Symmetry Selection in Artificial DNA Base Pairs - The Journal of

Apr 14, 2007 - We report the results of density functional theory (DFT) studies on the formation of the complex H1-−Cu2+−H1- consisting of two dep...
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J. Phys. Chem. B 2007, 111, 5357-5361

5357

Symmetry Selection in Artificial DNA Base Pairs Radi A. Jishi Department of Physics, California State UniVersity, Los Angeles, California 90032

Joseph Bragin* Department of Chemistry, Missouri Western State UniVersity, St. Joseph, Missouri 64507 ReceiVed: NoVember 5, 2006; In Final Form: February 11, 2007

We report the results of density functional theory (DFT) studies on the formation of the complex H1-Cu2+-H1- consisting of two deprotonated hydroxypyridone ligands (H1-) and a Cu2+ ion. We compare the total energies of three possible structures with different symmetries and show that the structure with plane reflection symmetry has the lowest energy. The electronic structure of the periodic extended DNA-like double helix consisting of stacked H1--Cu2+-H1- units is then calculated within the density functional method, and the double helix is found to be an insulating ferromagnet.

Introduction DNA plays an essential role in biological systems as the carrier of the genetic code. The electronic structure of DNA has been a controversial subject for some time with conflicting claims ranging from its being an insulator to its being an excellent conductor.1-10 Besides the relevance of this issue to important biological processes such as DNA damage and repair,11 the drive to construct nanoscale devices increases the interest in the electrical conducting properties of molecules like DNA. The DNA chain consists of two strands wound around each other to form a double helix structure. Each strand consists of a repeating sequence of a sugar molecule and a phosphate group; the sugar molecule, in turn, is attached to one of four possible bases: adenine (A), cytosine (C), guanine (G), and thymine (T). There is selectivity in pairing, however, due to a tendency to form hydrogen bonds; a guanine will only pair with a cytosine to form a G-C pair, and adenine will only pair with thymine to form an A-T pair. The particular sequence of these bases along a strand constitutes the genetic code. It takes about 10 bases along the helical strand to make one complete turn of the helix. The search for alternative pairs is motivated by various reasons. Though the four bases A, C, G, and T provide the structural solution to the problem of genetic code expression, this solution is not necessarily unique. Synthesis of additional base pairs that could be incorporated into the DNA structure leads, not only to the expansion of the genetic alphabet, but also to novel nanoscale structures with interesting physical and chemical properties. Different binding schemes that dictate the form of the bases include hydrogen bonding, hydrophobic packing interactions, and metal complexation. Recently, the hydrophobic molecule 3-fluorobenzene was found to form a pair with itself.12 Furthermore, it was shown that this artificial pair can be replicated by DNA polymerase; some mistakes do occur, however, with about one mistake for every thousand pairs that are copied. On the other hand, several new artificial base pairs that bind together through complexation with a transition metal * Address correspondence to this author. Phone: (816) 271-4534. Fax: (816) 271-4525. E-mail: [email protected].

have been synthesized,13-17 and synthesis of other structures consisting of DNA chains with metal atoms inserted into the double helix, in between the strands, have also been reported.18-20 In this work we study a particular unnatural base pair bound together through metal complexation. H1--Cu2+-H1- is a neutral complex involving Cu2+ ions where H1- is a deprotonated hydroxypyridone nucleobase that acts as a bidentate ligand. A single-site incorporation of the H1--Cu2+-H1- complex into a 15-nucleotide DNA duplex has led to an increase in the thermal stability of the duplex. More recently, the successful synthesis of very short right-handed double helices of the oligonucleotides nCu2+‚d(5′-G(H1-)nC3′)2 (n ) 1 to 5) was reported.14-16 The total number of base pairs within these helices ranges from 3 to 7, the two base pairs at the ends being G-C pairs. To align the complexes into a stack with the metal ions along the helix axis, the number of H1bases was increased, one by one, in the middle of 3- to 7-nucleotide single DNA strands d(5′-G(H1-)nC-3′) (n ) 1 to 5). In the absence of Cu2+ ions the duplex could not form and the single short strands remained dissociated. But upon the addition of Cu2+ ions into the solution, short double helices were formed; the process of the complexation of Cu2+ ions with the deprotonated hydroxypyridone was monitored by examining the resulting change in ultraviolet absorption. Continuous-wave electron paramagnetic resonance exhibited a fine structure splitting from which the distance between copper ions along the helix axis is estimated to be 3.7 ( 0.1 Å. Furthermore, it was found in these studies that the copper ions form a magnetic chain whereby the electron spins on adjacent copper ions couple ferromagnetically. In solution, the situation is complicated by the presence of hydration shells, and any complete model should take that into account when exploring the possible reaction pathways that lead to the formation of H1--Cu2+-H1complex. Recently, first-principles calculations within the density functional theory (DFT) framework, using plane-wave basis and ultrasoft pseudopotentials, have been reported.21 The calculations are simplified by truncating the H molecule at the joint of the sugar backbone; the sugar molecule and the phosphate-like group are replaced by a hydrogen atom, thus reducing the

