Interactions of Cations with RNA Loop-Loop Complexes

Abstract

RNA loop-loop interactions are essential in many biological processes, including initiation of RNA folding into complex tertiary shapes, promotion of dimerization, and viral replication. In this article, we examine interactions of metal ions with five RNA loop-loop complexes of unique biological significance using explicit-solvent molecular-dynamics simulations. These simulations revealed the presence of solvent-accessible tunnels through the major groove of loop-loop interactions that attract and retain cations. Ion dynamics inside these loop-loop complexes were distinctly different from the dynamics of the counterion cloud surrounding RNA and depend on the number of basepairs between loops, purine sequence symmetry, and presence of unpaired nucleotides. The cationic uptake by kissing loops depends on the number of basepairs between loops. It is interesting that loop-loop complexes with similar functionality showed similarities in cation dynamics despite differences in sequence and loop size.

Introduction

Ribonucleic acid (RNA) is a biopolymer comprised of adenine (A), guanine (G), cytosine (C), and uracil (U) nucleotides that can fold into complex tertiary structures essential for cellular processes. RNA loop-loop complexes, otherwise referred to as kissing loops (KL), result from Watson-Crick basepairings between unpaired nucleotides in partially or fully complementary RNA hairpins or stem loops. These KL interactions control key processes of biological activity in all organisms and are crucial for initiating RNA folding into complex tertiary shapes, formation of protein recognition or catalytic sites, promotion of multimerization of RNAs, and viral replication (1). KL interactions can also be used to facilitate the self-assembly of various nucleic-acid-based nanoparticles and nanomaterials (2–5).Yet there is a limited understanding of the rules of KL complex formation.

Assembly of both natural and synthetic RNA molecular architectures requires an ionic environment that compensates for the electrostatic repulsion of the phosphate backbones and assists in ion-mediated chain folding (1,6–10). It has been proposed that specific nonbonding interactions of Mg²⁺ ions with the phosphate clusters within the RNA loop-loop complex stabilize the human immunodeficiency virus type 1 (HIV-1) dimerization initiation site (DIS) (11), trans-activation response (TAR-TAR^∗) (12), and ColE1 plasmid (13) loop-loop structures. However, subtle differences between loop-loop sequences can affect Mg²⁺binding (11,14). For example, dimerization of HIV-1 subtype A with the loop sequence of AGGUGCACA requires divalent cations unlike that of subtype B with the loop sequence of AAGCGCGCA (11).Moreover, several studies have shown that loop-loop interactions can form without divalent cations (9,10,15). For these cases, similar complex stabilities for the HIV-1 DIS RNA loop-loop were obtained in NaCl and MgCl² solutions where concentrations differed by three orders of magnitude (10,15). In addition, the TAR-TAR^∗ complex was shown to be stable in 0.2 M NaCl solution (9).These observations raise interesting questions about the roles of divalent and monovalent ions in RNA KL stability, the factors affecting metal cation binding to KL, and whether cationic uptake can be predicted based on the sequence and function of a KL.

To address these questions, we performed all-atom explicit-solvent molecular-dynamics (MD) simulations of five distinct RNA loop-loop complexes. MD simulations are capable of providing detailed information on interactions between RNA and solvent atoms to show functionally relevant motions and RNA conformational changes (16–21). Previous simulation studies of RNA KLs demonstrated strong interactions of monovalent cations with RNA due to high negative-charge densities and observed electronegative pockets that selectively bind cations (3,9,22,24). Simulations of TAR-TAR^∗ KL complex showed that an asymmetric distribution of counterions around hairpins is inversely correlated with experimental observations of cation-induced TAR-TAR^∗ stability (25).

