Interpreting DNA Vibrational Circular Dichroism ... - ACS Publications

Nov 14, 2006 - B 2003, 107, 9165 and Krummel, A. T.; Zanni, M. T. J. Phys. Chem. B 2006, 110, 13991). Here, we extend the coupling model derived from ...
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J. Phys. Chem. B 2006, 110, 24720-24727

Interpreting DNA Vibrational Circular Dichroism Spectra Using a Coupling Model from Two-Dimensional Infrared Spectroscopy Amber T. Krummel and Martin T. Zanni* Department of Chemistry, UniVersity of Wisconsin at Madison, Madison, Wisconsin 53706-1396 ReceiVed: May 25, 2006; In Final Form: September 18, 2006

Two-dimensional infrared spectroscopy was recently used to measure the vibrational couplings between carbonyl bonds located on DNA nucleobases (Krummel, A. T.; Mukherjee, P.; Zanni, M. T. J. Phys. Chem. B 2003, 107, 9165 and Krummel, A. T.; Zanni, M. T. J. Phys. Chem. B 2006, 110, 13991). Here, we extend the coupling model derived from these 2D IR experiments to simulate the vibrational absorption and vibrational circular dichroism (VCD) spectra of three double-stranded DNA oligomers: poly(dG)-poly(dC), poly(dGdC), and dGGCC. Using this model, we determine that the VCD spectrum of A-form poly(dG)-poly(dC) is dominated by interactions between stacked bases, whereas the coupling between base pairs and stacked bases carries equal importance in the VCD spectrum of B-form poly(dG-dC). We also simulate the absorption and VCD spectra of dGGCC, which is a combination of A- and B-form configurations. These simulations give insight into the structural interpretation of VCD and absorption spectroscopies that have long been used to monitor DNA secondary structure and kinetics.

Introduction Vibrational absorption, circular dichroism, and two-dimensional infrared (2D IR) spectroscopies are three techniques used to monitor the structures of proteins and nucleic acids in various environments.1-14 These three techniques are sensitive to oligomer structure because the normal modes of the repeating units (such as the carbonyl stretches of the peptides or bases) are coupled by the curvature of the potential energy surface, creating delocalized vibrational eigenstates with characteristic infrared frequencies and spectral intensities.15-18 The frequencies and intensities are often sufficient to determine the oligomer secondary structure for systems whose coupling/structure relationship is well-understood or at least well-characterized with empirical correlations.19-23 But in practice additional unknowns such as hydrogen bonding make absorption spectroscopy unreliable for structure determination and worse for establishing a reliable coupling model. A better approach is to measure the couplings directly. In this regard, vibrational circular dichroism (VCD) and 2D IR spectroscopies are preferable. Vibrational circular dichroism measures the rotational strength of vibrational modes, which is directly proportional to the coupling in systems where the magnetic and electric transition moments of the repeating basis modes are orthogonal (such as for vibrational modes localized on carbonyl stretches).1,18,24-28 In fact, vibrational circular dichroism was one of the first experiments to definitively show that the carbonyl stretch modes of stacked nucleic acid bases are coupled.18 In contrast to linear spectroscopies, 2D IR spectroscopy measures the diagonal and offdiagonal anharmonicities of the potential energy surface.29-32 These anharmonicities give the curvature of the potential and thus are related to the coupling. Considering that all three techniques probe the same part of the potential energy surface, it stands to reason that a single model should exist that accurately * Author to whom correspondence should be addressed. E-mail: zanni@ chem.wisc.edu.

describes the coupling/structure relationship for all of these spectroscopies. Coupling models have been proposed to explain the carbonyl absorption and VCD spectra of nucleic acids, but there does not currently exist a single model that describes both.24,33-36 In large part this is because neither VCD nor absorption measurements are sensitive to both stacked and base-pair couplings. The very fact that there is strong signal in the VCD spectra of helical oligomers establishes that stacked bases are coupled. But VCD spectra are inconclusive for hydrogen-bonded bases, not because hydrogen-bonded bases are uncoupled but because the nearly planar geometry of base pairs gives little rotational strength.37 The situation is reversed for infrared absorption studies. The use of isotope labeling has established that the bases in guanine/ cytosine base pairs are strongly coupled.33,38 However, the absorption studies cannot conclusively assign the isotope frequency shifts to base-pair coupling as opposed to stacked coupling. Considering VCD and absorption experiments together it would appear that both stacked and base-pair couplings contribute. Both stacked and base-pair couplings have been accounted for in simulations of VCD and absorption spectra using transition dipole coupling (TDC) between carbonyl groups, but the spectra could not be adequately fit.1,2,18,24,36 Better agreement between VCD and absorption spectra were obtained by Self and Moore, who included ring vibrational modes in their calculations, coupled to the carbonyl groups with TDC.27,28 TDC is a reasonable model when the vibrational modes are wellseparated in space and not covalently bonded. As a result it is still unclear how vibrational coupling contributes to VCD and absorption spectra of nucleic acids, leaving the interpretation of the spectra largely empirical. In two recent publications we have explored the coupling in double-stranded guanine/cytosine nucleic acid oligomers using 2D IR spectroscopy and electronic structure calculations.39,40 Unlike one-dimensional VCD and absorption spectroscopies, 2D IR spectroscopy is sensitive to both stacked and hydrogenbonded bases through the diagonal and cross-peaks. For double-

