Intramolecular Base Stacking of Dinucleoside Monophosphate Anions in Aqueous Solution

Abstract

Time-dependent motions of 32 deoxyribodinucleoside and ribodinucleoside monophosphate anions in aqueous solution at 310 K were monitored during 40 ns using classical molecular dynamics (MD). In all studied molecules, spontaneous stacking/unstacking transitions occured on a time-scale of 10 ns. To facilitate the structural analysis of the sampled configurations we defined a reaction coordinate for the nucleobase stacking that considers both the angle between the planes of the two nucleobases and the distance between their mass-centers. Additionally, we proposed a physically meaningful transient point on this coordinate that separates the stacked and unstacked states. We applied this definition to calculate free energies for stacking of all pairwise combinations of adenine, thymine (uracil), cytosine and guanine moieties embedded in studied dinucleosides monophosphate anions. The stacking equilibrium constants decreased in the order 5’-AG-3’ > GA ~ GG ~ AA > GT ~ TG ~ AT ~ GC ~ AC > CG ~ TA > CA ~ TC ~ TT ~ CT ~ CC. The stacked conformations of AG occurred ten-times more frequently than its unstacked conformations. On the other hand, the last five base combinations showed a greater preference for the unstacked than the stacked state. The presence of an additional 2’-OH group in the RNA–based dinucleoside monophosphates increased the fraction of stacked complexes but decreased the compactness of the stacked state. The calculated MD trajectories were also used to reveal prevailing mutual orientation of the nucleobase dipoles in the stacked state.

Introduction

Stacking interactions between aromatic bases contribute to stabilization of DNA and RNA secondary structures in aqueous solution ¹ and DNA replication fidelity ². The relationships between the chemical properties of nucleobases and their stacking free energies in solution have been thoroughly studied both experimentally ^3-11 and theoretically ^{12-22, 23}. In general, base stacking in nucleic acids is a net outcome of a delicate balance of steric, London and electrostatic forces among the bases and the solvent molecules that is subject to conformational constraints imposed by the phosphodiester linkage ^24-26. Thus stacking of nucleobases should be studied in the proper biological context, including aqueous solution, counterion, dynamical, and entropic effects.

Previous molecular dynamics (MD) studies of ribo- ^16,22, and deoxyribo-dinucleoside monophosphates ¹⁷ indicated that their stacking propensity decrease in the order (5’-XpY-3’): purine-purine > purine-pyrimidine > pyrimidine-purine > pyrimidine-pyrimidine^16,17 and correlated the measured and calculated NMR scalar spin-spin coupling constant to the torsional angles ²². Furthermore, MD and NMR studies of dinucleoside polyphosphates revealed a strong stacking dependence on the length of the backbone¹¹. Investigation of stacking in the adenosine trimer showed stacking cooperativity ²⁷, but this cooperativity does not seem to involve the electrostatic preorganization ²⁸.

In this study, we used classical MD simulations to investigate conformational dynamics of dinucleoside monophosphates (Figure 1) in aqueous solution on a 40 ns timescale. Our examination of the populations of the stacked and unstacked dimer, which is based on a novel definition of the stacking coordinate, yields equilibrium constants for stacking of all 16 deoxyribodinucleoside monophosphates formed by four DNA nucleosides: deoxyadenosine, deoxythymidine, deoxycytidine and deoxyguanosine, and their 16 RNA counterparts from adenosine, cytidine, uridine, and guanosine. Our study provides stacking free energies and activation free energies for unstacking of the dimers and shows that the dipole moments of the bases of d(ApA), d(CpC), d(GpG) and d(TpT) dinucleotides in stacked states self-orient to the twist angle intrinsic to the B-DNA molecule.

Figure 1.

Studied dinucleoside monophosphates; 5’-XY= 5’-d(ApT) is shown as a representative example, hydrogen atoms are not shown.

Methods

MD simulations were carried out at a temperature of 310K in a spherical water droplet of 24 Å radius, which also contained one Na⁺ counterion. Potential energies of solute and solvent molecules were approximated using Amber ff94 ²⁹ and TIP3P ³⁰ molecular mechanical force fields that were implemented in program Q ³¹. Production trajectories of each simulated system were run for 40 ns using 2 fs integration stepsize. The solvent molecules within 3Å of the edge of the simulation sphere were subjected to spherical boundary conditions ^31,32 designed to mimic bulk solvent ³³. The non-bonding interactions of the atoms of the two stacked nucleobase moieties with the remaining part of the simulated system were explicitly evaluated for all distances. Remaining electrostatic and van der Waals interactions were treated explicitly for distances shorter than 10 Å, whereas for distances longer than 10 Å, a local reaction field (LRF) approximation was used ³⁴. The LRF approximation represents an effective alternative ³³ to a more common particle-mesh Ewald method ³⁵.

