Dependence of B-DNA Groove Bending Anisotropy - ACS Publications

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[KCl] Dependence of B-DNA Groove Bending Anisotropy Ning Ma, and Arjan van der Vaart J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 08 May 2017 Downloaded from http://pubs.acs.org on May 17, 2017

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The Journal of Physical Chemistry

[KCl] Dependence of B-DNA Groove Bending Anisotropy Ning Ma and Arjan van der Vaart* Department of Chemistry, University of South Florida, 4202 E. Fowler Ave. CHE 205, Tampa, FL 33620, U.S.A. Abstract The energetics of B-DNA bending toward the major and minor grooves were quantified by free energy simulations at four different KCl concentrations. Increased [KCl] led to more flexible DNA, with persistence lengths that agreed well with experimental values. At all salt concentrations, major groove bending was preferred, although preferences for major and minor groove bending were similar for the A-tract containing sequence. Since the phosphate repulsions and DNA internal energy favored minor groove bending, the preference for major groove bending was thought to originate from differences in solvation. Water in the minor groove was tighter bound than water in the major groove, and harder to displace than major groove water, which favored the compression of the major groove upon bending. Higher [KCl] decreased the persistence length for both major and minor groove bending, but did not greatly affect the free energy spacing between the minor and major groove bending curves. For sequences without Atracts, salt affected major and minor bending to nearly the same degree, and did not change the preference for major groove bending. For the A-tract containing sequence, an increase in salt concentration decreased the already small energetic difference between major and minor groove bending. Since salts did not significantly affect the relative differences in bending energetics and hydration, it is likely that the increased bending flexibilities upon salt increase are simply due to screening. * Corresponding author. Email: [email protected]. Phone: +1-813-974-8762.

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Introduction Many proteins bend DNA upon binding, and this bending often serves a biological purpose1 (for example in DNA packaging,2 regulation through DNA looping,3 and DNA repair4). Moreover, since DNA is a relatively stiff molecule, bending plays an important role in the binding energetics and strongly influences affinities.5-6 B-DNA, the most common form of DNA, has two grooves spiraling along its length that are geometrically and chemically distinctly different.7 The minor groove is narrow and forms at the N3 side of the purines and C2 side of the pyrimidines, while the major groove is wider and forms at the opposite side of the bases. B-DNA can therefore bend in two distinct directions: either toward the major groove, or toward the minor groove.8 The protein data bank has many examples of protein-DNA complexes in which DNA is bent towards either groove; proteins typically9 (but not always10) bind to one groove and bend DNA toward the other. While experiments can quantify the stiffness of DNA towards bending,1 the direction of bending is much harder to control experimentally. Insights into the anisotropy of DNA bending have therefore not come from experiments, but from statistical analyses of protein-DNA structures11-15 and from modeling studies.8-10, 16-20 We recently presented detailed computer simulations that provided the first quantitative comparison of the free energy cost of major versus minor groove bending for a number of DNA sequences.10 The simulations showed that bending toward the major groove is favored, except for the A-tract, which has a similar propensity for minor groove bending. Major groove bending was favored because of a free energy offset, which favors slight bending towards the major groove at equilibrium, and smaller stiffness toward major groove bending. Simulation data also suggested that water may play a much more active role in determining the direction of bending than previously thought. Major groove bending compresses the major groove, while the minor groove is compressed upon minor groove bending. Water may therefore play a role in determining the relative stiffnesses, since water is more easily liberated from the major than the minor groove.10, 21-28 An unanswered question is how salts affect the anisotropy of bending. Experiments have shown that DNA becomes more flexible at higher salt concentration,29-30 which is due to a more effective screening of the negatively charged phosphate backbone. It remains unclear however, how salts affect the relative difference between major and minor groove bending; how it impacts the free energy offset, and stiffnesses for major and minor groove bending. To address these questions, free energy simulations of DNA bending were performed at different salt concentrations. The results of these simulations will be presented, the effect of salt concentration will be discussed, and the origins of the bending anisotropy will be further examined. Methods Bending simulations. Potentials of mean force as a function of DNA bending were calculated from umbrella sampling31 simulations of total roll (ΘR) and tilt (ΘT). The methodology has been described in detail in Ref. 10, and will only be briefly summarized here. The method is based on


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the Madbend formalism,9 which calculates the DNA bending angle as ϕ = Θ 2R + Θ T2 . Bending is toward the major groove for positive values of ΘR, and toward the minor groove for negative ΘR; bending irrespective of direction will be named global or overall bending. Total roll and tilt are obtained by accumulating the roll (ρ) and tilt (τ) of all base steps (indicated by j in the following sums), while projecting out the twist: Θ T = ∑ j τ j cos γ j + ρ j sin γ j , and

(

(

)

)

Θ R = ∑ j −τ j sin γ j + ρ j cos γ j . The total twist (γ) is obtained by accumulating all base step

twists (Ω) relative to the central DNA step (NC): γ j = − ∑ i=N j

C +1

Ω i for j ≥ N C and

γ j = − ∑ i=1 Ω i otherwise. Roll, twist, and tilt are the angles that describe the relative orientation N C −1