The selected RNA motifs in our study differ by sequence and number of basepairs, and each are involved in distinct biological processes (Fig. 1). The KL complexes in Fig. 1 are arranged by increasing number of basepairs between loops. Moloney murine leukemia virus (Mo-MuL) genomic RNA KL complex can trigger viral RNA dimerization through the basepairing of two DIS hairpins with identical self-complementary sequences that are held together by two Watson-Crick basepairs (Fig. 1 a) (26). This KL is unique, since two basepairs between loops do not form a confined tunnel; instead, it has a pocketlike channel. The TAR kissing hairpin complex from the HIV-2 genome (HIV TAR-TAR^∗), which is part of the transcriptional activation region of the HIV RNA (12), has all six loop residues basepaired with residues in another loop (Fig. 1 b). The ribosomal subunit of Haloarcula marismortui (HM) KL complex, which mediates contacts with the adjacent stem loop of 23S rRNA (27), also has six basepairs between the loops, but each loop has one flanking unpaired nucleotide (Fig. 1 c). RNA dimerization initiation sites of HIV-1 subtypes A and B (HIV-1 DIS) KL complex promote genome dimerization (28) through the formation of a KL complex between DIS hairpins with identical sequences held together by six basepairs. In this case, each loop has three unpaired flanking nucleotides (Fig. 1 d). Escherichia coli RNA (ColE1) KL complex regulates the replication of the ColE1 plasmid (13) and has seven basepairs in the loop-loop region (Fig. 1 e).

Figure 1.

Secondary and tertiary structures with mapped solvent-accessible tunnels of the RNA kissing loop structures for (a) Mo-Mul, (b) TAR RNA of HIV-2, (c) HM RNA, (d) HIV-1 RNA DIS, and (e) E. coli RNA.

Materials and Methods

Molecular dynamics simulations

The initial coordinates for all the RNA molecules were obtained from the Protein Data Bank (PDB). The kissing-loop dimer of the Moloney murine leukemia virus' genomic RNA has been resolved by NMR (PDB entry 1f5u (Fig. 1 a)) (26). The coordinates of the TAR kissing-hairpin complex from the HIV-2 genome was obtained by NMR (PDB entry 1kis (Fig. 1 b)) (12). The coordinates of the KL complex from 23S rRNA of H. marismortui were extracted from the x-ray structure of the large ribosomal subunit (PDB entry 1s72 (Fig. 1 c)) (30). The structure of RNA dimerization initiation sites of HIV-1 subtypes A and B was determined by x-ray crystallography (PDB entry 2b8r (Fig. 1 d)) (28). The coordinates of ColE1 plasmid of E. coli RNA loop-loop complex were taken from the NMR structure (PDB entry 2bj2 (Fig. 1 e)) (13).

All molecular dynamics simulations were performed using Amber 9.0 software (31) and a modified version ff99 of the Cornell force field for RNA (32). Using this force field, RNA structures in solvent have been shown to dynamically converge to an energy minimum with approximate crystallographic structures (18,19) and model functionally significant conformations that transform from highly kinked structure to open unfolded conformations in ionic environments (20). In this force field, the ions are treated as van der Waals spheres with point charges without polarization and charge-transfer effects. Hence, the representation of monovalent ions is relatively more accurate than that of divalent ions (16,18). The cations were modeled based on Aqvist parameters (33). Over the course of the simulations we did not observe any clustering between Na⁺ and Cl⁻; moreover, due to electronegativity of RNA, no chlorine ions were observed inside the RNA KL tunnels.

All five KL complexes were thus simulated in 0.1 M of NaCl solvent. Sodium ions were chosen for our simulations primarily because magnesium ions are poorly described by pair additive forces and possess diffusion constants on timescales inaccessible with our computational resources (16,34). Furthermore, sodium ions can occupy some of the same locations as magnesium in the RNA major groove (35), and RNA loop-loop complexes can form in the presence of monovalent ions alone (9,10,15). To address the difference in interactions of magnesium and sodium ions, the ColE1 KL complex was also simulated at two different concentrations, 0.013 M and 0.1 M of MgCl₂.

