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Calculations of the Energetics of Oxidation of Aqueous Nucleosides and the Effects of Prototropic Equilibria David M. Close, and Peter Wardman J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b02653 • Publication Date (Web): 24 May 2016 Downloaded from http://pubs.acs.org on June 4, 2016

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Calculations of the Energetics of Oxidation of Aqueous Nucleosides and the Effects of Prototropic Equilibria

David M. Close* Department of Physics, East Tennessee State Univ., Johnson City, TN 37614

Peter Wardman formerly of the Gray Cancer Institute, CRUK/MRC Oxford Institute for Radiation Oncology, University of Oxford, Oxford OX3 7DQ, United Kingdom; present address: 20 Highover Park, Amersham, Buckinghamshire HP7 0BN, United Kingdom

Abstract

Recently the calculated standard reduction potentials of the radical-cations of N-methyl substituted DNA bases have been reported that agree fairly well with the experimental results. However there are issues reflecting the fact that the experimental results usually relate to the couple Eo(Nuc•,H+/NucH+) whereas the calculated results are for the Eo(Nuc•+/Nuc) couple. To calculate the mid-point reduction potential at pH 7 (Em7) it is important to have accurate acid dissociation constants (pKs) for both ground-state bases and their radicals, and the effects of uncertainty in some of these values (e.g. that of the adenosine radical) must be considered. Calculations of the pKs of the radicals of the nucleic acid bases (as nucleosides) have been performed to explore the effects the various pKs have on calculating the values of Em7, and to see what improvements can be made with the accuracy of the calculations.

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Introduction Reduction of the radicals from one-electron oxidation of DNA bases is of considerable biological interest because the reactions represent chemical repair of damage including that from photoionization and the direct effect of ionizing radiation. An important parameter that describes the behavior of compounds in electron transfer reactions is the standard reduction potential of the base radical; this also effectively defines the ultimate ‘sink’ for the radical center or positive ‘hole’ in DNA upon one-electron oxidation. Although the reduction potential of guanyl radicals in DNA is not well characterized, the mid-point reduction potential at pH 7, Em7 = 1.29 ± 0.03 V has been determined for the radical of the monomer guanosine.1 Modern theoretical calculations can provide estimates of the standard reduction potential o

(E ) of DNA base radicals. However use of these values to estimate the potential at pH 7 (Em7), which is of greatest interest, requires accurate dissociation constants of prototropic equilibria of both the bases and their radicals (all dissociation constants here are acid dissociation constants pKa but the suffix ‘a’ has been generally omitted for simplicity when using multiple suffixes). Since a free energy change ∆G of only 1.4 kcal/mol is equivalent to a difference in a pK of 1 unit, and the pKs of radicals, in particular, may be subject to some uncertainty, extrapolation of calculations to estimate values relevant to physiological conditions may not be as reliable or accurate as is desirable. This application of theoretical calculations is an important area since experimental approaches are not without problems. Thus Steenken and Jovanovic,1 from measurements at pH 7 of redox equilibria involving reference compounds of known reduction potential, estimated a standard potential Eo for the guanosine radical which was 0.26 V higher than calculated from earlier, similar experimental measurements with different redox indicators at pH 13.2 While the later study is undoubtedly more reliable than the former, the value derived by Steenken and Jovanovic for the standard reduction potential of guanosine (1.58 V) actually relates to the couple Eo(Nuc•,H+/NucH+) and not Eo(Nuc•+/Nuc), where Nuc = the neutral, unprotonanted/ undissociated nucleoside, as noted by Schroeder et al.3 The experimental data provides a value of Eo(Nuc•+/Nuc) = 1.47 ± 0.03 V using the same values for ground state and radical pKs and neglecting uncertainties in the latter.3 Unless the couple involved in calculating the standard