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5358 J. Phys. Chem. B, Vol. 111, No. 19, 2007 number of atoms in the H1--Cu2+-H1- complex by a factor of 2, and leading to a significant reduction in the computational resources required to carry out the calculations. The authors consider a stack of this truncated complex and study its electronic properties. In this work we report a theoretical investigation of the binding of two deprotonated hydroxypyridones (H1-) through complexation with a copper ion (Cu2+) in the gas phase. To begin with, we search for the equilibrium structure by energy minimization. Toward this end we compare the total energies of three possible structures each with a distinct symmetry. No truncation of the H molecule structure is considered in this work because the atomic arrangement of the backbone atoms is directly influenced by the overall symmetry of the H1--Cu2+H1- complex†. (The H1- stereochemistry used here is different from that of the model in ref 15 and nucelosides in polymeric natural DNA but the monomeric H1--Cu2+-H1- duplex energetics and configuration around Cu2+ are not affected by this configurational difference in the ligand.) In the first structure the copper ion sits at a center of inversion (point symmetry Ci), while the second structure has a 2-fold symmetry axis of rotation (C2), and the third structure has plane reflection symmetry (Cs). We find that while the Ci and C2 structures have approximately equal energies, the Cs structure is lower in energy than the other two by about 1.6 eV. Next we consider the double helix consisting of stacked H1--Cu2+-H1- units, each unit with a Cs structure. We calculate the electronic energy bands of the helix, considered an infinite one-dimensional crystal, and discuss our results. Computational Method We carry out first-principles, all-electron calculations, within density functional theory (DFT), on the deprotonated hydroxypyridone H1-, and on the H1--Cu2+-H1- complex. All calculations are performed with the B3LYP method, which has proven to be very successful in computations on molecules. The B3LYP method uses an exchange functional, developed by Becke,22 which is a linear combination of Hartree-Fock, local, and gradient-corrected correlation functional developed by Lee, Yang, and Parr.23 For the sake of consistency, the calculations on all structures are carried out in two steps, using the Gaussian program.24 First, the structures are optimized by using the 6-31G(d) Gaussian basis set. Next, the total energy is calculated at the optimized structure with use of much larger basis sets; for copper(II) we use the 6-311+G(3df) basis set, whereas for the lighter atoms of the first row we use the 6-311+G(2df,2p) basis set. In the 6-31G(d) basis set, there are 2 S-type Gaussian functions on the H atom, 3 S-, 2 P-, and 1 D-type Gaussian functions on the first row atoms, and 5 S-, 4 P-, 2 D-, and 1 F-type Gaussian functions on Cu2+. In the larger basis set used to calculate the total energy at the optimized structure there are 3 S- and 2 P-type Gaussian functions on H, 5 S-, 4 P-, 2 D-, and 1 F-type Gaussian functions on first row atoms, and 10 S-, 7 P-, 4 D-, 3 F-, and 1 G-type Gaussian functions on Cu2+. The basis set used in the calculation of the total energy of H1-Cu2+-H1- has a total of 1489 basis functions making the calculation very time-consuming. To check that the structure obtained by optimization is not overly sensitive to the size of the Gaussian basis set, we repeated the optimization step using the somewhat smaller 6-31G Gaussian basis set. Indeed, similar optimized structures were obtained to those resulting from the use of the 6-31G(d) Gaussian basis set. The electronic energy band calculations of the periodic extended system were carried out by using a first-principles,

Jishi and Bragin

Figure 1. The structure of deprotonated hydroxypyridone (H1-) as obtained by the optimization procedure outlined in the text. The hydrogen atoms are not shown in this figure.

