Conformational Control of TT Dimerization in DNA Conjugates. A

Mar 22, 2010 - Zhengzheng Pan , Mahesh Hariharan , Joshua D. Arkin , Almaz S. Jalilov , Martin McCullagh , George C. Schatz , and Frederick D. Lewis...
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J. Phys. Chem. B 2010, 114, 5215–5221

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Conformational Control of TT Dimerization in DNA Conjugates. A Molecular Dynamics Study Martin McCullagh, Mahesh Hariharan,† Frederick D. Lewis,* Dimitra Markovitsi,‡ Thierry Douki,§ and George C. Schatz* Department of Chemistry, Northwestern UniVersity, EVanston, Illinois 60201 ReceiVed: February 2, 2010; ReVised Manuscript ReceiVed: March 1, 2010

The paper presents quantum yield results for the [2+2] and 6-4 photodimerization of TT steps in several DNA structures, including hairpins where the context dependence of the photodimerization yield is determined, and it develops a theoretical model that correctly describes the trends in dimerization yield with DNA structure. The DNA conjugates considered include dT20, dA20dT20, and three alkane-linked hairpins that contain a single TT step. The theoretical modeling of the [2+2] process is based on CASSCF electronic structure calculations for ethylene + ethylene, which show that photoexcitation of low-lying excited states leads to potential surfaces that correlate without significant barriers to a conical intersection with the ground state surface at geometries close to the dimer structure. The primary constraint on dimerization is the distance d between the two double bonds, and it is found that d < 3.52 Å leads to quantum yield trends that match the observed trends within a factor of 3. Constraints on the dihedral angle between the two double bonds are not as important, and although it is possible to generate better dimerization yield predictions for some structures by including these constraints, the best overall picture is obtained with no constraint. For 6-4 dimerization, a distance g < 2.87 Å and no constraint on dihedral angle provide an accurate description of the yield. Introduction Ground state conformation can control both the products and efficiency of photochemical reactions.1,2 In cases where the barrier for interconversion of two reactive conformations is smaller than those for their photochemical reactions, the product ratios will be determined by the difference in energy between the transition states leading to these products and not by the ground state conformational populations (Curtin-Hammett principle).3,4 In cases where the barrier for interconversion of conformations is larger than the barrier for their photochemical reactions, product ratios will be determined by ground state conformational populations. Solid state [2+2] photodimerization provides a classic example of ground state conformational control, product formation being governed by the orientation of adjacent molecules (distance and dihedral angle, Figure 1), as described by the “topochemical rules” formulated over 50 years ago by Schmidt and co-workers.5,6 Irradiation of single strand and duplex DNA possessing adjacent thymines (TT steps) results in the formation of a cissyn cyclobutane dimer TT formed via a [2+2] addition of the thymine CdC bonds and lesser amounts a 6-4 adduct that is formed via addition of the CdC bond of one thymine with the CdO bond of the adjacent thymine (a Paterno-Buchi reaction) followed by thermal ring-opening of the oxetane intermediate (Figure 2).7–9 The formation of the major TT dimer has been proposed to occur from a minor subset of * Corresponding authors. E-mail: F.D.L.: [email protected]; G.C.S., [email protected]. † Current address: School of Chemistry, Indian Institute of Science Education and Research-Thiruvananthapuram, Trivandrum, Kerala, India 695 016. ‡ Laboratoire Francis Perrin, CEA/DSM/IRAMIS/SPAM - CNRS URA 2453, CEA/Saclay, 91191 Gif-sur-Yvette, France. § Laboratoire des Le´sions des Acides Nucle´iques, CEA/DSM/DRFMC/ SCIB - UJC UMR E 3, 38054, CEA/Grenoble, France.

