J. Phys. Chem. 1996, 100, 13837-13843
13837
Cyclic Voltammetry Studies of Polynucleotide Binding and Oxidation by Metal Complexes: Homogeneous Electron-Transfer Kinetics Dean H. Johnston† and H. Holden Thorp* Department of Chemistry, UniVersity of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3290 ReceiVed: January 25, 1996; In Final Form: April 30, 1996X
The cyclic voltammetry of Ru(bpy)32+ in the presence of calf thymus DNA has been studied. Theoretical simulations using DigiSim were performed for the voltammetry of the metal complex in the presence of DNA where the only interaction between the metal complex and DNA was electrostatic binding to the polyanion. The expected binding isotherm was obtained from the simulated voltammetry with input affinities similar to that of Ru(bpy)32+. The expected binding isotherm was not obtained for simulations with high affinities (>106 M-1) expected for intercalating complexes that exhibit neighbor exclusion, because the commercially available version of DigiSim treats only simple equilibria and cannot treat exclusion of binding to adjacent sites. Simulations were then performed for the case where the +3 state of the metal complex oxidizes the guanine base in DNA in a catalytic mechanism. The dependence of icat/id on scan rate and the second-order rate constant for the homogeneous chemical step was determined for the conditions where the metal complex does not bind to DNA, such as at high salt concentration. Under these conditions, there is an optimum scan rate where the catalytic current depends steeply on the homogeneous rate constant, allowing for the most accurate determinations in fitting experimental voltammograms. These considerations were applied to fitting cyclic voltammograms for the case of no DNA binding (high salt) and weak, but significant, DNA binding (50 mM salt). The rate of homogeneous electron transfer from the guanine nucleobase to the metal complex was 10 times faster in the low salt case, indicating a shorter electron-transfer distance and a more intimate association of the metal complex with the DNA.
A new generation of tools is being designed for the rapid and inexpensive determination of sequence and structural information from heterogeneous DNA and RNA samples.1-5 The development of these powerful new techniques is driven by applications in areas of gene therapy, genome sequencing, drug discovery, medical diagnostics, environmental monitoring, and forensics.6-10 Electrochemical techniques for detecting DNA hybridization involve signals from electrostatically bound redox-active probe molecules11,12 or detection of electrogenerated chemiluminescence (ECL).13,14 Such techniques are potentially applicable to DNA-derivatized surfaces that could be extended to multiplexed electrode arrays that would resemble known “biochips” designed for rapid sequencing or gene detection using fluorescence.6-8 We have reported recently on an alternative approach where simple redox-active molecules such as Ru(bpy)32+ can act as sensitive probes of DNA structure via electrochemical detection of DNA base oxidation.15 The redox potential for the guanine nucleobase in DNA is about 1.1 V vs SSCE.15,16 A number of simple M(bpy)33+ complexes are therefore capable of oxidizing the nucleobase to the radical cation,17 and we have shown using high-resolution electrophoresis that the formation of the radical cation leads to a piperidine-labile lesion specifically at guanine.18 The detection method therefore involves monitoring the M(bpy)33+/2+ redox couple by cyclic voltammetry, which is enhanced in the presence of DNA due to catalytic oxidation of guanine:
Ru(bpy)32+ f Ru(bpy)33+ + e-
(1)
(2) Ru(bpy)33+ + DNA f DNAox + Ru(bpy)32+ where DNAox contains an oxidized guanine site. The rate † Present address: Chemistry Department, Otterbein College, Westerville, OH 43081. X Abstract published in AdVance ACS Abstracts, July 15, 1996.
