Calculated pKa's of the DNA Base Radical Ions - American Chemical

Article pubs.acs.org/JPCA

Calculated pKa’s of the DNA Base Radical Ions David M. Close* Department of Physics, Box 70652, East Tennessee State University, Johnson City, Tennessee 37614, United States ABSTRACT: For the DNA bases the pKa’s of the neutral molecules have been measured, and a review article by Steenken provides a convenient summary of the experimental pKa’s of the DNA radical ions. The purpose of the present work is to attempt to calculate the pKa’s of the DNA radical ions and to compare these results with the experimental values. The agreement between the calculated and experimental pKa's for the guanine, cytosine, and thymine cations is very good but the pKa calculation on the adenine cation is not close to the experimental value. It is tempting to suggest that the pKa of the adenine cation is not actually ≤1 but is more likely somewhere near the calculated value of 3.9. Problems were encountered in calculating the pKa's of the one-electron reduced nucleobases because optimizations tend to produce nonplanar structures. The calculations presented show close agreement between the calculated and experimental pKa's for the thymine, cytosine, and adenine anions. Although there are no experimental data for the pKa of the guanine reduction product, the calculated value of 17.6 seems to be too high, given that for thymine the protonation is also at oxygen and results in a rather low pKa.

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INTRODUCTION An important review article by Steenken discussed the changes in acidity/basicity of the DNA bases upon one-electron gain or loss.1 If a base is one-electron oxidized, its acidity is increased. If a base undergoes one-electron addition, its basicity is increased. For example, Steenken and co-workers produced the adenine cation, A•+, from deoxyadenosine in aqueous solution employing laser photolysis and determined that the pKa of A•+ was ≤1. This value is very much lower that the pKa of the corresponding N6−H atom, which is ≥14 in neutral deoxyadenosine. This means that the acidity of the adenine moiety is increased by ca. 13 orders of magnitude upon one-electron oxidation. These reactions are important in understanding the radiation chemistry of the DNA bases in that they are useful in understanding which radicals are likely to be trapped in irradiated DNA constituents. There does not seem to be much in the literature about calculating the changes the pKa's of the DNA bases undergo upon one-electron gain or loss. It is of course relatively difficult to calculate accurate pKa's.2,3 For the DNA bases the pKa's of the neutral molecules have been measured, and Steenken’s article provides a convenient summary of the pKa's of the DNA radical ions.1 The purpose of the present work is to attempt to calculate the pKa's of the DNA radical ions, and to compare these results with the experimental values. Previous Work on Calculating the pKa's of the DNA Bases. Some time ago Goddard and co-workers attempted to compute the three pKa's of guanine denoted pKa1 ([G+H]+ → G°), pKa2 (G° → [G−H]−), pKa3 ([G−H]− → [G−2H]2−).4 Results within 0.2 units of the experimental values were obtained by adjusting the polarizable continuum model (PCM) parameter α (the electrostatic scaling factor of the radii of each sphere centered on the atoms), and by treating the free energy of solvation of a proton in water as an adjustable parameter.5 © 2012 American Chemical Society

This paper concludes with several important appendices that treat the basis set dependence on calculating the gas phase proton affinity, the basis set dependence on calculating the pKa's, and the extension of the techniques presented to calculating the pKa's of cytosine. More recently Verdolino et al.6 have calculated the pKa's of all the DNA bases and have supplied extensive Supporting Information on the details of all of their calculations. The computational methods used by Verdolino et al.6 are adopted herein, and consist of the following steps: (1) The geometry of each tautomer was optimized at the B3LYP/6-31+G(d,p) level of theory and frequencies were calculated. (2) A gas phase single-point calculation was conducted on the gas phase optimized geometry at the B3LYP/aug-cc-pVTZ level of theory. (3) 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. The α value was 1.00 (default setting). (4) A gas phase single-point calculation was conducted on the aqueous phase optimized geometry at the B3LYP/aug-ccpVTZ level of theory. (5) The free energy of solvation for the solution phase optimized geometry was obtained via a single-point calculation at the IEFPCM/B3LYP/6-31+G(d,p) level of theory using α values of 0.91 for the neutral and cationic tautomers and 0.83 for the anions. (6) The free energy in solution of each tautomer and pKa's were calculated as shown in Figure 1. Received: October 10, 2012 Revised: December 11, 2012 Published: December 14, 2012 473

