Molecular Dynamics Study of the Hybridization between RNA and Modified Oligonucleotides

Abstract

MicroRNAs (miRNAs) are attractive drug candidates for many diseases as they can modulate the expression of gene networks. Recently, we discovered that DNAs targeting microRNA-22–3p (miR-22–3p) hold the potential for treating obesity and related metabolic disorders (type 2 diabetes mellitus, hyperlipidemia and non-alcoholic fatty liver disease (NAFLD)) by turning fat-storing white adipocytes into fat-burning adipocytes. In this work, we explored the effects of chemical modifications, including phosphorothioate (PS), locked nucleic acid (LNA) and peptide nucleic acid (PNA), on the structure and energy of DNA analogs by using molecular dynamics (MD) simulations. To achieve a reliable prediction of the hybridization free energy, the AMOEBA polarizable force field and the free energy perturbation technique were employed. The calculated hybridization free energies are generally compatible with previous experiments. For LNA and PNA, the enhanced duplex stability can be explained by the preorganization mechanism, i.e. the single strands adopt stable helical structures similar to those in the duplex. For PS, the S and R isomers (Sp and Rp) have preferences for C’2-endo and C’3-endo sugar puckering conformations, respectively, and therefore Sp is less stable than Rp in DNA/RNA hybrids. In addition, the solvation penalty of Rp accounts for its destabilization effect. PS-LNA are similar to LNA as the sugar puckering is dominated by the locked sugar ring. This work demonstrated that MD simulations with polarizable force fields are useful for the understanding and design of modified nucleic acids.

Graphical Abstract

Introduction

Oligonucleotide Therapeutics (ONTs) hold great potential for treating various diseases, including those lacking druggable targets for conventional small-molecule drugs.¹ The target for ONTs is largely determined by its base sequence, which opens the possibility of rational design and rapid development of ONT drugs.² ONTs can interfere with gene expression through several mechanisms, such as antisense oligonucleotides (ASOs), small interfering RNAs (siRNAs), microRNA (miRNA) mimics, anti-microRNAs (antagomirs), or DNA-targeting triplex-forming and strand-invading ONTs.¹ Several ASO drugs have been approved by the Food and Drug Administration (FDA),³ siRNA and miRNA drugs have entered clinical trials, while other ONT drugs are under active research and development.¹

MiRNAs are small non-coding RNAs encoded in the genome that regulate post-transcriptional gene expression by binding to complementary target mRNAs.^4–5 Over 2000 human miRNAs have been discovered and they are estimated to regulate more than half of genes of the human genome.⁶⁷ Dysregulation of miRNAs is a common feature in cancer, central nervous system diseases, inflammation, cardiovascular diseases and metabolic disorders, suggesting the therapeutic potential of miRNA targeting. In addition, miRNAs typically have hundreds of mRNA targets within cellular networks, which means the entire pathway can be modulated by targeting miRNAs.^6–7 There are two strategies for modulating miRNA activity: restoring miRNA activity by synthetic miRNA mimics and inhibiting miRNA activity by complementary antagomirs or miRNA sponges.^{6, 8} Recently, we and other groups discovered that miRNAs play roles in brown adipogenesis and antagomirs targeting miRNAs are promising for treating obesity and related metabolic disorders.^9–13

To achieve favorable pharmacokinetic properties and clinical efficacy, the chemical structure of oligonucleotides (ON), including backbone, sugar, nucleobase and terminals, needs to be optimized.² Chemical modifications of RNA and DNA in nature have long been recognized.¹⁴ Notably, the 2’-O-methylation of RNA improves the binding affinity and nuclease resistance.² Various synthetic modifications have also been developed. Phosphorothioate (PS) is the first synthetic chemical modification which increases nuclease resistance.² Each PS modification introduces a chiral center and the stereoisomers have different thermodynamic properties and clinical efficacy.^15–17 Locked nucleic acid (LNA) enhances binding affinity through preorganization.² Peptide nucleic acids (PNAs) are ON analogs where the sugar and phosphate backbone is replaced by a peptide-like scaffold, which imparts resistance to nuclease and proteases and strong binding affinity.^18–19 Despite its neutral charge, PNA cannot be readily taken up by cells, and conjugation to peptides is used for cellular delivery.^19–20 Figure 1 lists examples of the common chemical modifications.

Figure 1.

Common chemical modifications of nucleic acids.