S0022-3654(96)00252-3 CCC: $12.00
constant for eq 2 can be obtained using square-wave voltammetry19 or cyclic voltammetry20 in conjunction with digital simulation. Because of the exponential dependence on the electron-transfer distance, this rate constant is highly sensitive to the solvent accessibility of the guanine bases in DNA and can selectively detect and identify a single mismatched base in a 15-mer oligonucleotide.15 A number of factors influence the electrochemical response associated with DNA-metal electron transfer.17,21-24 The diffusion coefficients of the metal complex free in solution and bound to DNA will influence the total measured current. Since these two diffusion coefficients are different by an order of magnitude, the absolute concentrations of bound and free metal complex, as determined by the DNA binding constant, will also play an important role. If the metal complex is a cation, understanding the role of the buffer in controlling the binding equilibrium is also vital. Finally, the chemical mechanism of the oxidation must be fully understood. Further development of electrochemical DNA biosensors therefore requires a detailed understanding of nucleotide binding, DNA diffusion, and oxidation mechanisms. We have made extensive use of the powerful cyclic voltammetry simulation program DigiSim20 in understanding and fitting our DNA oxidation data. In this paper, we demonstrate the simulation and fitting of cyclic voltammograms that detect DNA binding and oxidation by metal complexes in cases where the metal complex is not bound to DNA and where significant quantities of the metal complex are associated with the DNA. Experimental Section Materials. All metal complexes, DNA, and solutions were obtained, purified, and handled as described elsewhere.15 Voltammetry. Cyclic voltammograms were collected using an EG&G PAR 273A potentiostat/galvanostat with a single © 1996 American Chemical Society
13838 J. Phys. Chem., Vol. 100, No. 32, 1996
Johnston and Thorp
SCHEME 1 + DNA, kf(II)
M2+ +e–
– DNA, kb(II)
–e–
M3+
+ DNA, kf(III)
M2+/DNA +e–
–e–
M3+/DNA
– DNA, kb(III)
compartment voltammetric cell25 equipped with an indium tin oxide (ITO) working electrode (area ) 0.32 cm2), Pt-wire counter electrode, and a Ag/AgCl reference electrode. In a typical experiment, a sample containing 50 µM metal complex and 3.0 mM calf thymus DNA (per nucleotide-phosphate) dissolved in buffered aqueous solutions containing either 50 mM Na-phosphate buffer (pH ) 6.8, [Na+] ) 80 mM) or 50 mM Na-phosphate buffer and 700 mM NaCl (pH ) 6.8, [Na+] ) 780 mM) was scanned at 25 mV/s from 0.0 V to at least 200 mV beyond the redox couple of the metal complex. A range of scan rates (between 10 and 1000 mV/s) was used to verify the kinetic analyses. Scans of polynucleotides in the absence of metal complex showed no appreciable oxidative current to 1.3 V vs Ag/AgCl. A freshly cleaned ITO electrode was used for each experiment, and a background scan of buffer alone was collected for each electrode and subtracted from subsequent scans. Concentrations of DNA (per nucleotide phosphate) were determined spectrophotometrically (260 ) 6600 M-1 cm-1).26 Simulations. Cyclic voltammograms were simulated using the DigiSim 2.0 software package from BAS running on a Gateway P90 system. Simulations that considered metal complex binding used Schemes 1-3. The forward rate constants for all binding steps were assumed to be diffusion limited and were fixed at 1.0 × 109 M-1 s-1. Those simulations for which binding was unimportant used simpler EC′ or EC′C′ mechanisms as outlined later. All other simulation parameters are given in the text or the figure captions. The default simulation parameters (β ) 0.5, potential step ) 0.005 V) were used in all simulations except for those used to generate Figure 3 (k2 > 105 M-1 s-1) where β was set to 0.1 and the potential step was set to 0.002 V. For simulations that returned homogeneous guanine-metal electron-transfer rate constants, the input DNA concentrations was in terms of guanine concentration. Since calf thymus DNA is 20% guanine,26 the guanine concentration is [DNA]/5. Second-order guanine oxidation rate constants were determined by fitting of cyclic voltammetric data using the listed mechanisms. All parameters other than the oxidation rate (binding constants, redox potentials, diffusion coefficients, and heterogeneous electron-transfer rates) were determined from previous work15,22 or from a scan of the metal complex alone on the same electrode. Results and Discussion Metal Complex Binding to DNA. There has been extensive research on the binding of transition metal complexes to DNA via electrostatic and hydrophobic interactions.27-29 Bard and co-workers first proposed electrochemical techniques as a means for determining metal complex binding constants.23,24 We have recently shown that the strong intercalative interaction of a redox probe with DNA can be used to determine the diffusion coefficients of various polynucleotides22 and that normal pulse voltammetry is an excellent technique for determining concentrations of bound and free metal complexes over a wide range of binding affinities.21 Before attempting to simulate the more complex DNA oxidation reactions, we wanted to ensure that DigiSim could
Figure 1. Weak binding case, K2+ ) 700 M-1, K3+ ) 3500 M-1. (A) Simulated cyclic voltammograms using Scheme 1, T ) 298.15 K, area (planar) ) 0.088 cm2, ν ) 100 mV/s, E° ) 0.856 V, ks(free) ) ks(bound) ) 104 cm/s, R(free) ) R(bound) ) 0.5, kf(II) ) kf(III) ) 109 M-1 s-1, [M2+] ) 1.0 × 10-4 M, DM2+ ) DM3+ ) 1.0 × 10-5 cm2/s, DDNA ) 2.0 × 10-7 cm2/s. (1) [DNA] ) 0.0 M, (2) [DNA] ) 1.0 × 10-3 M, and (3) [DNA] ) 5.0 × 10-3 M. (B) Binding isotherm from simulated cyclic voltammograms for weak binding case with best fit to territorial binding equation (eq 6) with Kb2+ (from fit) ) 682 ( 3 M-1; ia ) current measured at a given DNA concentration, ib ) isat, if ) i0.