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potential is clearly defined, there is much scope for confusion in comparing calculation with experiment, as clearly described by Schroeder et al. in their Supplementary Data.3 In the present work the standard reduction potentials Eo(Nuc•+/Nuc) of the N-methyl substituted DNA bases have been calculated and compared with values calculated from experimental measurements of mid-point potentials in aqueous solution at various pH values and in aprotic solvents. The effects of uncertainties in pK values are illustrated, particularly with respect to adenosine. Until recently the calculation of dissociation constants of acids yielded results that were not in good agreement with experiment. In an extensive review, SadlejSosnowska computed the pKs of nine model compounds to study the influence of factors such as the SCRF model applied, choice of thermodynamic cycle, atomic radii used to build a cavity in the solvent, optimization of geometries, inclusion of electron correlation, and the dimension of the basis sets on the solvation free energies and the calculated pK values;4 this work includes ca. 60 pages of Supplementary Material. As an example, for phenol, calculated pKs were in the range of 18–20 compared to the experimental value of 10.0. Likewise, there are similar problems with the calculations of the acidic dissociation constants of DNA bases and their radicals. Thorp and co-workers used density functional theory along with the COSMO solvation model5 to calculate the pKs of the base radical cations.6 Their results for guanine, cytosine and adenine are reasonably close to the experimental values, but differ by 2.8 units for thymine. Reviews of similar calculations can be seen in Table 3 of Psciuk et al.7 and the paper by Close.8 Psciuk et al.7 calculated reduction potentials and acid dissociation constants of the nucleobases; they used the SMD polarizable continuum model to compute the solvation free energies.9 Thapa and Schlegel calculated the pKs and redox properties of the nucleobases with up to four explicit water molecules to augment the SMD solvation calculations.10 Verdolino et al. calculated the pKs of nucleobases with rather good agreement with experimental values.11 Their methods are the basis of the calculations described below. Overall then, while the reduction potentials for the purine radicals are fairly well established, those for the pyrimidine nucleosides are not. Data for both purines and pyrimidines in acetonitrile are available,12 but good data comparing all five DNA bases in aqueous solution remain elusive. We have attempted to address these problems in the present study.



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Computational Methods The standard reduction potential Eo is given by ∗ = - /nF

(1)

where F is Faraday’s constant (23.06 kcal/(mol V), n is the number of electrons in the redox process. The Gibbs energy for the reduction of the radical cation in solution is7 +•

-

∗ ∗ ∗ = (B) - (B ) - (e )

(2)

The standard state Gibbs energy in solution ∗ ∗ = ( + ∆ → ) +

(3)

is the sum of the standard state Gibbs energy in the gas phase = and the standard state ∗ along with the term ∆ → ) for converting from standard Gibbs energy of solvation

state concentration of 1 atm in the gas phase to the standard state concentration of 1 mol/L in the aqueous state. The notation here is that the standard state at 1 atm is denoted as and the ∗ standard state at 1 mol/L as ∗ . The Gibbs energy for the solvation energy ∆ of this one

electron reduction reaction is determined by using the thermodynamic cycle in Fig. 1 to yield Eq. 4. The abbreviations used here can be found in an article by Sutton et al.13

Fig. 1. Thermodynamic Cycle Used to Calculate Reduction Potentials. ∗ ∗ ∘ ∆ = ( (B) + ∆ → + ∆ (B)) ∘ - ( (B

+•

-

+• ∗ ∘ ) + ∆ → (B ) - ( (e )


(4)

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To study reactions in a physiological environment it is important to have the reduction potential at pH 7 which means that one has to have the acid dissociation constant (K), which are directly proportional to the Gibbs energy for deprotonation ∗

pK = 2.303%&

(5)

∗ The thermodynamic cycle in Fig. 2 is used to calculate ∆' in Eq. 6.14

Fig. 2. Thermodynamic Cycle Used to Calculate pK. ∗ ∗ ∘ ∆' = ( (A−) + ∆ → + ∆ (A−)) ∘ ∗ + ( (H+) + ∆ → (H+)) ∗ ∘ - ( (HA) + ∆ → ()* HA

(6)

Calculations were first performed on the N-methyl substituted DNA bases. Briefly, (i) The geometry of the dominant tautomer (as determined by Psciuk et al.7) was optimized at the B3LYP/6-31+G(d,p) level of theory and frequencies were calculated. (ii) the gas phase singlepoint calculation was conducted on the gas phase optimized geometry at the B3LYP/aug-ccpVTZ level of theory; and (iii) the geometry of each tautomer was optimized in aqueous solution at the IEFPCM/ B3LYP/6-31+G(d,p) level of theory using the gas phase optimized geometry as a starting point, cavity scaling parameter (alpha) value of 0.91 for the neutral and cationic species and 0.83 for the anions. The gas phase free energy for each model was obtained by the first two steps outlined above. Thus