of base pairs in a DNA step (shown in Fig. S1 of the Supporting Information); a step consists of two adjacent base pairs.32 In our implementation,33-34 the roll, twist and tilt angles are obtained from local coordinates, avoiding the costly overlays with idealized base pairs that are used in the formal definitions,32 yielding analytical forces and showing excellent agreement with the original definitions. Systems, setup, and analysis. We previously studied the bending of 8 double stranded DNA sequences in 0.15 M KCl;10 because of the large computational expense, we only considered four of these sequences here (Table 1). Sequence 1 is the Dickerson dodecamer,35 in sequence 2 the central AT base pairs of the Dickerson dodecamer are mutated to CG, sequence 3 consists of an inner TATA motif followed by an A-tract, that is bent toward the major groove in the crystal structure of the TBP-DNA complex (PDB entry: 1CDW36), and sequence 4 is bent toward the minor groove in the crystal structure of the HiPB-DNA complex (PDB entry: 4YG137). The strands were selected to form a minimal representation of sequence space, and include GC and AT-rich sequences. Each of the systems was simulated in four different KCl concentrations of 0.04, 0.15, 0.5, and 0.8 M. Based on the results of the persistence length analyses, simulations for sequence 1 at 0.5 and 0.8 M, and sequence 2 at 0.15 and 0.8 M were replicated, starting from the build. Because of the expense of the simulations, only four different concentrations and a limited number of duplicates could be considered. -- Table 1 Here -Unbent DNA structures were prepared by X3DNA,38 and solvated into rectangle water boxes using a minimum margin of 18 Å between DNA atoms and the side of the box. The particle mesh Ewald (PME) method39 was used for long-range electrostatics, except for the simulations at 0.04 M. This concentration was so low that the amount of K+ ions was insufficient to neutralize the system in the given box. To avoid the large computational expense of using much larger water boxes, this salt concentration was not treated by PME. Instead, a large cutoff of 12 Å for the non-bonded interactions with an atom-based force shift was used, which was previously shown to be an accurate replacement of PME at relatively low computational cost.40 To verify that the large cutoff approach was indeed appropriate, the Dickerson dodecamer sequence at 0.15 M KCl was simulated with both PME and with the large cutoff method. The free energy maps


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generated from these two methods were indeed highly similar, with differences in free energy below 0.25 kcal/mol at all bending angles of the 1D free energy bending curves (Fig. S2 of the Supporting Information). This agreement indicated the suitability of the large cutoff approach for low concentrations. After energy minimization, the systems were gradually heated from 120 K to 300 K over 1 ns with 1 kcal/(mol Å2) harmonic restraints applied on the heavy atoms of DNA, followed by a 1 ns equilibration during which the restraints were reduced from 1.0 to 0.5, to 0.25, to 0.1, and to 0.01 kcal/(mol Å2), and a 10 ns equilibrium without restraints. The final equilibrated structures were taken as starting point for the 2D umbrella sampling simulations, which applied harmonic restraints with a force constant of 0.04 kcal/(mol degree2) to the total roll and tilt. Because of possible fraying, only the inner base pairs were biased and the first and last two base pair steps were not included in the biasing. Targeted values of ΘR and ΘT each varied between -80˚ and 80˚ in steps of 10˚. For each window, a short equilibration of 0.1 ns was followed by a 1 ns production run. The final structure of each equilibration was used as starting point for the production run and also as starting point for the equilibration of the neighboring window. A total of 289 windows were simulated for each of the 16 systems. Since the DNA step parameter can only be calculated for properly formed base pairs, a flat bottom harmonic biasing potential was applied to the distance between the purine N3 and pyrimidine N1 of the inner base pairs, with a force constant of 10 kcal/(mol Å2) for distances larger than 3.3 Å, and a zero force constant for distances less than 3.3 Å. Analysis showed that this restraint was rarely active and did not impact the results. The simulations were performed with CHARMM41 (modified to enable umbrella sampling of total roll and tilt), and the CHARMM 36 force field.42 All simulations were performed in the NPT ensemble using the Nosé− Hoover thermostat,43 the leapfrog integrator with a time step of 2 fs, PME39 or the long cutoff method for different concentration as previously described, and SHAKE44 for all covalent bonds involving hydrogen atoms. Snapshots were saved every 2 ps. All free energy surfaces were calculated by the multistate Bennett acceptance ratio (MBAR)45 after decorrelation of the data sets; the MBAR uncertainty expressions45 were used for error analysis. One-dimensional free energy surfaces as a function of the DNA bending angle were obtained by integration of the 2-dimensional surfaces: F(ϕ ) = −kT ln ∫

Θ 2R +ΘT2 =ϕ

exp[−F(Θ R ,Θ T ) / k BT ]dΘ R dΘ T ; one-dimensional curves for bending

towards the major (minor) groove were obtained by restricting the integration over positive (negative) ΘR. Persistence lengths (A) were calculated from the curvature of the 1D free energy L ∂F curves using Mazur's method,46 using A = . The electrostatic repulsion between kT ∂(1− cosϕ ) the eight central phosphates was calculated using MBAR. MBAR was also used to calculate the total energy of the eight central base pairs with their phosphates and sugars; in both cases, data was first decorrelated. The eight central base pairs were used because of fraying (which affects the terminal base pairs); however, for completeness, the electrostatic repulsion and the total energy of the entire DNA were calculated as well. These energies are reported relative to the