accurately simulate the DNA binding steps. For these simulations we used the square scheme illustrated in Scheme 1. The cross reaction (eq 3) can influence the voltammetry under certain conditions;30 however, we have shown previously that this situation does not obtain for the complexes studied here.22
M3+ + M2+/DNA f M2+ ) M3+/DNA (3) In simulations that included binding, the binding steps were assumed to be diffusion controlled (kf ) 1.0 × 109 M-1 s-1);31 the reverse rate was then set by the simulation program according to the input equilibrium constant. We21,22 and others23,24 have shown previously that the square scheme for DNA binding does not destroy the reversibility of the cyclic voltammogram, which supports rapid binding and release of the metal complex.32 For the purpose of generating binding isotherms, the electrode reactions were assumed to be totally reversible. A series of cyclic voltammograms were simulated (selected voltammograms are shown in Figure 1A) using Scheme 1 (Kb2+ ) 700 M-1 and Kb3+ ) 3500 M-1), and the calculated peak current was determined as a function of DNA concentration. The relationship between Kb2+ and Kb3+ was determined from polyelectrolyte theory,33,34 which we have previously shown to obtain in this system.21 For cyclic voltammetry, the binding equilibrium affects the measured current because the effective diffusion coefficient of the bound metal complex is nearly an order of magnitude lower than that of the free form. The measured current is described as23,24
Polynucleotide Binding and Oxidation by Metal Complexes
i ) BCt(DfXf + DbXb)1/2
J. Phys. Chem., Vol. 100, No. 32, 1996 13839
(4)
where Ct is the total concentration of metal complex in mol/ cm3, Df is the diffusion coefficient of the free metal complex in cm2/s, Db is the diffusion coefficient of the bound metal complex in cm2/s, Xf is the mole fraction of metal complex free in solution, and Xb is the mole fraction of bound metal complex. The electrochemical constants are collected in the term B, which at 25 °C is equal to 2.69 × 105 n3/2Aν1/2, where n is the number of electrons in the redox couple, A is the electrode area in cm2, and ν is the voltammetric sweep rate in V/s. As we have discussed in detail elsewhere, the distribution of bound and free forms depends on the square of the measured current, so we can therefore calculate the mole fraction of bound complex as21
Xb ) (i2 - isat2)/(i02 - isat2)
(5)
where isat ()ib) is the current when all of the metal complex is bound to DNA and i0 ()if) is the current when no DNA has been added. A plot of the current expression for Cb/Ct (eq 5) versus the DNA concentration was constructed from the simulated voltammograms and is shown in Figure 1B. For relatively low binding affinities (K < 10 000 M-1), the mole fraction bound can be fit as
Xb ) K[DNA]/(K[DNA] + 1)
(6)
Fitting of the current function to eq 6 gives a Kb2+ of 682 ( 3 M-1, which is in acceptable agreement with the value of 700 M-1 that was input into the simulation. The alignment of the fit with the expected dependence on [DNA], and the reproduction of the input Kb2+ indicates that the simulation program is accurately modeling the current response for the weak binding case. A similar series of simulations were run using a much higher set of binding constants (Kb2+ ) 1.0 × 105 M-1 and Kb3+ ) 5.0 × 105 M-1). Selected simulated cyclic voltammograms are shown in Figure 2A, and the resulting binding isotherm is shown in Figure 2B. The DNA dependence was not fit well by the weak binding isotherm (eq 6), which was expected because at these binding constants, neighbor exclusion must be considered. Neighbor exclusion occurs when the extent of binding is limited by coverage of a finite number of base pairs by binding of a single complex, which prohibits binding of an additional complex in the same site. Binding isotherms in this regime are generally fit to a strong binding equation:21,22