Molecular modeling techniques, in particular molecular dynamics (MD) simulations, have been valuable tools for understanding the energetic and structural properties of modified nucleic acids since the early years of their discovery.^21–28 The effects of sequence and chirality on PS-modified oligonucleotides (ONs) were analyzed through simulations.^{23, 29–31} The destabilization of PS-DNA/DNA duplex by R-isomer PS (abbreviated Rp, and similarly for Sp) was explained by the stiffness of the backbone and the steric repulsion between the sulfur atom and the C-H group of sugar.^30–31 Rp and Sp were also shown to have the opposite effects on minor groove width.²⁹ The conformation and solvation of LNA were analyzed and compared with those of DNA and RNA.^32–35 LNA induced C’3-endo conformation of its complementary DNA strand, indicating its strong preference for A-form conformation.³² The inter-strand phosphate distances in LNA-containing duplexes were longer than those in DNA-RNA and RNA-RNA distances while the intra-strand phosphate distances in LNA-containing duplexes were shorter.³² The effect of LNA on triplex-forming ONs was also investigated.^36–37 The structure of PNA-DNA and PNA-RNA duplexes, as well as PNA single strands, were studied.^{21–22, 38–39} It was found that the PNAcontaining duplexes adopt different helical forms from the canonical A- or B-form, and the backbone of PNA is more flexible which may contribute to the duplex stability.^21–22 By using MD simulations with enhanced sampling technique, Verona et al. showed that functionalization of PNA backbone can facilitate preorganization of single strand and further enhance duplex stability.³⁸

Despite the development and application of MD in various modified nucleic acids,^40–43 recent studies^44–46 have pointed out the deficiency of the energy functions (also called force field) for MD simulations of nucleic acids. MD simulations of RNA tetranucleotides using several versions of the AMBER force field favored the unphysical intercalated conformations,⁴⁶ which were also observed in PNA simulations.³⁸ Traditional force fields employed by previous simulations lack some essential features in nucleic acid interactions, such as polarization and anisotropic electrostatics.^47–48 By including explicit terms to represent these features, polarizable force fields can significantly improve the accuracy of MD simulations.^49–53 Recently, we have shown that the AMOEBA force field^54–55 accurately predicts binding free energies even for challenging systems such as phosphate and calcium binding.^56–59 The base-base stacking and hydrogen bonding interactions described by AMOEBA are also systematically improved compared to the traditional force field.^{49, 51}

In this work, we extended the AMOEBA force field to study the hybridization between modified nucleic acids and an RNA target. We considered both the structural properties and binding free energies. Our analyses revealed insights into the factors contributing to duplex stability. Free energy perturbation (FEP) with MD simulations has been a standard approach for predicting drug potency and for evaluating simulation protocol. Calculations of hybridization free energy by FEP^60–62 or approximate approaches^63–64 such as MM/GBSA⁶⁴ or structure-property relationships^65–66 have been reported previously. Here we first validated our force field on PS systems with available experimental data. Then we took the antagomirs targeting miR-22–3p as an example to study the effect of chemical modifications by using FEP. Modifications under study include PS with different stereoisomers, LNA, combinations of LNA and PS, and PNA.

Methods

Force field.

The AMOEBA nucleic acid force field^{50, 55} was used for unmodified DNA and RNA. For chemical modifications not covered by the force field, the established protocol was followed to derive parameters.^{57, 67–68} The POLTYPE program was used to generate the initial parameters.⁶⁹ The structures were optimized at the MP2/cc-pVTZ level. Atomic multipole moments were initially assigned from QM electron density calculated at the MP2/6–311G** level via Stone’s distributed multipole analysis⁷⁰ and then optimizations were done with Tinker’s POTENTIAL program to fit to electrostatic potential calculated at MP2/aug-cc-pVTZ level. The van der Waals parameters for sulfur were optimized to capture the ligand-water interaction energy at different orientations calculated at the MP2/CBS level extrapolated from aug-cc-pVTZ/QZ. The fitting results are shown in Figure S1. The torsional parameters for PS were manually fitted by reproducing QM energy at the wB97x-D/6-311++G(2d,2p)/PCM level. Both QM and AMOEBA calculations were with implicit solvation (PCM or GK) and at the same QM-optimized geometry. Quantum mechanics calculations (QM) were performed using Gaussian 09⁷¹ and psi4 program.^72–74 All molecular mechanics (MM) calculations were performed using TINKER 8 Software.⁷⁵

Molecular dynamics simulations.