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-./0123 2442'567//-./01/92.:;,'

=

-./01/92.:;,'

+=>-./01/92.:;,' + ∆?→@ABC

(7)

The solvation free energy is computed using the SMD implicit solvation model instead of the IEFPCM method described above in step 3.9 Thus -./0123 2442'567//-./01/92.:;,'

∗ =

-./01/92.:;,'

+=>-./01/92.:;,' + ∆?→@ABC ∗DE/-./01/92.:;,'

+ → +

(8)

The calculations presented here were originally performed on the Gaussian 03 suite of programs.15 Later on new calculations involving optimizations in aqueous solution were performed at the SMD/B3LYP/6-31+G(d,p) level of theory using the Gaussian 09 suite of programs.16 Psciuk et al.7 have pointed out that a more accurate method for computing gas phase free energies is the CBS-QB3 compound model chemistry. However, herein only calculations at the B3LYP level of theory were performed. Results and Discussion The first step was to tabulate the standard reduction potentials Eo(Nuc•+/Nuc) of the Nmethyl substituted DNA bases calculated by Psciuk et al.7 and to compare these results with the results reported by Schroeder et al.3 (summarized in Table 1). For the present study it was important to reproduce the results of these two groups, and then to populate spreadsheets so that one can see the influence of the various pKs on Eo and Em7. Table 1 shows that at the level of theory used in the present study to compute standard potentials Eo(Nuc•+/Nuc) yields an estimate for guanosine that is ~ 0.1 V below the experimentalbased value, although this base is clearly by far the most-easily oxidized, in agreement with concensus from many studies. For thymidine, theoretical calculations and experimental-based estimates of the standard reduction potential of the radical are in quite good agreement, although the uncertainty in the experimental value is much higher than that for guanosine. However, computed values for adenosine and cytidine are around 0.2–0.3 V higher than expectation.


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Table 1. Calculated Reduction Potentials of the DNA Nucleosides and comparison with values derived from experimental data.

Eo(Nuc•+/Nuc) / V Base

Em7(base radical/base) a / V From

Calculated

From

(B3LYP) b

experiment c

Guanine

1.37

1.47

0.96

1.29 ± 0.03

Adenine

1.79

1.61

1.38

1.44 ± 0.02

Cytosine

2.07

~1.8

1.67

~1.6

Thymine

1.86

~1.9

1.45

~1.7

a

calculation (B3LYP)

d

From experiment e

Mid-point potential at pH 7 of the radical/ground state couple, including protons in the

half-reaction. b Calculations by Psciuk et al.7 on N-Methyl substituted DNA bases. c Based on experimental values in aqueous solution taking into account prototropic equilibria using pK values in Schroeder et al.3

d

From standard potentials calculated in

the present study taking into account prototropic equilibria using pK values in Schroeder et al.3

e

Steenken and Jovanovic.1

It should be noted that the standard potential Eo(Nuc•+/Nuc) calculated for adenosine from the experimental data at pH 5 is rather sensitive to the value assumed for the pK of the radical. One-electron oxidation of deoxyadenosine produces a radical whose absorption spectrum does not change for pH ~ 11 down to pH ~ 1, from which it was originally concluded that the pK of the radical is ≤1,17 although a later comment by Candeias and Steenken suggested “the previously given value for the pK of ≤1 is probably too low”.18 As discussed below, it has recently been reported that the radical pK is actually ~4.2, a value used in the calculations of Schroeder et al.3 and assumed in the calculation ‘From experiment’ in Table 1. If the value of the radical pK is actually, e.g. 1, 2, or 3 then the value of the standard potential for adenosine, Eo(Nuc•+/Nuc), based on experiment changes from 1.61 V to e.g. 1.80, 1.73 V, or 1.68 respectively. This uncertainty is discussed further below. There is some uncertainty in the value of the pK of the adenosine radical, the value of 4.2 being used to derive the value of the standard potential based on the experimental data obtained