dx.doi.org/10.1021/jp310049b | J. Phys. Chem. A 2013, 117, 473−480

The Journal of Physical Chemistry A

Article

(close to the 8.76 calculated by Verdolino et al.6) Both calculated values, however, are below the experimental pKa of 9.2−9.67). Also shown in Table 1 is the reaction G(N7+H)+ → G(−H) which represents the proton accepting ability of the native guanine molecule. The calculated pKa is 3.5, which compares well with the experimental pKa value of 3.2.7) The next entry in Table 1 is for deprotonation of thymine at N3−H. The pKa calculated here is 10.60, which compares closely with that of Verdolino et al.6 but both values are greater than the experimental value of 9.9.7 Also under thymine in Table 1 is a calculation on the proton accepting ability of the native thymine moiety at N3. The calculated pKa is −4.6 and agrees well with the experimental value of −5.9 The results in Table 1 show that the procedures detailed by Verdolino et al. give reasonable agreement between the calculated and the experimental pKa's of the DNA bases.6 The next step is to apply these procedures to the calculations of the pKa's of the radical ions of the DNA bases. We know that both Goddard and co-workers4 and Verdolino et al.6 had to alter the default PCM parameters to obtain satisfactory agreement with the experimental pKa's. Goddard and coworkers point out that calculations using the standard PCM parameters produce a pKa1 for guanine that is 1.4 units too low, and a pKa3 for guanine that is 1 unit too high.4 Thus for the cations the calculations were too acidic, and for the anions the calculations were too basic. This suggested that the atomic radii used to separate the continuum solvent from the explicit charges may be too large and therefore were adjusted as discussed in Verdolino et al’s. procedure above.6 There is no guarantee, however, that the PCM parameters they used will be suitable for calculations on the DNA radical ions. Previous Work on Calculating the pKa's of the DNA Base Radical Ions. Thorp and co-workers used density functional theory along with the COSMO solvation model10 to calculate the pKa's of the DNA base radical cations.11 Their results for guanine, cytosine, and adenine are reasonably close to the experimentally observed pKa values but differ by 2.8 units for thymine. Tureček and co-workers have calculated the pKa of the adenine cation radical using coupled-cluster methods for the reaction free energies in the gas phase, and several PCM models for the reaction free energies in solution.12 They report pKa's of 2.5 and 3.9 for deprotonation of the adenine cation radical at N6H2.13 The acid−base properties of the adenine cation radical have also been reported by Sevilla and co-workers.14 The concern Sevilla and co-workers had with Steenken’s1 original result was that further studies on dinucleosides of ApG and GpA determined that the rate of hole migration from one-electron oxidized A to G decreased from pH 2.3 to pH 7. Sevilla and coworkers have calculated that the pKa of A•+ is ≤1, using geometry optimizations at the B3LYP/6-31G(d) level of theory and PCM calculations with UAHF radii.14 Computational Methods. The results obtained by Verdolino et al.6 were performed on a development version of the Gaussian series of programs they called version E05. The author’s give the following details about their PCM calculations: Tight convergence criteria and the “nosymm” options were used for all optimizations. The solution phase optimizations employed a solvent excluding surface cavity model, UFF radii, and tesserae with an average area of 0.200 Å2. The initial calculations performed here were conducted on G03Rev E01,8 and agree well with the results of Verdolino et al.6 as shown in Table 1.

Figure 1. Thermodynamic cycle used to calculate pKa.

Here one sees that the standard free energy of solvation, ΔG(sol) * has been partitioned into a deformation term ΔE(dis) and a free energy of solvation term ΔGR(sol) ′ . This approximation was used to avoid problems of calculating the normal modes in solution. Then the pKa becomes 1.0 R′ ° (AR−) + ΔG(sol) ° (A−) pK a = (G(g) (A−) + ΔE(dis) 2.303RT R′ ◦ ° )(HAR) − ΔE(dis) − (G(g) (HA) − ΔG(sol) (HA) − 270.29)

As a check, Table 1 was populated with new calculations performed using these procedures, and with occasional use of Table 1. Calculated and Experimental pKa's of the Nucleobases nucleobase

reaction

adenine

A(N1+H) → A(−H) A → A(N6−H)− C(N3+H)+ → C(−H) C → C(N4-H)− G → G(N1−H)− G(N7+H)+ → G(−H) T → T(N3−H)− T(N3+H)+ → T(−H)

cytosine guanine thymine

+

calc pKaa 3.96 20.00 4.00 18.66 8.66 3.50 10.60 −4.6

(3.99) (4.15) (8.76) (10.67)

exp pKab 4.15 >14 4.45 >13 9.2−9.6 3.2 9.9 −5.0

a

Calculations by Verdolino et al.6 are in parentheses. bExperimental pKa values were taken from ref 7.

