Electron Spin Resonance Study of Electron Transfer in DNA: Inter

In this work, we employ frozen glassy aqueous (D2O) solutions of DNA at various concentrations in order to test for inter-DNA-double-strand electron t...
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J. Phys. Chem. B 2000, 104, 6942-6949

Electron Spin Resonance Study of Electron Transfer in DNA: Inter-Double-Strand Tunneling Processes Zhongli Cai and Michael D. Sevilla* Department of Chemistry, Oakland UniVersity, Rochester, Michigan 48309 ReceiVed: March 13, 2000; In Final Form: May 15, 2000

In this work, we employ frozen glassy aqueous (D2O) solutions of DNA at various concentrations in order to test for inter-DNA-double-strand electron transfer, i.e., transfer from one DNA double strand to another. Electrons generated by radiation are trapped on DNA and transfer to a randomly interspersed intercalator, mitoxantrone (MX). The monitoring of the buildup of the ESR signal of the MX radicals and the loss of the ESR signal of the DNA radicals with time at 77 K allows for the direct observation of the rate of electron transfer (ET). The fraction of MX radicals and the apparent ET distances after irradiation are found to increase with the concentration of DNA as well as with time. A model that assumes transfer both along and between DNA double strands (ds’s) is proposed and found to fit experimental results for the concentration dependence of apparent ET distances. Values for β and the ET distances found are in good agreement with our previous results for dilute aqueous glassy media. We find that extensive tunneling of electrons and holes in frozen D2O aqueous solutions (ices) and solid DNA (hydrated to 21 waters per nucleotide) can also be explained by inter-double-helix transfer. DNA in ices and DNA in hydrated solids give nearly identical results, suggesting that the DNA strands in ices are as closely packed as those in the hydrated solid DNA samples. Our results suggest that previous reports of extensive electron-transfer distances for DNA in icy media are found to be better explained by substantial inter-double-strand electron transfer. After correction for the inter-doublestrand electron/hole transfer, we find similar values of β and ET distances along one DNA ds (10 ( 1 bp at 1 min) in each medium (glass, ice, or hydrated DNA solid). Another simple tunneling model that assumes no difference in the transfer rates along the DNA helix, across it, or through the solution is found to give reasonable results for the ET distances, suggesting that at 77 K DNA is not an especially effective conduit for the transfer of excess electrons.

Introduction The transfer of the electrons and holes within DNA has attracted considerable recent interest.1-29 Various mechanisms such as single-step tunneling,20,30,31 multistep (phonon-assisted) hopping,20,30,32,33 clustering,34 and activation-energy-controlled transfer35 are proposed to explain either long- or short-range transfer of electrons and holes through DNA. Whereas most concern has been concentrated on transfer along the DNA double strands (ds’s), the possibility of transfer between DNA double strands has been largely neglected, with the exception of one recent report that found no evidence for such transfer.8 Because DNA is closely packed in chromatin, such potential inter-ds processes may be important in radiation damage to living systems. Pezeshk et.al. reported that the mean distance traveled by the ejected electrons prior to any type of capture in frozen aqueous solution of DNA intercalated by electron-affinic mitroxantrone was ca. 31 base pairs at 77 K.36 In contrast, our previous study showed that the mean distance traveled by the electrons in a frozen 7 M LiBr dilute aqueous solution of DNA intercalated by mitroxantrone at 77 K was only ca. 10 base pairs.37 In the frozen aqueous solution employed by Pezeshk et.al, two phases are formed, one comprising pure ice and the other containing closely packed DNA and associated water. In * Author to whom correspondence should be addressed. E-mail: sevilla@ oakland.edu. Fax: 248 370 2321.

a frozen 7 M LiBr aqueous solution, only one glassy phase is formed, in which DNA double strands are homogeneously distributed. One aim in this work is to answer the question: Does inter-double-strand electron transfer explain the difference in electron-transfer distances through DNA in frozen ices and in glassy aqueous solutions? In the present effort, we employ frozen aqueous glasses, frozen aqueous ices, and hydrated solid DNA plugs at low temperature (77 K) under conditions that allow single-step tunneling as the only likely mode of transfer. ESR spectroscopy is applied to directly observe both DNA and mitoxantrone (MX) electron adducts and holes as a function of time and average distances between adjacent DNA double strands. Our previous work at low DNA concentrations in glassy solutions suggested no inter-ds transfer; however, at the higher concentrations used in this work, we find that electron transfer (ET) between adjacent DNA double helices is an important process. A threedimensional model of electron transfer both along DNA double strands and across to adjacent DNA double strands is found to simulate the experimental dependence of electron transfer in DNA as a function of the distances between adjacent DNA double strands. Experimental Section Sample Preparation. Preparation of Mitoxantrone-Intercalated DNA Solids. Various molar ratios of salmon sperm DNA with MX were prepared by addition of ca. 1 mg/mL MX

10.1021/jp000956w CCC: $19.00 © 2000 American Chemical Society Published on Web 06/22/2000