10.1021/jp063227a CCC: $33.50 © 2006 American Chemical Society Published on Web 11/14/2006

Interpreting DNA VCD Spectra Using 2D IR

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stranded oligomers (dsDNA) that consist of two homo-polymers of identical bases such as poly(dG)-poly(dC), stacked couplings cause shifts in the frequency of the diagonal peaks whereas basepair couplings create cross-peaks. Multiple cross-peaks and diagonal peaks appear for double-stranded oligomers with more varied sequences. Through simulations of the spectra and electronic structure calculations of the couplings, we found that TDC between carbonyl groups is a poor model for two reasons: (a) because of the close proximity of the transition dipoles and (b) because of charge flow among the stacked bases. For hydrogen-bonded bases, charge flow is negligible, and the coupling can be computed using a transition dipole density model, which more accurately represents the charge distribution than two transition dipoles.40 Comparison of calculated couplings to those extracted from experimental 2D IR spectra indicates that both stacked and base-pair couplings can be reliably determined with appropriate electronic structure calculations. In this paper we use our experimentally derived coupling model39,40 to simulate and interpret the absorption and VCD spectra of several model double-stranded nucleic acids in the region of the nucleobase carbonyl stretches. We focus on the dsDNA molecules: poly(dG)-poly(dC), poly(dG-dC), and dGGCC. The VCD and absorption spectra of poly(dG)-poly(dC) and dGGCC have been previously reported by Diem and co-workers.24,35,36 The poly(dG-dC) VCD and absorption spectra were initially published by Keiderling and co-workers, then revisited by Bour and co-workers.4,8,25 The two polymeric DNAs have A- and B-form secondary structures, respectively, but the same Watson-Crick base-pair geometry.41-43 Thus, these two strands are expected to have the same base-pair coupling but different stacked couplings. Our model currently only includes coupling between nearest neighbors, an approximation that is investigated with dGGCC dsDNA. As compared to the poly(dG)-poly(dC) or poly(dG-dC) dsDNA, the dGGCC dsDNA sequence has a noncanonical form. This fact allows us to test our coupling model using NMR-derived structures and extend the model beyond idealized DNA forms. We find that VCD and absorption spectra for all three of these oligomers can be simulated within the uncertainties of the coupling model. That having been shown, we then discuss the physical origins of the frequency shifts and VCD peak patterns that underpin the well-established empirical relationships between these nucleic acid vibrational spectroscopies and secondary structure. Theory and Computational Approaches The approaches that we use to calculate the vibrational coupling constants and simulate the vibrational absorption spectra have been described in detail elsewhere,39,40 but a brief description is given here. The eigenvectors needed to compute the absorption spectrum and the VCD spectrum are obtained using the vibrational Hamiltonian written as

H)

1 2

βijBi+Bj ∑i ωiBi+Bi + ∑ i,j

(1)

where Bi and Bi+ are the harmonic oscillator raising and lowering operators, ωi is the mode energy, and βij are the couplings between modes i and j. Equation 1 references the quantum levels to the zero-point energy. The raising and lowering operators operate on modes qi that are localized on the bases and contain mostly carbonyl bond stretching motions. The interactions between oscillators are governed by the βij

coupling terms and are the focus of this paper. Diagonalizing eq 1 generates eigenstates Qk consisting of linear combinations of qi basis modes, representing vibrational modes that are delocalized over coupled guanine and cytosine bases. The eigenenergies of Qk give the measurable frequencies, although not all possible frequencies are observed because of symmetry. The absorption and the VCD spectra are determined from the eigenstate transition dipole and rotational strengths, respectively. The transition dipole strength of the kth eigenstate, Dk, is given by

| | ∂U ∂Qk

Dk )

2

(2)

Here, U is the electronic transition dipole of the eigenstate extended across multiple bases. Equation 2 can be expressed in terms of the qi basis modes using N

Dk )

( ) ∂µi ∂µj ‚ i ∂qj

N

∑ ∑ cikcjk ∂q i)1 j)1

(3)

where cik and cjk are the coefficients from diagonalizing the Hamiltonian in eq 1 and µi is the electronic transition dipole of the base i. The rotational strength is a measure of the molecular circular dichroism and depends on the interaction between the electronic and the magnetic transition dipoles in a molecule. Similar to the transition dipole strength, the rotational strength Rk can be written in either the eigenstate or the local mode basis. The rotational strength of the kth eigenstate is

Rk ) Im

[

∂U ∂M ‚ ∂Qk ∂Qk

]

(4)

where M is the magnetic transition dipole. Assuming the electronic and magnetic transition dipoles of the basis modes, qi, are orthogonal, the rotational strength of the kth eigenstate can be rewritten solely using the electronic transition dipoles

Rk ) -

() π c

n

n

[

∂µi

∑ ∑ cikcjk (υjXj - υiXi) ‚ ∂q i)1 j)1

i

×

]