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minimum energy value of each sequence to ease the comparison across multiple sequences. Hydration analysis was performed by considering water molecules/ions on the major groove side and within 5.5 Å of the major groove edge heavy atoms of the bases as major groove waters/ions, while those located within 5.0 Å of the minor groove edge heavy atoms of the bases and on the minor groove side as minor groove waters/ions. The terminal base pairs on each end were ignored to avoid overcounting. This analysis was only carried out for configurations with global bending angle less than 42.4˚ (up to ΘR/ Θt values of ±30˚). Beyond these angles the grooves were deformed so much, that a general definition for the groove waters that was satisfactory for all snapshots could not be found. Results Typical simulation snapshots are shown in Fig. 1; structures with negative ΘR were bent toward the minor groove, while structures with positive ΘR were bent toward the major groove. As the figure shows, the grooves had regular shapes for small and intermediate bending angles, but became highly deformed at large bending angles. Free energy surfaces as a function of ΘR and ΘT are shown in Fig. S3 of the Supporting Information. The global free energy minima were located near (ΘR, ΘT) = (15˚, -15˚) for most sequences, except for the A-tract containing sequence 3, which had its global minima near (5˚, -15˚). This sequence also differed in the direction of its principal axes: these were ~10˚ counter-clockwise from the ΘR axis for sequence 3, but ~30˚ counter-clockwise for the other sequences. The shape of the basins and locations of the minima indicate that most sequences preferred to slightly bend toward the major groove, while the sequence 3 had a near equal preference to bend toward either major or minor groove. The surfaces show that the ion concentration did not change the position of global minimum. The width of the basins was larger in the ΘR than in the ΘT axis direction, indicating that DNA was more flexible in roll than in tilt. -- Figure 1 Here -These effects were echoed in Fig. 2, which shows the integrated, one-dimensional free energy curves as a function of the DNA bending angle for overall bending and bending towards the major and minor grooves. The general shape of the overall one-dimensional free energy curves was similar among all sequences and all ion concentrations. Minima were at small bending angles (~20°), the free energy was quadratic in small and intermediate bending angle (up to ~50°) and linear at large bending angles (> 50°). Higher salt concentrations flattened the free energy curves, indicating that DNA became easier to bend as the salt concentration increased. Calculated persistence lengths (Table 2) confirmed this result, with a general downward trend in magnitude with increasing salt concentration. The only outliers were sequence 1 at 0.5 M and sequence 2 at 0.8 M, which showed small increases. Persistence lengths at 0.15 M agreed within error with previous results,10 except for sequence 2. This sequence showed a lower persistence length than previously reported, which was likely due to longer sampling. Overall persistence lengths agreed with Baumann and co-workers’ experimental work.30 Fig. 3 compares the experimentally measured persistence length of λ-bacteriophage DNA as a function of NaCl


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concentration, with the calculated persistence lengths of the four sequences as a function of KCl concentration. Despite the differences in monovalent salt that was used, and differences in sequence and length of the DNA strands, calculated persistence lengths followed the experimental trends. -- Figure 2 Here --- Table 2 Here --- Figure 3 Here -Fig. 2 shows that bending towards the major groove was generally preferred. For all non-A-tract containing sequences (i.e. sequences 1, 2 and 4), the major groove bending curve was lower in free energy than the minor groove bending curve; the difference was between 1-2 kcal/mol and stayed relatively constant as the bending angle was increased. Fig. 4A shows the free energy offset ∆Feq as a function of the salt concentration for the various sequences; ∆Feq is defined as the minimum free energy of the minor bending curve minus the minimum free energy of the major bending curve. The figure shows that while ∆Feq depended on sequence, it did not strongly depend on KCl concentration. For a given sequence, ∆Feq varied up to 0.3 kcal/mol with a change in [KCl]; however, the change in ∆Feq did not follow a particular trend, and the magnitude of the changes was within thermal energy. Persistence lengths for major and minor groove bending are listed in Table 2. In general, persistence lengths for bending toward the minor groove were larger than persistence lengths for bending toward the major groove, indicating a larger stiffness toward minor groove bending. The difference in persistence lengths of minor and major groove bending (∆A) as a function of the salt concentration are shown in Fig. 4B. For the non-A-tract containing sequences, ∆A was relatively constant within error, as one could infer from the relatively constant free energy spacings between the minor and major bending curve as the bending angle increases (Fig. 2). A-tract containing sequence 3 showed somewhat different behavior, however. ∆Feq was small, indicating similar propensities for major and minor groove bending; but like the other sequences, ∆Feq was nearly constant with salt concentration. For sequence 3 the difference in persistence length decreased as the salt concentration was increased, indicating a relative stronger decrease in stiffness toward minor groove bending. Fig. 3 shows that this behavior was mostly due to the bending over 50°: for this region, the difference between the minor and major bending curves decreased upon an increase in salt concentration. -- Figure 4 Here -Calculation of the phosphate repulsion energy suggests that the preference of major groove bending is not electrostatic in origin. Fig. 5 shows the total electrostatic energy between all phosphate groups of the inner 8 base pairs; the total phosphate repulsion energy for all phosphates of the DNA is shown in the Supporting Information (Fig. S4). Both curves are shown as a function of the bending angle for bending towards the major groove (right-hand-side curves) and bending towards the minor groove (left-hand-side curves). Each arm is parabolic in shape, but the curvature is typically larger for bending towards the major groove (Tables 3, S1),


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signaling a higher electrostatic expense for major groove bending. The repulsion plots over all DNA phosphate groups (Fig. S4) are more bumpy than the plots for the inner phosphates, which is due to DNA fraying (which affects the terminal base pairs). Fraying was also responsible for the higher curvature of minor groove bending, that was observed at some salt concentrations for sequence 3 when taking all residues into account (Table S1). Overall, the plots suggest that the electrostatics would generally favor minor groove bending. In a similar manner, plots of the total internal energy of the DNA (Figs. 6, S5) suggest that the total energy generally favored bending towards the minor groove. The arms were also parabolic in shape, and generally displayed a higher curvature for bending towards the major groove (Tables 3, S1). -- Figure 5 Here --- Table 3 Here --- Figure 6 Here -Fig. 7 shows the number of water molecules in the major and minor grooves upon bending toward the major and minor groove. The analysis was limited to bending angles up to 42˚, since no single geometrical criterion to define the extend of the grooves was satisfactory for larger angles. In general, the number of water molecules in the major groove decreased upon bending toward the major groove, since the major groove was compressed upon major groove bending. As the major groove was compressed, the minor groove was widened, which led to an increase in the number of water molecules in the minor groove upon major groove bending. The narrowing and widening of grooves can clearly be seen in the simulation snapshots of Fig. 1. A similar effect happened for minor groove bending, which gained water upon bending toward the major groove. However, loss of water in the minor groove upon minor groove bending was less apparent in this bending range, and in some cases numbers even appeared constant. Visual inspections were performed to investigate the behavior at higher bending angles, which indicated loss of water in the grooves to which DNA was bent, and gains of water to the opposite groove. Fig. 8 shows the average residence times of water molecules in the major and minor grooves upon bending toward either groove; these averages were taken over all residence times in the grooves, and include those for waters deep in the groove with long residence times and those for waters near the surface that frequently exchange with the bulk. Again, the analysis was limited to bending up to 42˚. There was a clear separation of the behavior of minor and major groove waters, with significantly higher average residence times in the minor groove. Trends showed that for bending toward the minor groove, average residence times for the minor groove water increased with bending angle, while the average residence times decreased for major groove water. This suggests the loss of the more mobile surface water or the tightening of water in the minor groove, and gain of surface waters in the major groove. A similar (but opposite) effect was seen for bending towards the major groove, although the increase in average residence times for the major groove water upon bending appeared less pronounced. Overall, trends in the number of groove water molecules and average residence times did not appear to strongly depend on the salt concentration.