ESR Study of Electron Transfer in DNA aqueous solution into an aqueous solution of 100 mg/mL DNA slowly with stirring under nitrogen. The mixture was allowed to sit in the dark for long periods (days to weeks), was stirred periodically with a vortex mixer, and then was freeze-dried when the solutions appeared uniform. Glassy Samples. Aqueous solutions containing 7 M LiBr were prepared by addition of 0.3 mL of D2O to various amounts of freeze-dried solid, followed by addition of 0.7 mL of 10 M LiBr. The resulting mixture was kept in the dark for several days and stirred daily with a vortex mixer until the solution appeared homogeneous. Solutions were drawn into thin-wall 4-mm Suprasil quartz tubes and then cooled to 77 K in liquid nitrogen, resulting in a glassy homogeneous sample. The glassy samples were gamma irradiated for the absorbed dose of 0.88 kGy (20 min). On irradiation of the 7 M LiBr glass, the majority of the initial ionization occurs in the solution and creates electrons and holes. The electrons are scavenged by the solutes, and the holes remain in the glass as Br2-•. This species has a very broad ESR spectrum, extending many hundreds of gauss, and does not interfere with the DNA and MX radical signals, which extend less than 75 G. Frozen Samples. Aqueous solutions were prepared by addition of 1 mL of D2O to various amounts of freeze-dried solid DNA intercalated with MX. The resulting mixture was allowed to stand in the dark for several days, with daily vortex mixing, until the solid was dissolved homogeneously. The solution was drawn into a glass tube with inner diameter of 4 mm and frozen in liquid nitrogen; the resultant ice plug was pushed out into liquid nitrogen after the glass wall was warmed sufficiently. The ice samples were irradiated for 2.6 kGy (60 min). Frozen aqueous solutions of MX-DNA consist of two phases: one is pure ice, and the other is a glassy region containing MX-DNA and glassy water. Irradiation of the frozen aqueous solution produces both electrons and holes within the DNA, as well as trapped •OH radicals in the ice. Ice samples were annealed at 125 K for 3 min to remove ice radical signals before ESR analysis was performed. Previous work has shown that the icephase •OH radicals do not attack the DNA, which is in its own separate phase.38 Hydrated Samples. About 100 mg of freeze-dried solid intercalated DNA was kept for 10 days in a desiccator containing D2O saturated with KCl under N2 gas. The hydrated solids (Γ ) 21 water molecules/nucleotide) were pressed into 4-mmdiameter solid plugs with an aluminum press in a N2 bag and then placed in liquid nitrogen. Hydrated DNA samples were irradiated for 2.6 kGy (60 min). Irradiation of the hydrated solids produces both electrons and holes within DNA. All preparations were performed under nitrogen. Irradiated samples were kept in the dark in liquid nitrogen through out all experiments. Methods of Analysis. Electron Spin Resonance. ESR spectra were taken on a Varian Century Series EPR spectrometer operating at X-band with a dual cavity and a 200-mW klystron and with Fremy’s salt (g ) 2.0056, AN ) 13.09G) as a reference. The spectra were recorded within a few minutes after irradiation and at increasing time intervals thereafter. Benchmark Spectra. Methods of analysis were similar to those used in our previous work.37 The ESR spectra of DNA and MX radicals in 7 M LiBr, D2O aqueous solutions, and hydrated solids at 77 K were produced as benchmark spectra (Figure 1). The similarity of the ESR spectrum of MX radicals in the 7 M LiBr glass (that consists of chiefly electron adducts) with the ESR spectra of MX radicals in ice and hydrated solids (that have

J. Phys. Chem. B, Vol. 104, No. 29, 2000 6943

Figure 1. First-derivative electron spin resonance “benchmark” spectra of MX radicals (left) and DNA radicals (right) used in the analyses of DNA-MX complex systems. Solid lines, in 7 M LiBr glasses; dotted lines, in a D2O ice (frozen D2O solutions); and dashed lines, in hydrated solid DNA. The spectra for both MX and DNA radicals in D2O ice and hydrated solid DNA are nearly identical, but they differ slightly from those in 7 M LiBr glasses. This is because only electron adducts to MX and DNA are produced in 7 M LiBr glasses (the holes are trapped within the glassy matrix), whereas both electron adducts and holes of MX and DNA are formed in D2O ices and hydrated solids. The three markers are each separated by 13.09 G. The central marker is at g ) 2.0056.

both electron adducts and holes) is considered good evidence that MX species with both one electron gain and one electron loss have similar ESR spectra in these systems. An advantage to our analyses is that the doublet ESR spectrum of DNA radicals and the single-line ESR spectrum of MX radicals are easily distinguished. This creates an excellent system for analyses of the relative fraction of each in a spectrum that is a combination of DNA radicals and MX radicals. Linear leastsquares fitting of benchmark spectra to experiment is employed to determine the fractional composition of DNA and MX radicals. The dashed lines in Figures 2 and 5 show the fits to experiment. The shape of the ESR spectrum of DNA radicals in frozen ice or hydrated solid, obtained by the subtraction of the spectrum of MX radicals from the mixed spectra of both DNA and MX radicals, does not change with time. Analysis for Apparent Transfer Distance along DNA Double Strands and Apparent Tunneling Constants. For random intercalation, when the mole ratio of MX to DNA base pairs (ν) is far smaller than 1, the probability that at least one MX is present within Da base pairs from the trapped electrons or holes is given by37

F(t) ) 1 - (1 - ν)2Da(t)

(1)

F(t) also represents the fraction of all electrons and holes captured by MX at time t relative to all electrons and holes originally captured by the DNA-MX system. The simple rearrangement of eq 1 leads to the relation for the apparent timedependent scavenging distance along DNA double strands, Da(t).