the starting geometries supplied by Verdolino et al.6 In these calculations very small changes in geometries can lead to local minima that contain imaginary frequencies, and therefore it is very helpful to have suitable starting geometries. The first entry in Table 1 involves adenine protonated at N1. The pKa for this species was calculated here to be 3.96, and by Verdolino et al.6 to be 3.99. Both calculations agree nicely with the experimental pKa of 4.15.7 The second entry under adenine involves information that is needed in the present work, that is, the pKa of the parent adenine moiety which is shown in Table 1 to be 20.0. Experimentally, it has only been determined that the pKa is greater than 14.1 The next entry in Table 1 involves a cytosine cation (protonation at N3). The pKa for deprotonation at N3 was calculated to be 4.0 compared to 4.15 calculated by Verdolino et al.6 The small differences arise from slight changes made to the PCM calculations in revisions of the Gaussian03 program.8 Also under cytosine in Table 1 is a calculation on the deprotonation of neutral cytosine at the C4−NH2 moiety. The calculated pKa is 18.66. All that is known experimentally is that the pKa for this reaction is >13.1 In Table 1 there is a calculation on the deprotonation of guanine at N1. The pKa for this reaction is calculated to be 8.66 474



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even at ∼10 K in single crystal experiments to yield a neutral G• radical.19 In single crystals of deoxyguanosine 5′-monophosphate, however, the G(−H)• radical is formed by deprotonation at the exocyclic N2, to yield a radical with hyperfine couplings at C8 and N2 (ρ(N2−H) = 0.33 and ρ(C8−H) = 0.175).19 The reaction is as shown here, along with a picture of the spin density of the G(N2−H)• radical (Figure 3).

One last concern is based on an observation by Goddard and co-workers.4 They show that simple changes such as ignoring diffuse functions in the calculation of the total energy of the molecule at 0 K can lead to a pKa that is off by 10 pKa units. However, what if one looks only at the end points, i.e., the comparison of the computed pK a compared with an experimental value? Might it be necessary to see if some of the steps in the calculations are based on improbable structures?15 For example, from Figure 1 one sees that the gas phase calculations are related to adiabatic ionization energy calculations and are known experimentally. There is an abundance of information on the structures of the anion and cation radicals involved in these calculations. Therefore, when relevant experimental data are available, they will be presented. Thus, when the one-electron oxidized guanine molecule deprotonates to produce a guanine radical, the computed structure will be examined to see if the spin densities agree with the experimental values, which are tabulated in a review article on the low-temperature defects identified by EPR/ENDOR spectroscopy on the X irradiated DNA bases.16

Figure 3. (a) Native guanine cation, (b) N2−H deprotonated cation, and (c) spin density of the N2−H deprotonated cation.

In the calculations performed here at the B3LYP/aug-ccpVTZ level of theory, the guanine cation deprotonated at the N2 position with the remaining hydrogen trans to N1 is lower in energy by 4.4 kcal/mol than the radical formed by deprotonation at N1. This agrees with calculations performed by Adhikary et al.20 They also performed calculations on these isomers with seven waters of hydration and found the N1 deprotonated isomer to be more stable than the N2 deprotonated isomer. The calculations for the deprotonation of the guanine cation are presented in Table 2. One sees that for deprotonation of

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RESULTS AND DISCUSSIONS It is important to point out that the experimental results discussed herein are mainly from the study of nucleosides, whereas the calculations presented are just on the nucleic acid bases without the ribose moieties.17 For the neutral bases, addition of the ribose only results in a small change in the pKa. For example the pKa of cytosine is 4.45, and the pKa of cytidine is 4.15.7 So as a first step calculations were performed to see what are the pKa's of the nucleobase radicals (anions and cations), and these are compared with experimental results. If there are only small differences in these comparisons, then this is a good check on the methods used in performing the calculations. If these efforts are successful, then they will be followed by calculations on the actual nucleosides. One-electron Oxidation of the DNA Bases. It is expected that radical cations will have lower pKa values than their parent compounds. Thus it is expected that the nucleobase radical cations should be much stronger acids than their parents. In this section calculations are performed to calculate the pKa's of the DNA bases after one-electron loss. Guanine. Deoxyguanosine is a weak acid with a pKa of 9.5.7 Upon one-electron oxidation the guanine cation has a pKa of 3.9.18 The difference in the pKa between the parent and the radical cation is −5.6, which represents a high driving force for deprotonation. The reaction envisioned by Steenken involved deprotonation of the guanine cation at the >N1−H position, as shown in Figure 2.1 This high driving force for deprotonation is likely the reason that the guanine radical cation deprotonates

Table 2. Calculated and Experimental pKa's of the Nucleobase Cations

a

nucleobase

reaction

calc pKa

guanine adenine cytosine thymine

G•+ → G(N1−H)• A•+ → A(N6−H)• C•+ → C(N4−H)• T•+ → T(N1−H)•

3.6 3.9 3.6−4.2 2.9−3.4

exp pKaa 3.9 ≤1 4.0 3.6

(Δ (Δ (Δ (Δ

= = = =

0.3) 2.9) 0.4) 0.2)

Experimental values are from ref 1.