Figure 1. Two CdC bonds showing the distance, d, and dihedral angle, η, which define their relative geometry.

conformations in which the thymine double bonds are appropriately aligned, in much the same way as described by Schmidt’s topochemical rules.10,11 Changes in the distance and torsional angles between adjacent thymines (Figure 1) are very rapid both in single strand and in duplex DNA (∼0.15 Å/ps and ∼3.75°/ps respectively); however, the nonradiative decay of the reactive thymine singlet state is even faster. A recent femtosecond time-resolved infrared study indicates that formation of the major cyclobutane dimer (TT) in the single strand oligomer dT18 is complete within ca. 1 ps following electronic excitation!12 Molecular dynamics (MD) simulations of dimerization of the dinucleotide dT-p-dT by Law et al. led to the conclusion that the dihedral angle, η, between thymine CdC bonds is smaller in dimerizable conformations than in canonical B-DNA (22° vs 36°).11 MD simulations of TT formation in the oligomer dT18 by Johnson and Wiest indicated that the best combination of distance and dihedral angle between thymine CdC bonds occurred between thymines located within a hairpin region of the single-stranded structure.10 Neither of these simulations addresses the more interesting and biologically relevant questions concerning TT dimerization in duplex DNA. These include the context dependence of TT dimerization and the competition between cyclobutane and oxetane formation.

10.1021/jp100983t  2010 American Chemical Society Published on Web 03/22/2010

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Figure 2. Formation of the TT dimer and 6-4 adduct upon absorption of light by a TT step.

Figure 3. Structures of the hairpins St1, St3, and St5 investigated in this paper.

We report here the results of a collaborative investigation of the products and efficiency of T-T dimerization in five systems: dT20, dA20dT20, St1, St3, and St5 (Figure 3). The first two systems allow us to probe the differences between single and double stranded systems while the last three systems allow us to probe the context dependence of TT dimer formation. The quantum yield for thymine dimer formation in dT20 was previously deduced from a time-resolved study.13 Here we report a more precise determination of these values, based on high performance liquid chromatography coupled to mass spectrometry, and we examine the effect of base pairing. St1, St3, and St5 are three mini-hairpins possessing an alkane linker connecting six A-T base pairs in which a single TT step is located either at the end or in the middle of the base pair domain (Figure 3). We previously reported that the relative yield of TT dimerization in hairpins is smaller when the TT step is located at the nonlinked end of the hairpin (St1) than for TT steps located midstrand (St3) or adjacent to the alkane linker (St5) and that formation of the 6-4 adduct derived from an oxetane intermediate is observed only for St5.14 Quantum yields were not determined in our previous study. We report here the use of this data to develop models for the dimerization process that are based on ground state molecular dynamics (MD) calculations together with results from completeactive-space self-consistent field (CASSCF) electronic structure methods that determine accessibility to the conical intersection for photodimerization. We also study 6-4 adduct formation with similar measurements and theory. Experimental Section Quantum Yield Measurements. Hairpins. Hairpins St1, St3, and St5 were synthesized, purified, and characterized as previously described.14 Solutions containing ca. 1-1.2 µM hairpin in 10 mM phosphate buffer (pH 7.2) with 1.0 M NaCl were irradiated at 280 nm using a Xenon arc lamp and monochromator (ca. 2 mW) at 10 °C in 1 cm path-length quartz cuvettes. Aliquots irradiated for different time intervals were analyzed by high performance liquid chromatography (HPLC; Waters 600) on a C18 reversed phase column (MICROSORB-MV 100-5 C18, 250 × 4.6 MM VALCO) equipped with a diode