All RNA structures were subjected to conjugate gradient energy minimization for 5000 steps. Minimized RNA structures were then neutralized with Na⁺ ions and immersed in a water box with a solvation shell ∼10 Å thick using the TIP3P water model (36). Additional Na⁺ and Cl⁻ ions were added to represent a 0.1 M effective salt concentration. Two simulations of ColE1 KL were performed, one with two Mg²⁺ ions (0.013 M MgCl₂) and another one with 11 Mg²⁺ ions (0.1 M MgCl₂). Charge neutrality for both samples was accomplished by adding Na⁺ ions. The equilibration of each RNA sample was carried out in 11 stages starting from a solvent minimization lasting10,000 steps while keeping the RNA restrained to 200 kcal/mol. The system was then gradually heated up to 300 K within 40 ps with the 200-kcal/mol restraint on the RNA. A 200-ps NPT equilibration was performed to ensure the homogeneous solvent density with the RNA restrained at 200 kcal/mol. Another 10,000-step minimization followed by a 20-ps NPT run was executed with the RNA restraint lowered to 25 kcal/mol. Subsequently, four additional sets of 1000 minimization steps were performed with the positional constraint relaxed from 20 kcal/mol to 5 kcal/mol. A final unconstrained 1000-step minimization was performed before heating the system to 300 K at a constant volume within 40 ps. The long-range electrostatic interactions were calculated by particle mesh Ewald summation (37) with a 0.00001 tolerance of Ewald convergence, and the nonbonded interactions were truncated at 9 Å. The temperature was maintained at 300 K using a Berendsen thermostat (38). SHAKE algorithm was used to constrain hydrogen-atom vibrations (39). The NVT production simulations were performed for 55 ns with a 2-fs time step. Control simulations of the 0.1 M NaCl solution and the RNA duplex in 0.1 M of NaCl were performed for 20 ns.

Analysis

The degree of convergence for molecular dynamics trajectories is measured by calculating a Pearson correlation coefficient, a bivariate analysis accounting for the strength of association between two variables. We calculated the Pearson correlation coefficient for ion occupancy around structurally similar RNAs, such as the palindromic sequences of DIS of HIV-1 subtypes A and B, where X and Y are the ion occupancy around subtype A and subtype B, respectively. Temporal ion occupancy calculated for the chosen ion was within 5 Å of the oxygen or nitrogen atoms of purines and pyrimidines. The Pearson correlation coefficient converged to 0.95 at the end of 10 ns (Fig. S1 a in the Supporting Material). Earlier studies showed a rank coefficient of 0.69 by 14 ns for palindrome DNA (40) and 0.94 in 15 ns for A-form RNA kissing loop (8), and poly guanine-cytosine RNA helix showed a correlation coefficient of 0.98 in 10 ns (41). To estimate the conversion of RNA structure, we performed four independent simulations of HIV-1 DIS KL complex. Temporal evolution of the root mean-square deviation of loop-loop residues show that the structural convergence of HIV-1 DIS occurs within 5 ns (Fig. S1 b). Thus, for analysis, we consider only the last 50 ns of production runs. Also, all KL complexes retained their basepairing and overall structure throughout the course of the simulations.

MD trajectories were processed using in-house scripts and PTRAJ, a standard tool suite accompanying Amber 9.0. The number of water molecules around cations was estimated by counting waters within 3.4 Å of cations that correspond to the first hydration shell (42). The diffusion coefficient of specific long-residency sodium ions was estimated by calculating the mean-square displacement during the time when the ion was residing inside the KL tunnel. The diffusion coefficient was calculated from the slope with a factor of 10/6 of the ionic mean-square displacements as a function of time.