Da(t) )

ln[1 - F(t)] 2ln(1 - ν)

(2)

Furthermore, we make use of the approximate relation for the time dependence of Da, successfully used for tunneling kinetics in glasses39 and in our previous work37 in DNA,

Da(t) ) (1/β) ln(k0t)

(3)

where k0 is the fundamental electron-transfer rate (constant) and Da and β are in units of base pair (bp) and inverse base pair (bp-1), respectively. For a tunneling process, plots of Da vs ln(t)

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Figure 2. First-derivative electron spin resonance spectra show spectra recorded 4 days after γ-irradiation of samples at various DNA concentrations in 7 M LiBr. All samples have a molar ratio of MX/bp of 1/52. The spectra clearly show that MX radicals increase in amount relative to the DNA radicals with increased concentration of DNA. The results suggest the possibility of electron transfer across adjacent DNA double strands. The fraction of electrons captured by MX is also found to increase with time. The dashed lines are the linear least-squares fits of benchmark ESR spectra of DNA and MX electron adducts to experimental spectra (solid lines).

are expected to be linear with the slope equal to 1/β. For samples with inter-double-strand electron transfer, Da becomes the total capture distance along the primary and near-neighbor double strands. In addition, the β value is artificially reduced by interdouble-strand electron transfer, and this apparent β value will be called R. A full model to account for the inter-double-strand transfer is given in a following section. Results Effect of DNA Concentration on Electron Transfer from DNA to MX in 7 M LiBr Glass. Figure 2 shows the ESR spectra recorded 4 days after γ-irradiation of three samples of MX-DNA in 7 M LiBr containing 20, 102, and 198 mg/mL DNA. All samples have a 1/52 molar ratio of MX/bp. As the concentration of DNA increases, the fraction of MX radicals in all radicals formed rises, e.g., from 38.5% at 20 mg/mL DNA to 59.4% at 198 mg/mL DNA. Similar results are also observed for lower MX loading (MX/bp ) 1/208). These results show a clear dependence of ET on DNA concentration and suggest electron transfer to adjacent DNA double helices as a possible source of this dependence. The fraction of electrons captured by MX increases with time. The apparent distances of electron transfer along DNA double strands are derived from eq 2. In Figure 3, plots of the apparent ET distance vs the natural logarithm of time at various DNA concentrations with MX/bp ) 1/52 are given. For a lower MX loading (MX/bp ) 1/208), similar results are obtained. The linearity in ET distance with ln(t) implies a tunneling process.37 Values of the apparent ET distance at one minute, Da(1min), and of R (the apparent β) derived from the linear least-squares fits of eq 3 to the data are provided in Table 1. Figure 4 shows plots of the apparent ET distances (Da) at 1 min and 15 days, the computed average distances between DNA double strands (Dds), and the tunneling distance decay constants (plotted in the insert) vs the concentration of DNA in 7 M LiBr glasses with a loading of MX to base pairs of 1/52 or 1/208 at 77 K. At the lowest concentration of DNA, 20 mg/mL, the apparent ET distance at 1 min and the R value are 9.2 ( 0.5 bp and 1.0 ( 0.4 Å-1, respectively. These results are consistent with our previous report that investigated DNA concentrations from 5-20 mg/mL.37 As the concentration rises to higher levels, the apparent transfer distance increases up to 13.6 ( 0.6 bp at 200 mg/mL and the R value falls to 0.27 ( 0.04 Å-1. This low

Cai and Sevilla

Figure 3. Plot of apparent electron-transfer distance vs natural logarithm of time (in minutes) for glassy samples of MX-DNA (frozen 7 M LiBr solutions) at various concentrations of DNA with a MX/bp mole ratio of 1/52. Lines are fits to eq 3. A clear dependence of the electron-transfer distance on concentration, as well as on time, is shown.

TABLE 1: Electron Tunneling Distances and Tunneling Decay Constants (r and β) vs DNA Concentration and MX Loading in a 7 M LiBr Glass at 77 Ka,b [DNA] 1/ν (g/mL) (bp/MX) n 0.22 0.10 0.053 0.025 0.010 average 0.198 0.150 0.102 0.052 0.020 average

208 208 208 208 208 208 52 52 52 52 52 52

average 208 & 52

Da(1min) (bp)

R (Å-1)

DI(1min) (bp)