Three sequences were simulated. (a) Double-strand hexamer DNA/RNA or DNA/DNA with two consecutive PS modifications on the DNA strand,⁷⁶ termed as PS-6. (b) Double-strand decamer DNA with one PS modification on each strand,¹⁶ termed as PS-10. (c) Fragments of miR-22–3p (miR-22 for short) containing 8–12 nucleotides and their complementary DNA strand with PS, LNA and/or PNA modifications. The structures of the PS10 were taken from the Protein Data Bank (PDB: 5J3F and PDB: 5J3I). Structures of other sequences were first generated by the make-na server (http://structure.usc.edu/makena/server.html) and then mutated to the modified structures by using an in-house script. The helical conformation was A-form for DNA-RNA hybrids and B-form for DNA duplexes. Single strand structures were extracted from their respective double strands. The duplexes or single strands were neutralized by sequentially adding Na+ ions to the grid point with the lowest electrostatic potential calculated by TINKER POTENTIAL program. The neutral complexes were solvated in periodic cubic water boxes of 74×74×74 ų such that the distance between the ON and its periodic images were at least 30 Å. NaCl was added to yield 0.15 M salt concentration.

The systems were gradually heated up to 298 K in 1 ns, then 0.5 ns NPT simulations at 298 K and 1 atm were performed to determine the equilibrium density. Production runs were in the NVT ensemble at 298 K.

The MD simulations were propagated by using the RESPA integrator⁷⁷ with a 3.0 fs time step and hydrogen-mass repartition.⁷⁸ Temperature and pressure were controlled by Bussi thermostat⁷⁹ and Monte Carlo barostat,⁸⁰ respectively. The van der Waals (vdW) iterations used a 12.0 Å cutoff, while the electrostatic interactions were treated by PME with a real-space cutoff of 7.0 Å. All molecular dynamics simulations were run using the Tinker-OpenMM program^{75, 81} on GPU.

Free energy calculation.

The relative hybridization free energies were calculated by the alchemical transition method.^{68, 81} The relative hybridization free energy ΔΔG_hyb can be expressed as

$$\Delta \Delta G_{hyb}=\Delta G_{\text{complex}}-\Delta G_{\text{solv}}$$ (1)

where ΔG_complex is the free energy change for mutating unmodified ONs to modified ONs in the duplex, and ΔG_solv is the free energy change of mutation of the single strand in solution. The thermodynamic cycles are shown in Figure S2 and S3. A series of artificial states, parameterized by λ, connecting the unmodified and modified states were created by interpolating the force field parameters. We used the notation that λ=0 corresponds to unmodified ONs and λ=1 corresponds to modified ONs. The free energy changes between adjacent states was estimated by the Bennett acceptance ratio (BAR) method.^82–84

For PS and LNA, ΔΔG_hyb due to the chemical modifications were calculated by the single topology approach, where the topology contains all connectivity information necessary for defining the two states, and only force field parameters changes during the alchemical transition.³⁵ The spacing of the alchemical states were chosen with the principle that the statistical errors for all steps are similar and therefore the computational resource is not wasted in well-sampled steps. For DNA to PS transition, the bonded and non-bonded parameters of the phosphate group were changed to those of the PS group. Linear interpolation of force field parameters was founded to be sufficient. For the mutation with 7 PS modifications, the lambda values were 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0; for the mutation with 4 or fewer PS modifications, there were 11 states equally spaced between 0 and 1. For DNA to LNA transition, it consists of increasing the non-bonded parameters and force constants of bonded parameters from zero to finite values. The following scheme for creating the C6’-O2’ bond in LNA was used to accelerate the convergence of free energy. For the bond parameters, first the force constant was exponentially increased from 0.0001 to ~5 kcal/mol/Ų accompanied by an exponentially decrease in bond length from the distance in DNA (~5 Å) to the equilibrium bond length in LNA (1.4565 Å), such that the change in equilibrium bond length at each step is inversely proportional to the force constant; then the force constant was linearly increased. For the angle parameters, the force constant was first exponentially increased from 0.0001 to 1 kcal/mol/deg² and then linearly increased to the desired value, while the equilibrium angle remained the same. For the dummy atoms H6’1 and H6’2, first the vdW lambda was linearly increased from 0 to 1 with softcore potential and electrostatic lambda was kept at 0; then the electrostatics lambda was linearly increased from 0 to 1. The lambdas for all the other parameters were linearly varied from 0 to 1. The lambda spacing was subject to further adjustment where necessary. Detailed settings are listed in Table S1. In total, 29 states were simulated for a smooth transition from DNA to LNA. For the combination of PS and LNA, ΔΔG_hyb was calculated as the sum of free energy change from DNA to LNA and the free energy change from LNA to PS-LNA. The simulations at all alchemical states started from the same initial structure. 10 ns simulations were performed for each state; the first 4 ns simulations were to allow for conformational reorganization, and the last 6 ns trajectories were used to calculate free energy and analyze structures. Two independent sets of simulations for the solvation free energy were conducted to better estimate the statistical error.