array detector (Waters PDA 996) using a column temperature of 60 °C with a UV detection wavelength of 260 nm, corresponding to the absorption maxima of the base pairs. A linear gradient of 20 mM ammonium acetate containing 0-30% CH3CN with a flow rate of 1 mL/min for 40 min was used. Under these conditions, starting material and the product(s) eluted with different characteristic retention time. The assignments of product peaks to cyclobutane and 6-4 adducts has been previously described.14 Product yields were determined from the initial slopes of plots of peak area vs irradiation time. Light intensities were determined using ferrioxalate actinometry.15 Quantum yields are the average of two or more measurements. Oligomers. Oligomers were purchased from Eurogentec. Single strands were lyophilized whereas dA20dT20 was provided after PAGE purification, as a double strand. They were dissolved in 0.1 mM phosphate buffer (pH ) 6.8) with 0.25 M NaCl. Irradiations were carried out at 266 nm in a Fluorolog-3 spectrofluorometer at 23 ( 1 °C. Solutions contained in 1 cm × 1 cm quartz cells were mildly stirred to avoid the formation of high local concentration of photoproducts. The power of the exciting beam was measured at the position of the sample by means of two different powermeters (Melles Griot 13PEM001; Ophir -NOVA2). It was confirmed a posteriori that less than 40% of the helices contained a thymine dimer. The concentration of thymine dimers was determined by HPLC associated to tandem mass spectrometry.16 Briefly, 10 µL of irradiated solution was diluted to 50 µL in water. Oligonucleotides were enzymatically hydrolyzed to release unmodified bases as nucleosides and photoproducts as dinucleoside monophosphates. Hydrolysis involved a first 2 h incubation (37 °C) step at pH 6 with phosphodiesterase II, DNase II, and Nuclease P1. Then, pH was adjusted to 8 and a second 2 h incubation (37 °C) was carried out in the presence of phosphodiesterase I and alkaline phosphatase. The resulting solution was injected onto a HPLC system (Agilent series 1100) equipped with a 150 × 2 mm octadecylsilyl silica gel column (particle size: 3 µm). The mobile phase was a gradient of acetonitrile in 2 mM TEAA. The eluent was then directed toward a tandem mass spectrometer (API 3000, Sciex-Applied Biosystems). Negative electrospray ionization was used. Detection was carried out in the multiple reaction monitoring mode using specific fragmentations for the thymine dimeric photoproducts (545432 and 545-447 for the (6-4) adducts and the CPDs, respectively). External calibration using authentic standards was used for both analytes. Computational Methods. The starting geometries for all systems were taken from the B-DNA structure (see Figure 4 and coordinates in Supporting Information). Charges were fit to the C12 linker using the restrained electrostatic potential fitting procedure (RESP).17 The C12 linker was optimized at the B3LYP/6-31G* level of theory followed by an electrostatic potential fitting at the HF/6-31G* level. Least squares fitting of the atomic charges to the calculated electrostatic potential was done using the resp module in Amber 8.18 Each system

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Figure 4. Starting structures for all five species investigated using MD: (a) dT20; (b) dA20dT20; (c) St1; (d) St3; (e) St5.

was neutralized with sodium ions and solvated with a box of TIP3P waters with a solvation length of 8 Å. An initial heating to 350 K, equilibration for 2 ns, followed by a production run of 6 ns was carried out on each system. Ten geometries were taken from the 350 K trajectory as starting geometries for simulations at 300 K. Each 300 K trajectory was equilibrated for 2 ns and then a production run of 6 ns was carried out. This yielded a total of 60 ns of simulation time to be analyzed for each system. The SHAKE algorithm was used to constrain all hydrogens in water.19 An integration time step of 2 fs was used for all simulations along with a particle mesh Ewald treatment of the long-range electrostatics.20,21 Isotropic pressure coupling to 1 bar was employed. A 10 Å van der Waal cutoff was used. Geometries were sampled every 2 ps. All simulations reported here were done using the CHARMM27 force field22,23 in the NAMD program.24 CASSCF calculations on ethylene + ethylene were done as a model system for the [2+2] cyclobutane dimer TT formation. The active space was chosen to be 4 electrons in twelve orbitals in accord with the CASSCF(2,6) ethylene monomer calculations done by Ben-Nun et al.25 The active space included some of the low-lying 3s and 3p C Rydberg orbitals as well as the necessary π* orbitals. The calculations were carried out using the MOLPRO program.26 All calculations reported here were done in D2 symmetry with the aug-cc-pVDZ basis set.27 A total of 15 states were monitored in a state averaged rigid scan of the dihedral angle (η) and ethylene separation distance (d). Results and Discussion TT Dimerization Products and Efficiency. Our previous study of TT dimerization in alkane linked mini-hairpins established that no dimer is observed when the base pair domain has an alternating (AT)3 sequence.14 Thus hairpin dimerization occurs exclusively for intrastrand TT steps, as previously observed for both native and synthetic duplex DNA.28 Quantum yields for TT dimerization in the Stn hairpins are reported in Table 1 along with values for TpT,29 dT20, and dA20dT20. The

