Free Energy Coupling between DNA Bending and Base Flipping

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Free Energy Coupling between DNA Bending and Base Flipping Ning Ma and Arjan van der Vaart* Department of Chemistry, University of South Florida, 4202 East Fowler Avenue CHE 205, Tampa, Florida 33620, United States S Supporting Information *

ABSTRACT: Free energy simulations are presented to probe the energetic coupling between DNA bending and the flipping of a central thymine in double stranded DNA 13mers. The energetics are shown to depend on the neighboring base pairs, and upstream C or T or downstream C tended to make flipping more costly. Flipping to the major groove side was generally preferred. Bending aids flipping, by pushing the system up in free energy, but for small and intermediate bending angles the two were uncorrelated. At higher bending angles, bending and flipping became correlated, and bending primed the system for base flipping toward the major groove. Flipping of the 6-4 pyrimidine-pyrimidone and pyrimidine dimer photoproducts is shown to be more facile than for undamaged DNA. For the damages, major groove flipping was preferred, and DNA bending was much facilitated in the 6-4 pyrimidine-pyrimidone damaged system. Aspects of the calculations were verified by structural analyses of protein−DNA complexes with flipped bases.

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various force fields34 for studying base flipping have been described as well. In addition to local distortions, global deformations such as DNA bending might also aid base flipping. In early computational work,35 energy minimizations in implicit solvent were used to show significant coupling between the DNA bending angle and base flipping of the central thymine in (A)5 double stranded DNA. This insight proved to be prescient, since in several structures of protein−DNA complexes with flipped out bases, DNA was bent, which suggests that DNA bending might facilite base flipping.36−38 The coupling between DNA bending and base flipping was tested in an experimental study of M.EcoKI methyltransferase, which used gapped duplexes to show that the strain in bent DNA is used to flip out bases.39 Coupling between bending and flipping was also inferred from structural analyses of a conformational flooding study of a 13mer,22 but the energetic effect was not quantified. Bending did not seem a prerequisite in a free energy study of base flipping in a GCGC containing dodecamer, however, although the correlation between bending and flipping was not systematically investigated.19 Bending was shown to facilitate flipping of the undamaged base across the thymine dimer,11 and simulations of the flipping of a G:U wobble base pair showed an open bent state, with reduced bending flexibility.12 Probability distributions in both studies were obtained from normal MD though, which limited the sampling. Enhanced bending upon opening was also seen in structural analyses of a free energy study of base flipping in poly-GA, poly-CT, and an A-tract containing strand.21,26 In the latter studies, sampling was enhanced for base opening but not for DNA bending, even though bending is energetically costly.40,41

INTRODUCTION Base flipping, the process by which a base moves out of its base paired position within the double helix to an extrahelical position,1 is essential for a large number of biological processes including epigenetic control,2 transcription initiation,3,4 DNA replication,4,5 and repair.6,7 Experimental measurements have indicated that spontaneous base flipping occurs in Watson− Crick base paired DNA, with lifetimes of tens to hundreds of nanoseconds.8,9 Flipping has significant activation energies that depend not only on the identity of the flipped base but also on the surrounding sequence.8−10 Barriers for mismatched bases and for various forms of DNA damage are lower than for undamaged DNA,11−17 which is thought to speed up recognition and repair by the proteins and enzymes involved in the various repair pathways. Computer simulations have played an important role in understanding the flipping process.17 Particularly insightful are free energy simulation studies, in which sampling along certain order parameters is enhanced in order to obtain accurate distributions.18 These simulations have been used to quantify the equilibrium free energy difference between closed and open states, the free energy barriers for flipping, and the mechanism of the reaction in bare19−26 and protein-bound DNA.23,27 Differences in relative energetic costs of flipping toward the major or minor groove side were examined, and the effect of mismatches16 and DNA damage13,14,28,29 on flipping barriers was quantified. Probability distributions and potentials of mean force have also been calculated from unbiased molecular dynamics (MD) simulations,11,12,15,30 although sampling in normal MD is much more limited. Simulations have detailed how proteins speed up flipping by locally distorting the DNA structure,23 where the local distortions are affected by electrostatic and van der Waals interactions with neighboring bases,31,32 and shown that in certain cases DNA flexibilities at the site of damage correlate with enzyme efficiency.30 Effects of polarization33 and the quality of © XXXX American Chemical Society

Received: April 17, 2017 Published: July 11, 2017 A

DOI: 10.1021/acs.jcim.7b00215 J. Chem. Inf. Model. XXXX, XXX, XXX−XXX

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Journal of Chemical Information and Modeling