Initial geometries of the stacked ribodinucleoside and deoxyribodinucleoside monophosphate anions were equilibrated for 75 ps with the temperature gradually increasing from 5 to 310K. Production trajectories of each simulated system were run for 40 ns using 2 fs integration stepsize and SHAKE algorithm. The phosphorus atom was constrained at the center of the simulation sphere using the harmonic potential with a force constant of 50 kcal/mol/Ų. One sodium counter ion was added to the simulated system to achieve overall zero charge. The distance between the phosphorus and sodium atoms was partly constrained by a flat-bottomed half-harmonic potential to prevent Na⁺ ion from entering the area of the sphere subjected to spherical boundary constraints. The flat part of this restraining potential reached from 0 to 20 Å. At these distances the Na⁺ ion did not experience any restraining force. Geometries of all atoms and energy data were saved every 400 and 40 fs, respectively.

The issue of overpopulation by the Amber force field of the g⁺t backbone for the α and γ torsional angles in simulations approaching 100 ns ³⁶ is known to us. However, our simulation time of 40 ns is much shorter. Although sampling of these torsional angles in the aberrant conformation (α≈100° and γ≈-160°) did occur during our MD trajectories, these conformations were not sampled exclusively (Figures 1S - 4S).

Stacking free energies were evaluated from the ratio of the number of stacked (N_stack) to unstacked (N_unstack) configurations as

$$\mathrm{\Delta }G=-\mathit{RT}\ln (\frac{N_{\mathit{Stack}}}{N_{\mathit{Unstack}}})=-\mathit{RT}\ln (K_{\mathit{Stack}})$$ (1)

where K_stack, R and T are the equilibrium constant for stacking, the universal gas-constant, and thermodynamic temperature. This direct approach of calculating K_stack was chosen instead of potential of mean force (PMF) calculations because a relatively small activation and ‘reaction’ free energies for the stacking process allowed both the stacked and unstacked configurations to be sampled in a single unconstrained MD simulation. The stacking coordinate, ξ, was chosen to be proportional to the vertical distance, R_M, between the centers of mass of the two bases (eq 2).

$$\xi =\frac{R_M}{S(\alpha )}$$ (2)

To eliminate T-shaped complexes and to enforce near coplanarity of the stacked bases this distance dependence was modulated by an angular term S(α) (Figure 2).

$$S(\alpha )=e^{-{\alpha }^4}+e^{-{(\alpha -\pi )}^4}+0.1e^{-{(\alpha -0.5\pi )}^4}$$ (3)

where α is an angle (in radians) between the planes of the two bases.

Figure 2.

Angular part of the stacking coordinate (eq 3).

Results and Discussion

The fraction of stacked nucleobase conformations depends on the definition of the stacked state or, in our case, on the transient value of the reaction coordinate for stacking. A straightforward approach is to define this coordinate as a distance between glycosidic nitrogen atoms of the two neighboring bases (R_NN). Norberg and Nilsson, who used this definition in their potential of mean force (PMF) simulations ^16,17, suggested R_NN = 4.5 or 5.0 Å to separate the stacked and unstacked states. While the calculated magnitudes of stacking equilibrium constants were affected by this distance, their order for 16 deoxyribonucleotide monophosphates was not¹⁶.

The use of the distance between glycosidic nitrogen atoms as a stacking coordinate oversimplifies stacking behavior of nucleic acids, which exhibit large structural flexibility. Therefore, Sychrovsky and coworkers ²² included two additional angles in their selection of stacked configurations. In their scheme, only configurations with the angle α between the planes of the two bases of less than 45° were considered as stacked. Additionally, the angle ϕ between the N9-C6 (purine) and N1-C4 (pyrimidine) vectors was required to stay below 60°. The second angular condition eliminated configurations, in which one of the bases would flip out of the DNA or RNA strand but remain parallel to the other base. These angular criteria were complemented by a less restrictive distance cut-off of R_NN < 6.4 Å.