TABLE 1: Quantum Yields and Product Ratios for TT Dimerization in Tn Hairpins, TpT,29 dT20, and dA20dT20 oligonucleotide

10-3ΦTT

St1 St3 St5 T pT a dT20 dA20dT20

0.39 0.92 1.1 13 50 22

a

10-3Φ6-4

TT/6-4

0.76 0.80 5.0 1.3

>20 >20 1.4 16 10 17

From Johns et al.29

lower values for the Stn hairpins may reflect the absorption of light by nonreactive adenines and by thymines that are not part of the TT step. The alkane linker does not absorb 280 nm UV light used for quantum yield measurements. Salient features of our quantum yield results are the lower value of ΦTT for St1 than for St3 or St5 and the relatively large value of Φ6-4 for St5. The low value of ΦTT for St1 may reflect hairpin end-fraying, which would reduce the extent of T1-T2 π-stacking.30 To our knowledge, the relative yields of TT dimerization at the ends vs interior of either single strand or duplex DNA have not been determined. We estimate that both our HPLC and UV analytical methods would have detected the formation of >5% 6-4 adduct from St1 or St3. The estimated TT/6-4 ratios for St1 and St3 are consistent with the values reported for TpT and dT20 (Table 1). The much smaller ratio for St5 is unprecedented. Models for [2+2] TT Dimerization. The method used to estimate dimerization quantum yields is related to methods used in previous studies by Law et al.11 and Johnson et al.10 TT dimers are assumed to be formed by the cycloaddition between the C5 and C6 atoms on adjacent thymines while 6-4 photoproducts are formed by fusing O4-C5 bonds and C6-C4 bonds. In both cases it is assumed that the reactants need to be “close enough” to the conical intersection that connects the initially excited state and the ground state of the photoproduct for reaction to occur. Two geometrical parameters were proposed as being vital in the [2+2] TT formation. These parameters are the distance between the midpoints of the C5-C6 bonds,

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Figure 5. Potential energy plots for a 25° dihedral angle for ethylene + ethylene as calculated by CASSCF(4,12)/aug-cc-pVDZ in D2 symmetry. Surfaces 2A-5A are all doubly excited states. Surface (π)2(π*)2 depicts where the CI vectors indicate significant population of the π* orbital appropriate for cyclobutane formation. Position b is the crossing between the (π)2(π*)2 state and the ground state. Position c is the early crossing between (π)3(π*)1 and a low lying doubly excited state.

d, and the absolute value of the C5-C6-C6-C5 dihedral angle, η. Law et al. suggest that geometries with d < 3.7 Å and η < 48.2° will dimerize,11 while Johnson et al. suggest that geometries with d ≈ 3.4 Å and η ≈ 27° will dimerize.10 For reference, the average d and η values obtained for dT20 in our B-DNA starting structure (Figure 4a) are 4.44 Å and 47.6°, respectively and the values for canonical duplex DNA are 3.37 Å and 36.0°, respectively.31 Both previously published models assume the need for two geometrical parameters to determine [2+2] photodimerization yields.10,11 To test this assumption, CASSCF calculations were carried out for ethylene + ethylene as a model [2+2] photodimerization system. Triplet mechanisms have been proposed for CPD formation;32,33 recent experiments, however, have shown that the singlet pathway is dominant.12,34 This CASSCF study is therefore only done for singlet surfaces. Assuming initial excitation of the separated ethylenes to a singly excited π* state, an eventual transition to a doubly excited π* state will lead to the formation of cyclobutane. The topology of the (π)3(π*)1 surface and the crossing between the (π)3(π*)1 and (π)2(π*)2 surfaces as a function of d and η will elucidate the [2+2] mechanisms dependency on d and η. Previous work by Bernardi et al. studied this reaction in detail but the surface dependence on η was never discussed.35,36 The dependence of the excited state surfaces on distance is investigated first. Select surfaces are plotted as a function of distance for a fixed dihedral angle of 25° in Figure 5. At infinite separation, there are four degenerate (π)3(π*)1 surfaces; for simplicity we only show one. The surfaces labeled 2A-5A are all 1A states in D2 symmetry while the surface labeled (π)3(π*)1 is 1B2 (and thus it could have been labeled 1B2) There is a diabatic surface with significant (π)2(π*)2 nature that we label in black in Figure 5. Unlike the other surfaces, which are adiabats, this surface is derived by examining the dominant configurations in the CASSCF calculations. At long distances this state is high in energy but rapidly decreases in energy as a function of d, eventually becoming the ground state at 2.0 Å. There is a crossing between the (π)2(π*)2 state and the (π)3(π*)1 surface at approximately 2.4 Å. This provides a mechanism whereby photoexcitation of the (π)3(π*)1 state can internally

