that only the quantum contribution remains there. Section 2 instead says there is no direct experimental measure for the degree of tunnelling and discusses the kinetic isotope effect as an approximation. (LLM, conf=0.84)
- Could not verifycites [38] Johannissen, L. O., Iorgu, A. I., Scrutton, N. S. & Hay, S. What are the signatures of tunnelling in enzyme-catalysed reactions? Faraday Discuss. 221, 367–378 (2020). sourceExperimental — accuracy not yet measured
The supplied passages contain only the title and bibliographic details. Searches for temperature-independent rates, cryogenic temperatures, and classical over-the-barrier contributions returned no relevant full-text passage; the substantive match was confined to the abstract, which is not admissible evidence under the stated rubric. (LLM, conf=0.66)
boosteddirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Partly supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“The approach of inserting the PES calculated from density functional theory into an OQS Hamiltonian has been successfully used before for proton transfer reactions 6 .”
§ An open quantum systems approach to proton tunnelling in DNA > Methods
What the sources say
- Supportedcites [6] Godbeer, A., Al-Khalili, J. & Stevenson, P. Modelling proton tunnelling in the adenine–thymine base pair. Phys. Chem. Chem. Phys. 17, 13034–13044 (2015). source
Section 2 says the authors used density functional theory to construct a proton-transfer potential energy surface, then used that potential in a time-dependent equation with environmental dissipation. Section 6 reports the resulting transition probabilities and finds that environmental coupling promoted tunnelling. The paper therefore exemplifies the approach described in the citing sentence. (LLM, conf=0.91)
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Supported
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“With this value, we obtain a forward and reverse reaction rate of k f = 7.61 × 10 5 s -1 and k r = 1.69 × 10 13 s -1 , respectively, whereas the half-life of the reactant and product is now 9.11 × 10 -7 and 4.09 × 10 -14 s, respectively.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus, the reaction is characterised by a ΔE (energetic asymmetry between the bottoms of the two potential wells) of 0.435 eV, a high forward barrier of 0.705 eV and a reverse barrier of 0.270 eV.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
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In the paper
“The classical equilibrium constant, K eq , is on the order of 10 -8 which is in agreement with Gheorghiu et al. 7 , whereas the half-lifes of the reactant and product are 0.0913 and 4.1 × 10 -9 s, respectively.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
What the sources say
- Not matchedcites Gheorghiu et al. 7
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
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In the paper
“Figure 2 also shows the first ten energy eigenvalues for a single proton in this potential, six of which are entirely local to the G-C canonical configuration, with the seventh eigenstate the first to have a nonzero amplitude in the shallow (tautomeric) well.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
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In the paper
“Comparatively, setting the quantum contribution in Eq. ( 8) to unity gives a classical forward and reverse reaction rate of k f = 7.596 s -1 and k r = 1.692 × 10 8 s -1 .”
§ An open quantum systems approach to proton tunnelling in DNA > Results
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In the paper
“At t → ∞, the thermal equilibrium distribution gives a probability of 1.73 × 10 -4 for the proton being in the tautomeric form, which is more than four orders of magnitude larger than that predicted by classical and semiclassical studies previously reported for this system.”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
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In the paper
“We performed a sensitivity analysis of the reaction barrier (see Supplementary Note 5) and determined that increasing the barrier height significantly impacts the rate of the thermally activated proton 'over-the-barrier' hopping dynamics; namely, it causes a striking reduction in classical rate, but it affects the quantum tunnelling rate much less.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
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In the paper
“The middle panel of Fig. 5 demonstrates that the high-temperature treatment becomes unphysical below ~600 K, whereby the distribution becomes increasingly point particle-like, violating the uncertainty principle.”