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-- Figure 7 Here --- Figure 8 Here -Discussion The free energy cost of DNA bending and its anisotropy toward major and minor groove bending were quantified for four sequences at four KCl concentrations. Calculated persistence lengths for overall bending (i.e. irrespective of the direction of bending) agreed well with experimental values, and showed a decrease upon an increase in salt concentration. Sequence 1 and 2 appeared somewhat stiffer then λ-bacteriophage DNA, which is consistent with the high GC content of these strands. Sequence 3 appeared less stiff than λ DNA, which is consistent with the known high flexibility of the TA motif.47 The free energy cost of overall bending was shown to be quadratic for small and intermediate bending angles, but became linear at high bending angles at all simulated concentrations. The relative ease of bending at high bending angles, a deviation from classical elastic theories like the worm-like chain model,48 is in agreement with previous studies.10, 34, 49 At all salt concentrations, bending toward the major groove was shown to be more facile than bending toward the minor groove, but for sequence 3 the preferences for major and minor groove bending nearly equaled. This is in agreement with the high tendency to bend toward the minor groove in experimental studies of A-tracts.50-53 Differences between major and minor groove bending are characterized by two factors: a difference in free energy offset (∆Feq; the difference in minimum free energies of the minor and major groove bending curves) and a difference in persistence lengths. ∆Feq depended on sequence, with a near-zero value for sequence 3 with the A-tract and 1-2 kcal/mol for the other sequences, but did not strongly depend on salt concentration. Persistence lengths also depended on sequence and were nearly always larger for minor groove bending. Differences in persistence lengths for major and minor groove bending were small however, with an average of 7% and a maximum of 28%, which suggests that ∆Feq is the most important factor in determining the preferred direction of bending. Moreover, for all but sequence 3, the difference in persistence lengths was not dependent on salt concentration. These observations indicate that while DNA became more flexible at higher salt concentration, for non-A-tracts, salt affected major and minor groove bending nearly to the same degree: it did not change the preference to bend toward the major groove, and only slightly affected ∆Feq, the free energy spacing, and difference in stiffness. For the A-tract, an increase in salt further decreased the already small difference in major and minor groove bending. Thus overall, salts did not significantly affect the relative differences in bending energetics, which indicates that electrostatics are not the underlying cause of the bending anisotropy. While DNA that is bent toward the major groove is structurally quite different from DNA that is bent toward the minor groove, the reason why major groove bending is favored was shown not to be due to differences in phosphate repulsion or DNA internal energy. Phosphate repulsion was shown to be ~quadratic in bending angle and generally less costly for bending in the minor groove direction, which indicates that the phosphate repulsions actually favor minor groove


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bending. The DNA internal energy (which includes electrostatics, base stacking and steric effects) was also ~quadratic in bending angle, and also generally less costly in the minor groove direction. This means that the internal energy is also not the reason why major groove bending is preferred. The elimination of the phosphate repulsion and DNA internal energy leaves solvation as plausible origin for the preference of major groove bending. Previous experimental and theoretical studies established the different behavior of water in the major and minor grooves, and showed that minor groove water is significantly less mobile than major groove water.10, 21-28 These differences were also observed here. In general, DNA lost water in the groove to which it was bent; the longer average residence times of water in the minor groove suggest that these water are more tightly bound and less facile to remove than waters in the major groove. This was echoed in the observations that sequence 3, which had the highest propensity to bend toward the minor groove, had the lowest average residence times for water molecules in the minor groove, and in the fact that in some of the simulations the number of minor groove waters appeared nearly constant in the 10 to 42˚ bending range while residence times increased upon bending. Thus, water in the grooves likely plays an important role in determining the favored direction of bending, and bending toward the minor groove is disfavored because the water molecules are harder to remove from the minor groove. The presented data showed that increased KCl concentration facilitates bending, but does not greatly affect the relative differences in major and minor groove bending energetics. Significant changes were only seen for sequence 3; however, differences between minor and major groove bending were small to start with for this sequence. Analyses showed that there are also no clear trends between differences in hydration and salt concentration. These observations suggest that while the preference of major groove bending is due to hydration, the ease of overall, major and minor groove bending upon the increase in [KCl] is largely due to the screening of salt. The lack of effect of salt on the preferred bending direction is likely important for biology, since proteinDNA complexes favor a particular bending direction, and the actual direction is important in processes like DNA looping or co-recruitment that require well-defined positioning of the DNA. While DNA bending angles have been observed to vary under different salt concentrations in protein-DNA complexes,54-56 the inherent resistance of DNA to change the direction of bending may add robustness to the geometry and energetics of protein-DNA complexes. The simulations presented here were performed with a fixed charge force field that lacks polarization. Given recent indications on the importance of polarization on minor groove widths,57-58 it will be interesting to refine our findings using a polarizable force field.