∂µj ∂qj

(5)

In these equations, cik and cjk are the coefficients from diagonalizing the Hamiltonian, c is the speed of light, υi is the unperturbed frequency, and Xi is the equilibrium position of the center of mass of the qi basis mode. We take Xi to be at the midpoint of the carbonyl bond. This expression for rotational strength has been well-characterized by Tinoco and others and was extended to nucleic acids by Diem and Keiderling.24,36,44-47 Because eq 5 predicts zero intensity for a single oscillator, it is appropriate to use it when the magnetic and electronic transition dipole moments of the local mode, qi, are orthogonal. To test for orthogonality, we calculated the electronic transition dipole and magnetic transition dipole moments for the carbonyl stretches in isolated cytosine and guanine bases using density functional theory employing the hybrid functional B3LYP and the 6-31++G** basis set (denoted DFT throughout this article). We found that the relative angles between the transition moments were 89.97° and 89.77°, respectively. Thus, (∂U/∂Qk)‚ (∂M/∂Qk) is very close to zero for a single oscillator, confirming the validity of eq 5. The advantage of using eq 5 to calculate rotational strengths versus more sophisticated methods is that it is only dependent on the geometry of the dsDNA oligomer

24722 J. Phys. Chem. B, Vol. 110, No. 48, 2006

Krummel and Zanni

Figure 2. Repeating units used to model B-form poly(dG-dC) dsDNA.

TABLE 1: Parameters Used to Calculate the Linear IR and VCD Spectra of Poly(dG-dC) dsDNAa Figure 1. (a) Calculated (dashed) and experimental (solid) VCD spectra of poly(dG-dC) dsDNA. (b) Calculated (dashed) and experimental (solid) IR spectra of poly(dG-dC) dsDNA. The stick spectra are also plotted. Experimental data are reproduced from ref 4.

and matrix elements µi of the basis modes qi and thus gives a more intuitive interpretation of the spectra. Parts of this paper refer to previous calculations that are described in detail in our earlier report on the 2D IR spectroscopy of DNA.40 In that paper, we performed geometry optimizations and frequency calculations using DFT. Full geometry optimizations were done on the cytosine (C) and guanine (G) free bases and a G:C base pair. The normal coordinates for C and G that contained the most carbonyl character serve as the qi basis modes referred to here. Single-point energy (SPE) calculations were one method used to calculate the coupling constants and transition dipole vectors in ref 40 for the bases, base pairs, and double-stranded DNA models. All quantum calculations were carried out in Gaussian 98 and Gaussian 03.48,49 Simulations In this section we present simulated VCD and absorption spectra for the dsDNA molecules, poly(dG-dC), poly(dG)poly(dC), and dGGCC, for comparison to previously published experimental VCD and absorption spectra. The experimental VCD and absorption spectra of poly(dG-dC) are shown in Figures 1a and 1b, as published by Bour and co-workers.4 Poly(dG-dC) is in the B-form and has alternating guanine and cytosine stacked bases. The experimental VCD spectrum in Figure 1a contains a couplet whose zero-crossing is at 1685 cm-1. The positive lobe is at a lower energy than the negative lobe, and their intensities are equal. The zero-crossing of this couplet is at the same position as the guanine carbonyl stretch absorption maximum in the linear IR spectrum shown in Figure 1b. The feature between 1640 and 1670 cm-1 in the absorption and VCD spectra is the cytosine carbonyl stretch. The assignment of these two features to the guanine and cytosine carbonyl stretches is historical.3 We know from 2D IR experiments that these modes also contain guanine and cytosine ring motions and, furthermore, are coupled to one another.40 Regardless, the absorption spectrum exhibits a flattened peak for the cytosine

site parameters

2D IRb d(GC)8

VCD poly(dG-dC)

ωG (cm-1) ωC (cm-1) θG θC µG (D Å-1 amu-1/2) µC (D Å-1 amu-1/2)

1666.2 1652.0 -2° -67° 3.8 3.8

1665.0 1655.6 32° -57° 3.8 3.8

βGC (cm-1) βSp (cm-1) βGp (cm-1) βCp (cm-1) βSpe (cm-1) βGpe (cm-1) βCpe (cm-1)

Coupling Parameters -10.6 -5.3 8.2 2.15 0.5 2.9 2.8

-9.5 -5.7 8.2 1.15 0.1 2.9 2.8

a The parameters extracted from the 2D IR spectra of d(GC) dsDNA 8 are listed for comparison. The electronic transition dipole angles, θG and θC, are depicted in Figure 3. b Values are taken from ref 40.