For PNA, since it shares few atoms in the backbone with DNA, the relative free energy calculation using the single topology approach is not efficient. Instead, the relative hybridization free energy between PNA octamer and dodecamer was computed by sequentially growing one nucleotide at a time. The same procedure could be used for DNA; however, because growing DNA involves a change in net charge, the free energy calculation would have some artifacts that are nontrivial to correct.⁸⁵ Therefore, the DNA and RNA hybridization free energies calculated by Mfold^86–87 were used for qualitative comparison. A total of 24 states were simulated for growing one nucleotide. First, the electrostatics lambda was kept at 0 while the vdW lambda was increased as 0, 0.5, 0.55, 0.58, 0.61, 0.64, 0.67, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, 1.0; then the electrostatics lambda was increased linearly from 0 to 1 in 10 steps. The choice of vdW and electrostatic lambdas were similar to that used for the calculation of protein-ligand binding free energy.^{58, 88} 6 ns simulations were performed for each state and the last 4 ns were used for analysis. Two independent sets of simulations for the complexation free energy were conducted. Representative structures from the end of simulations are included in the SI.

Results and Discussions

1. Double-strand hexamers and decamers with PS modifications

We first present our simulation results of the double-strand hexamers (PS-6, Figure 2) and decamers (PS-10, Figure 2) and compare them with experimental data. These two systems were chosen because they have few modifications (one or two PS modifications per strand), and experimental melting temperature data for DNA/PS-DNA and RNA/PS-DNA, as well as different stereoisomers are available. They serve as model systems to study the effect of PS modifications and to validate our force field.

Figure 2.

Structure of the (A) PS-6 [Rp,Rp]-DNA/RNA and (B) PS-10 Sp-DNA/Sp-DNA systems. The nucleotides connected to PS are shown in sticks, while others are shown in cartoon representation. The coordinates of PS-10 were taken from the Protein Data Bank (PDB: 5J3I).

The calculated relative hybridization free energies and experimental melting temperatures (Tm) are listed in Table 1 and Table 2. The melting temperature data suggests that in the case of PS-6, Sp modification is less stable than Rp modification for DNA/DNA duplex and the contrary is true for DNA/RNA, while both Sp and Rp are less stable than an unmodified duplex. For PS-10, Sp modification is more stable than unmodified DNA/DNA while Rp is less stable than the unmodified duplex. The trend between Sp and Rp modifications for DNA/DNA and DNA/RNA systems has also been confirmed by other experimental studies,^{15, 17} with the exception that the trend for dT-rich PS-DNA/DNA duplexes can be reversed.¹⁵ Our free energy calculations reproduced the relative stability between Sp and Rp for all three DNA/DNA or DNA/RNA systems. However, for PS-6, the calculated relative hybridization free energies have different signs for the two isomers, which is inconsistent with the experiment. Possible sources of the inconsistency include: (1) the fact that melting temperature and binding free energy at room temperature may not always agree; (2) force field error, in particular the error of torsion parameters which may favor the duplex conformation of the Sp isomer too much.

Table 1.

Comparison of experimental melting temperature and simulated relative hybridization free energy for the PS-6 system with sequence 5’-CGU(T)AGC-3’, 3’-GC_psT_psACG-5’.

Strand 1	Strand 2	Expt. Tm (°C)76	AAGhyb (kcal/mol)	sd (kcal/mol)
	DNA	44	0
	[Sp, Sp]-DNA	42	−2.03	0.42
DNA	[Rp, Rp]-DNA	40	1.23	0.45
	DNA	43	0
	[Sp, Sp]-DNA	38	0.27	0.42
RNA	[Rp, Rp]-DNA	42	−1.20	0.45

Table 2.

Comparison of experimental melting temperature and simulated relative hybridization free energy for the PS-10 system with sequence 5’-CG_psGCCGCCGA-3’, 3’-GCCG_psGCGGCT-5’.

Strand 1	Strand 2	Expt. Tm (°C)16	ΔΔGhyb (kcal/mol)	sd (kcal/mol)
DNA	DNA	76.55	0
Sp-DNA	Sp-DNA	77.53	−1.35	0.48
Rp-DNA	Rp-DNA	71.99	0.95	0.56

The structures of the duplexes were analyzed in terms of the helical, backbone and groove parameters calculated by the Curves+ program.⁸⁹ The structures of Rp and Sp modifications are both identical to those of the unmodified duplexes, which is consistent with NMR data.¹⁶ Therefore the effect of 1–2 PS modifications on the backbone is not strong enough to alter the conformational preferences of the duplexes.