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Figure 6. Contour plot of the (π)3(π*)1 surface of ethylene + ethylene as calculated by CASSCF(4,12)/aug-cc-pVDZ in D2 symmetry.

convert to (π)2(π*)2, either leading to photodimerization or leading back to the reactants. In Figure 5, the dimer structure shows up as a barrier in the ground state surface; however, if the bond distances in the ethylene structure were allowed to relax, the dimer geometry would become a minimum. Relaxation is also important to the energy of the crossing between the (π)2(π*)2 and (π)3(π*)1 states, which will move lower, making this intersection more favorable (i.e., downhill in energy starting from almost any geometry accessible from (π)3(π*)1). Note that the 2A state crosses (π)3(π*)1 at d ≈ 3.6 Å. This means that there is a conical intersection between these states at that point. This could provide a pathway for the initially excited (π)3(π*)1 state to decay back to the reactants if formed at distances larger than this. However, in reality, photoexcitation produces both states with some probability, so the maximum distance that would allow access to the (π)2(π*)2 state is difficult to estimate. In addition, in a solution reaction, the dependence of the dimerization probability on d is likely governed by additional issues, including solvent effects. In the analysis below we will vary d to optimize the agreement between theory and experiment. The dependence of the (π)3(π*)1 and (π)2(π*)2 surfaces on distance and dihedral angle are displayed in the contour plots shown in Figure 6 and 7, respectively. The contour plot in Figure 6 shows a shallow well excimer on the (π)3(π*)1 surface at 2.75 Å for a wide range of dihedral angles. Indeed, this surface does not display significant dependence on dihedral angle. Figure 7 displays a gradient toward zero dihedral angle at short distance for the (π)2(π*)2 state; however, more important than the topology of the separate states is the nature of the crossing between the (π)3(π*)1 and (π)2(π*)2 states as it is this crossing that results in the formation of the ground state of cyclobutane. The difference between these two states is plotted in Figure 8. As can be seen by the pink contour (0.0 difference), the doubly excited (π)2(π*)2 state crosses the singly excited (π)3(π*)1 state for all dihedral values plotted. The crossing ranges from 2.2 Å at small dihedral angles to 2.0 Å at large dihedral angles. Previous studies10,11 chose to limit the dihedral angle and the distance due to the necessary alignment of the carbon-carbon double bonds both in the products and in the conical intersection.37 The excited state topology presented here, however, suggests that there are pathways for the (π)3(π*)1 surface to cross the (π)2(π*)2 surface over a large range of dihedral angles (Figure 8). The topology of the (π)2(π*)2 surface, presented in

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Å Å Å Å

dT20

dA20dT20

47 52 57 63 50

27 29 34 40 22

TABLE 3: [2+2] Quantum Yields for St1, St3, and St5 Calculated from MD Simulations Using a Distance Cutoff of d < 3.52 Å 10-3 ΦTT

Figure 7. Contour plot of the (π)2(π*)2 surface of ethylene + ethylene as calculated in CASSCF(4,12)/aug-cc-pVDZ in D2 symmetry. Energy is relative to the ground state at infinite separartion.