Cb ) Ct
(
b - b2 -
)
2K2Ct[DNA] s 2KCt
b ) 1 + KCt + K[DNA]/2s
1/2
(7a) (7b)
where s is the site size in base pairs excluded by the bound metal complex. Fitting the simulated isotherm to eq 7 gave a very good fit, as shown in Figure 2B. The fit of the data in Figure 2B with both parameters varied gave a Kb2+ of (1.26 ( 0.04) × 105 M-1 and s ) 0.54. If the site size was fixed at 0.50, the resulting fit gave a Kb2+ of (1.01 ( 0.02) × 105 M-1. A site size of 0.5 is unrealistically small (intercalators exhibit site sizes of 2);22,35,36 however, the input of a simple equilibrium into DigiSim does not account for neighbor exclusion. The program therefore returns a site size of 0.5, which simply corresponds to a site size equivalent to a single nucleotide (onehalf of a base pair), since the DNA concentration is given in
Figure 2. Strong binding case, Kb2+ ) 1.0 × 105 M-1, Kb3+ ) 5.0 × 105 M-1. (A) Simulated cyclic voltammograms using Scheme 1, T ) 298.15 K, area (planar) ) 0.32 cm2, ν ) 25 mV/s, E° (free) ) 1.00 V, ks(free) ) ks(bound) ) 104 cm/s, R(free) ) R(bound) ) 0.5, kf(binding) ) 109 M-1 s-1, [M2+] ) 5.0 × 10-5 M, DM2+ ) DM3+ ) 6.0 × 10-6 cm2/s, DDNA ) 2.0 × 10-7 cm2/s. (1) [DNA] ) 0.0 M, (2) [DNA] ) 5.0 × 10-5 M, and (3) [DNA] ) 4.0 × 10-4 M. (B) Binding isotherm from simulated cyclic voltammograms for strong binding case with best fit to site binding equation (eq 7, s fixed at 0.5), Kb2+ (from fit) ) (1.01 ( 0.02) × 105 M-1; ia ) current measured at a given DNA concentration, ib ) isat, if ) i0.
nucleotides. Thus, DigiSim is somewhat limited for the strong binding case, although it would be straightforward to modify the code to account for the special equilibrium. This limitation should not have a significant effect on the modeling discussed here, because under most experimental conditions the concentration of available binding sites is much greater than the concentration of metal complex. All of the cases discussed here fall in the regime described by eq 6. DNA Oxidation: No Binding. We have previously shown that a variety of metal complexes oxidize the guanine bases in DNA electrocatalytically.15,17,18 To determine the solvent accessibility of the guanine base, the rate of guanine oxidation must be quantitated from the catalytic current enhancement observed in the cyclic voltammetry experiment.15 One approach would be to modify the square scheme in Scheme 1 by adding a step where the bound oxidized metal complex oxidizes the DNA followed subsequently by dissociation of the metal complex, and this case is discussed in detail below. A simpler model can be used for the case where electrostatic binding is insignificant, which was accomplished previously by increasing the ionic strength so that the majority of the complex (>95%) is free in solution.15 In this case, the voltammetry can be modeled using the two line mechanism given in eqs 8 and 9.
M2+ h M3+ + e-
(8)
M3+ + DNA h M2+ + DNAox
(9)
This mechanism is very much like the classic EC′ mechanism37 except that the DNA oxidation step is considered as a second-
13840 J. Phys. Chem., Vol. 100, No. 32, 1996
Johnston and Thorp
Figure 4. Cylic voltammograms and digital simulations (using eqs 10-13) for 50 µM Ru(bpy)32+ + 3.0 mM calf thymus DNA in 50 mM Na-phosphate + 700 mM NaCl. T ) 298.15 K, area (planar) ) 0.32 cm2, E° ) 1.059 V, ks) 3.6 × 10-3 cm/s, R ) 0.5, kf(11) ) 0.026 s-1, Keq(12) ) 1200, kf(12) ) 9000 M-1 s-1, Keq(12) ) 1200, kf(12) ) 1000 M-1 s-1, [M2+] ) 5.0 × 10-5 M, [guanine] ) 6.0 × 10-4 M, DM2+ ) DM3+ ) 6.6 × 10-6 cm2/s, DDNA ) DDNAox ) DDNAox′ ) 2.0 × 10-7 cm2/s. (A) ν ) 25 mV/s, (B) ν ) 250 mV/s, and (C) ν ) 1000 mV/s. Numbers in parentheses refer to the equation numbers in the text.
