Clasificación de los conflictos

Of all 16 cluster optimisations described above, only four resulted in significantly stronger (by ≥3.5 kcal/mol) base–water or water–water interactions, compared to the starting structures, after accounting for BSSE. One of these four was the base–water interaction in U(enol)W50 with M06-2X, which was clearly due to the ionic interaction between H3O

+

and U− in the final structure. The other three were base–water in U(enol)W50 with M05-2X, base–water in BrU(keto)W50 with PBE0, and water–water in BrU(keto)W50 with M05-2X. The observation that both interaction terms became weaker (or were essentially unchanged) in all four optimisations of BrU(enol)W50 can be related to

v_{The base–water interaction in BrU(enol)W50 is strengthened by a negligible 0.1 kcal/mol at the same level of} theory (Table 3.15).

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the fact that all four methods predicted enolisation of BrU to be less favourable in the optimised structures. Unfortunately, without a formal method of partitioning the interaction energy into physically meaningful terms (e.g. DFT-SAPT), it is difficult to establish the physical origin of these energy changes using the supermolecular method alone. In any case, the large influence of BSSE on the final geometries casts doubt on their validity.

However, the rare tautomer hypothesis of BrU mutagenicity does not require that the mutagenic tautomer be absolutely favoured over the canonical tautomer. Van Mourik et al.’s calculated reversal

of the tautomeric preference of BrU in nanodroplets was a remarkable finding, but all that is actually required by the rare tautomer model is that the equilibrium population of the enol form, under physiological conditions, be appreciably higher for BrU than for U (or T). The keto form could still dominate overall.

Loeb and Kunkel estimated that, in the absence of repair apparatus, an error rate of one in 10n base pairs required a free energy difference of 1.4n kcal/mol between correct and incorrect base pairs.19 Equivalently, Lasken and Goodman154 derived an energy difference of 2.7 kcal/mol for an error rate of one in 102.

Let us assume that the enolisation of aqueous BrU, though unfavourable, incurs a smaller energetic penalty than the enolisation of aqueous U. Then, BrU should form rare-tautomeric mispairs more often than U. Now, Loeb and Kunkel’s equation implies that, for BrU to increase the error rate by 10n

(neglecting repair apparatus), the enolisation energy of BrU must be lower than that of U by a margin of 1.4n kcal/mol, assuming that all mispairs formed by either base are rare-tautomeric. Experimentally, the increase in error rate induced by BrU varies widely, as a function of many variables, but is generally in the range 102– 104.53, 57, 61, 155 This, then, requires the enolisation energy of BrU to be 3 – 6 kcal/mol lower than that of U. However, since repair enzymes heavily reduce the mutation rate in vivo, this is probably an underestimate, representing the lower bound of the rare tautomer stabilisation needed to account for BrU-induced mutagenesis.

Note that Loeb and Kunkel’s equation is not exact here (even if free rather than potential energies are available), because our clusters only contain single U or BrU bases, not base pairs. However, let us assume that BrU and U form hydrogen bonds with roughly the same strength, and likewise for BrU* and U*. Then, consider the case of ATGC transitions, which are caused by substrate G (rather than A) mispairing with either U or BrU in the template. We have assumed that the energy difference between BrU*-G and BrU-A, and the energy difference between U*-G and U-A, differ from each other mostly due to the different enolisation energies of BrU and U, since the H-bonding patterns are the same. Hence the difference in base pair energies is approximately equal to the difference in enolisation energies. The same applies to the mispairing of substrate U and BrU, in competition with C, opposite template G: the difference between BrU*-G and C-G energies, and the difference between U*-G and C-G energies, should be roughly equal to the difference in enolisation energies of BrU and U.

Every method employed in this chapter, except for re-optimisation with M05-2X, found the tautomerisation of BrU to be more favourable than that of U by 8.7 kcal/mol or more. On this basis, we would expect BrU to induce mutations at at least 106 times the rate of U (8.7 / 1.4 = 6.2, cf. Loeb and Kunkel),19 in the absence of repair enzymes. Allowing for the subsequent effect of those enzymes, this is arguably consistent with the experimental rates of 102 – 104. Although it is disappointing that we did not have the time and resources to explore this line of enquiry further (e.g.

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using different starting structures), and that the results we obtained were contaminated by BSSE, our findings in this chapter confirm that water approaching the bulk limit has a large and favourable effect on the tautomerisation of BrU compared to U, which cannot be predicted by implicit solvent models alone.

A natural follow-up question is to ask what size of water cluster is needed to appreciably change the gas-phase tautomeric preference of BrU. In particular, it would be productive to investigate smaller clusters (e.g. up to 10 water molecules), with the water in positions corresponding to the most commonly occupied hydration sites in DNA as established by crystallography.45

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Chapter 4: CPMD study of tautomerism in a