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using pH 5, rather than the much lower value of ≤1 based on earlier experiments. Such a value, recently used in previous papers in this context6, 19 has some support, but uncertainty remains. A good discussion of this problem can be found in a paper by Adhikary et al.20 Calculations of the pK of the –N6-H deprotonated adenine cation have recently been performed.8 The lowest energy is for the isomer with the N6-H hydrogen cis to N1; for this isomer the calculated pK is 3.9.17 (For the isomer with the N6-H trans to N1 the computed pK = 4.1.) Kobayashi has recently reported that the pK of the radical cation of deoxyadenosine is 4.2, determined experimentally by transient spectroscopy.21 However, in these experiments the solutions contained 5 mM base together with 0.1 M tert-butanol, the latter to scavenge hydroxyl radicals and prevent base-•OH radical-adducts being formed. The problem is that tert-butanol is probably about an order of magnitude less reactive towards •OH than adenosine; kinetic database values22 for rate constants recommend values for reaction of •OH + tert-butanol of 6.0 × 108 M–1 s–1, compared with 6.3 × 109 (pH 5) or 1.9 × 109 (pH ~ 2) M–1 s–1for adenosine. Hence in these experiments, approximately 14–33 percent of •OH radicals are likely to react with adenosine rather than with tert-butanol. Further, the spectral changes upon which this assignment was made occurred over timescales of a few tens of nanoseconds.21 In solutions containing 5 mM adenosine, the half-life of oxidation by the SO4•– radical is around 30 ns at the pH values of relevance, a timescale not dissimilar to that associated the spectral changes and ascribed by the authors to deprotonation of the adenosine radical-cation. Until further studies are performed, it seems likely that the fast absorbance changes reported cannot be unequivocally or exclusively ascribed to the prototropic equilibrium involving the adenosine radical. The next step is to attempt new calculations on the pKs of the nucleic acid bases so that one can explore the effects the various pKs have on calculating the values of Em7, and to see what improvements can be made with the calculations. One problem to consider involves the models to be used. Psciuk et al.7 have calculated the pKs for the N1 or N9 methylated bases as presented in Table 1 (above). They also include calculations on complete nucleosides but do not report complete calculations of the pKs or Em7s. This is important because the actual experimental measurements were performed on the nucleosides. For these calculations one has to decide on an appropriate model. It is easy to find the geometries of the ribosides as they occur in a polymer. However if one tries to calculate the optimized structure of just a monomer, one encounters intramolecular H-bonds. Such structures are unlike the polymeric structures. For the


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monomers, there is a tendency of the C2′-OH to rearrange so as to hydrogen bond with an N or an N-H on the base. This is reminiscent of the intricate H-bonded structures exhibited in the xray structures of the nucleosides.23, 24 For the present study, the ribosides are optimized without constraints and so do exhibit intramolecular H-bonds as shown in Fig. 1. The structures and optimized coordinates are in the Supporting Material.

Fig. 2. Structures of Cytidine. Left: Structure of Cytidine as in RNA, the C2-N1-C1′-C2′ torsion angle is 141.7º. Right: Gas phase geometry optimized structure of Cytidine, the C2-N1C1′-C2′ torsion angle is 72.2º and the intramolecular H-bond C2′-OH···O-C2 is 2.03Å.

For the first step the Em7 is calculated for guanosine. The results are presented in Table 2. For each entry one sees the experimental pKs if they are known. Then Em7 is calculated for guanosine using the formula in Steenken and Jovanovic1 with pKr1 = 2.4, pKr2 = 9.5, pKr3 = 12.3, pKo1 = 3.9 and pKo2 = 10.9 (the formula used can be found in the Supporting Information along with the specific tautomer associated with each pK). One might assume that the third deprotonation (pKr3) would occur at the guanine >C2-NH2. However von Sonntag points out that at pH ˃ 12.0 in the nucleosides deprotonation likely involves deprotonation at the ribose.25, 26 However, high pKs such as pKr3 have no impact in calculating values of Em7 from data obtained at pH values much less than these higher pKas.27 The second row in Table 2 contains efforts to calculate Eo from the computed pKs. The notation here (α=1.00) indicates use of the default value of the PCM cavity scaling factor in the



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SMD calculations. The third row contains calculations involving small variations in alpha to bring the computed pKs more in-line with the experimental pKs.