The conformations of the modified single strands exhibit large variations. The optical tweezer experiment indicated that single-strand DNA (ssDNA) has an extended structure with persistence length similar to A-form;⁹⁰ it has also been postulated that ssDNA structure consists of random coil and stacking.⁹¹ In our simulations, both the unmodified and modified PS-6 ssDNA experienced unstacking between some of the bases. Preferences of PS modifications for sugar puckering conformations were identified. The sugar puckering conformation was characterized by the pseudo-rotation angle P.⁸⁹ The north conformation near 0 deg indicates C3’-endo, which is typical for A-form, while C2’-endo near 180 deg is typical for B-form. The sugar puckering conformations for PS-6 are compared in Figure 3. It can be seen clearly that Sp modifications prefer B-form and Rp modifications prefer A-form. As reported in a previous study, this is due to the steric repulsion between sulfur and the CH group of deoxyribose.³⁰ The sugar puckering conformation of unmodified ssDNA is between those of Rp and Sp modifications. The influence of the PS modifications on sugar puckering extends beyond the sugars adjacent to the PS. For example, the modifications are on the C8/T9 and T8/A10 linkages, while the sugar puckering of C11 is also affected.

Figure 3.

Sugar puckering conformation in the PS-6 single strand simulations. “PO” means unmodified phosphate linkage. “Sp” and “Rp” mean the two isomers of PS modification. “*” denotes the nucleotide with PS modification on 5’-end. The sugar puckering conformation is measured by pseudo-rotation angle P. An angle near 0 deg means the north conformation or C3’-endo, while an angle near 180 deg means the south conformation or C2’-endo.

For PS-10, both single strands were simulated. The modified and unmodified ssDNA showed either extended structures with partial unstacking or compact structures with hydrogen bonds between nucleobases and phosphate linkages. No systematic trends in the global conformation were observed between the isomers and the unmodified ssDNA. Similar to the case of PS-6, PS modifications also influence the sugar puckering conformation (Figure 4), i.e. Sp prefers B-form and Rp prefers A-form.

Figure 4.

Sugar puckering conformation in the PS-10 single strand simulations. The definition is in Figure 3 caption.

The preferences of Sp and Rp for different sugar puckering conformations in single strands explain their relative duplex stability. DNA/DNA duplexes have B-form conformations, so Sp is more stable; DNA/RNA duplexes are in A-form, so Rp is more stable. Our finding is consistent with a previous theoretical study which showed the stabilization/destabilization effect of Sp/Rp modifications on the backbones of DNA/DNA duplexes.³⁰

2. PS and PS-LNA antagomirs

After validation of our simulation protocol on PS-6 and PS-10, we investigated the effects of PS and LNA on the antagomirs. The target, 5’-AGCUGCCA-3’, is an octamer RNA taken from the 2–9 nucleotide of miR-22. The antagomirs are complementary DNAs with PS and/or LNA modifications. The calculated hybridization free energies relative to unmodified DNA/RNA are shown in Table 3. The simulation systems include full PS modifications on all nucleotides with Sp, Rp or alternating Sp and Rp isomers, full LNA modifications, full LNA modifications with partial PS modifications on two ends, full LNA and PS modifications, partial LNA modifications on two ends, partial LNA and partial PS modifications on two ends. The hybridization free energies ΔΔG_hyb were difficult to converge especially for PS modifications, because of the flexibility of the single strands. The standard deviations of ΔΔG_hyb estimated by the block average method, which provide lower bounds if the sampling is inadequate, are 1–2 kcal/mol. Nevertheless, some general trends of ΔΔG_hyb can be observed. The PS modifications either destabilize or have little effect on the duplex. The full Sp isomer has the strongest destabilization effect with a ΔΔG_hyb of +3.9 kcal/mol, while the full Rp isomer and mixed isomers have similar weak effects. The relative stability between full Sp and full Rp isomers is consistent with the simulation results on PS-6 and PS-10 systems as well as previous experimental results of full PS modifications on other DNA/RNA duplexes. It is also clear that the effects of Sp and Rp are not additive: the free energy does not correlate with the fraction of Rp in all PS modifications.

Table 3.

Computed relative hybridization free energies between miR-22 and antagomirs with PS, LNA or PS-LNA modifications.