7 14.1 ( 0.6 0.19 ( 0.02 10.2 ( 0.1 12 10.9 ( 0.8 0.33 ( 0.07 9.6 ( 0.3 6 10.0 ( 0.8 0.50 ( 0.17 9.5 ( 0.5 6 9.4 ( 0.6 0.73 ( 0.28 9.2 ( 0.4 6 9.9 ( 0.6 0.88 ( 0.44 9.8 ( 0.5 9.65 ( 0.25 8 13.6 ( 0.6 0.27 ( 0.04 10.0 ( 0.2 8 11.9 ( 1.1 0.35 ( 0.13 9.6 ( 0.4 7 11.2 ( 0.4 0.42 ( 0.06 9.7 ( 0.2 6 10.7 ( 0.2 0.78 ( 0.08 9.8 ( 0.1 15 9.2 ( 0.5 0.99 ( 0.38 9.1 ( 0.2 9.64 ( 0.14

β (Å-1) 0.73 ( 0.05 0.73 ( 0.14 0.77 ( 0.24 0.91 ( 0.33 0.98 ( 0.49 0.83 ( 0.20 0.91 ( 0.16 0.95 ( 0.35 0.90 ( 0.13 1.19 ( 0.15 1.10 ( 0.23 1.01 ( 0.13

9.65 ( 0.15 0.92 ( 0.20

a

Da(1min) is the apparent total tunneling distance at 1 min and includes inter-double-strand transfer to neighboring strands. R is the apparent tunneling distance decay constant. DI(1min) is the corrected tunneling distance along a single DNA double strand at 1 min (see text for model). β is the corrected tunneling distance decay constant. Values result from fits of Da and DI to ln(t) (eq 3). n is the number of data points. The data at 208 bp/MX is considered less reliable than that at 52 bp/MX. b The stacking distance between base pairs is assumed to be 3.4 Å.

value of the tunneling constant is not reasonable and suggests that uncorrected inter-strand tunneling is artificially lowering the value of the tunneling constant. Clearly, the probability of tunneling between adjacent double helixes increases as the concentration of DNA increases. The average separation between double helixes is about 206 Å at 10 mg DNA/mL and 46 Å at 200 mg DNA/mL; as a consequence, a significant fraction of the DNA strands at higher concentrations should be within tunneling distances, which are up to 50 Å at long times. We note that the influence of holes in the DNA (i.e., oneelectron-oxidized guanine) is expected at higher concentrations of DNA in LiBr glasses, and this issue needs to be addressed. As the concentration of DNA increases from 20 to 200 mg/ mL, the fraction of holes produced by direct ionization of DNA should increase from 0.7% to 6.2% of the total DNA radicals (holes and electron adducts) on the basis of mass fractions alone

ESR Study of Electron Transfer in DNA

Figure 4. Plot of apparent ET distances (Da) at 1 min and 15 days vs concentration of DNA in 7 M LiBr glasses, with a loading of MX to base pairs of 1/52 or 1/208. The average distance between DNA double strands (Dds) at each DNA concentration is also given. The lines of Da vs [DNA] are fits to a model, which assumes transfer along a central DNA double strand and six neighboring strands. The fits are based on eq 7, taking a ) 20 Å, DI(1min) ) 31.6 Å, and DI(15days) ) 43.9 Å. Inserted plot shows the dependence of apparent tunneling distance decay constants (R) on concentration of DNA in 7 M LiBr glasses at 77 K. Correction for transfer to neighboring strands gives a value for the distance decay constant, β, near 1 for all concentrations, as shown in the upper line in the insert.

(the density of 7 M LiBr is 1.41 g/mL). We find that a leastsquares fit of the ESR spectrum of DNA radicals in 200 mg DNA/mL 7 M LiBr glasses with appropriate benchmark functions, i.e., DNA radicals attained from 20 mg DNA/mL 7 M LiBr glasses and one-electron-oxidized guanine,40 suggests a 6.5% increase in one-electron-oxidized guanine as a fraction of total radicals. A 5.5% increase is expected from mass alone. As might be expected for such small amounts, we find that the fraction of MX in this analysis does not change significantly from that found in analyses without the inclusion of oneelectron-oxidized guanine. Thus, our results in glasses are not markedly affected by the direct ionization of DNA in aqueous glasses in the concentration range studied. Transfer of Radicals from DNA to MX in D2O Frozen Aqueous Solutions (Ices) and Hydrated Solid DNA. Experiments were performed in simple frozen aqueous solutions of DNA in order to ascertain the reasons for the apparent disagreement between our results in glassy solutions37 and a previous report in frozen ices.36 In Figure 5, we show ESR spectra recorded 4 days after γ-irradiation of samples of 20 and 100 mg DNA/mL in frozen D2O as well as hydrated DNA solid at 77 K. All three samples have a molar ratio of MX/bp of 1/200. The fraction of the total radicals captured by MX is 38.6% for a frozen 20 mg DNA/mL ice sample, 40.5% for a frozen 100 mg DNA/mL ice sample, and 38.0% for hydrated DNA solid (Γ ) 21 water molecules/nucleotide). In contrast to the results for glassy samples, in ice, no obvious dependence of the fraction of the total radicals captured by MX on the DNA concentration is observed. Moreover, the fraction of the total radicals captured by MX is similar to that obtained in hydrated solid DNA. Previous work has shown that DNA in frozen D2O aqueous solution separates into two phases, one similar to a hydrated solid and the other a pure crystalline ice phase.36 As a result, the DNA phase remains similar to a hydrated pure DNA solid even though the overall solution concentrations vary by a factor of 10.