N1−H the pKa is calculated to be 3.6, which compares well with the experimental pKa of 3.9.18 For completeness the two cases of deprotonation at N2 were also calculated. For the deprotonation that leaves an N2−H trans to N1, the pKa is calculated to be 5.2, and for the remaining proton cis to N1, the calculated pKa is 5.8. One can compare the experimental hyperfine couplings for the N2−H2 radical with the couplings calculated at the aug-ccpVTZ level of theory. The experimental C8−Hα isotropic hyperfine coupling is −13.8 MHz19 whereas the calculated coupling is −16.6 MHz. Likewise, the experimental N2−Hα isotropic coupling is −27.0 MHz19 and the computed coupling is −23.0 MHz. This is good evidence that the calculated spin density of the G(N2−H)• radical depicted in Figure 3 (pz-type orbital) accurately represents the known features of this radical as determined by detailed EPR/ENDOR experiments in the solid state. Adenine. One-electron oxidation of deoxyadenosine produces the radical cation of A•+ whose absorption spectrum does not change for pH ∼ 11 down to pH ∼ 1, from which it was originally concluded that the pKa of A•+ ≤1.1 Taking the

Figure 2. (a) Native guanine cation, (b) N1−H deprotonated cation, and (c) spin density of the N1−H deprotonated cation. 475



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pKa of adenine to be ≥14,21 the ΔpKa (A/A•+) ≥−13. Therefore, the acidity of adenine is increased by ≥13 orders of magnitude upon one-electron oxidation. This strong driving force is likely the reason that the adenine cation deprotonates in single crystals even at helium temperatures. For example, in X irradiated adenosine at 10 K, the dominate feature of the EPR spectrum is the −N6−H deprotonated adenine cation with spin densities ρ(N6−H) = 0.42 and ρ(C8−H) = 0.162.22 The scheme for deprotonation of the adenine radical cation of A•+ is as shown in Figure 4, along with the computed spin density of the N6 deprotonated radical.

Figure 5. (a) Native cytosine cation, (b) N4−H deprotonated cation, and (c) spin density of the N4−H deprotonated cation.

would be expected to have appreciable spin density at N1, N3, and N4 as shown by Geimer et al.24 There are no comparable experimental results from the solid state. In crystals of cytosine nucleotides for example, the cytosine is protonated at N3, and after one-electron oxidation, the cation deprotonates at N3.16 Calculations on the deprotonation of the cytosine cation are presented in Table 2. One sees that for deprotonation of N4− H2 the pKa is calculated to be 3.6 for the arrangement of the remaining N4−H hydrogen cis to N3, and 4.2 for the arrangement of N4−H trans to N3. The cis isomer is lower in energy than the trans isomer and the computed pKa agrees with the experimental pKa value which is 137 and the pKa of the radical cation (C−H)•+ ∼4.1 Therefore, one-electron oxidation leads to a ΔpKa (C/C•+) ≥ 9 orders in magnitude change in acidity. The cytosine radical cation (C−H)•+ deprotonates reversibly at N4 and has been characterized by Geimer et al.24 This reaction is shown in Figure 5. This radical

Figure 6. (a) Native thymine cation, (b) N3−H deprotonated cation, and (c) spin density of the N3−H deprotonated cation.

expected to have appreciable spin density at N1 and C5 as shown by Geimer et al.26,27 This radical has not been detected in the solid state. In the solid state there seems to be a preference for the thymine cation to irreversibly deprotonate at the >C5−CH3 yielding an allyl radical with spin density on both C5 and C6.16 Figure 6c shows the calculated spin density for the (T−H)•+ cation radical. Some explanation is needed here. If calculations are performed on this radical in the gas phase, this radical becomes very nonplanar and no longer has characteristics of a π-radical (as previously reported by Naumov et al.28) However, calculations on this structure in a PCM cavity result in a planar π-radical. This was the structure chosen for Figure 6c. Here the computed isotropic hyperfine couplings are 57.0 MHz for the C5−CH3 and 22.3 MHz for the nitrogen N1 coupling. These compare favorably with the respective experimental couplings of 57.8 and 17.7 MHz.28 476



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The calculated pKa of the N3 deprotonated (T−H)•+ cation is shown in Table 2 to be 3.4. This is in good agreement with the experimental pKa of 3.6.25 Revisiting the One-electron Oxidation of Adenine Problem. Looking at the results in Table 2, one sees that the agreement between the calculated and experimental pKa's for the guanine, cytosine, and thymine cations is very good. Small differences here (the Δ’s in column four) may be due to the fact that the calculations are for the nucleobases, whereas the experimental results are from studies on nucleosides. The problem here is that the pKa calculation on the adenine cation is not close to the experimental value. As pointed out in the Introduction, Sevilla and co-workers have done calculations on the pKa of the adenine cation and have produced results in agreement with the experimental value (≤1).14 There are several points to be considered here. Sevilla and co-workers calculated the pKa of the adenine cation by doing optimizations at the B3LYP/6-31G(d) level of theory and PCM calculations with UAHF radii.14 The PCMUAHF model was parametrized by Tomasi and co-workers at the HF/6-31G(d) level of theory using gas phase geometry.29 De Abreu et al. have looked at the effects of levels of theory on the calculations of the pKa's of histamine.30 They find that calculations at the B3LYP level of theory gives better results than does HF theory, but only when diffuse functions were used.31 Next one must consider the calculated results in Table 2. The pKa's for the guanine, cytosine, and thymine cations are all between 3.5 and 4.0. One should ask why the experimental value for the pKa of the adenine cation is so low (≤1)? For all four nucleobases the deprotonataion of the cation is at a nitrogen. Why then should there be such a big difference in the pKa between adenine and the other three nucleobases? Finally, one should ask how the calculations of pKa's with the PCM-UAHF method compared to the methods suggested by Verdolino et al.6 Table 3 shows calculations of the pKa's of all