Our design of the stacking reaction coordinate avoids the necessity to limit the angle ϕ by replacing the R_NN distance by the distance between the centers of mass of the two bases (R_M). This is because a parallel flipping of a base out of the double-helix, which may occur at constant R_NN, always increases R_M. In addition, cutoffs in R_NN and α were replaced by a function ξ that depends on both R_M and α via eq. 2. Because the angular term S(α) (eq. 3) has the same broad S(α) = 1 plateau near both α = 0 and 180° (Figure 2) our stacking function treats equally face-to-face and face-to-back orientations of the two bases. The decrease of S(α) that occurs for non-parallel arrangement of the two bases works alongside the increase in R_M; both these geometric changes result in larger ξ. Thus configurations with small and large ξ values correspond to stacked and unstacked conformations, respectively.

The magnitude of ξ fluctuates significantly in the course of simulations as the stacked complexes open and vice-versa. We observed at least one opening and closing event for each of the 32 dinucleotides; these time-dependent structural fluctuations were quantified by counting of each occurrence of a certain ξ value. The resulting histograms of the total number of sampled dinucleotide configurations N(ξ) are presented in Figures 3 and 4. These histograms feature bell-shaped N(ξ) profiles for 3.2 < ξ < 5 Å, followed by a slower decay in the 5 < ξ < 6 Å interval, and a plateau for ξ > 6 Å. Since two non-hydrogen atoms that are not covalently bonded are sterically prevented from coming closer than 3.2 Å, our simulations did not sample any dinucleotide conformation having ξ below this limit. The most tightly stacked conformations are characterized by ξ in the 3.2 - 3.4 Å range. This ξ range agrees well with the average vertical interbase distance of 3.4 Å observed in B-DNA crystals ³⁷. However, since a near-perfect vertical alignment of the base mass-centers, yielding R_M < 3.4 Å, is a rare event only a small fraction of the calculated configurations have ξ in the 3.2 - 3.4 Å range. The majority of the stacked configurations occur for ξ in the 3.8 - 4.4 Å range (Table 1S), which allows the two bases to slide and tilt with respect to each other. Thus, the conformations in this bin feature average vertical separation between their planes of less than 3.6 Å.

Figure 3.

Distribution of the configurations of deoxyribodinucleoside monophosphates in aqueous solution as a function of the stacking coordinate.

Figure 4.

Distribution of the configurations of ribodinucleoside monophosphates in aqueous solution as a function of the stacking coordinate.

The nucleobase chemical structure alters the stacking histograms to a greater extent than the 2’-substituent (H or OH) on the sugar ring (c.f. Figure 3 and 4). On average, the most populated stacked conformations of deoxyribodinucleotides have their ξ values 0.1 Å smaller than the corresponding ribodinucleotides (Table 1). Thus, the 2’-OH group on the sugar seems to be accommodated by a slightly larger slide and tilt of the nucleobases. Judging by the magnitude of N when N(ξ) reaches its maximum (N_max), deoxyribo- and ribodinucleotides have, on average, similar stacking propensity. The T -> U substitution has no effect if the other base is adenine (A), it decreases N_max for GT and CT, and increases N_max for TG and TC dinucleotides. In addition, UU stacking was calculated to occur about two-times more frequently than TT stacking. The reduction in the number of stacked TT complexes is probably due to steric repulsion between their 5’-CH₃ groups.

Table 1.

Calculated structural and thermodynamic parameters for base stacking interactions in dinucleoside monophosphates in aqueous solution at 310 K.

dinucleotidea	d(NpN)b				NpNc
5’-XpY-3’	ξmaxd	Kstacke	ΔGf	ΔGexpg	ξmaxd	Kstacke	ΔGf
ApA	3.9-4.1	5.6	-1.1	-1.5h	4.0-4.2	5.8	-1.1
ApC	3.8-4.0	1.1	-0.1	-0.9h	3.8-4.0	3	-0.7
ApG	3.8-4.0	25.2	-2.0	-1.3i	4.0-4.2	6.7	-1.2
ApX	3.8-4.0	1.5	-0.3	-0.9h	3.8-4.0	2.9	-0.7
CpA	4.0-4.2	0.5	0.4	j	4.2-4.4	0.9	0.1
CpC	4.1-4.3	0.1	1.3	0.1h	4.1-4.3	0.4	0.6
CpG	3.8-4.0	1.2	-0.1	-0.7i	3.9-4.1	1.1	-0.1
CpX	3.8-4.0	0.5	0.4	0.1h	4.2-4.4	0.4	0.6
GpA	3.8-4.0	1.8	-0.4	j	3.8-4.0	9.5	-1.4
GpC	3.8-4.0	2.2	-0.5	j	4.0-4.2	2	-0.4
GpG	3.8-4.0	8.7	-1.3		3.8-4.0	9.1	-1.4
GpX	3.8-4.0	2.9	-0.7		3.8-4.0	2.7	-0.6
XpA	4.0-4.2	1.5	-0.2	j	4.0-4.2	0.9	0.1
XpC	4.0-4.2	0.3	0.6	0.1h	4.0-4.2	1.9	-0.4
XpG	4.0-4.2	2.7	-0.6		4.1-4.3	2.1	-0.5
XpX	4.0-4.2	0.3	0.7	0.1h	4.0-4.2	0.8	0.1

^aX denotes thymine(T) in d(NpN) and uracil(U) in NpN

^bdeoxyribodinucleoside monophosphates (see also footnote g).