Table 2. Calculations of mid-point reduction potential (Em7) of the Ribosides Base pKr1 pKr2 pKr3 pKo1 pKo2 a Guanosine 1.9 9.25 12.33 3.9 10.9 3.5b (α=1.00) 12.9 (α=1.00) 21.5 (α=1.00) 2.8 (α=1.00) 16.8 (α=1.00) 2.3c (α=1.01) 9.6 (α=0.96) 12.9 (α=0.90) 4.2 (α=0.99) 10.4 (α=0.93) Adenosine 3.6d >13.75 ≤1 e 12.5 4.2 3.6 5.0b (α=1.00) 25.4 (α=1.00) 3.6 (α=1.00) c 3.8 (α=1.01) 16.6 (α=0.90) 0.4 (α=1.03) Cytidine 4.5e ~4.0 b 4.3 (α=1.00) 5.5 (α=1.00) 4.4c (α=1.01) d Thymidine 9.9 3.6 11.5b (α=1.00) 2.1 (α=1.00) 10.1c (α=0.98) 3.3 (α=0.98) a The experimental pKs listed here are from Steenken and Jovanovic.1 b The solvation free energies calculated here are with the SMD solvation model using default parameters.

c

The

solvation free energies calculated here are with the SMD solvation model using the cavity scaling factor α listed. d The experimental pKs listed here are from Steenken.17 e The experimental pKs listed here are from Psciuk et al.7

The next entry in Table 2 is for adenosine. The formula for computing Em7 is as shown by Schroeder et al.3 Their data included pKr1= 3.6, pKr2 = 12.5 and pKo1 = 4.2. For the pKr2 = 12.5 one again has to consider several sites of deprotonation. In the literature one sees that this deprotonation occurs at the C6-NH2,17 though as noted above, high pKs have no impact in calculating values of Em7. As discussed above there are reasons to question the pKo1 = 4.2. Using these three values Schroeder et al.3 calculated Em7 = 1.61 V. The other values for pKo1 in Table 2 show just how much this parameter varies with small changes in the pK obtained by small variations in alpha. The third entry in Table 2 is for cytidine. The formula for computing Em7 is as shown by Schroeder et al.3 and here in the Supporting Information. Their data included pKr1= 4.2, and a pKo1 = 4.0, with the pKo1 being the most sensitive term. Here one sees that the calculated pKs are


Em7 /V 1.29 1.22 1.30 1.79 1.61 1.64 1.83 1.78 1.69 1.75 1.90 1.99 1.92

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close to the experimental values even with the default α = 1.0 parameter. As such the three computed Em7 values cluster around 1.7 V. The last entry in Table 2 is for thymidine. Using the experimental pKr1 = 9.8, and a pKo1 = 3.6, Schroeder et al.3 compute Em7 = 1.90 V. Using the pKs calculated here yield very similar results. Conclusions The first part of this study dealt with calculations performed on model systems of the Nmethyl substituted nucleic acid bases as originally studied by Psciuk et al.7 The results in Table 1 shows that at the level of theory used in the present study to compute standard potentials E(Nuc•+/Nuc) yields an estimate for guanosine of 1.47 that is ~ 0.1 V below the experimental

value 1.58 determined from the Eo(Nuc•,H+/NucH+) couple. In their study of adenosine Schroeder et al. have calculated Eo(Nuc•+/Nuc) = 1.61 V and Eo(Nuc•,H+/NucH+) = 2.03 V.3 As discussed herein, much of this difference results for the choice for the pKo1 of adenosine being ~4.0 but there are uncertainties about the experimental value of this pKo1. The second part of the present study involves calculations of the pKs of the nucleic acid bases in order to explore the effects of the pKs have on the calculated values of Em7. Calculations were performed on the ribosides. Using the default parameters in the SMD solvation model the calculated values of Em7 are in good agreement with the experimental values and with only small changes in the cavity scaling factor (alpha) even better agreement is achieved.

Supporting Information The Supporting Information is available free of charge on the ACS Publication website. The supporting information contains: the formulas used for computing Em7; the specific tautomers associated with each pK; and the xyz coordinates of the optimized nucleosides used, along with intramolecular H-bonds.