Solvent-accessible tunnels in Fig. 1 were calculated using CAVER software (43), where a skeleton search of a path that connects a cavity within a macromolecule with a bulk solvent is based on a reciprocal distance function grid (44) and plotted using PyMol software (45). The tunnel radius for the structures (see Fig. 3) was evaluated using HOLE software (46), which adopts a Monte Carlo simulated annealing procedure for cavity estimation. The algorithm adopted by HOLE includes an initial guess of the probe point inside the cavity and assigns a vector presuming a tunnel direction. The probe then moves in a plane normal to the tunnel vector and searches for the largest sphere that can fit without an overlap within the van der Waals surface of any atom. The series of such spheres constitute the tunnel. Tunnel profiles were obtained by performing HOLE calculations on 300 snapshots from the last 10 ns of the trajectory. Average solvent-accessible tunnel radii were obtained by fitting a cubic spline. The spline function calculates individual segments between two data points and then minimizes the oscillation by curve fitting. However, in some cases, data with unknown oscillations may result in a nonzero second derivative which generates a poor polynomial fit. Spline function allows harmonic solutions that retain functional form for such data. Our data (Fig. 3, a–e, gray lines) had unknown oscillations, so cubic spline fit was a natural choice to represent an average radius.

Figure 3.

(a–e) Solvent-accessible tunnel's radius, where light gray bars represent the radius for individual snapshots and the black solid line is a cubic spline fit of the data. (f–j) Cylindrical distribution of cationic occupancy within the Mo-MuL RNA (a and f), HIV TAR-TAR^∗ (b and g), HM (c and h), HIV-1 DIS (d and i), and ColE1 (e and j) KLs. Zero is the cylinder's center.

Cationic occupancy counting (see Fig. 3) was performed using an in-house PERL script, which constructs a cylindrical volume based upon the position of phosphates in distal apposition at the opening of each KL (Fig. S2). The median bisector of the line connecting each pair forms the cylindrical axis. The midpoint of the line between the medians forms the center of the cylinder. For all KL complexes, the same length of the cylinder was used. The calculation for the cylindrical geometry and ion frequency counts were performed via an in-house script that also binned ion frequencies by radius and length of cylinder. Ion frequency counts were incremented based on the distance from the atomic center of the ion to the nearest atomic center of a residue if it was within a cutoff distance of 5 Å.

Results and Discussion

We observed that all RNA KLs possess solvent-accessible tunnels that pass through the inner major groove of loop-loop complexes (Fig. 1). These tunnels, which are irregular cylinders with varying diameters and anisotropic minima along the cylindrical axis, attract and retain Na⁺ ions. The calculated number of ions inside the KL tunnel (cationic occupancy) was compared to the cationic occupancy within a similar volume of the counterion cloud surrounding the RNA (Table 1). In our simulations, each KL complex accommodated between one and four sodium cations simultaneously within the tunnel. For example, we found that the ColE1 KL can accommodate up to four positive charges inside its tunnel, which can be either Mg²⁺ or Na⁺ ions (Fig. S4); this may explain why loop-loop complexes can form in both NaCl and MgCl₂ solution (9,10,15). Additional simulations of ColE1 at 1 M NaCl indicated that the number of cations in the tunnel is independent of salt concentration. This observation is in agreement with the experimental observations; for example, ultraviolet melting analysis also estimated three sodium ions bound to HIV-1 DIS complex (10), and formation of ColE1 KL had been shown to coincide with an uptake of approximately two magnesium ions per complex (7).

Table 1.

Interactions of sodium ions with RNA loop-loop complexes

	Longest Na+ residence time (ns)	Average number of Na+ in KL∗	Na+ diffusion coefficient ((m2/s) × 10−9)	Direct Na+ binding† to specific atoms within the 3.2 Å
				Site	Occupancy (%)	Time (ns)
Ion cloud	0.016	0.124	1.33‡	O1P	NA	0.28
Mo-MuL KL	7.5	1.95	0.28	G11A@O6	7.86	0.11
HIV TAR-TAR∗ KL	20	2.20	0.0031	G9A@N7	56.58	0.45
				G8A@N7	37.13	0.27
				A11A@N7	34.63	0.43
				G9A@O6	31.12	0.71
				G10A@N7	23.42	0.20
				U6B@O4	19.17	0.43
				G10A@O6	17.52	0.27
				G8A@O6	16.32	0.32
HM KL	18	2.69	0.0014	G422@N7	37.74	0.75
				A423@N7	35.19	0.65
				U420@O4	26.55	0.54
				U2444@O4	12.21	0.28
HIV-1 DIS	17	2.69	0.00125	C11A@N3	5.87	0.05
ColE1 KL	40	3.05	0.0065	G12A@N7	83.23	0.42
				G11A@N7	83.11	0.77
				A9A@N7	52.24	1.45
				A7B@N7	16.74	0.52

^∗Occupancy was calculated within a cylindrical space (radius, 6 Å; length, 20 Å).