^cribodinucleoside monophosphates

^dthe range of the stacking reaction coordinate ξ (Å) (eq. 2) for which N(ξ) reaches a maximum. ξ_max characterizes the structure of the most stable stacked conformations.

^eK_stack= N(stacked)/N(unstacked) = N(ξ < 6 Å)/ N(ξ > 6 Å), where N(ξ) is the total number of configurations that have reaction coordinate ξ in the given range.

^fCalculated stacking free energy (kcal/mol) (T = 298K, eq 1). By comparing ΔG values obtained from the 20 ns and 40 ns trajectories (Table 2S) we estimate that the data presented here are converged to ±0.3 kcal/mol.

^gExperimental free energies at 298K for the association of 1 M deoxyribonucleosides in aqueous solution ^7,38. Because monomers were used in these experiments and the measured free energies refer to the formation of various complexes that may have different geometries (stacked or hydrogen-bonded), molecularity, or protonation state, these data provide only qualitative framework for the comparison with the calculated data.

^hThermal osmometry ⁷

ⁱSolubility measurements ³⁸

^jΔG_exp (5’-YpX) = ΔG_exp (5’-XpY)

Both TT and UU stacking histograms feature a shallow minimum near ξ = 6.4 Å. The corresponding activation barrier for unstacking, which can be estimated from the ratio of number of configurations at the N(ξ) maximum and minimum, is about 1.4 kcal/mol at 310K. Most other dinucleotides do not feature a distinguisheable N(ξ) minimum. However, using a value of N at ξ=6.4 Å as a reasonable transition state approximation we can characterize the unstacking of pyrimidine-pyrimidine- and purine-pyrimidine-containing dinucleotides by the activation free energy of 1 to 2 kcal/mol; a larger activation barrier of about 2 to 3 kcal/mol is characteristic for unstacking of purine-purine dinucleotides.

The presence of the N(ξ) minima or a flat region for ξ > 6 Å makes it reasonable to postulate ξ = 6 Å as the transient point that separates the pools of the stacked and unstacked configurations. Using this transient point allows us to determine equilibrium constants (K_stack) and free energies for stacking (Table 1). The calculated K_stack values are only little affected by shifting the transient point on the reaction coordinate from 6 to 7 Å (Table 1S).

The most stable stacking interaction was calculated for the AG deoxyribodinucleotide (-2 kcal/mol), and GA and GG ribodinucleotides (-1.4 kcal/mol). On the other hand, very weak stacking was obtained for the CC, TC and TT dinucleotides. The large difference between stacking free energies of AG and GA deoxyribonucleotides appears to be structurally related to unfavorable face-to-face geometry (almost no overlap) of nucleobases in GA. In addition, the back-to-face geometries of GA often sample a less advantageous 90° angle between the two nucleobase dipoles (Figure 5). The purine-purine > purine-pyrimidine > pyrimidine-pyrimidine order of the stacking stability agrees well with the results of ab initio¹⁸ calculations in aqueous solution (Table 2). However, lesser agreement, both in relative and absolute terms, was obtained with the results of PMF calculations of Norberg and Nilsson. Their definition of the transient point (R_NN = 5 Å) yields significantly smaller K_stack values because R_NN = 5 Å corresponds to the position of the maximum of N(ξ)²⁸. However, the smaller K_stack calculated for CA ribodinucleotide by us (K_stack = 0.9) than by Norberg and Nilsson (K_stack = 9.6) indicates that differences in the MD trajectory lengths employed in these two studies are also significant.

Figure 5.

Scatter plots of the angles between dipole moments of nucleobase moieties sampled along a 40ns MD trajectory. Representative geometries are drawn to the right. The purple and green arrows represent dipole moments of the 3’ and 5‘ base, respectively. The 3’-deoxynucleoside base is outlined more heavily and is placed anterior to the 5’ deoxynucleoside base. The sugar-phosphate backbones are symbolized by the solid black circles. Only amino group hydrogens are shown. Dipole vectors, |m(A)| = 0.55 eÅ, |m(G)| = 1.40 eÅ, |m(C)| = 1.65 eÅ, |m(T)| = 1.05 eÅ, have been scaled by a factor of three for illustrative purposes.