TABLE 1: Geometric Parameters in Three Hydroxypyridone Copper II Structures H1--Cu2+-H1bond O2-Cu32 O4-Cu32 C3‚‚‚Cu32 C1‚‚‚Cu32 O2‚‚‚O4 C1-O2 C3-O4 C1-C3 C3-C7 C1-C5 angle O4-Cu32-O2 O2-Cu32-O36 O34-Cu32-O36 O4-Cu32-O34 sum C5-C1-C3 O2-C1-C5 O2-C1-C3 sum C1-C3-C7 O4-C3-C1 O4-C3-C7 sum C1-O2-Cu32 C3-O4-Cu32 O2O4O34O36 O2O4Cu32O34 O2O4O36Cu32

H1-

Ci

C2

Cs

2.799 1.244 1.261 1.512 1.429 1.448

1.836 2.545 3.046 2.714 2.794 1.281 1.267 1.508 1.416 1.419

1.918 1.934 2.668 2.648 2.647 1.298 1.302 1.463 1.406 1.414

1.895 1.905 2.660 2.645 2.608 1.304 1.310 1.445 1.406 1.417

115.6 122.2 122.1 359.9 117.5 119.7 122.8 360

77.4 102.6 77.4 102.6 360 114.5 122.4 123 359.9 120.3 117.6 122.1 360 120.1 100.7 0.0 180

86.8 98.8 86.8 98.8 371.2 116.8 125.3 117.9 360 121.7 116.3 121.9 359.9 109.3 109.5 134.6 -16.7

86.7 93.8 86.7 93.8 361 117.6 125.3 117.1 360 122 115.8 122.2 360 110.1 110.3 -180 -179.6 0.3

all-electron, self-consistent local density functional method in which local Gaussian-type orbitals are used.25,26 In this work the 6-31G Gaussian basis set is employed. The double helix consisting of stacked H1--Cu2+-H1- units is treated as a onedimensional crystal with a screw symmetry operation S(a,φ) consisting of a translation a down the helical axis followed by a rotation φ about that axis. Because the symmetry group generated by the screw operation S is isomorphic with the onedimensional translation group, it is possible to define a helical unit cell consisting of a single H1--Cu2+-H1- unit. This makes a first-principles calculation feasible: our helical unit cell consists of 63 atoms whereas, on the other hand, the translational unit cell, taking φ ) π/5 radians, is 10 times bigger, consisting of 630 atoms. Results/Discussion To begin with, we optimize H1-, the deprotonated hydroxypyridone, using the procedure outlined above. The resulting optimized structure is shown in Figure 1 and some of the data

Symmetry Selection in Artificial DNA Base Pairs

Figure 2. The structure of the H1--Cu+2+-H1- complex optimized under the constraint that it has an inversion symmetry (Ci) about the site of the Cu2+ cation, numbered 32 in the figure. The Cu2+ cation is surrounded by four oxygen atoms forming a planar structure. Here, oxygen atoms 2 and 34 are equivalent by symmetry. Hydrogen atoms are not shown.

regarding bond lengths and angles are given in Table 1. As for the H1--Cu2+-H1- complex, we consider three models with distinct symmetries. In each model the structure of the complex is optimized subject to the only constraint that the structure has a particular symmetry. In the first model the copper ion sits at a center of inversion. The calculated optimized structure is shown in Figure 2, and some bond lengths and angles are shown in Table 1. We note that the atomic arrangement surrounding the copper ion is planar, but Cu2+ is not equidistant from the four surrounding oxygen atoms. To understand the difference in the bond lengths we note that in the H molecule a proton is attached to the O atom numbered 4 in Figure 2, and similarly to atom number 36. Upon deprotonation, these two sites will each have an extra electron, and so when the complex with copper is formed, and because inversion symmetry requires that atoms 4 and 36 are equivalent to each other, but not to atoms 2 and 34, it is natural that the distance of atoms 4 and 36 to copper will be different than the distance of the other two O atoms, numbers 2 and 34, to copper. Indeed, Mulliken population analysis reveals that oxygen atoms 2 and 4 in Figure 2 have charges given by -0.27 e and -0.46 e, respectively. Clearly, the charge of the two extra electrons is redistributed among various atoms, but the charge redistribution is still asymmetrical, showing a still larger negative charge on the sites where the protons were removed. In this structure, the highest occupied molecular orbital (HOMO) is separated from the lowest unoccupied molecular orbital (LUMO) by an energy gap of 3.2 eV; furthermore, the spin parts of the wave functions of these two spin orbitals are of different types, one being a spin-up orbital while the other is a spin-down orbital. Most of the contribution to the wave function of the HOMO results from s-type Gaussian orbitals centered at the carbon atoms 7, 8, 15, and 17, and atoms equivalent to these by inversion symmetry, with smaller contributions from the p-type Gaussian orbitals centered on carbon atoms 1 and 3, oxygen atoms 2 and 4, and the corresponding equivalent atoms. In the second model, the H1--Cu2+-H1- complex is constrained to have the symmetry group C2, with a 2-fold axis of rotation through Cu2+. The optimized structure is shown in Figure 3. The Cu2+ ion is nearly equidistant from the four surrounding oxygen atoms. Here, oxygen atoms 4 and 36, equivalent by symmetry, are separated by a relatively short distance compared to the case of the inversion symmetry case. To reduce electrostatic repulsion the negative charge on these two atoms is more uniformly distributed, leading to approximately equal negative charge, about -0.4 e, on each of oxygen atoms 2, 4, 34, and 36, and consequently, approximately equal distance of these atoms from the central copper ion. In