The DNA molecules were solvated in rectangular 0.15 M KCl TIP3P water50 boxes, with a minimum margin of 14 Å between the DNA and the edge of the water box. The overall charge on the systems was zero. After energy minimization with the default NAMD conjugate gradient minimizer, the systems were gradually heated from 120 to 300 K, over a 1 ns period. During heating, a harmonic restraint with a force constant of 1 kcal/(mol Å2) was applied to all DNA heavy atoms. This restraint force was gradually reduced to 0.5, 0.25, 0.1, 0.01, and finally to 0 kcal/(mol Å2) in blocks of 0.2 ns equilibriation. During heating and equilibration, harmonic restraints with force constants of 0.04 kcal/(mol Å2) between the centers of mass of the bases that form a base pair were in effect to ensure proper hydrogen bonding. The equilibrated structures were taken as starting points of twodimensional umbrella sampling simulations. The first order parameter for the umbrella sampling was the DNA bending angle, here defined as the angle among the centers of mass of the central two base pairs backbone and the centers of mass of each of the two base pairs backbone at the termini. The second order parameter described base flipping, defined as the pseudodihedral angle among four mass centers: the center of mass of the base ring of residue 6 of the main chain (or the center of mass of the (6-4)PP or CPD residues for the damaged systems), the center of mass of the backbone of main chain residue 6 (or the backbone of the damage for the damaged systems), the center of mass of the backbone of main chain residue 8, and the center of mass of the backbone of complementary chain residue 6. The same pseudodihedral has been used in studies of base flipping before;19 negative angles describe flipping on the major groove side, and positive angles describe flipping on the minor groove side. Force constants for the harmonic restraints on both angles were set to 0.04 kcal/(mol deg2). A total of 144 umbrella windows were used per system, with the DNA bending angle between 0 and 90 deg, the base flipping angle between −180 and 180 deg, and intervals of 15 degrees for each angle. Each window was equilibrated for 1 ns, followed by a production simulation of 5 ns, for a total production time of 720 ns per system. The first simulated window had a pseudodihedral angle of 10 degrees, and a DNA bending angle of 15 degrees. The final configuration of each equilibriation run was used to start the equilibration of neighboring windows at ±15 degrees for the dihedral angle and ±15 degrees for DNA bending angles. All simulations were performed with NAMD,51 using the colvar module,52 and the CHARMM36 force field44 for the standard residues. Simulations were performed in the NPT ensemble with the Langevin piston Nosé−Hoover method,53,54 using a damping coefficient of 1 ps−1 and a time step of 2 fs. Periodic boundary conditions were in effect, the particle mesh Ewald method was used for long-range electrostatics,55 and SHAKE was used for covalent bonds involving hydrogen atoms.56 Coordinates were stored every 0.5 ps, and visual analyses were performed with VMD.57 Gibbs free energy surfaces and associated statistical errors were calculated by the multistate Bennett acceptance ratio (MBAR) estimator after decorrelating the trajectories.58 All reported DNA bending angles correspond to the definition used in the umbrella sampling. A search of the Protein Data Bank was performed to identify protein−DNA complexes in which a single base at the protein− DNA interface was flipped out. Complexes in which A, G, T, and C were flipped out were identified, as well as complexes with UV damaged DNA with (6-4)PP or CPD flipped out. Bending and flipping angles were calculated for these structures, using similar definitions as in the simulations.

To systematically assess free energy coupling between DNA bending and flipping, we present two-dimensional umbrella sampling simulations of the base flipping of a central thymine and DNA bending of DNA 13mers. The effect of neighboring sequences was systematically assessed by performing the simulations for all 16 base pair combinations directly upstream and downstream from the central T:A base pair. Simulations will also be presented for the flipping of the damaged base pair in two sequences with thymine dimers: the cyclobutane pyrimidine dimer (CPD) and 6-4 pyrimidine-pyrimidone photoproducts (64)PP, which are common UV light induced, mutagenic damages (Figure 1).42

Figure 1. Structure of (6-4)PP and CPD damaged bases.