feature, in agreement with other recent Fourier transform IR data.4 The flattened feature is created by multiple overlapping modes. The 2D IR spectrum of the dsDNA d(GC)8, a shortened version of the poly(dG-dC) with the same secondary structure, exhibits two sets of cross-peaks, thereby resolving the two overlapped cytosine modes.40 The secondary structure of the poly(dG-dC) dsDNA can be broken into a repeating block of stacked base pairs, which consists of two units, A and B. Units A and B are depicted in Figure 2. Unit A is a C:G base pair on top of a G:C base pair, whereas, unit B is the G:C base pair stacked on top of another C:G base pair. The nearest neighbor couplings used to model a sequence 40 base pairs in length are denoted in Figure 2. The parameters extracted from the 2D IR experiments on d(GC)8 dsDNA are also given in Table 1.40 Through the use of these values, the VCD and absorption spectra of the poly(dG-dC) dsDNA sequence were simulated, which give the long-dashed lines in Figures 1a and 1b, respectively. These spectra are calculated from eqs 1, 3, and 5 and convoluted with Voigt line shapes as described previously in ref 31 of Krummel et al.39 The stick spectra prior to convolution are also shown. Our model does a good job of calculating the features of both experiments centered at 1685 cm-1. The features that lie between 1640 and 1670 cm-1 are difficult to reproduce because they overlap and

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Figure 3. Hydrogen-bonded G:C base pair. The electronic transition dipole vectors are set at the midpoint of the carbonyl bonds and rotated by θG and θC.

interfere, but our model reproduces the experiment reasonably well. The overlapping cytosine bands, resolved with 2D IR, are also predicted by the simulations. The site parameters and coupling parameters used to simulate the VCD spectrum are given in Table 1. Only minor modifications from the canonical B-form coupling values were needed to fit the spectra. The coupling constants required to calculate the VCD spectrum all lie within 1 cm-1 of those extracted from the 2D IR data. Furthermore, the site parameters required to reproduce the VCD spectrum are all within the expected experimental error constraints from the dsDNA d(GC)8. Thus, it appears that the vibrational coupling in arbitrarily long oligomers can be broken into small repeating units of stacked bases. The one exception to this statement is the orientation of the guanine transition dipole relative to its carbonyl bond, which lies outside of the dsDNA d(GC)8 error bars. This angle was altered for better agreement in the intensities of the bands. The transition dipole angle is one of the least accurate parameters to obtain from the 2D IR spectra, because it changes the peak intensities but not their frequencies. The difference may also indicate that nearest neighbor couplings alone are not adequate, a point discussed in more detail below. The experimental VCD spectrum of the A-form dsDNA poly(dG)-poly(dC) is presented in Figure 4a, as taken from Zhong et al.24 Notice that this spectrum is similar to that of B-form poly(dG-dC) even though the sequence and secondary structures are different. While VCD is not terribly sensitive to the differences between these two oligomers, the 2D IR spectra of these sequences are remarkably different,40 testament to the enhanced structural sensitivity of 2D versus 1D IR spectroscopies. Nonetheless, the primary difference between the spectra in Figures 1a and 4a is in the feature centered at 1650 cm-1. In Figure 4a, the VCD spectrum of poly(dG)-poly(dC) exhibits a negative lobe that is lower in energy than the positive lobe, and their intensities are equal. The dashed line in Figure 4a is the VCD spectrum that we simulated with eqs 1 and 5 and can be modeled using a single repeating unit of two stacked G:C base pairs, as depicted in Figure 5. The local mode and coupling parameters used in the simulations of the spectra for a 28 base-pair model of poly(dG)-poly(dC) dsDNA are given in column two of Table 2. As can be seen in Figure 4a, the simulated VCD spectrum reproduces the experimental VCD spectrum nicely. Comparing columns 1 and 2 in Table 2 shows the similarity of the input parameters used to simulate the 2D IR spectra of the selfcomplimentary dG5C5 dsDNA40 and the VCD spectrum of the poly(dG)-poly(dC) dsDNA molecule. Again, the variation in

Figure 4. (a) Calculated (dashed) and experimental (solid) VCD spectra of poly(dG)-poly(dC) dsDNA. (b) Calculated (dashed) and experimental (solid) IR spectra of poly(dG)-poly(dC) dsDNA. The stick spectra are also plotted. Experimental data are digitized from ref 24.

Figure 5. Repeating unit used to model A-form poly(dG)-poly(dC) dsDNA.

the coupling terms used to simulate the VCD spectrum of poly(dG)-poly(dC) dsDNA is minimal. The only notable difference is in the guanine local mode frequency, ωG, used in the 2D IR simulations versus the VCD calculations. This difference is likely a result of electron transfer, which is discussed below. We also simulated the absorption and VCD spectra of the double-stranded oligomer dGGCC. According to the NMR structure of dGGGCCC, this dsDNA sequence adopts an A-form-like structure at the ends and a B-form structure in the middle.43,50,51 The experimental VCD and absorption spectra are shown in Figures 6a and 6b, respectively, and were taken from Birke et al.35 Like the other strands, the absorption spectrum contains peaks located at 1678 and 1647 cm-1 that correspond to the guanine and cytosine carbonyl stretches, respectively. But unlike the other oligomers, the cytosine peak intensity is now larger than that of the guanine, which is also reflected in the experimental VCD spectrum of dGGCC dsDNA. Also, the feature centered at 1650 cm-1 no longer appears as a couplet with a positive and negative lobe as it does in the previous oligomers studied, but rather it only exhibits a single positive lobe.