Figure 8. Difference between (π)2(π*)2 and (π)3(π*)1 states of ethylene + ethylene as calculated by CASSCF(4,12)/aug-cc-pVDZ in D2 symmetry.

Figure 7, displays a large gradient toward zero dihedral angle; however, this is only accessed after the surface crossing, at a point where cyclobutane formation is guaranteed. It is thus possible for an ethylene + ethylene system at large dihedral angles to undergo excitation to the (π)3(π*)1 surface and rapidly form cyclobutane. [2+2] Quantum Yields of dT20 and dA20dT20. Experimental quantum yields for the [2+2] and 6-4 dimer formation are reported in Table 1. The dT20 and dA20dT20 systems are used as benchmarks for our MD studies. The difference in quantum yields between dT20 and dA20dT20 may reflect competitive absorption by dA and energy transfer between dA and dT as well as differences in the ground state conformation between the single strand and duplex. Thymine absorbs more strongly than adenine at the excitation wavelengths used in our quantum yield measurements (280-290 nm).38 Furthermore, fluorescence quantum yields are independent of excitation wavelength over the range 245-285 nm, suggesting that energy transfer between adenine and thymine takes place.39 However, these factors appear to be insufficient to account for the lower quantum yields for dA20dT20 vs dT20. Table 2 shows quantum yield results for MD simulations of dT20 and dA20dT20 for four different distance cutoffs. Given the excited state topologies discussed above, limits on the C5-C6-C6-C5 dihedral angle were ignored and a distance

d < 3.52 Å exp

St1

St3

St5

1.5 0.39

1.5 0.92

0.9 1.05

cutoff giving agreement with the experimental dT20 result is sought. The MD cutoff yielding the smallest percent error from experiment for dT20 is d < 3.52 Å. This same cutoff value gives a quantum yield of 29 × 10-3 for dA20dT20, which is in good agreement with the experimental yield of 22 × 10-3. Thus, geometrical arguments can explain the [2+2] quantum yield discrepancy between dT20 and dA20dT20. A separation of 3.52 Å for ethylene + ethylene on the (π)3(π*)1 surface shows a negative gradient that would allow for excimer formation based on the CASSCF results (Figure 6), and it is inside the conical intersection that would lead to nonreactive decay on the 2A surface. Johnson and Wiest concluded on the basis of their MD simulations of TT dimer formation in dT18 that dimer formation is more efficient in transiently formed hairpin conformations having intrastrand T-T base pairing than in extended regions resembling the poly(dT) strand of a duplex (Figure 4a).10 Analysis of our results for dT20 indicates that the terminal base pairs T1-T2 and, to a lesser extent, T19-T20 have the highest predicted dimerization quantum yields (Figure S11, Supporting Information). The terminal bases can insert themselves between adjacent bases forming mini-hairpins (Figure S12), which allow for noncanonical stacked geometries to be sampled. In contrast to the results of our analysis of dT20, we find that probabilities of dimer formation are similar for each of the thymines in dA20dT20 except for T1 and T20, which have only one neighboring T and thus a lower probability of dimer formation (Figure S11). [2+2] Quantum yields of St1, St3, and St5. Using the distance cutoff for [2+2] dimerization found above (d < 3.52 Å), the quantum yields for St1, St3, and St5 are calculated. The results are shown in Table 3. Upon comparison of the d < 3.52 Å results and the experimental results, two things are immediately apparent. First, the order of magnitude predicted by our one parameter model is correct. The percent error is only 14% for St5. The second major observation is that experiment predicts a trend of increasing [2+2] quantum yield from St1 to St3 to St5, while the MD results predict the opposite trend. There are a couple of possible reasons for this, all stemming from the limitations of the model. First, the model depends on the accuracy of the force field employed. The geometries leading to dimer formation are rarely populated, a situation that can be especially difficult for a force field to sample accurately. Second, energy flow, excited state quenching via other pathways, and preferential excitation of certain bases are completely ignored. While these factors are not thought to be hugely important,