§ An open quantum systems approach to proton tunnelling in DNA > The low-temperature limit
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In the paper
“whereas the half-lifes of the reactant and product are 0.0913 and 4.1 × 10 -9 s, respectively.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
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“At low temperatures, the KIE rapidly increases, providing further evidence that the transfer process becomes increasingly dependent on the quantum (tunnelling) contribution.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
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In the paper
“However, in our OQS approach, the tunnelling factor obtained is on the order of 10 5 , suggesting that the system readily interconverts between the canonical and tautomeric configuration via quantum effects.”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
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In the paper
“On the other hand, incorporating the correction prevents the compression of the distribution in phase space at lower temperatures -demonstrating an asymptotic convergence to 0.5.”
§ An open quantum systems approach to proton tunnelling in DNA > The low-temperature limit
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In the paper
“At low temperature, the linear trend continues to the origin, implying that at 0 K, the distribution is perfectly point-like, with zero uncertainty.”
§ An open quantum systems approach to proton tunnelling in DNA > The low-temperature limit
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In the paper
“The experimental rates reported are much faster than the rates reported here, which is likely due to the initial ultraviolet pulse modifying the reaction profile.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
hedgedconditional- Asserted: passes — The authors put it forward as true.
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In the paper
“We show that the double proton transfer process takes place so quickly (in comparison with biologically relevant timescales) that the lifetimes of the tautomeric states do not play a significant part in determining the likelihood of a base pair mismatch.Rather, it is the ratio between the concentration of tautomeric base pairs to canonical base pairs present at chemical equilibrium that matters.”
§ An open quantum systems approach to proton tunnelling in DNA > Abstract
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In the paper
“Due to the significance of the quantum tunnelling even at biological temperatures, we find that the canonical and tautomeric forms of G-C inter-convert over timescales far shorter than biological ones and hence thermal equilibrium is rapidly reached.”
- Also stated in: § Results · hedged
“These quantum corrected half-lives are significantly shorter than the classical estimates, indicating the protons are sufficiently delocalised along the hydrogen bond and populate both states; the forward and reverse reaction rates are so quick that the system continuously converts between the canonical and tautomeric forms.”
§ An open quantum systems approach to proton tunnelling in DNA > Abstract
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- Also stated in: § Results · hedged
In the paper
“However, the experiment suggests that the proton transfer reaction rate can be fast and have a quantum component.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
What the sources say
- Not checked — no full text of the sourcecites [36] Douhal, A., Kim, S. & Zewail, A. Femtosecond molecular dynamics of tautomerization in model base pairs. Nature 378, 260–263 (1995). source
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Which is exclusively a nonclassical activity coefficient containing effects such as thermally enhanced tunnelling, zero-point energy, decoherence and dissipation, leading to an activity coefficient that is far from unity, in the same way that solvent effects can shift equilibrium 15 .”
§ An open quantum systems approach to proton tunnelling in DNA > Abstract
What the sources say
- Not matchedcites [15] Hill, T. Thermodynamics of small systems. in Dover Books on Chemistry (ed. Benjamin, W. A.) (Dover Publications, 1994). https://books.google.co.uk/books?id=Xa-yAAAAQBAJ.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
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- Not matched
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In the paper
“The first 50 structural evidence for the rare tautomer hypothesis was observed using X-ray crystallographic analysis of a DNA polymerase.Whereby the polymerase was observed mismatching C with A.”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Therefore, the G-C base pair enters the active site of the helicase in thermal equilibrium between canonical and tautomeric states with its eigenstates populated according to a Maxwell-Boltzmann distribution, W eq (q, p) = W(q, p, t → ∞).”