Figure 3. Second-order EC′ case. (A) Simulated cylic voltammograms for the second-order oxidation of DNA (eqs 8 and 9), varying the second-order oxidation rate constant, kf(9). T ) 298.15 K, area (planar) ) 0.32 cm2, ν ) 25 mV/s, E° ) 1.06 V, ks) 104 cm/s, R ) 0.5, Keq(9) ) 105, [M2+] ) 5.0 × 10-5 M, [guanine] ) 5.0 × 10-4 M, DM2+ ) DM3+ ) 6.0 × 10-6 cm2/s, DDNA ) DDNAox ) 2.0 × 10-7 cm2/s. (1) kf(9) ) 0.0 M-1 s-1, (2) kf(9) ) 104 M-1 s-1, and (3) kf(9) ) 108 M-1 s-1. (B) Ratio of catalytic current (circles, primary peak, triangles, prepeak) to diffusion-limited current for simulations of the secondorder EC′ case as a function of the second-order rate constant, kf(9). All other conditions as in (A). Numbers in parentheses refer to the equation numbers in the text.
order reaction. In most cases, it is difficult to obtain solution conditions where DNA is in large excess, so the data cannot be analyzed using the method of Nicholson and Shain38 or any other technique that assumes pseudo-first-order conditions. For calf thymus DNA, the concentration of oxidizable substrate is less than the total concentration of nucleotide phosphate since only about 20% of the bases in calf thymus DNA are guanine. The DNA concentration that was actually input into the simulation was therefore the total guanine concentration ()[DNA]/5), so all second-order rate constants are given in terms of guanine concentration. Under conditions of weak binding, we have previously fit the current response for the oxidation of calf thymus DNA by a variety of metal complexes with widely differing redox potentials.15 The driving force dependence follows the predictions of Marcus theory for outersphere electron transfer, giving a slope of 1/2 for the plot of RT ln k versus ∆G. To ensure that a significant change in rate constant results in a significantly different response, a series of simulations were run to explore the relationship between the catalytic peak current and the second-order rate constant for the EC′ mechanism listed in eqs 8 and 9. Selected simulated cyclic voltammograms for the cases where the forward rate for eq 9 (kf) varies from 0 to
108 M-1 s-1 are shown in Figure 3A. A plot of the calculated catalytic peak current divided by the diffusion-limited current (icat/id) versus the second-order rate constant is shown in Figure 3B. As shown by Nicholson and Shain,38 the catalytic current for the pseudo-first-order case rises indefinitely as the rate constant is increased; however, Figure 3B shows that this is not the case for the second-order mechanism. The numbers calculated for the plot in Figure 3B were not reduced to dimensionless units, so the plot directly addresses the precise experimental conditions of interest here. The plot in Figure 3B was calculated for a scan rate of 25 mV/s, but an equivalent graph that is shifted to higher scan rate is obtained at any value. For example, the same icat/id is obtained for k2 ) 1 × 105 M-1 s-1 at 25 mV/s and k2 ) 1 × 106 M-1 s-1 at 250 mV/s, and it is straightforward to obtain such a plot for any scan rate. The important feature in the plot shown in Figure 3B is that a maximum in catalytic peak current is observed. Just beyond this peak, the current response actually splits into two peaks. This prepeak is typical in cases where kf is particularly fast and results from depletion of the reactant (DNA in this case) at the electrode prior to depletion of the catalyst; this scenario has been discussed in detail elsewhere.39,40 For the plot shown (scan rate ) 25 mV/s, [guanine]/[M] ) 10) the largest slope is observed in the range k2 ) 103-104 M-1 s-1, so it is best to fit reactions with rate constants in this range for this scan rate. Fitting of a range of scan rates therefore allows the region of highest variation to be located (see below). A system with a rate constant around 105 M-1 s-1 would not be well determined at 25 mV/s, since many different rate constants would give similar current responses. The rate constants observed for the oxidation of calf thymus DNA were all in the range 102-104 M-1 s-1, so most of the data were collected over a range of scan rates that included 25 mV/s. The curve generated for Figure 3B appears to be general for any EC′ case where the reactant in the second (homogeneous) step is in limited quantity. Additional simulations at different [guanine]/[M] ratios showed very similar curves with a slight shift in the position of the peak current to higher rate constants with a larger excess of guanine. No attempt was made to explore the effect of changing the ratio of diffusion coefficients
Polynucleotide Binding and Oxidation by Metal Complexes SCHEME 2
J. Phys. Chem., Vol. 100, No. 32, 1996 13841 SCHEME 3
+ DNA, kf(II)
M2+ +e–
– DNA, kb(II)
–e–
M3+
+ DNA, kf(II)
M2+/DNA +e–
+ DNA, kf(III)
M2+
–e–
+e–
M3+/DNA
–e–
M3+
– DNA, kb(III)
+ DNA, kf(II)′
+e–
+ DNA, kf(III)
–e–
M3+/DNA
– DNA, kb(III)
kb
M2+
M2+/DNA
– DNA, kb(II)
kb
kf + DNA, kf(II)′
M2+/DNA′
M2+
– DNA, kb(II)′