^†Direct binding ignores angular dependencies.

^‡Empirical value of 0.1 M sodium in bulk water.

Our simulations show that these cations resided within the tunnel on a timescale orders of magnitude longer than cations within the counterion cloud. To illustrate the difference in cationic movement within the counterion cloud and inside a KL region, we calculated the mean-square displacement of the longest-residency Na⁺ ion around HIV-1 DIS complex over the entire trajectory (Fig. 2). The ion is colored by the simulation time from 0 ns (red) to 50 ns (blue). In the beginning of that simulation, the ion was located in the bulk and was attracted to RNA due to electrostatic forces. At ∼9 ns, the ion enters the loop region and stays there for ∼17 ns (red-to-silver color transition) before exiting into the bulk (blue). The sodium ion shows a significant decrease in its diffusion coefficient from 1.33 × 10⁻⁹ m²/s in the bulk to 0.00125 × 10⁻⁹ m²/s inside the KL complex (Table 1). Overall, the observed characteristics of resident ions were distinct from those in the counterion cloud in terms of the binding site preferences, hydration profiles, and residence times. Ions in the loop-loop region may contribute to KL structure stabilization and promote the KL interactions (1,6–10); hence, their exact role warrants closer scrutiny.

Figure 2.

Mean-square displacement of the longest-resident ion inside HIV-1 DIS kissing loops. The longest-residence ion's trajectory is mapped into the RNA structure snapshot. The ion color is based on its trajectory time from the initial time to the final time.

Our simulations indicate that the ion dynamics inside these tunnels depend primarily on the KL structure and sequence. We represent the spatial and temporal profile of a tunnel by calculating the solvent-accessible radius averaged over the trajectory that is mapped along the tunnel axes (Fig. 1).The distribution function of ion occupancies was calculated along a cylindrical axis as described in the analysis section (Fig. 3, f–j). The tunnel radius and ionic occupancy are mapped to the common center. The light gray lines are the radius of the individual snapshots taken at 100-ps intervals, whereas the black line is the average tunnel radius, derived from a cubic spline fit of the data. The extent of the oscillation in gray lines reflects the structural flexibility of the KL tunnel. All RNA structures showed a skewed average tunnel profile that narrows near the center of the KL region. However, the specific geometry of the ionic tunnel differs from one KL assembly to another and is governed by the spatial arrangement of basepairs. The molecular geometry of the Mo-MuL open channel is dynamic, as evidenced by the variability in radius (Fig. 1 a, gray lines). The cylindrical cationic distribution in the Mo-MuL KL region is shown in Fig. 3 f, where the highest bulk Na⁺ occupancy is situated on the B-hairpin side. However, the intensity of this peak is not high. This tunnel accommodated up to two sodium ions (Table 1), which can reside on either side, as indicated by short direct binding events with G_11A on the A-hairpin side. Earlier studies suggested that N7 atoms of adeninesA_9A and A_9B were the most frequent binding sites during a 16-ns simulation time (22).The TAR-TAR^∗ tunnel radius varies less than that of Mo-MuL (Fig. 3 b, gray lines), which may be attributed to the fact that all residues between the loops are paired. The cylindrical cationic distribution in the TAR-TAR^∗ KL region shows a sharp cationic peak on the side of a guanine-adenine pair and peaks that are more spaced out on the side with higher purine content (Fig. 3 g). We determined that up to three Na⁺ ions can reside inside the TAR-TAR^∗ KL complex with the longest observed time of 20 ns. However, the maximum specific cationic binding to any atom within KL was only 706 ps (Table 1). The HM KL (Fig. 3 c, gray lines) and HIV-1 DIS regions (Fig. 3 d, gray lines) show greater tunnel flexibility than TAR-TAR^∗, which might account for the cationic distribution profile. Their distribution profiles show multiple peaks, which indicate nonspecific occupancy and areas of extended cationic residence (Fig. 3, h and i). The ColE1 tunnel displayed the highest cationic occupancy (Fig. 3 j), with its radius fluctuating much less intensely than those of either HM or HIV-1 DIS (Fig. 3 e). Despite the sequence differences among RNA motifs, there is a correlation between ionic occupancy and average local structure compaction (Fig. 3). Moreover, in simulations in both NaCl (Fig. S5) and MgCl₂ solutions (Fig. S4), as compared to those in pure water, the local RNA structure compaction is also present. It is known that multivalent cations can induce RNA compaction more efficiently than monovalent cations (34,47,48).