Supporting Information A schematic of the rotational step parameters, differences in PME and long-range cutoff treatment, two-dimensional free energy surfaces, and phosphate repulsions and internal energies for the full length DNA sequences with their curvatures are presented in the Supporting Information.


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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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(17) Sanghani, S. R.; Zakrzewska, K.; Harvey, S. C.; Lavery, R. Molecular Modelling of (a(4)T(4)Nn)(N) and (T(4)a(4)Nn)(N): Sequence Elements Responsible for Curvature. Nucleic Acids Res. 1996, 24, 1632-1637. (18) Beveridge, D. L.; Barreiro, G.; Byun, K. S.; Case, D. A.; Cheatham, T. E., III; Dixit, S. B.; Giudice, E.; Lankas, F.; Lavery, R.; Maddocks, J. H., et al. Molecular Dynamics Simulations of the 136 Unique Tetranucleotide Sequences of DNA Oligonucleotides. I. Research Design and Results on D(Cpg) Steps. Biophys. J. 2004, 87, 3799-3813. (19) Dixit, S. B.; Beveridge, D. L.; Case, D. A.; Cheatham, T. E., 3rd; Giudice, E.; Lankas, F.; Lavery, R.; Maddocks, J. H.; Osman, R.; Sklenar, H., et al. Molecular Dynamics Simulations of the 136 Unique Tetranucleotide Sequences of DNA Oligonucleotides. II: Sequence Context Effects on the Dynamical Structures of the 10 Unique Dinucleotide Steps. Biophys. J. 2005, 89, 3721-3740. (20) Curusku, J.; Zakrzewska, K.; Zacharias, M. Magnitude and Direction of DNA Bending Induced by Screw-Axis Orientation: Influence of Sequence Mismatches and Abasic Sites. Nucleic Acids Res. 2008, 36, 2268-2283. (21) Kubinec, M. G.; Wemmer, D. E. Nmr Evidence for DNA Bound Water in Solution. J. Am. Chem. Soc. 1992, 114, 8739-8740. (22) Liepinsh, E.; Otting, G.; Wüthrich, K. NMR Observation of Individual Molecules of Hydration Water Bound to DNA Duplexes: Direct Evidence for a Spine of Hydration Water Present in Aqueous Solution. Nucleic Acids Res. 1992, 20, 6549-6553. (23) Liepinsh, E.; Leupin, W.; Otting, G. Hydration of DNA in Aqueous Solution: Nmr Evidence for a Kinetic Destabilization of the Minor Groove Hydration of D-(TTAA) 2 Versus D(AATT) 2 Segments. Nucleic Acids Res. 1994, 22, 2249-2254. (24) Denisov, V. P.; Carlström, G.; Venu, K.; Halle, B. Kinetics of DNA Hydration. J. Mol. Biol. 1997, 268, 118-136. (25) Johannesson, H.; Halle, B. Minor Groove Hydration of DNA in Solution: Dependence on Base Composition and Sequence. J. Am. Chem. Soc. 1998, 120, 6859-6870. (26) Phan, A. T.; Leroy, J.-L.; Gu ron, M. Determination of the Residence Time of Water Molecules Hydrating B -DNA and B-DNA, by One-Dimensional Zero-Enhancement Nuclear Overhauser Effect Spectroscopy. J. Mol. Biol. 1999, 286, 505-519. (27) Jana, B.; Pal, S.; Bagchi, B. Enhanced Tetrahedral Ordering of Water Molecules in Minor Grooves of DNA: Relative Role of DNA Rigidity, Nanoconfinement, and Surface Specific Interactions. J. Phys. Chem. B 2010, 114, 3633-3638. (28) Saha, D.; Supekar, S.; Mukherjee, A. Distribution of Residence Time of Water around DNA Base Pairs: Governing Factors and the Origin of Heterogeneity. J. Phys. Chem. B 2015, 119, 11371-11381. (29) Hagerman, P. J. Flexibility of DNA. Annu. Rev. Biophys. Biophys. Chem. 1988, 17, 265286. (30) Baumann, C. G.; Smith, S. B.; Bloomfield, V. A.; Bustamante, C. Ionic Effects on the Elasticity of Single DNA Molecules. Proc. Natl. Acad. Sci. USA 1997, 94, 6185-6190. (31) Torrie, G. M.; Valleau, J. P. Non-Physical Sampling Distributions in Monte-Carlo FreeEnergy Estimation - Umbrella Sampling. J. Comput. Phys. 1977, 23, 187-199. (32) Olson, W. K.; Bansal, M.; Burley, S. K.; Dickerson, R. E.; Gerstein, M.; Harvey, S. C.; Heinemann, U.; Lu, X.-J.; Neidle, S.; Shakked, Z. A Standard Reference Frame for the Description of Nucleic Acid Base-Pair Geometry. J. Mol. Biol. 2001, 313, 229-237.