of the different reactants, since we have firmly established that DM/DDNA ) 30.21,22 Another implication of the graph in Figure 3B is the importance of collecting and fitting data at several different scan rates. Figure 4 shows the experimental cyclic voltammograms collected for 50 µM Ru(bpy)32+ and 3.0 mM calf thymus DNA at scan rates from 25 to 1000 mV/s overlaid with simulations under the same conditions. To achieve satisfactory fits, two additional chemical steps other than those shown in eqs 8 and 9 were added to the simulation mechanism. First, a reaction was added that accounted for slow conversion of the oxidized metal complex back to the reduced form (eq 11), which is known for M(bpy)33+ complexes at neutral pH.41 Second, oxidation of DNAox also had to be considered (eq 13), as many guanine oxidation products are known to be more easily oxidized than guanine itself.42 The new mechanism required to fit the scan rate dependence is given in eqs 10-13:
M2+ h M3+ + e-
(10)
M3+ h M2+
(11)
M3+ + DNA h M2+ + DNAox
(12)
M3+ + DNAox h M2+ + DNAox′
(13)
where DNAox′ contains a guanine that has undergone two oxidations. The experimental voltammograms shown in Figure 4 are overlaid with the simulations using eqs 10-13 at scan rates from 25 to 1000 mV/s. For these simulations, the best fit for ν ) 250 mV/s was obtained, and then the only parameter that was varied between the simulations was the scan rate. As apparent in Figure 4, the simulated curves at 25 and 1000 mV/s reproduce the experimental curves reasonably well without redetermining the rate constant. However, if separate fits were performed for each scan rate, fits as good as that shown for the 250 mV/s scan were obtained. The determined rate constants then varied only over a factor of 3, which is acceptable for determining solvent accessibilities that depend logarithmically on the rate constant.15 DNA Oxidation: Weak Binding. We can now consider the case where binding of the metal complex to the DNA is important. As mentioned above, this situation can be modeled using a modification of Scheme 1 where the bound oxidized metal complex oxidizes the DNA. This modified scheme is shown in Scheme 2. As in the simulations using Scheme 1, the binding step is assumed to be diffusion controlled (kf(II) ) kf(III) ) kf(II)′ ) 1.0 × 109 M-1 s-1), and the equilibrium constants for the binding reactions are given by the known binding constants K2+, K3+, and K2+′, respectively. The difference in potential for oxidation of the bound complex is determined in a Nernstian fashion by K2+ and K3+,21-24 so the
+e–
M2+/DNA′
– DNA, kb(II)′ +e–
–e–
M3+
kf
+ DNA, kf(III)′
–e–
M3+/DNA′
– DNA, kb(III)′
kb′
kf′
+ DNA, kf(II)′′
M2+
M2+/DNA′′
– DNA, kb(II)′′
oxidation of the bound form can be considered as a thermodynamically superfluous reaction (TSR), as defined by Feldberg et al.20,43 The overoxidation reaction that occurs with highly oxidizing complexes such as Ru(bpy)32+ can be simulated by expanding Scheme 2 as shown in Scheme 3. One problem arises from the fact that the concentration of oxidizable substrate is the concentration of guanine bases and not the total concentration of nucleotide bases, while the known binding constants are given in terms of total nucleotide phosphate concentration. Since the input concentration of DNA was actually the guanine concentration, this discrepancy was overcome by multiplying the binding constants by a factor of 5, which is valid as long as eq 6 describes the binding isotherm. The rate constant is therefore in terms of the guanine concentration while the binding equilibrium is still calculated for the total nucleotide concentration. Cyclic voltammograms were collected for solutions of 50 µM Ru(bpy)32+ and 2.0 mM calf thymus DNA in 50 mM Naphosphate buffer. A binding constant at this ionic strength of 400 M-1 was determined by earlier measurements.36 The voltammetric results at three different scan rates are shown in Figure 5 overlaid with simulations obtained using Scheme 3 with kf ) 100 s-1 and kf′ ) 20 s-1. As in the case with no binding, the close agreement between the actual and simulated cyclic voltammograms at several different scan rates supports the given mechanism and rate constants, and the range of rate constants obtained by independent fitting at each scan rate is the same as that discussed above for Figure 4. An important issue is how the intimacy of binding affects the measured rate constants. It would therefore be instructive to compare the rate constants from the low ionic strength case with those obtained in the case where binding is not significant. It is straightforward to derive that the relationship between the first order (binding) and second-order (no binding) rate constants is given by
k2 )
K3+ k1 K [DNA] + 1 3+
(14)
where k2 is the second-order rate constant, and k1 is the corresponding first-order rate constant obtained from simulation. The value of kf determined in Figure 5 therefore gives an equivalent second-order rate constant of k2 ) 1.4 × 105 M-1 s-1.