24724 J. Phys. Chem. B, Vol. 110, No. 48, 2006 TABLE 2: Parameters Used to Calculate the Linear IR and VCD Spectra of Poly(dG)-Poly(dC) dsDNAa

Krummel and Zanni TABLE 3: Comparing Couplings Used for dGGCC dsDNA to Canonical A- and B-Form Couplings

site parameters

2D IRa dG5C5

VCD poly(dG)-poly(dC)

site parameters

2D IRa dG5C5

2D IRa d(GC)8

VCD dGGCC

ωG (cm-1) ωC (cm-1) θG θC µG (D Å-1 amu-1/2) µC (D Å-1 amu-1/2)

1664.0 1655.6 -2° -92° 3.8 3.8

1675.0 1655.0 -2° -92° 3.8 3.8

ωG (cm-1) ωC (cm-1) θG θC µG (D Å-1 amu-1/2) µC (D Å-1 amu-1/2)

1664.0 1655.6 -2° -92° 3.8 3.8

1666.2 1652.0 -2° -67° 3.8 3.8

1664.0 1651.0 32° -68° 3.8 3.8

-9.5 9.6 -0.7 -1.9 -2.7

βGC (cm-1) βG (cm-1) βC (cm-1) βGCx (cm-1) βGCx2 (cm-1) βSpe (cm-1) βGpe (cm-1) βCpe (cm-1)

Coupling Parameters -9.6 -10.6 9.5 n/a 0.8 n/a -1.9 n/a -2.7 n/a n/a 0.5 n/a 2.9 n/a 2.8

-10.6 10.4 -0.7 -1.9 -2.7 -0.5 5.9 4.8

βGC (cm-1) βG (cm-1) βC (cm-1) βGCx (cm-1) βGCx2 (cm-1)

Coupling Parameters -9.6 9.5 0.8 -1.9 -2.7

a The parameters extracted from the 2D IR spectra of dG5C5 dsDNA are listed for comparison. b Values are taken from ref 40.

a

Figure 6. (a) Calculated (dashed) and experimental (solid) VCD spectra of dGGCC dsDNA. (b) Calculated (dashed) and experimental (solid) linear IR spectra of dGGCC dsDNA. The stick spectra are also plotted. Experimental data are digitized from ref 35.

To simulate the spectra, we truncated the dGGGCCC dsDNA NMR structure43 to dGGCC dsDNA, assigned transition dipoles to each carbonyl bond as we did for the other oligomers, and started with a Hamiltonian built from the canonical A- and B-form couplings where appropriate. The simulations shown in Figure 6 utilize couplings that are only slightly different than those of the canonical DNA forms. In Table 3, the canonical coupling constants and the constants used in Figure 6 are given. All coupling constants used to simulate the VCD and absorption spectra lie within the experimental uncertainty of the values extracted from the 2D IR spectra. Discussion The primary problem with the interpretation of VCD and IR absorption spectra is the lack of observables. Both VCD and IR absorption spectra contain frequency information. However, frequency shifts created upon double helix formation can be caused by coupling between either stacked bases or between hydrogen-bonded bases.39 In that regard, frequency information

Values are taken from ref 40.

alone is not enough. VCD spectra also contain rotational strengths that are a more direct measure of vibrational coupling. Still, VCD spectra are only really sensitive to the coupling between stacked bases simply because the geometry of hydrogenbonded bases gives little signal intensity.37 As a result, it is difficult to understand the vibrational coupling of DNA from these two spectroscopies alone. In this report, the spectra were simulated from a coupling model developed from 2D IR spectra. The 2D IR spectra have provided enough additional observables (overtone and combination band frequencies as well as crosspeak intensities that depend on relative transition dipole orientations) that both the stacked and base-pair couplings could be estimated. Now, with the VCD and IR absorption spectra of these three oligomers adequately reproduced, we can use the coupling model to interpret their spectral features. Consider the dsDNA poly(dG)-poly(dC). The best way to envision the motions in the DNA is as vibrational modes delocalized along the individual strands that are then coupled to each other. The simulations of poly(dG)-poly(dC) relied primarily on the couplings βGC, βG, and βC. These couplings correspond to the hydrogen-bonded bases in base pairs, the coupling between stacked guanine bases, and the coupling between stacked cytosines bases (Figure 5), respectively. Each coupling has a different effect on the spectra. Couplings between stacked bases on the same strand produce two infrared transitions (E| and E⊥). E| is shifted in frequency equal to the coupling, at least according to the analytical solution for a perfect and infinitely long helix, and E⊥ is nearby.39,52-54 The equations for E| and E⊥ are explicitly written below in eqs 6 and 7. Therefore, for βG ) 10.4 cm-1, the observed IR frequency of the coupled guanine exciton appears approximately 10 cm-1 above the vibrational frequency of the single guanine base. In contrast, βC ) -0.7 cm-1, so only a small shift is observed in the cytosine band to lower frequencies. For the three doublestranded oligomers studied here, the coupling between guanines ranges from βGpe ) 2.9 cm-1 to βG ) 10.4 cm-1, and the coupling between cytosines ranges from βCpe ) 2.8 cm-1 to βC ) -0.7 cm-1. Guanine coupling is always larger than that of cytosine in A- and B-form DNA because the secondary structure of all three double-stranded oligomers puts the guanine carbonyl bonds on the inside of the helix and the cytosine carbonyl groups on the outside. As a result, the distance from one base to the next is much smaller for guanines than cytosines (Figures 2 and 5), and hence guanines are more strongly coupled. Frequency shifts are also caused by βGC, but the shifts are small