§ An open quantum systems approach to proton tunnelling in DNA > Results
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In the paper
“A high tunnelling factor and KIE has been observed in other models of OQSs 18,40 probing proton transfer reactions.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
What the sources say
- Not checked — no full text of the sourcecites [18] Liu, Y., Yan, Y., Xing, T. & Shi, Q. Understanding the large kinetic isotope effect of hydrogen tunneling in condensed phases by using double-well model systems. J. Phys. Chem. B 125, 5959–5970 (2021). source
- Not checked — no full text of the sourcecites [40] Xie, W., Xu, Y., Zhu, L. & Shi, Q. Mixed quantum classical calculation of proton transfer reaction rates: from deep tunneling to over the barrier regimes. J. Chem. Phys. 140, 174105 (2014). source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“single-stranded RNA phage replicases have error rates on the order of 10 -4”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
What the sources say
- Not checked — no full text of the sourcecites [56] Eigen, M. & Schuster, P. A principle of natural self-organization. Naturwissenschaften 64, 541–565 (1977). source
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
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In the paper
“Within the atomic unit system, a minimally uncertain distribution will take on a value of 0.5, with a value less than this violating the uncertainty principle.”
§ An open quantum systems approach to proton tunnelling in DNA > The low-temperature limit
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- The authors state this as an assumption: Heisenberg's position-momentum uncertainty principle must be upheld.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The high tautomer occupation probability might also be relevant to address the role of mutations in several theories of the origin of life”
§ An open quantum systems approach to proton tunnelling in DNA > Discussion
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“These quantum corrected half-lives are significantly shorter than the classical estimates, indicating the protons are sufficiently delocalised along the hydrogen bond and populate both states; the forward and reverse reaction rates are so quick that the system continuously converts between the canonical and tautomeric forms.”
§ An open quantum systems approach to proton tunnelling in DNA > Results
hedgeddirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For a pure, unmixed state, the S 2 entropy takes on a value of zero.”
§ An open quantum systems approach to proton tunnelling in DNA > The low-temperature limit
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Depending on the reaction pathway, if the two protons transfer simultaneously or not, the reduced mass of the system can tend to one or two proton masses 62 .”
§ An open quantum systems approach to proton tunnelling in DNA > Methods
What the sources say
- Not checked — no full text of the sourcecites [62] Schweiger, S. & Rauhut, G. Plateau reactions: double proton-transfer processes with structureless transition states. J. Phys. Chem. A 107, 9668–9678 (2003). source
plainconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Studies on other proton transfer reactions suggest that the reduced mass at the transition state is dependent on the proton transfer process and can fluctuate to a much heavier mass far from the transition state 62 .”
§ An open quantum systems approach to proton tunnelling in DNA > Methods
What the sources say
- Not checked — no full text of the sourcecites [62] Schweiger, S. & Rauhut, G. Plateau reactions: double proton-transfer processes with structureless transition states. J. Phys. Chem. A 107, 9668–9678 (2003). source
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The apparent single-dimensionality of the PES is due to the application of transition state theory to this system, which results in a single effective reaction coordinate being displayed to represent the minimum energy reaction pathway for tautomerisation.”
§ An open quantum systems approach to proton tunnelling in DNA > Methods
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Here, the back-to-back double Morse potential captures these requirements while maintaining the reaction profile obtained from high-level density functional theory calculations.”
§ An open quantum systems approach to proton tunnelling in DNA > Methods
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Negative entropy implies that the system can be in a more ordered state than an unmixed, pure state, which is problematic.”
§ An open quantum systems approach to proton tunnelling in DNA > The low-temperature limit
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The authors state this as an assumption.
The two protons in G-C undergo asynchronous transfer, with the rate-determining process being the transfer of a single proton across the barrier, and the other proton then moving in the opposite direction to preserve electroneutrality.
“We assume, as previously observed 6,14 , that the two protons undergo asynchronous transfer, suggesting that the ratedetermining process is the transfer of a single proton across the barrier, with the other proton then moving in the opposite direction to preserve electroneutrality.”
The authors state this as an assumption.
The bath is dominated by the thermal fluctuations of the surrounding water molecules.
“Assuming that the bath is dominated by the thermal fluctuations of the surrounding water molecules, we can estimate the value of γ.”
The paper relies on this without support.
Experimental measurements of tautomerisation rates for G-C double proton transfer reaction are still not available.
“Experimental measurements of tautomerisation rates for G-C double proton transfer reaction are still not available.”