13842 J. Phys. Chem., Vol. 100, No. 32, 1996
Johnston and Thorp
Figure 5. Cylic voltammograms and digital simulations (using Scheme 3) for 50 µM Ru(bpy)32+ + 2.0 mM calf thymus DNA in 50 mM Naphosphate. T ) 298.15 K, area (planar) ) 0.32 cm2, E° (free) ) 1.09 V, E° (bound) ) 1.05 V (TSR), ks(free) ) ks(bound) ) 0.1 cm/s, R(free) ) R(bound) ) 0.5, Kb2+ ) 2000 M-1, Kb3+ ) 104 M-1, kf(II) ) kf(III) ) kf(II)’ ) kf(III)′ ) kf(II)′′ ) 109 M-1 s-1, kf ) 100 s-1, kf′ ) 20 s-1, [M2+] ) 5.0 × 10-5 M, [guanine] ) 4.0 × 10-4 M, DM2+ ) DM3+ ) 1.0 × 10-5 cm2/s, DDNA (all forms) ) 2.0 × 10-7 cm2/s. Calculated (using eq 14) second-order oxidation rate kf(2) ) 1.4 × 105 M-1 s-1. (A) ν ) 25 mV/s, (B) ν ) 250 mV/s, and (C) ν ) 1000 mV/s.
TABLE 1: Summary of DNA Oxidation Experiments and Experimental Conditions oxidant
buffer
K2+ (M-1)a
k2 (M-1 s-1)b
scan rate (mV/s)
Ru(bpy)32+ Ru(bpy)32+
50/700c 50d
10 400
1.0 × 104 1.4 × 105
10-1000 10-1000
a Binding constants calculated from polyelectrolyte theory or experimentally determined. For simulations with binding, the entered binding constants were multiplied by 5 because the concentration of oxidizable DNA (guanine) is only 20% of the total DNA concentration. Binding constants are therefore in terms of total nucleotide concentration, while rate constants are in terms of guanine concentration. b The second-order rate constant for the high salt case was determined directly from the fitting, and the second-order rate constant for the low salt case was calculated from the first-order rate constant using using eq 14. c Buffer consisting of 50 mM Na-phosphate and 700 mM NaCl, pH ) 6.8, [Na+] ) 780 mM. d 50 mM Na-phosphate, pH 6.8.
As shown in Table 1, the equivalent second-order rate constant for the case with binding is a factor of 10 higher than that obtained at high salt. At high salt, the electron transfer probably occurs in an encounter complex where the metal complex and DNA are separated by a large number of counterions and solvent molecules. As discussed elsewhere, electron tunneling through highly polar media proceeds with a large value of the parameter β,44 so the distance dependence of electron transfer can be described according to eq 15:
kls/khs ) exp(-β∆r)
(15)
where kls and khs are the rate constants for electron transfer at low salt and high salt, respectively, and ∆r is the difference in electron-transfer distance between the two cases. If the value of β ()3 Å-1)15 is the same for both cases, we can estimate that the electron-transfer distance is ∼0.9 Å shorter in the low salt case. Although ionic strength effects on β can be expected to be small, the parameter would likely increase at higher ionic strength, since more polar media exhibit higher β values. This increase would lead to an even larger value for ∆r, supporting the contention that the electron-transfer distance is shorter in the low ionic strength case. We have taken advantage of the high value of β for polar media to probe finely the solvent accessibility of the guanine