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Figure 3. The optimized structure of the H1--Cu2+-H1- complex with a 2-fold rotational symmetry axis through the Cu2+ cation, numbered 32 in the figure. Here oxygen atoms 2 and 34 are equivalent by symmetry as are oxygen atoms 4 and 36. Hydrogen atoms are not shown.

Figure 4. The optimized structure of the H1--Cu+2-H1- complex with a plane-mirror reflection symmetry through the Cu2+ cation, numbered 32 in the figure. Oxygen atoms 2 and 34 are equivalent by symmetry as are oxygen atoms 4 and 36. Hydrogen atoms are not shown.

this model, the total energy of the complex is only 0.06 eV lower than that in the Ci structure. The HOMO-LUMO gap is found to be 3.3 eV, and the main contribution to the HOMO wave function arises from s-type orbitals centered on carbon atom 3 and its symmetry equivalent, and d-type Gaussian orbitals centered on the copper site; the main contribution to the LUMO wave function, on the other hand, is due to s-type Gaussian orbitals centered on carbon atoms 3, 15, and 17, and the atoms equivalent to them by symmetry. The spin type of the LUMO is again opposite to that of the HOMO. In the third model the structure of the H1--Cu2+-H1complex is optimized under the constraint that it has the symmetry group Cs with a reflection symmetry plane passing through Cu2+. The optimized structure is shown in Figure 4. The four oxygen atoms surrounding copper are found to form a square with Cu being at the square center at a distance of 0.19 nm from each oxygen atom. The single-point calculation gives a total energy for this structure, which is 1.6 eV lower than the other two cases, indicating that this structure with the Cs symmetry group is more stable than the structures with Ci and C2 symmetry groups. The HOMO-LUMO gap was found to be 3.8 eV, which is larger than the gaps in the first two structures, reflecting the higher stability of this model compared to the previous two considered above. The HOMO and LUMO have opposite spin types, and the HOMO wave function has a large contribution from orbitals centered on the four surrounding oxygen atoms and carbon atoms 7, 15, and their symmetry equivalent. The largest contributions to the LUMO come from orbitals centered on carbon atoms 7, 15, 17, and their symmetry equivalent, and on the nitrogen atoms. It should be noted that in the three different structures considered in this work, the copper ion and the four surrounding oxygen atoms are almost coplanar; this is consistent with results obtained by El-Jammal et al.27 for two related systems, one consisting of a copper ion complexed to two units of 1,2-dimethyl-3-hydroxypyridin-4one, while in the other system a 1,2-diethyl analogue is used instead.

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Figure 5. Total energy per H1--Cu2+-H1- unit (Cs structure) fit to a Morse potential curve with an energy minimum occurring at a copper-copper distance of 3.59 Å. The zero of energy corresponds to the case of isolated H1--Cu2+-H1- units.

In treating the extended periodic system we fixed the bond lengths and angles in the H1--Cu2+-H1- unit to those obtained by optimization with the 6-31G Gaussian basis set. In the helical symmetry operation S(a,φ), which is the fundamental symmetry operation of the double helix, the angle φ is held fixed at π/5 radians while a, which represents the distance between copper ions along the helix axis, is varied to determine the optimal value. This is accomplished by calculating the total energy of the system with first-principles, all-electron calculations within the local density approximation as described earlier. This approach has been applied successfully to one-dimensional systems, both metallic, such as carbon nanotubes,28,29 and insulating, such as peptide nanotubes.30 Our results for the calculated total energy per H1--Cu2+-H1- unit are shown in Figure 5 in which the zero of energy corresponds to the case of isolated H1--Cu2+-H1- units. A Morse potential curve provides a reasonable fit to the calculated total energy values, with an energy minimum occurring at a copper-copper distance of 3.59 Å; this is in very good agreement with the experimental value given by 3.7 ( 0.1 Å. The resulting electronic energy bands for the double helix are shown in Figure 6. In this figure, the Fermi energy level is taken as the zero-energy level, the solid lines represent the energy bands of the majority-spin (taken here as spin-up) electrons, while the dashed lines represent the energy bands of the minority-spin electrons. The bands are very narrow, displaying very little dispersion; this results from the weak coupling between the stacked units along the helix. Similar narrow bands were also calculated30 in the case of peptide nanotubes where