ID	Antagomir sequence	Description	ΔΔGhyb (kcal/mol)	sd (kcal/mol)
A-0	5’-dT-dG-dG-dC-dA-dG-dC-dT-3’	DNA	0	--
A-11	5’-dTSpdGSpdGSpdCSpdASpdGSpdCSpdT-3’	Sp 7	3.9	1.9
A-12	5’-dTRpdGRpdGRpdCRpdARpdGRpdCRpdT-3’	Rp 7	0.4	2.0
A-13	5’-dTSpdGRpdGSpdCRpdASpdGRpdCSpdT-3’	Sp 4 Rp 3	0.9	2.0
A-14	5’-dTRpdGSpdGRpdCSpdARpdGSpdCRpdT-3’	Sp 3 Rp 4	−0.4	1.8
A-20	5’-lnT-lnG-lnG-lnC-lnA-lnG-lnC-lnT-3’	Ln 8	−3.2	1.1
A-21	5’-lnTSplnGSplnG-lnC-lnA-lnGSplnCSplnT-3’	Ln 8, Sp 4	−3.7	1.2
A-22	5’-lnTRplnGRplnG-lnC-lnA-lnGRplnCRplnT-3’	Ln 8, Rp 4	−2.4	1.6
A-31	5’-lnTSplnGSplnGSplnCSplnASplnGSplnCSplnT-3’	Ln 8, Sp 7	−2.6	2.4
A-32	5’-lnTRplnGRplnGRplnCRplnARplnGRplnCRplnT-3’	Ln 8, Rp 7	−2.8	2.2
A-40	5’-lnT-lnG-dG-dC-dA-lnG-lnC-lnT-3’	Ln 5	−1.4	0.7
A-41	5’-lnTSplnGSpdG-dC-dA-lnGSplnCSplnT-3’	Ln 5, Sp 4	−3.2	0.9
A-42	5’-lnTRplnGRpdG-dC-dA-lnGRplnCRplnT-3’	Ln 5, Rp 4	−1.6	1.2

The LNA modifications all stabilize the duplex. The ΔΔG_hyb introduced by 8 LNAs (−3.2 kcal/mol) is larger than that of ΔΔG_hyb for 5 LNAs (−1.4 kcal/mol). The combinations of LNA and PS are also more stable than unmodified DNA/RNA. PS modifications have smaller effects on LNA than on DNA, consistent with a previous experimental study.⁹² Sp-LNA is more stable than Rp-LNA, which is different from the trend in pure PS modifications.

The conformations of the full Sp and Rp single strands resemble B-form and A-form except for the flipping of terminal bases (Figure 5, Figure 6), respectively. This is reflected by their sugar puckering (Figure 7). The mixed isomers (A-13 and A-14) have more disordered structures, likely due to the mismatch between adjacent sugar puckering conformations. For comparison, ssDNA has extended structure with partial unstacking, which is compatible with a previous optical tweezer study that ssDNA is more extended than B-form.⁹⁰ The sugar puckering distribution in ssDNA is also broader than that of PS. In duplexes, due to the constraint on the helical structure, the sugar puckering of PS-DNA and DNA is mostly C3’-endo, while Sp modifications have slightly higher fractions of C2’-endo conformation.

Figure 5.

Structures of DNA and PS antagomirs from MD simulations. The structures from left to right are (A) DNA/RNA, (B) DNA, (C) Sp, (D) Rp and (E) mixed Sp/Rp isomer, corresponding to A-0, A-0, A-11, A-12, and A-14, respectively.

Figure 6.

Solvation structures of the 3’-terminal bases of DNA and Rp antagomir (A-12) from MD simulations. In the duplex, the sulfur atoms are not well solvated (B) due to the steric effect of nearby nucleobases compared to DNA (A). In the single strand (C), the steric effect on solvation is less severe since the backbone is more flexible. For example, the sulfur atoms can have close interaction with nucleobases, which compensates for the under-solvation. Therefore, the under-solvation leads to a penalty for duplex formation.

Figure 7.

Sugar puckering conformation in the simulations of antagomirs A-0, A-11, A-12, A-13 and A-14. The five antagomirs are labeled as PO, Sp7, Rp7, Sp4Rp3, Sp3Rp4, respectively. The definition is in Figure 3 caption.

The preferences of Sp and Rp for different sugar puckering conformations are in line with their relative stability for hybridization. However, the Rp/RNA hybrid is not more stable than DNA/RNA hybrid even though single strand Rp is more ordered. The solvation structure around PS modifications also affects its duplex stability. The sulfur atoms of Rp in duplex, pointing towards the major groove, are not well solvated due to its bulky size and steric hinderance of neighboring bases, so the PS linkage in the duplex is less favorable than the phosphate linkage. In single strands, the sulfur atoms can form close contact with the nucleobases (e.g. C7 and T8, see Figure 6) to compensate for the under-solvation.

Since the sugar in LNA is locked in A-form, single strands containing full LNA modifications (A-20, A-21, A-22, A-31, A-32) maintain helical structures resembling that in the duplex. The sugar puckering has a narrow distribution near C3’-endo, consistent with previous MD simulations.³³ The single strand with 5 LNAs (A-40) also has a regular A-form structure, while the partially modified PS-LNA single strands (A-41, A-42) has base-base unstacking at the junction between LNA and DNA nucleotides. This can be attributed to the steric interaction between PS and the locked sugar and the flexibility of the deoxyribose.