Table 2.

Comparison of the calculated average free energies (kcal/mol) for dinucleoside monophosphate stacking in aqueous solution.

Dinucleotide	d(NpN)a	NpNa	CHARMMa	Ab initiob
5’-Purine-Purine-3’	-1.2	-1.2	0.2	-0.9
5’-Purine-Pyrimidine-3’	-0.4	-0.6	-0.1	-0.5c
5’-Pyrimidine-Purine-3’	-0.1	-0.1	0.0
5’-Pyrimidine-Pyrimidine-3’	0.8	0.2	1.4	-0.2

^aPresent simulations, d(NpN) and NpN denote deoxyribo- and ribo-dinucleoside monophosphates, respectively.

^bPMF calculations of ribodinucleoside phosphates ¹⁶. Equilibrium constants for stacking that were reported by Norberg and Nilsson for using R_NN < 5Å stacking condition ¹⁶ were converted by us to free energies using eq 1.

^cMP2/6-31+G*/Langevin-dipoles calculations of nucleobase dimers with empirical enthalpy-entropy compensation corrections from DNA melting thermodynamics¹⁸.

^d5’-3’ order of mixed dimers were not distinguished because of the absence of the explicit phosphodiester linkage in the model.

Unfortunately, this theoretical discrepancy cannot be resolved using relevant experiments, because obtaining experimental thermodynamical data for intramolecular stacking of dinucleoside monophosphates has so far presented insurmountable challenge for spectroscopic or calorimetric methods due to low sensitivity of these methods. In fact, it has been easier to determine association thermodynamics for nucleoside monomers (from the observed colligative properties of their aqueous solutions) ^7,38. Interestingly, the calculated free energies are quite close to their experimental counterparts (Table 1) despite the presence of the phosphodiester linkage, a higher temperature (310 K vs 298 K), and a higher effective molarity.

The stacked nucleobases create a net dipole through vector addition of their individual dipoles. According to Onsager solvation model ³⁹ the solvation free energy of the stacked base-pair is proportional to the square of this net dipole moment. Thus, aqueous solvation tends to stabilize a parallel orientation of the nucleobase dipoles. However, this conformation also results in greater repulsion between the individual dipoles. To minimize this dipole-dipole repulsion, an antiparallel orientation should result. Thus, to lower their total free energy in solution, the dipoles of the nucleobases must orient themselves in order to balance dipole-dipole repulsion of the gas phase and net dipole solvation in water ¹². In balancing these terms, an energetic minimum occurs near twist angle between the dipoles of the two bases equal to 30° ¹⁸. To include also the effects of the phosphodiester linkages, we examined mutual orientation of dipole moments of the stacked bases (Figure 5). We found that AA, CC, GG and TT dinucleotides that are stacked in face-to-back orientation favor twist angles between 20° and 60°, the direction that is consistent with the right-handedness of B- and A-DNA. An important role in the preferential stabilizing of these conformations is probably played by both the phosphodiester linkage and electrostatic interactions, whereby contributing to the observed 36-degree helical rotation per step in B-DNA or 33-degree rotation in A-DNA. Ab initio investigation of stacking in DNA base-pair steps as a function of angular twist show clear energetic minima around an average of 34° and 3.5 Å, in agreement with this study ⁴⁰, although specific sequence can influence the preferred twist angle in the presence of the backbone linker ⁴¹. Thus, the observed trend could be further reinforced when polarizable force fields or solutions with higher ionic strengths are were considered in explicit simulations.

Base flipping that occurred during the MD simulations of all dinucleotides resulted in two separate populations of twist angles. The face-to-back population features smaller twist angles whereas the larger angles occur for face-to-face or back-to-back stacking arrangement, in which one base is flipped around its glycosidic bond. Two distinct twist-angle populations occur in most dinucleotides with the exception of TA, TG, TC and CA dinucleotides (Figure 5).

In conclusion, past studies have shown that van der Waals or dispersion forces determine the strength of stacking interactions in aqueous solution ^15,18,42. Our results indicate that electrostatic interactions help to determine the specific twist angle in the stacked complexes. The stacking free energies presented here may serve as benchmarks for calibration of the simplified force fields and solvation models for nucleic acids.