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because the frequency difference between the guanosine and cytosine bases is large (ωG ) 1675.0 cm-1, ωC ) 1655.0 cm-1, Table 2). For Watson-Crick base pairs, βGC ) -10.6 cm-1. If the cytosine and guanine carbonyl frequencies were degenerate, then a 21.2 cm-1 splitting would be observed for a single base pair. Including βGC in the calculations only causes a 3.5 cm-1 shift of the two E| bands, although their intensities change by ∼30%. Thus, the frequencies are more sensitive to base stacking couplings than to base-pair couplings whereas the intensities reflect both contributions. The frequencies measured in the IR absorption spectra are also present in the VCD spectra because both spectroscopies probe the same vibrational eigenstates. However, VCD intensities will differ because the VCD spectra are proportional to the rotational strengths instead of the transition dipole moment magnitudes. According to eq 5 the rotational strength for a linear combination of coupled oscillators depends on two characteristics: (a) their relative orientation and (b) the magnitude of their coupling. Consider a single pair of degenerate coupled oscillators. The absorption spectrum of such a pair consists of a symmetric and an antisymmetric stretch. The relative intensities of these modes depend on the orientation between the two electric transition dipole vectors, given by D( ) (1 - cos θij), where θij is the angle between the two transition dipoles. Therefore, the IR absorption intensities differ by 2 cos θij. An analogous relationship exists for the magnetic transitions that give symmetric and antisymmetric combinations. Through the use of eq 5, the cross product of the electronic and magnetic transition dipoles gives the rotational strengths R( ) (sin θij. Thus, the symmetric and antisymmetric stretches are equal in intensity but opposite in sign, regardless of θij, creating the signature doublet often seen in VCD spectra. Since these formulations for the absorption and VCD intensities are drawn from a case of degenerate oscillators, this scenario is exact for stacked guanines or cytosines and can be generalized for nondegenerate oscillators. To understand the VCD spectra of dsDNA, consider the two individual strands contained in poly(dG)-poly(dC). If poly(dG) were infinitely long and a perfect helix, then it would have three infrared active transitions, one parallel to the helical axis and the other two degenerate and perpendicular to the helix axis. The frequencies of these transitions are given by

βm ∑ m

(6)

βm cos(χ) ∑ m

(7)

E | ) E0 + and

E⊥ ) E0 +

where χ ) 2πm/N. Here, N is the number of bases per turn of the helix, and m denotes the mth neighbor.53,54 Because these two modes are orthogonal, positive and negative features appear in the VCD spectrum analogous to the symmetric and antisymmetric stretch modes of two coupled oscillators. But unlike two coupled oscillators, the splitting between the two peaks is only a fraction of the coupling strength set by χ. The splitting between E| and E⊥ for poly(dG) is approximately 2.5 cm-1 even though βG ) 9.6 cm-1. The small eigenstate splitting can be seen in the stick spectrum in Figure 4a. In poly(dG), the higherfrequency transition at 1698 cm-1 is the symmetric stretch and is negative because βG is positive. In poly(dC), βC is negative, making the symmetric stretch the lower-frequency mode. This is also the reason that the signs of the cytosine modes are opposite to the guanine peaks in the VCD spectra. As for their