Effect of basepairing between loops

Tabulated results (Table 1), arranged by increasing number of basepairs between loops, revealed a putative relation between the number of basepairs that hold the complex together and the number of cations inside the tunnel and longest residency time. Specifically, ColE1, with seven basepairs between loops, possessed the highest cationic occupancy and the longest ion residency time, whereas the Mo-MuL KL complex had the shortest ion residency time. A similar trend was observed in HIV TAR-TAR^∗, HIV-1 DIS, and HM KL complexes, which were held together by six basepairs between the loops.

Unpaired nucleotides in a loop play an important role in the ionic distribution and structural changes of a tunnel. One can observe that radius fluctuations were much greater for the Mo-MuL, HM, and HIV-1 DIS KL complexes with unpaired nucleotides (Fig. 3, a, c, and d) as compared to the radius fluctuations of complexes with all loop residues basepaired (Fig. 3, b and e). The cationic occupancy also follows this trend, as the KL complexes with unpaired residues showed greater distribution of small cationic intensity peaks, whereas loops with all bases paired show sharp and high intensity peaks. The presence of unpaired bases near the loop region seems to have a dominating influence on cation distribution.

Effect of sequence

Among all structural characteristics, we observed that KL complexes with a lopsided purine distribution between the loops will attract cations more strongly toward the purine-rich loop. This is best observed in the ColE1 KL complex, with its strong and sharp cationic intensity peak in the loop with four purines (including three guanines and one adenine) and a smaller double peak on the opposite side, where there are only three adenines (Fig. 3 j). The HIV TAR-TAR^∗ complex has two cations localized within the purine-rich region of the loop, which has three guanine bases and one adenine base (Fig. 3 g). This is in agreement with previous observations (25) of asymmetric accumulation of the counterions along the guanine tract on the TAR side.

The KL complexes with high sequence symmetry between loops (HIV-1 DIS and Mo-MuL) show a reduced ionic intensity, multiple peak occupancies, and a more equal distribution of ions along the tunnel (Fig. 3, f and i). Mo-MuL has an open tunnel and shows a strong binding for up to two cations. In a similar way, previous molecular dynamic simulations (22) observed a cation binding pocket occupied by one or two long-resident and diffusive Na⁺ cations. For HIV-1 DIS, it was observed that in the absence of Mg²⁺ions, three Na⁺ ions may remain coresident in this pocket (22). Despite the difference in the number of basepairs between the loops, the cationic distribution profiles are similar for both HIV-1 DIS and Mo-MuL. Moreover, the direct binding of the cations to RNA atoms is determined to be <10% occupancy and seems to be much less relevant in the symmetrical loop-loop complexes (Table 1). These complexes also have the smallest tunnel radius among all KL complexes, which may be related to the similar functions that these two KL complexes undertake in a cellular environment.

HM KL represents an interesting case (Fig. 3 h), as it does not have a symmetrical sequence but has a relatively even distribution of purines between loop bases. Due to neighboring G and A bases in both loops, the cationic intensity is high, as in TAR-TAR^∗ and ColE1. However, the unpaired flanking bases cause multiple cationic occupancy peaks, as in Mo-MuL and HIV-1 DIS KL.