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Figure 5. First-derivative electron spin resonance spectra recorded 4 days after γ-irradiation of samples of 20 and 100 mg DNA/mL in frozen aqueous D2O solutions and for a hydrated DNA solid sample at a hydration level of 21 water molecules/nucleotide. The loadings of MX to DNA base pairs are all identical at 1/200. The spectra show that the fraction of MX is independent of DNA concentration in frozen D2O solutions. In fact, the results found are identical to those for hydrated solid DNA. These results suggest that the DNA in frozen D2O solutions is in a separate phase equivalent to hydrated solid DNA. The fraction of electrons and holes captured by MX also increases with time. The dashed lines are linear least-squares fits of benchmark ESR spectra of DNA and MX radicals to experimental spectra (solid lines).

Figure 6. Plot of apparent transfer distance along DNA double strands vs natural logarithm of time (in minutes) for frozen D2O solutions (icy samples) and hydrated solid samples of MX-DNA as a function of concentration of DNA and loading of MX. Circles and solid line: ice, 100 mg DNA/mL with MX/bp ) 1/200. Squares and dotted line: ice, 100 mg DNA/mL with MX/bp ) 1/400. Solid circles and dot-dashed line: ice, 20 mg DNA/mL with MX/bp ) 1/200. Solid triangle and dashed line: hydrated solid DNA with MX/bp ) 1/200. Lines are leastsquares fits to eq 3.

As with the glassy samples, the transfer of radicals from DNA to MX in the frozen ices and hydrated DNA solids was monitored over time by analyses of the ESR spectra. Figure 6 shows a plot of the apparent transfer distances versus the natural logarithm of time in minutes found for DNA-MX in D2O frozen ice and hydrated DNA solids at 77 K with two concentrations of DNA (20 and 100 mg/mL) and at two ratios of MX to DNA base pairs (1/200 and 1/400). The linear dependence of the distances on the ln(t) is again in accord with a tunneling process. The results found for the R values and the apparent tunneling distances at 1 min, derived from the leastsquares fits of the data in Figure 6 to eq 3, are given in Table 2. The apparent distance at 1 min is found to be 34 ( 3 bp, with an R value of 0.16 ( 0.04 Å-1. This distance is in accord with a similar study on frozen aqueous solutions by Pezeshk et al.36 Both values (D and R) are found to be independent of the

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Cai and Sevilla

TABLE 2: Results for Tunneling Distance and Tunneling Distance Decay Constants vs Concentration of DNA and Loading of MX in D2O Ices and Hydrated Solid DNA at 77 K [DNA] (g/mL) 0.020 0.100 0.100 1.27

1/ν (bp/MX) 200 200 400 200

sample

n

Da(1min) (bp)

R (Å-1)

DI(1min) (bp)

β (Å-1)

icea ice ice hydrated solidb

7 12 6 6

32 ( 1 35 ( 2 35 ( 2 33.5 ( 0.5

0.16 ( 0.05 0.16 ( 0.07 0.17 ( 0.08 0.16 ( 0.03

9.6 ( 0.3 10.1 ( 0.5 10.0 ( 0.5 9.8 ( 0.1

1.1 ( 0.3 1.1 ( 0.5 1.2 ( 0.5 1.1 ( 0.2

34 ( 3

0.16 ( 0.04

9.87 ( 0.25

1.15 ( 0.25

average a

Frozen DNA solution at concentration given in the first column with MX intercalated at the bp/MX ratio given in the second column. b Salmon sperm DNA with intercalated MX hydrated to about 21 water molecules per nucleotide.

Figure 7. Schematic diagram depicting the spatial arrangement of DNA in a glass (frozen 7 M aqueous solution), an ice (frozen aqueous solution), and a hydrated solid (21 D2O/nucleotide).

concentration of DNA and the loading of MX, as well as being independent of whether the DNA is in a frozen ice or is a pure hydrated solid DNA. This verifies that the DNA phase in a frozen aqueous solution yields results similar to a hydrated solid and suggests that the local environments and DNA-DNA separation distances in the two systems are similar. The apparent transfer distances in icy and solid samples are far greater than in glassy samples. For example, even the highest concentration in the glassy matrix (198 mg DNA/mL) has much shorter apparent transfer distances than the lowest concentration (20 mg/mL) in a DNA-ice sample. On the other hand, the R values for icy and solid DNA samples are far smaller than those for glasses. These results imply that inter-ds electron transfer is greater in icy samples than in glasses. This finding is reasonable, because the average separation between DNA double helices in a solid DNA sample is about 20 Å, far smaller than the average distances estimated for glassy solutions. Figure 7 shows a schematic diagram of the spatial arrangement of DNA in a glass, an ice, and a hydrated solid. Discussion Our experiments yield results for apparent electron-transfer distances and apparent β (R) values in frozen aqueous glasses that are concentration-dependent. At lower DNA concentrations (10-25 mg DNA/mL), we find results that are in accord with our previous work;37 however, at higher concentrations (50200 mg/mL), we find increasingly larger apparent ET distances and decreasingly lower apparent β values. These unreasonable values result from the consideration of electron transfer along only a single DNA double helix. We show below that this apparent concentration dependence is in accord with tunneling between adjacent double helices, and when properly modeled, the results yield the same distances and β values as found in dilute solutions. To simulate the experimental dependence of electron and hole transfer in DNA as a function of average distance between adjacent DNA double strands, a three-dimensional model for the transfer of electrons and holes in DNA is proposed.