The paper relies on this without support.
DNA repair mechanisms are highly efficient.
“the well-known presence of highly efficient DNA repair mechanisms”
The authors state this as an assumption.
Heisenberg's position-momentum uncertainty principle must be upheld.
“We note additionally that Heisenberg's position-momentum uncertainty principle must also be upheld”
The authors state this as an assumption.
Changes to the transfer energy landscape due to isotopic substitutions (such as zero-point energy and free energy contributions) are neglected; only mass effects on the reaction rate are considered.
“We neglect any changes to the transfer energy landscape due to isotopic substitutions, such as zero-point energy and free energy contributions, and consider only the effect on the reaction rate due to modifications of the mass terms in Eq. ( 1).”
The authors state this as an assumption.
The third-order potential terms in Eq. (1) are dropped to simplify numerical calculations.
“To simplify the numerical calculations, we drop the third-order potential terms in Eq. ( 1).”
The authors state this as an assumption.
The mass of the proton is, in a very good approximation, the effective mass of the tunnelling particle in the asynchronous concerted process.
“it is acceptable to assume that the mass of the proton mass is in, a very good approximation, the effective mass of the tunnelling particle in the asynchronous concerted process 5 .”
The authors state this as an assumption.
The collective classical rearrangement of the rest of the atoms of both bases can be neglected.
“Furthermore, the collective classical rearrangement of the rest of the atoms of both bases can be neglected.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ An open quantum systems approach to proton tunnelling in DNA > Results
“This timescale of the proton transfer (10 fs-100 ns) is significantly shorter than the cleavage timescale in the helicase (t ≫ 100 ns).”
§ An open quantum systems approach to proton tunnelling in DNA > Results
“whereas the half-life of the reactant and product is now 9.11 × 10 -7 and 4.09 × 10 -14 s, respectively.”
Citations
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Toda-like Hamiltonian as a probe for quantized prey-predator dynamics
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Quantum Biology—New Perspectives, Insights, and Frontiers in the Field of Medicine: A Review Article
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Quantum and anharmonic effects in hydrogen-bonded crystals, surfaces and biological systems
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On the Role of Nuclear Quantum Effects in Reactive Dynamics Simulations
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An Open-Quantum-Systems Theory of Quantum-Biological Communication Channels
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Quantum‐Level Influences on Enzyme Reactions and Their Ripple Effects on Biological Phenomena
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Plant Phenomics—the unrecognized rise of a scientific discipline
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Quantum biology and ultraweak photon emission: an overlooked intersection?
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Quantum Biology 2.0: Traversing and harnessing protein superhighway networks of light and life
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Metadata
- Authors
- Slocombe, L., Sacchi, M., & Al-Khalili, J.
- Affiliations
- University of Surrey (GB)
- Corresponding author
- Slocombe, Louie
- Sacchi, Marco
- Al-Khalili, Jim
- Venue
- Communications Physics
- Published
- 2022-05-05
- Volume
- 5
- Issue
- 1
- ISSN
- 2399-3650 (ISSN-L)
- OpenAlex
- W3204256293
- Semantic Scholar
- 0339b0872e10e7bcb07ebb38d3c28b16cae727e6
- Cited by
- 122
- References
- 63
- Citations by year
- 2026: 30 · 2025: 31 · 2024: 24 · 2023: 30 · 2022: 7
- FWCI
- 6.35
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Communications Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- arXiv (Cornell University) (cc-by)
- Funders
- Leverhulme Trust (DS- 2017-079)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › DNA and Nucleic Acid Chemistry
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Spectroscopy and Quantum Chemical Studies
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Photochemistry and Electron Transfer Studies
- Keywords
- proton tunneling, DNA, hydrogen bonding, guanine-cytosine base pair, DNA mutations, open quantum systems, decoherence, energy dissipation, quantum tunneling, point mutations, genetic stability
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-19, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-19 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
Statistics and arithmetic are recomputed, not judged.
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