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METHODS Initial structures of double stranded DNA molecules with sequence 5′-CGCGAX6T7Z8CGCCC-3′ were generated with X3DNA.43 X and Z were varied to include all 16 combinations of the standard DNA bases; strands will be referred to by the identity of base pairs 6-8 of the main strand. In addition, simulations were performed on double stranded DNA molecules of the same sequence, but in which bases 6 and 7 of the main strand were replaced by (6-4)PP and CPD, and Z corresponded to G. In these two systems, the two bases in the complementary strand across the damage were adenines. Initial parameter values for the CPD and (6-4)PP residues consistent with the CHARMM36 nucleic acid force field44 were generated with ParamChem,45−47 after which the parameters were further optimized by following the standard CHARMM force field optimization procedure.48 For (6-4)PP, only a dihedral angle involving the C6 and C7 atoms of the thymine dimer was further optimized. For CPD, parameters for the two base rings and the cyclobutane ring were further optimized. The Gaussian09 software49 was applied to acquire quantum target data. The energy minimized geometry and dipole moments were calculated at the HF/6-31G(d) level. Potential energy scans (PES) were calculated at the B3LYP/6-31G(d) level. Atomic charges were optimized until the calculated dipole moment agreed within 30% of the quantum calculations. Next, force constant for bonds and angles were optimized based on geometrical criteria. The force constants for dihedral angles were subsequently optimized by matching the force field PES to the quantum mechanical PES. Normal modes were matched as well. Parameters were further fine-tuned by following an iterative approach;47 final parameters are listed in the Supporting Information. B

DOI: 10.1021/acs.jcim.7b00215 J. Chem. Inf. Model. XXXX, XXX, XXX−XXX

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Figure 2. Free energy surface of DNA bending and base flipping for the inner thymine in double stranded, Watson−Crick base paired 13mers. Sequences are identified by the identity of bases 6−8 of the main strand. Negative flipping angles indicate flipping toward the major groove, positive flipping toward the minor groove. Free energies are in kcal/mol. Error bars are not shown, but these were below 0.1 kcal/mol.

Figure 3. Representative simulation snapshots. Backbone atoms in gray, minor groove side facing atoms in blue, major groove side facing atoms in red, flipped thymine shown as wireframe. A, D) flipped toward major groove, B, E) unflipped, base paired with adenine of complementary strand, C, F) flipped toward minor groove. A−C for unbent DNA, D−F for 70 degree bent DNA.

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RESULTS AND DISCUSSION

angular restraint on the centers and termini of the DNA; while this restraint maintained the bending angle, it did not control the direction of bending (i.e., whether DNA is bent toward the major or minor groove). Consequently, in all systems DNA was bent toward the major groove, the direction for which bending is

Figure 2 shows the two-dimensional free energy surfaces of DNA bending and base flipping of the central thymine of 5′CGCGAX6T7Z8CGCCC-3′ dsDNA, while Figure 3 shows representative structures. DNA bending was controlled by an C

DOI: 10.1021/acs.jcim.7b00215 J. Chem. Inf. Model. XXXX, XXX, XXX−XXX

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Journal of Chemical Information and Modeling easiest.59 The free energy surfaces generally converged after 3 ns of production time per window; error bars for the surfaces of Figure 2 (calculated after 5 ns of production time per window) were below 0.1 kcal/mol. Figure 1 shows a significant sequence dependent effect on DNA bending and flipping. The highest bending flexibility in the absence of flipping was observed for the GTA sequence (sequences are named by base pairs 6-8 of the main strand), while the lowest was observed in the TTT sequence. These observations are consistent with the known flexibility of the TA step and known rigidity of the TT step.60 On average, the highest bending flexibility was observed for upstream G (irrespective of the identity of the eighth base pair) or downstream A (irrespective of the identity of the sixth base pair), with the downstream base having a slightly higher effect on the bending flexibility. In its minimum free energy configuration, the DNA strands were slightly bent (∼25 degrees), consistent with other simulation studies.59,61,62 Free energies for flipping were also sequence dependent (Table 1). Mimimum free energy costs for flipping toward the