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(33) Karolak, A.; Vaart, A. Enhanced Sampling Simulations of DNA Step Parameters. J. Comput. Chem. 2014, 35, 2297-2304. (34) Spiriti, J.; Kamberaj, H.; de Graff, A. M. R.; Thorpe, M. F.; van der Vaart, A. DNA Bending through Large Angles Is Aided by Ionic Screening. J. Chem. Theory Comput. 2012, 8, 2145-2156. (35) Dickerson, R. E. Crystal Structure Analysis of a Complete Turn of B-DNA. Nature 1980, 287, 755-758. (36) Nikolov, D. B.; Chen, H.; Halay, E. D.; Hoffman, A.; Roeder, R. G.; Burley, S. K. Crystal Structure of a Human Tata Box-Binding Protein/Tata Element Complex. Proc. Natl. Acad. Sci. USA 1996, 93, 4862-4867. (37) Schumacher, M. A.; Balani, P.; Min, J.; Chinnam, N. B.; Hansen, S.; Vulić, M.; Lewis, K.; Brennan, R. G. Hipba-Promoter Structures Reveal the Basis of Heritable Multidrug Tolerance. Nature 2015, 524, 59-64. (38) Lu, X. J.; Olson, W. K. 3dna: A Software Package for the Analysis, Rebuilding and Visualization of Three Dimensional Nucleic Acid Structures. Nucleic Acids Res. 2003, 31, 5108-5121. (39) Darden, T.; York, D.; Pedersen, L. Particle Mesh Ewald: An NŊ Log (N) Method for Ewald Sums in Large Systems. J. Chem. Phys. 1993, 98, 10089-10092. (40) Norberg, J.; Nilsson, L. On the Truncation of Long-Range Electrostatic Interactions in DNA. Biophys. J. 2000, 79, 1537-1553. (41) Brooks, B. R.; Brooks, C. L., 3rd; Mackerell, A. D., Jr.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S., et al. Charmm: The Biomolecular Simulation Program. J. Comput. Chem. 2009, 30, 1545-614. (42) Hart, K.; Foloppe, N.; Baker, C. M.; Denning, E. J.; Nilsson, L.; MacKerell Jr, A. D. Optimization of the Charmm Additive Force Field for DNA: Improved Treatment of the Bi/Bii Conformational Equilibrium. J. Chem. Theory Comput. 2011, 8, 348-362. (43) Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nosé–Hoover Chains: The Canonical Ensemble Via Continuous Dynamics. J. Chem. Phys. 1992, 97, 2635-2643. (44) Ryckaert, J.-P.; Ciccotti, G.; Berendsen, H. J. Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of N-Alkanes. J. Comput. Phys. 1977, 23, 327-341. (45) Shirts, M. R.; Chodera, J. D. Statistically Optimal Analysis of Samples from Multiple Equilibrium States. J. Chem. Phys. 2008, 129, 124105. (46) Mazur, A. K. Wormlike Chain Theory and Bending of Short DNA. Phys. Rev. Lett. 2007, 98, 218102. (47) El Hassan, M. A.; Calladine, C. R. Propeller-Twisting of Base-Pairs and the Conformational Mobility of Dinucleotide Steps in DNA. J. Mol. Biol. 1996, 259, 95-103. (48) Kratky, O.; Porod, G. Röntgenuntersuchung Gelöster Fadenmoleküle. Rec. Trav. Chim. Pays-Bas 1949, 68, 1106-1123. (49) Spiriti, J.; van der Vaart, A. DNA Bending through Roll Angles Is Independent of Adjacent Base Pairs. J. Phys. Chem. Lett. 2012, 3, 3029-3033. (50) MacDonald, D.; Herbert, K.; Zhang, X.; Polgruto, T.; Lu, P. Solution Structure of an aTract DNA Bend. J. Mol. Biol. 2001, 306, 1081-1098. (51) Zinkel, S. S.; Crothers, D. M. DNA Bend Direction by Phase Sensitive Detection. Nature 1987, 328, 178-181.


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(52) Stefl, R.; Wu, H. H.; Ravindranathan, S.; Sklenar, V.; Feigon, J. DNA A-Tract Bending in Three Dimensions: Solving the Da(4)T(4) Vs. Dt(4)a(4) Conundrum. Proc. Natl. Acad. Sci. USA 2004, 101, 1177-1182. (53) Barbic, A.; Crothers, D. M. Comparison of Analyses of DNA Curvature. J. Biomol. Struct. Dyn. 2003, 21, 89-97. (54) Dragan, A. I.; Read, C. M.; Makeyeva, E. N.; Milgotina, E. I.; Churchill, M. E. A.; CraneRobinson, C.; Privalov, P. L. DNA Binding and Bending by Hmg Boxes: Energetic Determinants of Specificity. J. Mol. Biol. 2004, 343, 371-393. (55) Cherny, D. I.; Striker, G.; Subramaniam, V.; Jett, S. D.; Palecek, E.; Jovin, T. M. DNA Bending Due to Specific P53 and P53 Core Domain-DNA Interactions Visualized by Electron Microscopy. J. Mol. Biol. 1999, 294, 1015-1026. (56) Schroth, G. P.; Gottesfeld, J. M.; Bradbury, E. M. TFIIIa Induced DNA Bending - Effect of Low Ionic-Strength Electrophoresis Buffer Conditions. Nucleic Acids Res. 1991, 19, 511-516. (57) Savelyev, A.; MacKerell, A. D. Differential Deformability of the DNA Minor Groove and Altered BI/BII Backbone Conformational Equilibrium by the Monovalent Ions Li+, Na+, K+, and Rb+ Via Water-Mediated Hydrogen Bonding. J. Chem. Theory Comput. 2015, 11, 44734485. (58) Savelyev, A.; MacKerell, A. D. Differential Impact of the Monovalent Ions Li+, Na+, K+, and Rb+ on DNA Conformational Properties. J. Phys. Chem. Lett. 2015, 6, 212-216.