base in duplex oligonucleotides that contain mismatches at guanine. In this case, the greater the penalty for transfer through polar solvent, the more sensitive the electron-transfer rate constant to the solvent accessibility of the base. This phenomenon is also apparent in comparing the k2’s in Table 1. At low ionic strength, electron transfer occurs within an associated complex where the metal complex is likely to be in more intimate contact than at high ionic strength, which increases the rate constant for electron transfer by an order of magnitude. The ability to modulate these rate constants predictably using changes in ionic strength and to measure the different rate constants conveniently using cyclic voltammetry and digital simulation may provide a means for further tuning the dependence of the rate constant on the solvent accessibility of the nucleobase dictated by the DNA structure. Acknowledgment. This research was supported by the David and Lucile Packard Foundation. H.H.T. thanks the Camille and Henry Dreyfus Foundation for a Camille Dreyfus TeacherScholar award and the Alfred P. Sloan Foundation for a Fellowship. References and Notes (1) Jenkins, Y.; Barton, J. K. J. Am. Chem. Soc. 1992, 114, 87368738. (2) Ried, T.; Baldini, A.; Rand, T. C.; Ward, D. C. Proc. Natl. Acad. Sci. U.S.A. 1992, 89, 1388-1392. (3) Du, Z.; Hood, L.; Wilson, R. K. Methods Enzymol. 1993, 218, 104121. (4) Tizard, R.; Cate, R. L.; Ramachandran, K. L.; Wysk, M.; Voyta, J. C.; Murphy, O. J.; Bronstein, I. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 4514-4518. (5) Kaiser, R.; Hunkapiller, T.; Heiner, C.; Hood, L. Methods Enzymol. 1993, 218, 122-153. (6) Fodor, S. P. A.; Rava, R. P.; Huang, X. C.; Pease, A. C.; Holmes, C. P.; Adams, C. L. Nature 1993, 364, 555-556. (7) Noble, D. Anal. Chem. 1995, 67, 201A-204A. (8) Bains, W. Chem. Br. 1995, 122-125. (9) Scholin, C. A.; Villac, M. C.; Buck, K. R.; Krupp, J. M.; Powers, D. A.; Fryxell, G. A.; Chavez, F. P. Nat. Toxins 1994, 2, 152-165. (10) Holodniy, M.; Mole, L.; Margolis, D.; Moss, J.; Dong, H.; Boyer, E.; Urdea, M.; Kolberg, J.; Eastman, S. J. Virol. 1995, 69, 3510-3516. (11) Millan, K. M.; Mikkelsen, S. R. Anal. Chem. 1993, 65, 23172323. (12) Millan, K. M.; Saraullo, A.; Mikkelsen, S. R. Anal. Chem. 1994, 66, 2943-2948. (13) Xu, X.-H.; Yang, H. C.; Mallouk, T. E.; Bard, A. J. J. Am. Chem. Soc. 1994, 116, 8386-8387. (14) Xu, X.-H.; Bard, A. J. J. Am. Chem. Soc. 1995, 117, 2627-2631. (15) Johnston, D. H.; Glasgow, K. C.; Thorp, H. H. J. Am. Chem. Soc. 1995, 117, 8933-8938. (16) Lecomte, J.-P.; Kirsch-De Mesmaeker, A.; Feeney, M. M.; Kelly, J. M. Inorg. Chem. 1995, 34, 6481-6491. (17) Johnston, D. H.; Welch, T. W.; Thorp, H. H. Met. Ions Biol. Syst. 1996, 33, 297-324. (18) Johnston, D. H.; Cheng, C.-C.; Campbell, K. J.; Thorp, H. H. Inorg. Chem. 1994, 33, 6388-6390. (19) Osteryoung, J. Acc. Chem. Res. 1993, 26, 77. (20) Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589a. (21) Welch, T. W.; Thorp, H. H. J. Phys. Chem. 1996, 100, 13829. (22) Welch, T. W.; Corbett, A. H.; Thorp, H. H. J. Phys. Chem. 1995, 99, 11757-11763. (23) Carter, M. T.; Rodriguez, M.; Bard, A. J. J. Am. Chem. Soc. 1989, 111, 8901. (24) Carter, M. J.; Bard, A. J. J. Am. Chem. Soc. 1987, 109, 75287530. (25) Willit, J. L.; Bowden, E. F. J. Phys. Chem. 1990, 94, 8241. (26) Maniatis, T.; Fritsch, E. F.; Sambrook, J. Molecular Cloning: A Laboratory Manual, 2nd ed.; Cold Spring Harbor Press: Plainview, NY, 1989. (27) Pyle, A. M.; Barton, J. K. Prog. Inorg. Chem. 1990, 38, 413. (28) Thorp, H. H. AdV. Inorg. Chem. 1995, 43, 127-177. (29) Satyanarayana, S.; Dabrowiak, J. C.; Chaires, J. B. Biochemistry 1993, 32, 2573. (30) Blauch, D. N.; Anson, F. C. J. Electroanal. Chem. 1991, 309, 313.
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