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TABLE 4: 6-4 Quantum Yields for All Five Systems Investigated in This Paper 10-4Φ6-4 g < 2.87 Å exp

dT20

dA20dT20

2St1

St3

St5

53 50

21 13

3 0

3 0

14 8

hence the correctly predicted order of magnitude, they may be necessary to explain the subtle differences between St1, St3, and St5. A more detailed investigation for these systems, including analysis of models that include for the dihedral angle dependence of the reaction probability is given in Supporting Information. However, none of these more complex models leads to results for all five molecules in Table 1 that are in better agreement with experiment than is found in Tables 2 and 3. Comparison between the calculated results in Table 2 (d < 3.52 Å) and Table 3 can be made by computing an average quantum yield per TT step. The values for dT20 and dA20dT20 are 2.7 × 10-3 and 1.5 × 10-3, respectively. St1, St3, and St5 have only one TT step so the results in Table 3 do not require normalization. The results suggest that the TT steps in St1 and St3 are as likely to be in dimerizable geometries as the average TT step in the longer dA20dT20 system. The St5 TT step deviates from the average dA20dT20 result, suggesting a special effect for constraints associated with the C12 linker, which is also reflected in the high yield of 6-4 adduct from this hairpin. The dT20 system has a higher quantum yield per TT step than the four base paired systems, demonstrating the importance of a more flexible structure in achieving d < 3.52 Å. 6-4 Quantum Yields. Following a similar prescription to the [2+2] calculations, a cutoff for the C5-O4 distance, g, giving good agreement between the calculated and experimental 6-4 quantum yields for the dT20 system is sought. The optimal cutoff value was found to be g < 2.87 Å. As a point of comparison, the average g (C5(5′)-O4(3′)) value in the starting B-DNA structure for dT20 is 4.24 Å. Thus both average distance and cutoff are shorter for oxetane formation vs cyclobutane formation (Figure 2). The 6-4 quantum yields for all five systems using this cutoff shown in Table 4 give good agreement with their corresponding experimental values. Of equal importance is that the calculated values follow the same trend as experiment. The 6-4 quantum yield for dT20 is found to be over twice that of dA20dT20 and the 6-4 quantum yield for St5 is found to be much greater than the result for either St1 or St3. The correct prediction of both the order of magnitude and experimental trends suggest that the 6-4 reaction is better correlated with a single geometric parameter, the ground state distance between reactive double bonds, than is cyclobutane formation. Conclusions The importance of ground state geometry on the excited state dimerization of thymines in single strand and duplex DNA has been investigated, including both [2+2] and 6-4 products. CASSCF calculations for ethylene dimerization show that the important geometrical parameter for the [2+2] reaction is the distance, d, between the midpoints of the C5-C6 double bonds (Figure 1). Determining a cutoff for d by fitting to experimental data for the dT20 system suggests geometries with d < 3.52 Å will form a dimer. This cutoff value gives quantum yields of the correct order of magnitude for all five systems investigated (dT20, dA20dT20, St1, St3, and St5). The experimental trend for variation of the [2+2] quantum yield with dimer location relative to the C12 linker for St1, St3, and St5 is not reproduced by