GTG, and a near equal preference for either direction for ATT, all other sequences favored major groove flipping by 1 or 2 kcal/ mol. Downstream G appeared to somewhat favor minor groove flipping, by having lower barriers in half the cases. While the free energy barriers for flipping out were large, the barrier for flipping back in was generally around 1 kcal/mol, in some cases 2 kcal/ mol. In most cases, the free energy surface for the flipped state was relatively flat and wide, with no deep basins. Small barriers for flipping back in and flatness of the flipped out state were also observed in simulations of flipping irrespective of DNA bending.17,19,24,25 This indicates that DNA is generally easier to bend once the base is flipped out. Since interactions between the flipped base and the rest of DNA are weakened, the origin of this flatness is mainly entropic. Figure 2 shows that the barriers for flipping were generally quite wide along the bending direction. For many sequences, the minimum cost for flipping in a particular direction was nearly constant (within a fraction of 1 kcal/mol) within a wide range of DNA bending angles, typically between ∼10 and ∼50 degrees. This behavior was generally observed for both major and minor groove flipping. Only a few sequences had a reduced width of the barrier along the bending direction: ATG and ATC for minor groove flipping, TTC, GTA, CTT, and CTC for major groove flipping. The minimum barrier region was generally centered around the bending angle corresponding to the optimal bending angle of the unflipped state, suggesting that DNA flipping is relatively insensitive of the bending angle around the equilibrium structure and indicating a lack of correlation between bending and flipping. This was also reflected in the shape of the free energy basins at these bending angles: tilted inverted Gaussians (with free energies for flipping in the minor groove direction generally going up steeper than in the major groove direction) with principal axes aligned with the bending and flipping axes. While bending aided flipping by pushing the system higher in free energy, which lowered the cost for flipping, flipping and bending behaved more or less independently of each other in this region. At higher bending angles, the Gaussian shape of the basins generally became distorted, with a widening toward the major groove side and rotation of the principal axes toward the major groove side indicating a positive correlation between bending and major groove flipping. This effect occurred for nearly all sequences and was particularly pronounced for ATC, TTG, and CTT. This observation indicates that at higher bending angles, the systems became primed for flips toward the major groove: upon bending, the central thymine was pushed toward the major groove side. At very large bending angles, the isocountours became nearly aligned with the flipping angle, indicating low or even absent costs for flipping once the DNA was heavily bent. Analysis of the flipping and DNA bending angle in structures of protein−DNA complexes with flipped bases in the Protein Data Bank (Figure 4) showed an interesting correspondence to some of these findings. For flipped out thymines with an upstream and downstream G (indicated by the white circle in Figure 4), all five experimental data points were on the minor groove side, which was also the preferred flipping direction for the GTG sequence (Figure 2). For the other flipped thymines, a slight preference for major groove flipping was observed, which was also seen in the calculations (Table 1). Of note is the wide range of DNA bending angles in the structures. This seems to suggest that overall, bending and flipping are not so tightly correlated for undamaged DNA, echoing the simulation results.

Table 1. Minimum Free Energies for Flipping of Central Thymine in Undamaged DNA Strandsa minimum free energy of flipping (kcal/mol) sequence

toward major groove

toward minor groove

ATA ATT ATG ATC TTA TTT TTG TTC GTA GTT GTG GTC CTA CTT CTG CTC

8.2 9.5 8.5 10.4 8.5 8.6 10.9 10.8 9.0 8.4 8.5 8.3 8.1 11.9 10.1 8.9

9.4 9.7 9.9 11.3 10.2 10.1 10.1 11.6 10.0 10.5 7.5 9.4 10.2 12.5 11.7 11.1

Large barriers (between 10 and 12 kcal/mol for flipping toward major, between 11 and 13 kcal/mol for flipping toward minor groove) are indicated in bold. a

major groove side were between 11 and 12 kcal/mol for CTT, between 10 and 11 kcal/mol for ATC, TTG, TTC, and CTG, between 9 and 10 kcal/mol for ATT and GTA, and between 8 and 9 kcal/mol for the other sequences. For minor groove flipping, minimum free energy costs were between 12 and 13 kcal/mol for CTT, between 11 and 12 kcal/mol for ATC, TTC, CTT, CTG, and CTC, between 10 and 11 kcal/mol for TTA, TTT, TTG, GTA, GTT, and CTA, and between 9 and 10 kcal/ mol for all other sequences, except GTG for which the cost was between 7 and 8 kcal/mol. Generally, a trend was seen in which flipping of the central thymine was harder for sequences with upstream C; upstream T or downstream C also tended to make flipping more energy costly. On the other hand, upstream G and downstream A tended to ease flipping of the central thymine. Flipping toward the major groove was generally more facile than flipping toward the minor groove. While a preference for flipping toward the minor groove was observed for TTG and D

DOI: 10.1021/acs.jcim.7b00215 J. Chem. Inf. Model. XXXX, XXX, XXX−XXX

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out (6-4)PP and CPD damaged bases are shown in Figure 4. Data for both is very sparse, but CPD is shown to prefer flipping toward the major groove, and (6-4)PP showed relatively large bending angles.