Author Information Corresponding Author *E-mail: [email protected] Telephone: 423-439-5646



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Notes The authors declare no competing financial interest. Acknowledgements The idea for this study came about during a ACS symposium On Calculating pKs and Redox Potentials at the ACS Meeting in Boston last summer (arranged by H.B. Schlegel and M.L. Coote). After one of us (DMC) presented some of the ideas about the pK of the adenosine radical, Michael Sevilla (Dept. of Chemistry, Oakland, Univ.) suggested that many in the audience may not be aware of all the problems associated with measuring pKs. So thanks to Berny Schlegel and Michelle Coote for inviting me to their symposium, and thanks to Michael Sevilla for suggesting the present topic, and for helpful discussions. Thanks also to Anil Kumar (Dept. of Chemistry, Oakland, Univ.) for help with the calculations, and thanks to Einar Sagstuen (Dept. of Biophysics, Univ. of Oslo) for helpful suggestions. The Gaussian 09 calculations reported here were supported by the Extreme Science and Engineering Discovery Environment (XSEDE) allocation number MCB150023. Thanks for the generous computer time allocation (to DMC) to complete this project, and many thanks to Mahidhar Tatineni, San Diego Super Computer, for much help with calculations on Comet.

References and Notes 1.

Steenken, S.; Jovanovic, S. V., How Easily Oxidizable Is DNA? One-Electron Reduction

Potentials of Adenosine and Guanosine Radicals in Aqueous Solution. J. Am. Chem. Soc. 1997, 119, 617-618. 2.

Jovanovic, S. V.; Simic, M. G., One-Electron Redox Potentials of Purines and

Pyrimidines. J. Phys. Chem. 1986, 90, 974-978. 3.

Schroeder, C. A.; Pluhařová, E.; Seidel, R.; Schroeder, W. P.; Faubel, M.; Slaviček, P.;

Winter, B.; Jungwirth, P.; Bradforth, S. E., Oxidation Half-Reaction of Aqueous Nucleosides and Nucleotides via Photoelectron Spectroscopy Augmented by ab initio Calculations. J. Am. Chem. Soc. 2015, 137, 201-209. 4.

Sadlej-Sosnowska, N., Calculation of Acidic Dissociation Constants in Water: Solvation

Free Energy Terms. Their Accuracy and Impact. Theor. Chem. Acc. 2007, 118, 281-293.


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5.

Klamt, A.; Schüürmann, G. J., COSMO: A New Approach to Dielectric Screening in

Solvents with Explicit Expressions for the Screening Energy and its Gradient. J. Chem. Soc., Perkin Trans. 2, 1993, 799-805. 6.

Baik, M. H.; Silverman, J. S.; Yang, I. V.; Ropp, P. A.; Szalai, V. A.; Yang, W. T.;

Thorp, H. H., Using Density Functional Theory to Design DNA Base Analogues with Low Oxidation Potentials. J. Phys. Chem. B 2001, 105, 6437-6444. 7.

Psciuk, B. T.; Lord, R. L.; Munk, B. H.; Schlegel, H. B., Theoretical Determination of

One-Electron Oxidation Potentials for Nucleic Acid Bases. J. Chem. Theo. Comput. 2012, 8, 5107-5123. 8.

Close, D. M., Calculated pKa's of the DNA Base Radical Ions. J. Phys. Chem. A 2012,

117, 473-480. 9.

Marenich, A. V.; Cramer, C. J.; Truhlar, D. G., Universal Solvation Model Based on

Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113, 6378-6396. 10.

Thapa, B.; Schlegel, H. B., Calculations of pKa's and Redox Potentials of Nucleobases

with Explicit Waters and Polarizable Continuum Solvation. J. Phys. Chem. A 2014, 119, 51345144. 11.

Verdolino, V.; Cammi, R.; Munk, B. H.; Schlegel, H. B., Calculation of pKa Values of

Nucleobases and the Guanine Oxidation Products Guanidinohydantoin and Spirominodihydantoin using Density Functional Theory and a Polarizable Continuum Model. J. Phys. Chem. B 2008, 112, 16860-16873. 12.

Seidel, C. A. M.; Schultz, A.; Sauer, M. H. M., Nucleobase-Specific Quenching in

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One might assume that the third deprotonation would occur at the guanine >C2-NH2. So

herein pKr3 for guanosine was calculated for deprotonation at C2'-OH. Calculations show that deprotonation at C2'-OH of guanosine is indeed lower in energy than for deprotonation at >C2NH2.

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