Kobayashi has recently reported that the pKa of the radical cation of deoxyadenosine is 4.2, as determined by transient spectroscopy.33 One-Electron Reduction of the DNA Bases. All of the nucleic acid bases are good electron traps. Due to the increase in electron density, the electron adducts are considerably stronger bases than their neutral precursors. In this section calculations are performed to calculate the pKa's of the DNA bases after one-electron reduction. Attempts will be made to compare the calculations with experimental results. As for the structure of the various anions and protonated anions, one can compare these radicals with the structure of radicals in the literature. Some caution must be used because of the tendency of gas phase calculations to yield nonplanar structures. These same structures may not be present in the experimental literature. On the other hand, there are numerous experimental results that show large out-of plane hyperfine couplings that are not present in optimized calculations where for example protonation of an oxygen would generally be confined to the molecular plane. Thymine. The electron adduct of thymidine T•− is negatively charged at pH above 7.34 At lower pH values the electron adduct rapidly protonates reversibly at O4 to give a neutral radical T(O4)•. The pKa = 6.9.35 Because the pKa of the parent is −5,9 the basicity of the electron adduct increases by 12 orders of magnitude upon one-electron reduction. This reaction is shown in Figure 7. The C4−OH protonated thymine anion has been detected and characterized in the solid state.16 The calculated distribution of the spin density is shown in Figure 7c.

Table 3. Calculated and Experimental pKa's of the Nucleobase Cations

a

nucleobase

reaction

calc pKa

guanine adenine cytosine thymine

G•+ → G(N1−H)• A•+ → A(N6−H)• C•+ → C(N4−H)• T•+ → T(N1−H)•

2.11 −1.04 −1.58 1.23

3.9 ≤1 4.0 3.6

exp pKaa

Figure 7. (a) Native thymine anion, (b) O4−H protonated anion, and (c) spin density of the O4−H nonplanar protonated anion.

(Δ (Δ (Δ (Δ

Calculations on the pKa T•− protonation at C4−OH are given in Table 4. The calculated pKa = 7.2, which is close to the

= = = =

1.79) ∼2.00) 5.58) 2.37)

Table 4. Calculated and Experimental pKa's of the Nucleobase Anions


four nucleobase cations using the methods of Sevilla and coworkers compared with the experimental results.14 Comparing the results in Table 2 with the results in Table 3, one sees that the methods used by Verdolino et al.6 to calculate pKa's of the nucleobases give better agreement with the experimental results. In comparing the results in Tables 2 and 3, one sees that the calculated pKa's in Table 3 are too low compared to the experimental values. This is in part due to calculation of the gas-phase reaction free energy (which on average are 5 kcal/ mol lower in Table 3 than in Table 2.) There are also differences in the calculation of the free energies of solvations.32 Based on the results presented here, it is tempting to suggest that the pKa of the adenine cation is not actually ≤1 but is more likely somewhere near the calculated value of 3.9 as shown in Table 2. There is experimental evidence that this is so.

nucleobase thymine cytosine adenine guanine a

reaction •−

•

T → T(O4+H) C•− → C(N3+H)• A•− → A(N1+H)• G•− → G(O4+H)•

calc pKa

exp pKaa

7.2 16.3 12.6 17.6

6.9 >13 12.1 unknown


experimental value of 6.9 determined by pulse radiolysis.35 The major site of spin density in the C4−OH protonated electron adduct would be at C6. The experimental C6−Hα hyperfine coupling is −39.8 MHz,36 in excellent agreement with the calculated value here of −38.9 MHz. As for the small hyperfine couplings, we have the N3−Hα experimental hyperfine coupling of 6.0 MHz36 compared to the calculated value of 3.4 MHz. The calculated C4−OH hyperfine coupling is large 477