Figure 8. Diagram depicting three-dimensional tunneling model. DI is the total ET distance along the primary double strand. DJ is the distance of migration on the neighboring double strand; DJ ) DI - x, where x is the center-to-center inter-double-strand distance.

Three-Dimensional Model for the Transfer of Electrons and Holes in Glassy, Icy, and Hydrated DNA. For onedimensional tunneling, Da(t) in eq 1 can be directly interpreted as the tunneling distance along a DNA double strand. However, when the tunneling of electrons and holes to adjacent DNA double strands is competitive with the tunneling along an individual DNA double strand, tunneling samples all strands within the tunneling distance at time t. In a sense, the problem increases from tunneling along one strand to tunneling along several strands. Under these circumstances the probability of capture is still F(t) ) 1 - (1 - ν)2Da, but Da(t) can be modified to

Da(t) ) DI(t) + nDJ(t)

(4)

where n is the number of double strands adjacent to the strand containing the electron or hole; Da(t) is the apparent total tunneling distance, including tunneling distances along neighboring strands following inter-double-strand transfer; DI(t) is the distance of tunneling along a single DNA double helix; and DJ(t) is the average distance of transfer along each adjacent double strand. Of course, this assumes that the tunneling is limited to distances that take in only near-neighbor strands. We find that this is a reasonable assumption, even for solid DNA samples. Assuming that P(x) is the probability that a DNA double helix is located a center-to-center distance x from the primary double helix, for the tunneling route shown in Figure 8, DJ can be expressed as

DJ(t) )

∫aD (t) [DI(t) - x]P(x) dx I

(5)

where a is the diameter of DNA double helix, 20 Å. For frozen 7 M LiBr aqueous solutions, we make the simplifying assumption that DNA can be considered as homogeneously distributed rods with hexagonal packing.41 Thus, the

ESR Study of Electron Transfer in DNA

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average center-to-center separation between adjacent DNA double helices (Dds) is estimated to be

Dds ) xj )

{

2 × 1024 M(bp) 31/2NDst[DNA]

}

1/2

) 21[DNA]-1/2 (Å) (6)

where M(bp) is the average molecular weight of a base pair (sodium salt, 2.5 D2O/base), 762; N is Avogadro’s number, 6.023 × 1023; Dst is the stacking distance of DNA bases, 3.4 Å; and [DNA] is the concentration of DNA in g/mL and not larger than 1 g/mL (practically, 0.25 g DNA/mL is the maximum concentration at which a homogeneous LiBr aqueous solution can be made). To fit the experimental dependence of the apparent ET distance on the concentration of DNA in 7 M LiBr glasses, as shown in Figure 4, several distribution functions are examined, assuming Dds as the mean and 0 and 2Dds as the lower and upper limits of x, respectively. We take DI(1min) ) 31.6 Å and DI(15days) ) 43.9 Å, derived from Da(1min) and Da(15days) as [DNA] approaches zero. We find that a simple, continuous, linearly increasing distribution with P(x) ) cx for 0 e x e Dds and P(x) ) c(2Dds - x) for Dds e x e 2Dds gives reasonable fits to experimental data. Assuming that ∫D0 dsP(x) dx ) 0.5, we find that c is 1/Dds2. Because the diameter of a DNA double helix is 20 Å, the maximum center-to-center separation between two adjacent DNA double strands should be close to 20 Å. When DI < Dds, eq 4 is reorganized as

Figure 9. Plot of electron-transfer distance along individual DNA double helices corrected for inter-double-strand transfer vs natural logarithm of time (in minutes) for glassy samples of MX-DNA at various concentrations of DNA. All samples have a molar ratio of MX/ bp of 1/52. The values of Da in Figure 3 are replotted here after correction for electron transfer to adjacent DNA double strands via a three-dimensional transfer model that assumes transfer to only nearneighbor strands (see text). Lines are least-squares fits to eq 3.