these calculations. Thus while the ground state structure gives a good estimate of the [2+2] quantum yield, it does not describe the subtle differences between the St1, St3, and St5 systems. The 6-4 dimer formation was investigated in a similar fashion. It was found that a distance cutoff of g < 2.87 Å gave good agreement with experiment for the dT20 system. This cutoff also gave good agreement for the four other systems investigated as well as retaining experimental trends. Ground state geometry is thus a controlling factor in 6-4 dimer formation. Acknowledgment. Financial support for this research was provided by the National Science Foundation (CHE-0628130) to G.C.S. and F.D.L. and the French Agency for Research (ANR PCV07_194999). Supporting Information Available: Further analysis of dihedral angle dependence of [2+2] quantum yields for all five species. A detailed analysis of where the [2+2] dimers form in dT20 and dA20dT20. Starting structures for all five species in pdb format. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Liu, R. S. H.; Turro, N. J.; Hammond, G. S. J. Am. Chem. Soc. 1965, 87, 3406. (2) Dauben, W. G.; Williams, R. G.; Mckelvey, R. D. J. Am. Chem. Soc. 1973, 95, 3932. (3) Lewis, F. D.; Johnson, R. W.; Johnson, D. E. J. Am. Chem. Soc. 1974, 96, 6090. (4) Anslyn, E.; Dougherty, D. A. Modern Physical Organic Chemistry; University Science Books: Sausalito, CA, 2006. (5) Cohen, M. D.; Schmidt, G. M. J. J. Chem. Soc. 1964, 1996. (6) Ramamurthy, V.; Venkatesan, K. Chem. ReV. 1987, 87, 433. (7) Cadet, J.; Vigny, P. In The Photochemistry of Nucleic Acids; Morrison, H., Ed.; Wiley: New York, 1990. (8) Setlow, R. B. Science 1966, 153, 379. (9) Beukers, R.; Berends, W. Biochim. Biophys. Acta 1960, 41, 550. (10) Johnson, A. T.; Wiest, O. J. Phys. Chem. B 2007, 111, 14398. (11) Law, Y. K.; Azadi, J.; Crespo-Hernandez, C. E.; Olmon, E.; Kohler, B. Biophys. J. 2008, 94, 3590. (12) Schreier, W. J.; Schrader, T. E.; Koller, F. O.; Gilch, P.; CrespoHernandez, C. E.; Swaminathan, V. N.; Carell, T.; Zinth, W.; Kohler, B. Science 2007, 315, 625. (13) Marguet, S.; Markovitsi, D. J. Am. Chem. Soc. 2005, 127, 5780. (14) Hariharan, M.; Lewis, F. D. J. Am. Chem. Soc. 2008, 130, 11870. (15) Murov, S. L. Handbook of Photochemistry; Marcel Dekker: New York, 1973. (16) Douki, T.; Court, M.; Sauvaigo, S.; Oden, F.; Cadet, J. J. Biol. Chem. 2000, 275, 11678. (17) C. I. Bayly, P. C.; Cornell, W. D.; Kollman, P. A. J. Phys. Chem. 1993, 97, 10269. (18) Case, D. A.; T., A. D.; Cheatham, T. E., III; Simmerling, C. L.; Wang, J.; Duke, R., R. E.; Luo, K. M. M.; Wang, B.; Pearlman, D. A.; Crowley, M.; Brozell, S.; Tsui, V.; Gohlke, J., H.; Mongan, V. H.; Cui, G.; Beroza, P.; Schafmeister, C.; Caldwell, J. W.; Ross, W. S. and; Kollman, P. A. AMBER 8; University of California: San Francisco, 2004. (19) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Chem. 1977, 23, 327. (20) Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 10089. (21) Petersen, H. G. J. Chem. Phys. 1995, 103, 3668. (22) Foloppe, N.; MacKerell, A. D., Jr. J. Comput. Chem. 2000, 21, 86. (23) MacKerell, A. D.; Banavali, N. K. J. Comput. Chem. 2000, 21, 105. (24) Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale´, L.; Schulten, K. J. Comput. Chem. 2005, 26, 1781. (25) Ben-Nun, M.; Martinez, T. J. Chem. Phys. 2000, 259, 237. (26) H.-J. Werner, P. J. K.; Lindh, R.; Manby, F. R.; Schu¨tz, M.; Celani, P.; Korona, T.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B.; Amos, R. D.; Bernhardsson, A.; Berning, A.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.; Goll, E.; Hampel, C.; Hetzer, G.; Hrenar, T.; Knizia, G.; Ko¨ppl, C.; Liu, Y.; Lloyd, A. W.; Mata, R. A.; May, A. J.; McNicholas, S. J.; Meyer, W.; Mura, M. E.; Nicklass, A.; Palmieri, P.; Pflu¨ger, K.; Pitzer, R.; Reiher, M.; Schumann, U.; Stoll, H.; Stone, A. J.; Tarroni, R.;

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