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calculated to be 7.7 kcal/mol above the minimum energy (nonplanar) structure described above. Because there are three experimental structures of the N3 protonated adenine anion in the literature,16 it was decided to compute the pKa of this structure to compare the results with the calculations on the N1 protonated anion. This reaction is depicted in Figure 10. Calculations on this structure showed

here because the hydrogen is out of the molecular plane, as was detected in the solid state (as shown in Figure 7c).16 The evidence then is that the calculations on the C4−OH adduct are well represented by the spin density shown in Figure 7c. Cytosine. The deoxycytidine N3H radical C(N3H) • remains unaltered from pH 6 to pH 13, which means that the pKa of the protonated electron adduct is >13.35 The pKa of cytosine(N3+H)+ is 4.4. Therefore, the ΔpKa upon electron addition is >9 orders of magnitude. The reaction is as shown in Figure 8. The N3−H protonated cytosine anion has been

Figure 10. (a) Native adenine anion, (b) N3−H protonated anion, and (c) spin density of the N3−H planar protonated anion. Figure 8. (a) Native cytosine anion, (b) N3−H protonated anion, and (c) spin density of the N3−H planar protonated anion.

that the amino hydrogen’s remained in the molecular plane. However, the protonation at N3 lead to a nonplanarity at this site. Therefore, the spin densities shown in Figure 10c were calculated from a planar structure. The calculated energy of this structure is only 0.6 kcal/mol above the nonplanar minimum energy structure. The computed spin densities are shown in Figure 10c. A comparison of the calculations with the experimental results22 (in parentheses) has the major isotropic hyperfine couplings as C2−H −39.8 (−29.8) MHz, C8−H −11.9 (−11.4) MHz, and N3−H 12.8 (−9.8) MHz. The evidence then is that the calculations on the N3−H adduct are well represented by the spin density shown in Figure 10c. In Table 4 one sees that the computed pKa of the adenine electron adduct A•− protonated at N1 is 12.6, which is slightly above the experimental pKa of 12.1.38 Calculations on the adenine electron adduct A•− protonated at N3 yields a pKa = 14.6. Guanine. The radical anion of deoxyguanosine has not been fully studied in solution. In the solid state the electron adduct is protonated at O6, as shown in Figure 11.16 There are also studies of the guanine anion protonating at carbon C8.40

observed and characterized in cytosine monohydrate, and in 1MeCytosine.16 The distribution of spin density of this radical is as shown in Figure 8c. Calculations on the pKa of the cytosine anion for protonation at N3 are given in Table 4. The calculated pKa is 16.3. The experimental value of the pKa is said to be >13. The major site of spin density in the N3−H protonated electron adduct would be at C6. The experimental C6−Hα hyperfine coupling is −38.6 MHz, in agreement with the calculated value here of −40.1 MHz.16 The calculations also show a large hyperfine coupling to one of the C4−NH2 hydrogen’s due to pyramidilization, as previously noted by Wetmore et al.,37 but in the solid state these hydrogen’s are in the molecular plane. The spin density depicted in Figure 8c was calculated with the C4−NH2 hydrogen’s constrained to be in the molecular plane. This structure is calculated to be 3.2 kcal/mol above the minimum energy (nonplanar) structure described above. Adenine. The adenosine electron adduct A•− pKa is 12.1,39 whereas the pKa of the protonated parent is 3.5.7 Therefore, the ΔpKa (A(NH)+/A(NH)•) = 8.6. The reaction involving the N1H is shown in Figure 9. The problem here is that after

Figure 11. (a) Native guanine anion, (b) O6−H protonated anion, and (c) spin density of the O6−H planar protonated anion. Figure 9. (a) Native adenine anion, (b) N1−H protonated anion, and (c) spin density of the N1−H planar protonated anion.

The same problems arose here on attempts to optimize the O6−H protonated anion as discussed above under adenine. Basically, if allowed to optimize without constraints, the results converge to a C6−OH σ-radical. The results are similar to the nonplanar radical discussed by Wetmore et al.41 Because there is no experimental evidence of a σ-radical on guanine, calculations were performed on a structure optimization to preserve Cs symmetry. This results in a planar radical with a majority of the spin density on C8. The experimental isotropic hyperfine coupling for C8−Hα is −8.5 MHz,19 and the

electron capture and protonation at N1 calculations show that the molecule undergoes changes in the geometry of the ring at C6. The molecule becomes nonplanar, and the amino group rotates out of the plane (as described by Wetmore et al.39). Unfortunately there are no experimental studies to support these observations because in the solid state protonation of the electron adduct A•− is observed to be at N3. To complete Figure 9, the spin density shown is for a calculation with the NH2 protons confined to the molecular plane. This structure is 478



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computed value of this coupling is −7.1 MHz. Thus Figure 11c depicts a π-radical that exhibits the features described by the experimental results on the O6−H protonated anion. This structure is calculated to be 2.6 kcal/mol above the minimum energy (nonplanar) structure. The calculated pKa of the O6−H protonated anion is 17.6. If one chooses the nonplanar structure that converges to a C6− OH σ-radical, the calculated pKa is 10.6. There is no experimental value in the literature, so there is no way to know which of these calculated values is likely to be closer to what one would actually measure experimentally.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Most of the calculations presented here were performed with the help of William Nelson at Georgia State University who provided access to three 64-bit quad core computers. Sadly Bill died before this work was completed. Special thanks here to Duke Windsor (GSU) for help in keeping these machines up and running till this work was completed. Thanks also to Anil Kumar, Oakland University, for sending examples of calculations used for calculating the pKa of the adenine cation as described in ref 14. Thanks to Roman Zubatyuk and Oleg Shishkin, NAS of Ukraine, for providing help in improving the calculations presented here. Also, thanks to Mike Sevilla, Oakland University, for suggesting the use of ref 33 herein.