The relatively weak effects of PS on LNA is due to the conformational stability of LNA. Since the sugar puckering in LNA is always A-form, PS modifications on LNA does not affect the hybridization free energy by altering the sugar puckering conformations. For Rp-LNA, the under-solvation penalty similar to Rp-DNA (Figure 6) was also observed, although this effect is weaker because of the conformation restraint of LNA.

3. PNA antagomirs

PNAs have distinct features from unmodified or modified nucleic acids such as the neutral charge and flexibility of the backbone. The structural dissimilarity between PNA and DNA also poses a challenge for directly computing the relative free energy by using the single topology approach. We calculated the hybridization free energy change for increasing the length of the PNA antagomir from 8 to 12. In addition, the calculation of free energy involving a change in net charge can be problematic.^{85, 93} Therefore, the simulation results for PNA were compared with empirical data for DNA/DNA and RNA/RNA hybridization obtained from the Mfold server.^86–87 DNA/RNA hybrids are generally less stable than RNA/RNA duplex and similar to DNA/DNA duplex. Exceptions are that the stability of DNA/RNA hybrids with a high pyrimidine fraction in DNA is close to that of RNA/RNA duplex.⁹⁴

As shown in Table 4, the lowering of free energy due to growing four nucleotides to PNA/RNA hybrid is even larger than that for RNA/RNA duplex. The free energies of adding single nucleotides for RNA/RNA and DNA/DNA duplexes predicted by Mfold are relatively uniform, whereas the free energies for PNA/RNA vary significantly. The free energy change of PNA/RNA correlates with the type of nucleobases. When stacking between two purines is formed (from 10 to 11), there is substantial stabilization effect; when stacking between two pyrimidines (from 8 to 9) or between a pyrimidine and a purine (from 9 to 10 or from 11 to 12) is formed, the free energy gain is less significant. This result suggests that PNA can enhance the stacking between nucleobases.

Table 4.

Comparison of hybridization free energies (kcal/mol) relative to those of octamers from simulations and Mfold. The sequence of the target strand is 5’-AAGCU(T)GCCAGU(T)U(T)GA-3’. SD is the standard deviation.

Length	Sequence	Mfold86–87		Simulation
		RNA/RNA	DNA/DNA	PNA/RNA	SD
9	5’-CT(U)GGCAGCT(U)-3’	−1.68	−1.97	−0.66	0.45
10	5’-ACT(U)GGCAGCT(U)-3’	−3.56	−3.20	−2.33	0.50
11	5’-AACT(U)GGCAGCT(U)-3’	−5.39	−4.84	−6.48	0.53
12	5’-CAACT(U)GGCAGCT(U)-3’	−6.63	−6.16	−7.24	0.58

The PNA single strands showed A-form-like helical structures (Figure 8). The helical structures were stable even after extended 60-ns simulations. In contrast, DNA single strands adopted Bform-like extended conformations (Figure 5B and 7). The preorganization of the PNA single strands could explain the stability of the PNA/RNA duplexes. Previous MD simulations of PNA single strands using the AMBER force field (ff19SB and parmbsc0 parameters) produced intercalated and unstacked structures.^{27, 38} As noted by Bergonzo et al.,⁴⁶ the intercalated structures may be an artifact of those AMBER force fields and they are not specific to PNA. More recent developments of the AMBER force fields have eliminated the artificial intercalated structures by using improved water models and/or tuning phosphate-sugar interactions.^95–96 NMR data on a hexamer single-strand PNA indicate slow exchanges between cis and trans conformations of the amide bond χ1,⁹⁷ which could be beyond the time scale of our MD simulations.

Figure 8.

Structures of dodecamer single-strand PNA (B) and PNA/RNA hybrid (A) from MD simulations.

The helical parameters of the PNA single strands are similar to those of the PNA/RNA hybrids, both of which resemble typical A-form DNA/RNA hybrids (Table 5). It should be noted that in general X-ray crystal structures of ONs are more reliable than NMR structures, although they are also affected by crystalline packing and ensemble averaging. Compared to the PNA/RNA hybrids, the PNA single strands have larger incline and tip angles and axis bending. PNA single strands are also more flexible than the hybrids as evidenced by the larger standard deviations.

Table 5.