intensities, the bases in DNA are nearly orthogonal to the helical axis, so most of the transition intensity appears in the symmetric stretches in the IR absorption spectra. The cytosine and guanine base frequencies are nondegenerate, which is why the basepair coupling, βGC, has little influence on the VCD spectrum. This conclusion is consistent with Birke et al.37 In a similar manner, the other two double-stranded oligomers can be approximately classified into parallel and perpendicular modes, although the resulting VCD and IR absorption spectra are more complicated. As the symmetry of a dsDNA sequence is lowered and/or its length becomes finite, more eigenstates are IR-allowed. Therefore, spectra of poly(dG-dC) dsDNA contain more features than poly(dG)-poly(dC) dsDNA because poly(dG-dC) dsDNA has a lower symmetry. The dsDNA sequence dGGCC also lacks symmetry and does not have a full helical turn. As a result, the spectra of dGGCC dsDNA contains eight eigenstates that carry oscillator strength. In this case, the spectra are best understood by examining each eigenstate obtained by explicit diagonalization of the Hamiltonian. Our interpretation of the VCD spectrum is qualitatively similar to that by Diem and co-workers.24,35,37 However, the Diem group and others relied on the TDC model to calculate the coupling between the oscillators. According to our 2D IR work, the TDC model underestimates the coupling between hydrogen-bonded bases and overestimates the coupling between stacked bases, at least when employing transition dipole vectors that lie along the guanine and cytosine carbonyl bonds.40 Therefore the small rotational strength calculated with TDC for a base pair is underestimated, and the large rotational strength calculated for stacked bases is exaggerated. Although the magnitudes are inaccurate, TDC correctly predicts the signs of the coupling terms,39 which is why the earlier models correctly predict the sign of the of the couplet at 1685 cm-1 in poly(dG)-poly(dC) dsDNA. Using more precise coupling parameters has allowed us to more accurately interpret the VCD and IR absorption spectra. It is also interesting to compare our results to those of Self and Moore who used DeVoe Theory to calculate the VCD and absorption spectra of poly(rG)-poly(rC). Their approach used TDC coupling like Diem and co-workers36 but also included coupling between the carbonyl and ring modes, leading to better agreement with experiment. Indeed, our 2D IR work revealed that the ring modes are strongly coupled to the carbonyl vibrations in cytosine but not guanosine bases. Although TDC is typically not a good model for covalently coupled modes, inclusion of the ring modes effectively rotates the carbonyl transition dipole directions, to which the absorption, VCD, and especially 2D IR spectra are very sensitive. As demonstrated in these studies, our Hamiltonian and nearest neighbor coupling model provide quantitative insights to the physical origins of the absorption and VCD spectra of poly(dG-dC) dsDNA, poly(dG)-poly(dC) dsDNA, and dGGCC dsDNA However, there are still contributions to the spectra that need to be explored further. We note that this coupling model has only been examined for guanine/cytosine sequences in D2O. In D2O, labile NH2 protons exchange with deuterium atoms. This exchange simplifies the coupling because ND2 modes are at a much lower frequency than the carbonyl modes. However, if these sequences were studied in H2O, then the NH2 stretches might need to be included in the model because NH2 bends lie ∼20 cm-1 away from the carbonyl modes.34,55-57 Structural disorder could also play a role by giving rise to a range of couplings that could localize the vibrational eigenstates. The vibrational dynamics might also be different for guanine

24726 J. Phys. Chem. B, Vol. 110, No. 48, 2006 and cytosine bases, which might be probed with stimulated IR photon echo experiments. DNA is also well-known to transfer electrons.58,59 In fact, our electronic structure calculations exhibit evidence for electron transfer along the DNA strands. When the middle base of three stacked bases is moved along its vibrational coordinate, qi, charge is transferred along the strand. This charge transfer induces dipoles on the top and bottom bases as well as alters their diagonal force constants. The effect is largest for stacked guanines in the A-form because they have the most significant overlap of their rings. Following a procedure outlined in our previous paper, we used DFT/B3LYP methods to calculate transition dipoles, induced transition dipoles, and force constants by stretching one of three stacked bases along its carbonyl normal mode, qi. Electron-transfer effects are included in the coupling calculations.40 When the middle base of three stacked guanosines in the A-form is stretched, we calculate that the middle base has a transition dipole of 4.67 D/(Å amu1/2). In addition, we also find transition dipoles that have been induced on the unstretched bases; in a stack of guanines their magnitudes are 0.49 D/(Å amu1/2). The force constants of the three guanine bases also differ; the force constant of the middle base is 21.5 cm-1 lower than the forces constants of either of the bases on the end. Induced transition dipoles are also present in stacked cytosine bases. In comparison, stretching the middle of three stacked cytosine bases in the A-form creates an induced transition dipole strength of 0.38 D/(Å amu1/2) versus 4.53 D/(Å amu1/2) on the middle base. But in constrast to guanosine, the force constants differ by less than 1 cm-1 for three stacked cytosines. While the VCD and 2D IR measurements do not directly detect charge flow, these calculations suggest that the force constants of the bases change with sequence length, the magnitude of the change depending on the overlap of the stacked bases. This may explain why ωG ) 1664 cm-1 in dG5C5 dsDNA and ωG ) 1675 cm-1 in poly(dG)-poly(dC) dsDNA. The site energies in the double-stranded poly(dG-dC) DNA are consistent with those in dG5C5 dsDNA, because the guanine bases poly(dG-dC) dsDNA are not stacked on top of each other. Conclusions We recently used 2D IR spectroscopy to measure the coupling between base pairs and stacked bases in short guanine/cytosine dsDNA sequences.39,40 Through the use of two short, doublestranded oligomers that have A- and B-form DNA secondary structures, the 2D IR experiments provided the necessary observables to develop a model that accurately describes the couplings between nearest neighbor bases. In this report we used this model to simulate the VCD and absorption spectra of poly(dG)-poly(dC) dsDNA, poly(dG-dC) dsDNA, and dGGCC dsDNA. Our work helps explain how the VCD and IR absorption spectra depend on couplings that are directly related to the secondary structures of DNA oligomers. Furthermore, our simulations of dGGCC dsDNA demonstrate the flexibility of our model to describe a sequence that contains mixed canonical nucleic acid forms. Perhaps more important is the fact that with these coupling models and simulations in hand insights as to the physical origins of features in the absorption and VCD spectra of these sequences were obtained. Using these coupling models to understand the origins of the IR and VCD signals for DNA, we find that the IR and VCD experiments give complementary information. Certainly future studies are needed to closely examine how electron-transfer and hydration effects contribute to these spectroscopies. However, our results dem-