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CONCLUSIONS Table 2 contains a comparison of the calculated and experimental pKa's of the nucleobase cations. The agreement between the calculated and experimental pKa's for the guanine, cytosine, and thymine cations is very good. This is not the case for calculating the pKa of the adenine cation. With the methods of calculating pKa's as prescribed by Verdolino et al.,6 the difference between the calculated and experimental pKa is ca. 3 pKa units. As noted above, the author of the original experimental value has said that “it is too low”.23 There is a new experimental pKa value for the adenine cation reported by Kobayashi of 4.2, which is close to the calculated value reported here.33 There are other methods for calculating pKa's described in the literature. For example Sevilla and co-workers calculated the pKa of the adenine cation by doing optimizations at the B3LYP/6-31G(d) level of theory and PCM calculations with UAHF radii.14 This approach did give a pKa of adenine near the original experimental value (≤1). However, as seen in Table 3, this method tends to considerably underestimate the experimental value of the other three nucleobases. So it seems as if for the cations of the nucleobases at least the methods described by Verdolino et al. give better agreement with the experimental results.6 Problems were encountered in calculating the pKa's of the one-electron reduced nucleobases. The primary problem is that optimizations tend to produce nonplanar structures. In the case of guanine, the nonplanarity is significant and results in a σradical, in which the spin density is in the molecular plane. The interest here is in a study of radicals that are present in irradiated DNA, for which only π-radicals are observed.16 So if σ-radicals were found upon optimization, calculations were performed on planar (Cs symmetry) structures. There are of course problems in comparing experimental results obtained in the solid state, and measurements made in solution with the calculations performed herein. The calculations presented in Table 4 show close agreement between the calculated and experimental pKa's for thymine cytosine and adenine. There is no experimental data for the pKa of the guanine reduction product. The calculated value of 17.6 seems to be too high, given that for thymine the protonation is at oxygen and results in a rather low pKa. Of course the guanine anion may not actually protonate at a heteroatom. Steenken has suggested that there is evidence the protonation is actually protonated at C8.1 Finally, it seems safe to say that the methods described by Verdolino et al.6 for calculating pKa's, and applied here to calculating the pKa's of the one-electron oxidized and oneelectron reduced nucleobases yield results that are reasonably close to the known experimental pKa's.

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REFERENCES

(1) Steenken, S. Free Radical Res. Commun. 1992, 16, 349−379. (2) The important thing here is to note that an error of 1.36 kcal/mol in the calculation of the free energy of reaction results in an error of 1 pKa unit. (3) Alongi, K. S.; Shields, G. C. Theoretical Calculations of Acid Dissociation Constants: A Review Article. Ann. Rep. Comput. Chem. 2010, 6, 113−138. (4) Jang, Y. H.; Goddard, W. A.; Noyes, K. T.; Sowers, L. C.; Hwang, S.; Cheng, D. S. J. Phys. Chem. B 2003, 107, 344−357. (5) In the 1990s the acceptable range was −254 to −261 kcal/mol. In 2010 the accepted value was −265.9 kcal/mol. See ref 3. (6) Verdolino, V.; Cammi, R.; Munk, B. H.; Schlegel, H. B. J. Phys. Chem. B 2008, 112, 16860−16873. (7) Ts’o, P. O. P. Bases, Nucleosides, and Nucleotides. In Basic Principles in Nucleic Acid Chemistry; Ts’o, P. O. P., Ed.; Academic Press: New York, 1974; Vol. 1, pp 454−584. (8) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant; et al. Gaussian 03, Revision E.01; Gaussian, Inc., Wallingford, CT, 2004. (9) Garcia, B.; Palacios, J. Ber. Bunsen-Ges. Phys. Chem. 1988, 82, 697−700. (10) Klamt, A.; Schuurmann, G. J. Chem. Soc., Perkin Trans. 1993, 799805. (11) Baik, M.-H.; Silverman, J. S.; Yang, I. V.; Ropp, P. A.; Szalai, V. A.; Yang, W.; Thorp, H. H. J. Phys. Chem. B 2001, 105, 6437−6444. (12) Chen, X.; Syrstad, E. A.; Nguyen, M. T.; Gerbaux, P.; Tureček, F. J. Phys. Chem. A 2004, 108, 9283−9293. (13) These differences arise because the authors have used two different PCM schemes, one involving proton transfer to water, and one involving proton transfer to OH−. (14) Adhikary, A.; Kumar, A.; Khanduri, D.; Sevilla, M. D. J. Am. Chem. Soc. 2008, 130, 10282−10292. (15) There are several problems that can appear. Optimizations can converge to σ radicals with a majority of the spin density in an oxygen 2Py orbital. Also, when one compares Hartree−Fock orbitals and Kohn−Sham orbitals involving oxygen, the HF method has the pz-type orbitals higher in energy that the pxpy-type orbitals, whereas the opposite is true for DFT calculations. (16) Close, D. M. Radiat. Res. 1993, 135, 1−15. (17) The problem here is that the nucleic acid bases, especially the purines, are not very soluble in water. The solubility can be increased by using the nucleosides. (18) Candeias, L. P.; Steenken, S. J. Am. Chem. Soc. 1989, 111, 1094. 479