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Tables Table 1. Simulated double stranded DNA sequences. Name Sequence 1 5'-CGCGAATTCGCG-3' 2 5'-CGCGCGCGCGCG-3' 3 5'-GCTATAAAAGGC-3' 4 5'-TATCCGCTTAAG-3'


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Table 2. DNA persistence lengths for overall bending and bending towards the major and minor grooves. Sequence [KCl] (M) overall (Å) major (Å) minor (Å) 1: CGCGAATTCGCG 0.04 624 ± 21 625 ± 16 618 ± 28 0.15 548 ± 16 547 ± 15 565 ± 21 a a 0.15 538.5 539.5 551.1a 0.5 562 ± 25 560 ± 24 580 ± 7 574 ± 20 575 ± 19 565 ± 11 539 ± 16 537 ± 15 568 ± 37 0.8 557 ± 20 553 ± 18 578 ± 16 2: CGCGCGCGCGCG 0.04 633 ± 45 625 ± 41 708 ± 13 0.15 549 ± 16 563 ± 18 623 ± 3 552 ± 35 545 ± 32 665 ± 9 0.15 590.6a 581.3a 625.5a 0.5 537 ± 33 534 ± 31 576 ± 9 0.8 598 ± 12 595 ± 12 654 ± 8 620 ± 15 617 ± 15 668 ± 13 3: GCTATAAAAGGC 0.04 534 ± 16 531 ± 7 680 ± 6 0.15 461 ± 70 440 ± 69 501 ± 7 0.15 473.1a 456.9a 533.1a 0.5 413 ± 21 388 ± 21 452 ± 6 0.8 347 ± 18 363 ± 24 330 ± 4 4: TATCCGCTTAAG 0.04 540 ± 22 540 ± 22 544 ± 5 0.15 502 ± 20 501 ± 19 512 ± 12 a a 0.15 512.0 511.1 506.1a 0.5 494 ± 12 494 ± 11 492 ± 16 0.8 457 ± 30 457 ± 29 498 ± 12 a From Ref. 10.


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Table 3. Curvature of phosphate repulsion and DNA total energy for central 8 base pairs with their sugars and phosphates for bending towards the major and minor groove. Highest values are shown in bold. [KCl] (M) Phosphate Repulsion DNA Total Energy (kcal/(mol deg2)) (kcal/(mol deg2)) Major Minor Major Minor 1: CGCGAATTCGCG 0.04 0.00360 0.00253 0.00404 0.00380 0.15 0.00381 0.00242 0.00411 0.00290 0.5 0.00400 0.00281 0.00437 0.00273 0.00415 0.00362 0.00528 0.00421 0.8 0.00428 0.00216 0.00342 0.00356 0.00532 0.00199 0.00594 0.00437 2: CGCGCGCGCGCG 0.04 0.00282 0.00331 0.00553 0.00492 0.15 0.00396 0.00286 0.00707 0.00460 0.00112 0.00189 0.00359 0.00573 0.5 0.00498 0.00338 0.00577 0.00485 0.8 0.00408 0.00407 0.00550 0.00474 0.00217 0.00129 0.00654 0.00627 3: GCTATAAAAGGC 0.04 0.00467 0.00143 0.00534 0.00454 0.15 0.00345 0.00314 0.00671 0.00521 0.5 0.00489 0.00279 0.00775 0.00393 0.8 0.00442 0.00354 0.00637 0.00469 4: TATCCGCTTAAG 0.04 0.00364 0.00256 0.00699 0.00376 0.15 0.00343 0.00381 0.00421 0.00353 0.5 0.00411 0.00249 0.00451 0.00222 0.8 0.00267 0.00175 0.00372 0.00297


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Captions for the Figures Figure 1. Representative simulation structures for sequence 2; structures of the other sequences were similar. θR and θT values as shown, backbone atoms in gray, base atoms on major groove side in red, on minor groove side in blue. Figure 2. Free energy curves of DNA bending. Columns indicate the KCl concentration, rows the different sequences. Black curves for overall bending, red for bending towards the major groove, blue for bending towards the minor groove; these curves are grey, orange, and cyan, respectively, for the duplicate simulations of sequence 1 and 2. For clarity, error bars are not shown; these were less than 0.2 kcal/mol for bending angles ≤ 50°, and less than 0.5 kcal/mol elsewhere. Figure 3. Comparison of experimental and calculated persistence lengths as function of monovalent salt concentration. Experimental data for λ-bacteriophage DNA as a function of [NaCl] is taken from Ref. 30; the data points show the different models by which the experimental measurements were interpreted (squares: inextensible worm-like chain model, circles: strong-stretching limit; triangles: extensible worm-like chain model).30 Filled downward triangles show calculated data for sequence 1-4 (indicated as S1-S4); unfilled downward triangles show simulation data from Ref. 10. Figure 4. Effect of [KCl] on ΔFeq (A) and the difference in persistence length between minor and major groove bending (B). Data for sequences 1-4 (indicated by S1-S4) are shown in black, red, green and blue, respectively. Lines connect average values; for clarity, error bars in (B) are slightly offset to avoid overlap. Data from Ref. 10 is indicated by thin circles. Figure 5. Electrostatic energy between DNA phosphate groups as a function of the bending angle. The energy is shown for the phosphates of the eight central base pairs and excludes phosphates of the terminal base pairs. Duplicate simulations are shown as thin lines. Figure 6. Total internal energy of DNA as a function of the bending angle. The energy is shown for the eight central base pairs (bases, sugar, and phosphates) and excludes the terminal base pairs. Duplicate simulations are shown as thin lines. Figure 7. Number of water molecules in major and minor groove as function of the bending angle, for bending towards the major and minor grooves. Duplicate simulations are shown as thin lines. Figure 8. Average residence time of water molecules in the major and minor grooves as a function of the bending angle, for bending towards the major and minor grooves. Duplicate simulations are shown as thin lines. Major and minor groove waters as indicated by text in grey; the residence time is significantly larger for minor groove waters.


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Figures

Figure 1


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Figure 2


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Figure 3


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Figure 4


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Figure 5


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Figure 6


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Figure 7


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Figure 8


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TOC Graphic


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Supporting Information for [KCl] Dependence of B-DNA Groove Bending Anisotropy Ning Ma and Arjan van der Vaart* Department of Chemistry, University of South Florida, 4202 E. Fowler Ave. CHE 205, Tampa, FL 33620, U.S.A.

Figure S1. Schematic definition of the rotational step parameters. Grey and white boxes indicate DNA bases; two adjacent base pairs (i.e. a DNA step) are shown.