Structural parameters of single-strand PNA and PNA/RNA hybrid from MD simulations. SD is the standard deviation between all bases and conformations. The parameters for several experimental structures are also listed for comparison. Ax-bend is the total axis bending angle divided by the number of base steps. The parameters were calculated by Curves+.⁸⁹

		Expt.			MD
	DNA/RNA	PNA/RNA		PNA/PNA	PNA		PNA/RNA
	(PDB: 1PJG)	(PDB: 176D)	(PDB: 5EMF)	(PDB: 1PUP)	Mean	SD	Mean	SD
Xdisp (Å)	−3.41	−3.60	−5.81	−7.87	−5.31	2.20	−6.01	0.85
Ydisp (Å)	−0.56	0.85	1.76	−0.05	1.23	2.34	0.95	0.78
Incline (°)	12.90	7.20	11.10	7.50	17.73	12.23	12.58	6.29
Tip (°)	1.40	−2.40	−0.70	−0.50	6.76	14.53	3.63	5.79
Ax-bend (°)	2.78	0.72	1.74	1.24	2.63	1.45	1.08	0.56
Shift (Å)	0.02	−0.42	−0.88	0.03	−1.11	1.79	−0.65	0.50
Slide (Å)	−1.20	−1.61	−2.08	−2.51	−1.86	0.92	−2.19	0.40
Rise (Å)	3.23	3.39	3.29	3.35	3.30	0.58	3.23	0.35
Tilt (°)	−0.90	2.60	0.00	0.30	−2.34	10.26	−1.53	6.11
Roll (°)	7.30	3.70	5.00	2.70	7.02	7.72	5.89	5.87
Twist (°)	31.40	30.00	24.50	20.00	26.69	17.41	25.22	4.51
Buckle (°)	−5.50	1.80	1.70	0.10	-	-	−1.36	6.83
Propeller (°)	−10.50	−15.30	−8.80	−8.10	-	-	−6.07	6.80
Opening (°)	3.20	2.60	1.20	0.40	-	-	1.17	3.60

The tilt and roll angles of the PNA/RNA hybrids are close to those of the experimental A-form DNA/RNA structure, while the X-displacement and the twist angle are between those of A-form DNA/RNA and P-form PNA/PNA duplexes and the intra-base pair parameters are close to those of 5EME/F. There are three experimental PNA/RNA duplex structures in the PDB, i.e. NMR structure 176D and recent X-ray structures 5EME/F, which exhibit some variations. The average X-displacement and twist angle of 176D are similar to those of DNA/RNA, while both parameters for 5EME/F are shifted towards typical P-helix conformation. The twist angles of all base steps in the recent X-ray structures 5EME/F are systematically smaller than those in 176D, indicating the effect of sequence length or crystal packing on the helix structure. The structures in our MD simulations of PNA/RNA are close to 5EME/F. Interestingly, an early MD simulation of the 176D PNA/RNA duplex²² reported twist angles of 23.2–23.7°, which is smaller than 30° in the NMR structure. This indicates a possible artifact of either previous simulation or the NMR structure.

Conclusion

We have performed all-atom MD simulations with the AMOEBA force field to study the hybridization between modified Nucleic Acids and RNAs. The calculated hybridization free energies are generally consistent with previous experimental data on other sequences. PS modifications destabilize the duplexes and Rp is more stable than Sp for DNA/RNA hybrids. LNA and PS-LNA modifications both have a stabilization effect. PNA can enhance hybridization in a sequence-dependent manner.

The effects of the chemical modifications can be rationalized through analyses of their conformations and solvation structures. LNA and PNA single strands have stable A-form-like conformations. This preorganization is responsible for the enhanced stability of the duplex. PS-LNA are similar to LNA since the sugar puckering conformation is dominated by locked deoxyribose. For pure PS modifications, Rp or Sp isomers resemble A-form or B-form, while mixed Rp/Sp isomers have more disordered structures. For comparison, the structure of unmodified DNA is more flexible and more extended. Therefore, pure Sp modification strongly destabilize the DNA/RNA duplex, which has an A-form structure. Besides sugar puckering conformation, solvation properties also affect Rp stability. The sulfur atoms of Rp in the duplex are not well solvated, which causes a solvation penalty for hybridization. So the Rp hybrids are slightly less stable than DNA/RNA hybrids. The destabilization effect of PS is a result of sugar puckering preferences and solvation properties.

This work demonstrated the utility of the FEP technique combined with a polarizable force field for understanding nucleic acid stability. FEP has been a standard method for the study of host-guest systems and protein-ligand binding⁹⁸ and was recently used to predict protein stability.⁹⁹ However, nucleic acids are still challenging because of the highly charged phosphate linkage and flexible backbone. Here we showed that by using polarizable force field and proper alchemical transition pathways, the free energy calculation results for nucleic acids can be directly related to experiments.