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(19) Hole, E. O.; Nelson, W. H.; Sagstuen, E.; Close, D. M. Radiat. Res. 1992, 129, 119−138. (20) Adhikary, A.; Kumar, A.; Becker, D.; Sevilla, M. D. J. Phys. Chem. B 2006, 110, 24171−24180. (21) Hissung, A.; von Sonntag, C.; Veltwisch, D.; Asmus, K.-D. Int. J. Radiat. Biol. 1981, 39, 63−71. (22) Close, D. M.; Nelson, W. H. Radiat. Res. 1989, 117, 367−378. (23) Candeias, L. P.; Steenken, S. J. Am. Chem. Soc. 1993, 115, 2437− 2440. (24) Geimer, J.; Hildenbrand, K.; Naumov, S.; Beckert, D. Phys. Chem. Chem. Phys. 2000, 2, 4199−4205. (25) Deeble, D. J.; Schuchmann, M. N.; Steenken, S.; von Sonntag, C. J. Phys. Chem. 1990, 94, 8186−8192. (26) Geimer, J.; Beckert, D. J. Phys. Chem. A 1999, 103, 3991−3998. (27) Geimer, J.; Brede, O.; Beckert, D. Chem. Phys. Lett. 1997, 276, 411−417. (28) Naumov, S.; Barthel, A.; Reinhold, J.; Dietz, F.; Geimer, J.; Beckert, D. Phys. Chem. Chem. Phys. 2000, 2, 4207−4210. (29) Barone, V.; Cossi, M.; Tomasi, J. J. Chem. Phys. 1997, 107, 3210−3221. (30) De Abreu, H. A.; De Almeida, W. B.; Duarte, H. A. Chem. Phys. Lett. 2003, 383, 47−52. (31) The experimental pKa2 of histamine is 9.2. At the HF/631G(d,p) level of theory pKa = 0.82 and is 5.9 at HF/6-31++G(d,p). At the B3LYP/6-31G(d,p) level of theory pKa = −0.50 and is 9.73 at B3LYP/6-31++G(d,p). See ref 30. (32) For cytosine and thymine the ΔGsol(cation) are close for either method, but the ΔGsol(neutral) differ more than 3 kcal/mol. For adenine both ΔGsol(cation) and ΔGsol(neutral) differ by ca. 4 kcal/ mol, and for guanine the ΔGsol(cation) calculations also differ by ca. 4 kcal/mol whereas the ΔGsol(neutral) values are fairly close. (33) Kobayashi, K. J. Phys. Chem. 2010, 114, 5600−5604. (34) Novais, H. M.; Steenken, S. J. Am. Chem. Soc. 1986, 108, 1−6. (35) Steenken, S.; Telo, J. P.; Novais, H. M.; Candeias, L. P. J. Am. Chem. Soc. 1992, 114, 4701−4709. (36) Sagstuen, E.; Hole, E. O.; Nelson, W. H.; Close, D. M. J. Phys. Chem. 1992, 96, 1121−1126. (37) Wetmore, S. D.; Himo, F.; Boyd, R. J.; Eriksson, L. A. J. Phys. Chem. B 1998, 102, 7484−4791. (38) Candeias, L. P.; Steenken, S. J. Phys. Chem. 1992, 96, 937−944. (39) Wetmore, S. D.; Boyd, R. J.; Eriksson, L. A. J. Phys. Chem. B 1998, 102, 10602−10614. (40) Hüttermann, J. Radical Ions and Their Reactions in DNA and its Constituents. In Radical Ionic Systems: Properties in Condensed Phases; Lund, A., Shiotani, M., Eds.; Kluwer Academic Publishers: Dordrecht/Boston/London, 1991; Vol. 6, pp 435. (41) Wetmore, S. D.; Boyd, R. J.; Eriksson, L. A. J. Phys. Chem. B 1998, 102, 9332−9343.

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Calculated pKa's of the DNA Base Radical Ions - American Chemical

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