Jishi and Bragin

Figure 6. Electronic energy bands for the double helix (H1--Cu2+H1-)x (Cs structure). The majority-spin (taken here as spin-up) electron bands are shown as solid lines, while the minority-spin electron bands are dashed. The zero of energy is the Fermi level.

TABLE 2: Energies of Three Hydroxypyridone Copper(II) Structures system Cu2+ H1H1--Cu2+-H1H1--Cu2+-H1H1--Cu2+-H1-

point symmetry

total energy (hartrees)

Ci C2 Cs

-1639.4117 -858.7764 -3358.0037 -3358.0060 -3358.0600

the stacked cyclic peptide rings couple via the weak van der Waals interaction. The double helix, viewed as a onedimensional crystal, is insulating, despite the presence of copper ions along the helix axis, and the fact that the total number of electrons per a helical unit cell is odd. Since the local density approximation is used, it is likely that the energy gap is underestimated in this calculation and that a more accurate calculation will yield a larger energy gap. The insulating property results from the relatively large distance between copper ions along the chain (3.6 Å) compared to the distance between nearest neighbor copper atoms in the fcc copper crystal (2.55 Å), and from the fact that in the copper ion in the helix, the valence electrons occupy the 3d orbitals whose wave functions are localized relatively close to the nucleus. The extremely small overlap between the 3d wave functions on neighboring copper ions along the helical axis leads to electron localization on the copper ion and surrounding ring; this is reflected in the particularly flat bands just below and above the Fermi level in Figure 6. These bands are formed from the hybridization of the 3d states on copper with the s and p states on its nearest neighboring oxygen and carbon atoms. The energy bands show that the double helix is ferromagnetic with one spin per helical unit cell, in agreement with experiment.14-17

Symmetry Selection in Artificial DNA Base Pairs The analysis of the orbital population of atoms in the helical unit cell of the double helix shows that about 2/3 of the spin density resides on the copper, while the remaining third is distributed over the p states of the four surrounding oxygen atoms. Conclusion The total energies of Cu2+, H1-, and the three structures of H1--Cu2+-H1- were calculated by using the large Gaussian basis sets discussed in the previous section. The calculated energies are shown in Table 2. It is seen that the structures with symmetry groups Ci and C2 have essentially the same energy, whereas the structure with Cs symmetry is lower in energy by 1.6 eV, making this structure more energetically favorable than the other two. Treating the double helix formed by stacking H1--Cu2+-H1- units in the Cs structure as a one-dimensional crystal, we calculate a separation between copper ions that is in agreement with experiment, and we show that the resulting electronic energy bands indicate that the helix is an insulating one-dimensional ferromagnet. Acknowledgment. This work was supported by an MBRSSCORE award to California State University, Los Angeles (NIH S06-GM 8101-30). References and Notes (1) Beratan, D. N.; Priyadarshy, S.; Risser, S. M. Chem. Biol. 1997, 4, 3. (2) Taubes, G. Science 1997, 275, 1420. (3) Arkin, M. R.; Stemp, E. D. A.; Holmlin, R. E.; Barton, J. K. Science 1996, 273, 475. (4) Murphy, C. J.; Arkin, M. R.; Jenkins, Y.; Ghatlia, N. D.; Bossmann, S. H.; Turro, N. J.; Barton, J. K. Science 1993, 262, 1025. (5) Wan, C.; Fiebig, T.; Schiemann, O.; Barton, J. K.; Zewail, A. H. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 6014. (6) Fink, H. W.; Shonenberger, C. Nature 1999, 398, 407. (7) Okahata, Y.; Kobayashi, T.; Tanaka, K.; Shimomura, M. J. Am. Chem. Soc. 1998, 120, 6165. (8) Porath, D.; Bezryadin, A.; de Vries, S.; Dekker, C. Nature 2000, 403, 635. (9) Kasumov, A.; Yu, C.; Kociak, M.; Gueron, S.; Reulet, B.; Volkov, V. T.; Klinov, D. V.; Bouchiat, H. Science 2001, 291, 280.

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