Figure S2. Comparison of free energy from PME and long-range cutoff method. Simulation results are shown for sequence 1 (Dickerson dodecamer) in 0.15 M KCl. A) 2D free energy surface calculated using PME, B) 2D free energy surface calculated using large cutoff method, C) difference in 2D free energy surface between PME and large cutoff method, D) 1D free energy surface calculated using PME, E) 1D free energy surface calculated using large cutoff method, E) difference in 1D free energy surface between PME and large cutoff method. Free energy surfaces of A-C as a function of ΘR and ΘT; color legend for A-B on the left, for C on the right. Free energy surfaces of D-F as a function of overall bending (black), bending towards major (red), and bending towards minor groove (blue); error bars as indicated.


S1


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Figure S3. Free energy surfaces (in kcal/mol) as a function of ΘR and ΘT (in degrees). Columns indicate the KCl concentration, rows the different sequences. Duplicates are shown on the right. Error bars are not shown for clarity; these were less than 0.4 kcal/mol in all cases.

Figure S4. Electrostatic energy between DNA phosphate groups as a function of the bending angle. Energies are shown for all phosphate groups (including those of the terminal bases). Duplicate simulations are shown as thin lines.


S2

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Figure S5. Total internal energy of DNA as a function of the bending angle. The energy is shown for the entire DNA (including the terminal bases). Duplicate simulations are shown as thin lines.


S3


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Table S1. Curvature of phosphate repulsion and DNA total energy for entire DNA (including the terminal base pairs) for bending towards the major and minor groove. Highest values are shown in bold. [KCl] (M) Phosphate Repulsion DNA Total Energy (kcal/(mol deg2)) (kcal/(mol deg2)) Major Minor Major Minor 1: CGCGAATTCGCG 0.04 0.00429 0.00316 0.00561 0.00513 0.15 0.00439 0.00314 0.00590 0.00557 0.5 0.00432 0.00330 0.00531 0.00395 0.00394 0.00351 0.00625 0.00345 0.8 0.00449 0.00228 0.00416 0.00404 0.00539 0.00181 0.00694 0.00474 2: CGCGCGCGCGCG 0.04 0.00427 0.00319 0.00638 0.00578 0.15 0.00380 0.00344 0.00678 0.00569 0.00309 0.00296 0.00794 0.00700 0.5 0.00496 0.00427 0.00444 0.00545 0.8 0.00439 0.00495 0.00634 0.00612 0.00287 0.00421 0.00965 0.01099 3: GCTATAAAAGGC 0.04 0.00471 0.00214 0.00589 0.00555 0.15 0.00290 0.00588 0.00689 0.00647 0.5 0.00581 0.00559 0.00871 0.00619 0.8 0.00458 0.00887 0.00657 0.00713 4: TATCCGCTTAAG 0.04 0.00453 0.00389 0.00829 0.00423 0.15 0.00284 0.00414 0.00571 0.00408 0.5 0.00474 0.00387 0.00540 0.00366 0.8 0.00325 0.00257 0.00349 0.00332


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Figure 1. Representative simulation structures for sequence 2; structures of the other sequences were similar. θR and θT values as shown, backbone atoms in gray, base atoms on major groove side in red, on minor groove side in blue. 548x570mm (72 x 72 DPI)



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Figure 2. Free energy curves of DNA bending. Columns indicate the KCl concentration, rows the different sequences. Black curves for overall bending, red for bending towards the major groove, blue for bending towards the minor groove; these curves are grey, orange, and cyan, respectively, for the duplicate simulations of sequence 1 and 2. For clarity, error bars are not shown; these were less than 0.2 kcal/mol for bending angles ≤ 50°, and less than 0.5 kcal/mol elsewhere. 701x723mm (72 x 72 DPI)


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Figure 3. Comparison of experimental and calculated persistence lengths as function of monovalent salt concentration. Experimental data for λ-bacteriophage DNA as a function of [NaCl] is taken from Ref. 30; the data points show the different models by which the experimental measurements were interpreted (squares: inextensible worm-like chain model, circles: strong-stretching limit; triangles: extensible worm-like chain model).30 Filled downward triangles show calculated data for sequence 1-4 (indicated as S1-S4); unfilled downward triangles show simulation data from Ref. 10. 652x518mm (72 x 72 DPI)



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Figure 4. Effect of [KCl] on (A) and the difference in persistence length between minor and major groove bending (B). Data for sequences 1-4 (indicated by S1-S4) are shown in black, red, green and blue, respectively. Lines connect average values; for clarity, error bars in (B) are slightly offset to avoid overlap. Data from Ref. 10 is indicated by thin circles. 488x711mm (72 x 72 DPI)


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Figure 5. Electrostatic energy between DNA phosphate groups as a function of the bending angle. The energy is shown for the phosphates of the eight central base pairs and excludes phosphates of the terminal base pairs. Duplicate simulations are shown as thin lines. 875x592mm (72 x 72 DPI)



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Figure 6. Total internal energy of DNA as a function of the bending angle. The energy is shown for the eight central base pairs (bases, sugar, and phosphates) and excludes the terminal base pairs. Duplicate simulations are shown as thin lines. 861x592mm (72 x 72 DPI)


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Figure 7. Number of water molecules in major and minor groove as function of the bending angle, for bending towards the major and minor grooves. Duplicate simulations are shown as thin lines. 1039x675mm (72 x 72 DPI)



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Figure 8. Average residence time of water molecules in the major and minor grooves as a function of the bending angle, for bending towards the major and minor grooves. Duplicate simulations are shown as thin lines. Major and minor groove waters as indicated by text in grey; the residence time is significantly larger for minor groove waters. 1042x681mm (72 x 72 DPI)


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Dependence of B-DNA Groove Bending Anisotropy - ACS Publications

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