Da(t) ) DI(t) + 6{

∫aD (t) P(x)[DI(t) - x] dx + [DI(t) - a)]∫0a P(x) dx} I

) DI(t) + [DI(t)3 - a3]/Dds2

(7)

where Da(t) and DI(t) are in Å and a is the diameter of DNA double helix, 20 Å. The fits to eq 7 are shown in Figure 4. The correlation coefficients between experimental data and calculated values based on eq 7 are 0.976 for Da(1min) and 0.973 for Da(15days), respectively. In hydrated DNA solid samples, DNA double strands are clearly tightly packed, with about 20 Å center-to-center separation between adjacent DNA double helices. The value of 20 Å is expected from the strand diameter of DNA, but we also find that a straightforward calculation based on the density of these samples (1.3 g/cm3) and the weights of water and DNA also yields a value near 20 Å for the center-to-center distances. Thus,

Da(t) ) DI(t) + n[DI(t) - 20]

(8)

where Da(t) and DI(t) are in Å and n is the number of the adjacent DNA double strands. If we assume hexagonal packing of the strands in hydrated solid DNA, n is 6.41 Equation 8 is also applied to frozen D2O aqueous solutions, as they are found to behave as hydrated DNA solid samples. Tunneling Constants along Individual DNA Double Strands. For glassy samples, the tunneling distance along individual DNA double helix, DI(t), can be derived from the apparent distance Da(t) according to eq 7. Figure 9 shows the replotted data of Figure 3 based on eq 7. A comparison of Figures 3 and 9 shows that the three-dimensional model substantially accounts for the concentration effects. The individual lines for different DNA concentrations are all within 1-2 bp in Figure 9 vs 10-12 bp in Figure 3. Values of DI(1min) and β derived from the linear least-squares fits of eq 3 to the derived DI(t) values are given in Table 1. Values of DI(1min) and β in glasses at 77 K are found to be 9.65 ( 0.15 bp and

Figure 10. Plot of the tunneling distance along individual DNA double helices (corrected for inter-double-strand transfer) vs natural logarithm of time (in minutes) for frozen D2O solutions (icy samples) and a hydrated solid sample of MX-DNA as a function of concentration of DNA and loading of MX. Circles and solid line: ice, 100 mg DNA/ mL with MX/bp ) 1/200. Squares and dotted line: ice, 100 mgDNA/ mL with MX/bp ) 1/400. Solid circles and dot-dashed line: ice, 20 mg DNA/mL with MX/bp ) 1/200. Solid triangle and dashed line: hydrated solid DNA with MX/bp ) 1/200. The values of Da in Figure 6 are replotted here after correction for electron and hole tunneling to adjacent DNA double strands via a three-dimensional transfer model (see text). Lines are least-squares fits to eq 3.

0.92 ( 0.20 Å-1, respectively. Both values are independent of the concentration of DNA, in good agreement with our previous report of results from work in dilute glassy media.37 For frozen D2O ices and hydrated DNA solids, the use of eq 8 also allows for correction of the transfer distances for transfer between adjacent double strands. Figure 10 shows the replotted data of Figure 6 based on eq 8. When so corrected, the values of DI(1min) and β in frozen D2O ice and hydrated solids at 77 K are found to be 9.87 ( 0.25 bp and 1.15 ( 0.25 Å-1, respectively. Thus, the values of DI(1min) and β for glassy, icy, and solid samples appear about the same within our error

6948 J. Phys. Chem. B, Vol. 104, No. 29, 2000 limits. Because holes are formed on DNA in the hydrated DNA samples, the similar values for DI(1min) and β suggest that both holes and electrons tunnel at similar rates. This is a hypothesis we hope to test in subsequent studies. Homogeneous 3D Model. The probability for electron capture by a homogeneously dispersed trap (MX) in three dimensions is given by F(t) ) 1 - exp(-Vt/VMX), where Vt is the tunneling volume, equal to 4/3πDIII3 and DIII is the tunneling distance in a homogeneous three-dimensional medium. VMX is the sample volume per MX molecule.39 This treatment assumes that MX is homogeneously dispersed in a medium and takes no account of the fact that the MX is actually intercalated in DNA; thus, a direct path for the transfer of the electron or hole to the intercalator is assumed. This straightforward tunneling relationship is applied to the solid hydrated DNA sample (21 water molecules/nucleotide, 1/200 ratio of MX to base pairs). The tunneling distance DIII at 1 min is found to be 30.2 ( 0.2 Å, compared to the value of 32.8 ( 0.5 Å found for travel along a single double strand in dilute solutions. This suggests that the β values are comparable for travel across and along the strands, as suggested in our other treatment. However, the homogeneous three-dimensional model results in β values of 2.2 ( 0.3 Å-1, which is not in agreement with our earlier work and which is too large to allow for travel of 30 Å in 1 min. This, we believe, is due to the facts that distances of 30 Å are simply not yet sufficient to assume homogeneity and that there are complications with the recombinations of the holes and electrons that are formed on DNA in the solid hydrated system. This model seems to give realistic distances in solid samples, which can be taken as rough approximations. We have also employed this model to compute DIII at 1 min for DNA in a glassy solution sample, i.e., 1/52 ratio of MX to base pairs at a DNA concentration of 200 mg/mL in the 7 M LiBr glass. In this case, the transfer of excess electrons dominates the process, and we find that the tunneling distance DIII at 1 min is 33.3 ( 0.4 Å, with β values of 1.5 ( 0.1 Å-1. This lower value of β is more realistic and is in keeping with other reports in the literature for solutions.42 Conclusions Our major findings are the following: 1. Inter-double-strand electron transfer is found to be an important process for DNA in the solid state, in frozen water solutions (ices), and in aqueous glasses at high concentrations of DNA that place DNA double strands within tunneling distances (up to 45 Å at our longest times). 2. A model of electron and hole transfer both along DNA double strands and across to near-neighbor DNA double strands is found to simulate the experimental dependence of electron and hole transfer in DNA as a function of the average distance between adjacent DNA double strands. This model makes the assumption that β is the same between the strands as within a strand. This possibly underestimates the size of β through the solvent, as it has been reported to be near 1.4 Å-1 in other work.42 3. A second model, which assumes homogeneous dispersion of the MX in three dimensions, is found to give reasonable estimates for electron-transfer distances in solid (hydrated) DNA samples and glassy solution-phase DNA; however, estimates of β are poor for the solid sample and more realistic for the solution-phase sample (1.5 Å-1). In this model, any differences in transfer along the DNA double strand, across it, or through the solution are ignored. The fact that realistic answers are