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CONCLUSION Coupling between flipping of the central thymine base and DNA major groove bending was investigated for 16 DNA 13mers. The identity of the neighboring up- and downstream base had a significant effect on the flipping energetics, modulating the free energy cost of flipping by up to 2 kcal/mol. Bending energetics were also dependent on sequence, in a manner consistent with the known relative flexibility of base pairs. Overall, major groove flipping was more favorable by 1−2 kcal/mol, although minor groove flipping was preferred for a couple of sequences. Barriers for flipping were generally quite wide in the bending direction, extending tens of degrees, and the free energy surface was generally relatively flat for the flipped out states, indicating that DNA bending is easier when bases are flipped out. While the free energy cost of flipping out was typically around 10 kcal/mol, the barrier for flipping back was low, typically near 1 kcal/mol. The data suggests no strong correlation between bending and flipping for bending angles up to 30 degrees from equilibrium. Bending is seen to help flipping, by pushing the system up in energy, which decreases the cost for flipping. However, the two behave more or less independently in this bending range. At higher bending angles, a noticeable correlation between flipping and bending developed, which primed the system for flipping toward the major groove. Bending and flipping became more coupled, until finally, at very large bending angles (>80 degrees), the cost of flipping became very small. Aspects of the calculations could be verified by an analysis of protein−DNA structures with flipped bases from the Protein Data Bank. A small preference was seen for major groove flipping in undamaged DNA, and no strong coupling between DNA bending and flipping angles was observed. Flipping of CPD and (6-4)PP was shown to be more facile than for thymine, especially for (6-4)PP. While bending of the CPD strand aided flipping by pushing the system higher in free energy, no strong correlations between bending and flipping were found. Bending of (6-4)PP damage was very facile; both CPD and (6-4)PP preferred flipping to the major groove side.

Figure 4. Distribution of flipping and DNA bending angles for protein− DNA complexes with flipped bases from the Protein Data Bank. In the undamaged panel, white circles indicate flipped out thymines with upand downstream G on the same strand, triangles indicate flipped out thymines for all other sequences, and black circles indicate strands in which an C, G, or A is flipped out. In the other panels, the damaged (64)PP or CPD is flipped out.

Two-dimensional free energy surfaces as a function of the DNA bending angle and flipping angle were also calculated for two UV damaged strands in which either the (6-4)PP or CPD damage was flipped out (Figure 5). Because of the large

Figure 5. Free energy surface of DNA bending and damage flipping of the (6-4)PP and CPD systems. Negative flipping angles indicate flipping toward the major groove and positive flipping toward the minor groove. Free energies in kcal/mol; error bars are not shown, but these were below 0.1 kcal/mol.

computational expense of the simulations, sequence effects were not investigated. Both damages preferred flipping toward the major groove, and for both damages an increase in DNA bending flexibility was observed, especially for the (6-4)PP damage. For CPD, the free energy surface in the flipped region on the major groove side was wide and relatively flat. At the minor groove side, the free energy surface showed an arm at a flipping angle between 50 and 60 degrees and a bending angle of 20 to 40 degrees, but at these angles the damage was still mostly inside the helix (Figure S3B). The fully flipped configuration on the minor groove side occurred for a bending angle between 10 and 30 degrees, an area less wide and higher in free energy than the flipped major groove side. The free enery cost for flipping was between 7 and 8 kcal/ mol on the major groove side and between 8 and 9 kcal/mol on the minor groove side or about 1 kcal/mol less in either direction compared to undamaged DNA. For (6-4)PP, the flipped out state was relatively wide with no discernible basin, and the free energy cost for flipping was significantly reduced compared to undamaged DNA. Flipping toward the major groove side was most facile at a bending angle of 20 degrees, while flipping toward the minor groove was favored at a higher angle of ∼50 degrees. For CPD no strong correlation was observed between DNA bending and flipping. For (6-4)PP the correlation was weak: the minimum cost of flipping toward the minor groove occurred at an overbending of 20 degrees from equilibrium, but the energetic effect was rather small. Bending of (6-4)PP was very facile, with low free energy costs for bending angles up to 60 degrees. Protein Data Bank statistics on protein−DNA complexes with flipped

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jcim.7b00215.

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Tables with force field parameters for the CPD and (64)PP damage, as well as figures showing atom numbering, atomic charges, and CPD structures (PDF)

AUTHOR INFORMATION

Corresponding Author

*Phone: +1-813-974-8762. E-mail: [email protected]. ORCID

Arjan van der Vaart: 0000-0002-8950-1850 Notes

The authors declare no competing financial interest. E

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ACKNOWLEDGMENTS Computer time was provided by USF Research Computing, sponsored in part by NSF MRI CHE-1531590.

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DOI: 10.1021/acs.jcim.7b00215 J. Chem. Inf. Model. XXXX, XXX, XXX−XXX