Krummel and Zanni onstrate the promise of 2D IR, 1D IR, and VCD spectroscopies to elucidate coupling/structure relationships of DNA and RNA oligomers. Models such as this one should help in monitoring the secondary structures of DNA and RNA in a wide range of studies, such as drug binding or fast kinetic studies. Note Added in Proof: Cho and co-workers recently published a series of papers on the vibrational coupling in DNA. They simulated FTIR, VCD, and 2D IR spectra of DNA double helices similar to the ones studied here.60-62 Acknowledgment. A.T.K. and M.T.Z. thank Petr Bour and Max Diem for providing us with the experimental data. We also thank Tim Keiderling for use of his equipment and helpful discussions. This research was supported by the Beckman Foundation and the National Science Foundation (Grant No. CHE0350518). Computational resources were provided to the University of Wisconsin Chemistry Parallel Computing Center through NSF Grant No. CHE0091916 and gifts from the Intel Corporation. A.T.K. also thanks the NSF for a Graduate K-12 Fellowship. References and Notes (1) Wang, L.; Keiderling, T. A. Biochemistry 1992, 31, 10265. (2) Wang, L. J.; Pancoska, P.; Keiderling, T. A. Biochemistry 1994, 33, 8428. (3) Liquier, J.; Taillandier, E. Infrared Spectroscopy of Nucleic Acids. In Infrared Spectroscopy of Biomolecules; Mantsch, H., Chapman, D., Eds.; John Wiley: New York, 1996; pp 131-158. (4) Andrushchenko, V.; Wieser, H.; Bour, P. J. Phys. Chem. B 2002, 106, 12623. (5) Tsankov, D.; Kalisch, B.; de Sande, H. V.; Wieser, H. J. Phys. Chem. B 2003, 107, 6479. (6) McClain, B. L.; Finkelstein, I. J.; Fayer, M. D. J. Am. Chem. Soc. 2004, 126, 15702. (7) Mukherjee, P.; Krummel, A. T.; Fulmer, E. C.; Kass, I.; Arkin, I. T.; Zanni, M. T. J. Chem. Phys. 2004, 120, 10215. (8) Bour, P.; Andrushchenko, V.; Kabelac, M.; Maharaj, V.; Maharaj, V. J. Phys. Chem. B 2005, 109, 20579. (9) Choi, J. H.; Hahn, S.; Cho, M. Int. J. Quantum Chem. 2005, 104, 616. (10) Chung, H. S.; Khalil, M.; Smith, A. W.; Ganim, Z.; Tokmakoff, A. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 612. (11) Hahn, S.; Kim, S.-S.; Chewook, L.; Cho, M. J. Chem. Phys. 2005, 123, 084905. (12) Kuimova, M. K.; Dyer, J.; George, M. W.; Grills, D. C.; Kelly, J. M.; Matousek, P.; Parker, A. W.; Sun, X. Z.; Towrie, M.; Whelan, A. M. Chem. Commun. 2005, 1182. (13) Massari, A. M.; Finkelstein, I. J.; McClain, B. L.; Goj, A.; Wen, X.; Bren, K. L.; Loring, R. F.; Fayer, M. D. J. Am. Chem. Soc. 2005, 127, 14279. (14) Kuimova, M. K.; Cowan, A. J.; Matousek, P.; Parker, A. W.; Sun, X. Z.; Towrie, M.; George, M. W. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 2150. (15) Tsuboi, M.; Takahashi, S.; Harada, I. Infrared and Raman Spectra of Nucleic AcidssVibrations in the Base Residues. In Physico-Chemical Properties of Nucleic Acids; Duchesne, J., Ed.; Academic Press: New York, 1973; Vol. 2; p 91. (16) Bandekar, J.; Krimm, S. Biophys. J. 1986, 49, A295. (17) Krimm, S.; Bandekar, J. AdV. Protein Chem. 1986, 38, 181. (18) Gulotta, M.; Goss, D. J.; Diem, M. Biopolymers 1989, 28, 2047. (19) Torii, H.; Tasumi, M. J. Chem. Phys. 1992, 96, 3379. (20) Hamm, P.; Woutersen, S. Bull. Chem. Soc. Jpn. 2002, 75, 985. (21) Choi, J. H.; Ham, S. Y.; Cho, M. J. Phys. Chem. B 2003, 107, 9132. (22) Moran, A.; Mukamel, S. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 506. (23) Wang, J. P.; Hochstrasser, R. M. Chem. Phys. 2004, 297, 195. (24) Zhong, W. X.; Gulotta, M.; Goss, D. J.; Diem, M. Biochemistry 1990, 29, 7485. (25) Wang, L. J.; Keiderling, T. A. Nucleic Acids Research 1993, 21, 4127. (26) Wang, L. J.; Yang, L. G.; Keiderling, T. A. Biophys. J. 1994, 67, 2460. (27) Self, B. D.; Moore, D. S. Biophys. J. 1997, 73, 339. (28) Self, B. D.; Moore, D. S. Biophys. J. 1998, 74, 2249.

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