Cai and Sevilla obtained with this model provides good evidence that DNA is not a particularly good conduit for excess electrons. 4. The contradiction in the literature between electron-transfer distances for DNA in frozen ices36 and glassy aqueous LiBr solutions37 is explained by the different distances between nearneighbor DNA double strands in two media. 5. Results for frozen aqueous solutions (ices), even as low as 20 mg DNA/mL, are found to be identical to those for hydrated solid DNA. This indicates phase separation in frozen aqueous solutions that places DNA strands at the same distances as in the neat hydrated DNA (i.e., ca. 20 Å center-to-center separations). 6. Once corrected for inter-double-strand transfer, our results give electron- and hole-transfer distances that are largely independent of the medium, i.e., glass, ice, or hydrated solid DNA, with a distance at 1 min of 10 bp. The tunneling distance decay constant β is found to be near 1 Å-1 at 77 K in each medium, which is in the “usual” range for a covalent system.42 Our work in glassy samples gives electron transfer distances, and values of β, averaged over individual sites of electron localization at cytosine and at thymine. For hydrated solid DNA our work gives the average for these sites for electron transfer and hole transfer from guanine. Attempts at distinguishing electron transfer from these individual radicals species, as well as determinining the effect of hydration levels on both electron and hole transfer in hydrated DNA, are currently under active study in our laboratory. Acknowledgment. The authors thank Yuriy Razskazovskiy for many helpful discussions and for pointing out the homogeneous three-dimensional model. This research was supported by NIH NCI Grant RO1CA45424 and by the Oakland University Research Excellence Fund. References and Notes (1) Milano, M. T.; Bernhard, W. A. Radiat. Res. 1999, 152, 196201. (2) Netzel, T. L. J. Chem. Educ. 1997, 74, 646-651. (3) Debije, M. G.; Milano, M. T.; Bernhard, W. A. Angew. Chem., Int. Ed. Engl. 1999, 38, 2752-2756 (4) Anderson, R. F.; Patel, K. B. J. Chem. Soc., Faraday Trans. 1991, 87, 3739-3746. (5) Sevilla, M. D.; Becker, D.; Razskazovskii, Y. Nukleonika 1997, 42, 283-292. (6) Meggers, E.; Michel-Beyerle, M. E.; Giese, B. J. Am. Chem. Soc. 1998, 120, 12950-12955. (7) Martin, R. F.; Anderson, R. F. Int. J. Radiat. Oncol., Biol., Phys. 1998, 42, 827-831. (8) Kelley, S. O.; Jackson, N. M.; Hill, M. G.; Barton, J. K. Angew. Chem., Int. Ed. Engl. 1999, 38, 941-945. (9) Lewis, F. D.; Zhang, Y.; Liu, X.; Xu, N.; Letsinger, R. L. J. Phys. Chem. 1999, 103, 2570-2578. (10) Fukui, K.; Tanaka, K.; Fujitsuka, M.; Watanabe, A.; Ito, O. J. Photochem. Photobiol. B: Biol. 1999, 50, 18-27. (11) Wan, C.; Fiebig, T.; Kelley, S. O.; Treadway, C. R.; Barton, J. K.; Zewail, A. H. PNAS 1999, 96, 6014-6019. (12) Kelley, S. O.; Barton, J. K. Science 1999, 283, 375-381. (13) Beratan, D. N.; Priyadarshy, S.; Risser, S. M. Chem. Biol. 1997, 4, 3-8. (14) Kelley, S. O.; Barton, J. K. Met. Ions Biol. Syst. 1999, 36, 211249. (15) Steenken, S. Biol. Chem. 1997, 378, 1293-1297. (16) Lewis, F. D.; Wu, T.; Zhang, Y.; Letsinger, R. L.; Greenfield, S. R. Science 1997, 277, 673-676. (17) Dandliker, P. J.; Holmlin, R. E.; Barton, J. K. Science 1997, 275, 1465-1468. (18) Razskazovskii, Y.; Swarts, S. G.; Falcone, J. M.; Taylor, C.; Sevilla, M. D. J. Phys. Chem. B 1997, 101, 1460-1467. (19) Kelley, S. O.; Barton, J. K. Chem. Biol. 1998, 5, 413-425. (20) Ratner, M. Nature 1999, 397, 480-481.

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