Purine bases were the most preferred sites for cationic interactions in all KL complexes (Table 1). A similar effect was observed recently in RNA helices where monovalent ions associated with polypurine stretches of adenine and guanine (41). Also, purine-rich stretches in RNA aptamers are shown to be crucial for the binding of Co²⁺ and are targets for 6-mer oligodeoxyribonucleotides (49). Ion localization around purine-rich regions could be explained by electronegative pockets formed by the N7 and O6 atoms of guanine and the N7 atom of adenine. Crystallographic studies of metal binding in HIV-1 RNA duplexes have demonstrated that divalent species such as Mg²⁺prefer the N7 and O6 atoms of guanine residues (50). A sodium ion can have an ideal octahedral arrangement of first-shell oxygen atoms in association with the O6 position of guanine (51). This might explain why partially hydrated ions in the tunnel would localize around purines as the entropic penalty of this interaction could likely contribute to the KL's stability (52). Density functional theory calculations of metal binding to DNA basepairs suggested that bare Na⁺ ion can infiltrate the major groove adjacent to the N7 site of purine bases (53).Of the two purines, guanine will have the highest propensity to sequester cations, since it has the largest dipole moment of all the nucleobases (54). Our simulations support the idea that cations have a high affinity for polypurine stretches within KL complexes.

Ion dynamics inside the KL complex

All RNA KL motifs exhibited some degree of direct binding of Na⁺ ions (Table 1). The direct binding sites are categorized by the cationic occupancy >10% over the trajectory. The symmetric loop sequences of Mo-MuL and HIV-1 DIS complexes showed less of a propensity for specific cationic binding, as indicated by their single-site occupancies of <8%. The most preferred ion binding site in Mo-MuL was the O6 atom of guanine; for HIV-1 DIS, direct binding was observed at the N3 atom of cytosine in loop A. RNA motifs including HIV TAR-TAR^∗, HM, and ColE1 showed multiple direct ion-binding sites with high occupancies. The location of the sites with direct cationic binding agrees well with the cylindrical ionic distribution of Na⁺ occupancy (Fig. 3, f–j). For example, the strongest intensity peak in ColE1 corresponds to Na⁺ interaction with the N7 atoms of G_12A, G_11A, and A_9A, and another peak corresponds to Na⁺ binding to A_7B at the N7 atom. In a similar way, in the HM KL complex, a major cationic occupancy peak arises from Na⁺ interaction with G₄₂₂, A₄₂₃ at N7, and U₄₂₀ at the O4 position. Another, smaller intensity peak is on the right side of a tunnel and relates to U₂₄₄₄ at the O4 position. However, the KL residency time of the longest specific ion does not correlate with any direct specific binding times. For example, the ColE1 KL complex had the longest direct binding time of ∼1.5 ns; however, the longest residency time of a cation inside its KL complex was 40 ns.

Ion hydration

A resident sodium cation does not remain bound to one RNA atom on one side of the loop for the entire trajectory. Our simulations show that the ion binds to different RNA atoms inside the loop-loop region and also can pass through the tunnel. The direct binding can be exemplified by the change in the first hydration shell of a Na⁺ ion just between 19 and 20.5 ns as it passes through the ColE1 KL tunnel (Fig. 4). The first hydration shell was calculated within the 3.4-Å distance between water oxygen and Na⁺. Direct binding of a sodium ion to RNA is always accompanied by the loss of a water molecule from its hydration shell. In the beginning of the transition, a Na⁺ ion intermittently binds to N7 at A_9A, consequently shedding one to two water molecules from its hydration shell. The ion then becomes fully hydrated by moving to the center of the opening, until it binds to the phosphate oxygen of A_9A. After moving away from the phosphate, the cation completes its hydration shell (Fig. 4 b) and starts to move through the tunnel. During this rapid movement through the tunnel (Fig. 4 c), the ion retains its hydration shell, with the exception of a short contact with O4 at U_10A where it loses a few of its first-shell waters. Simulations show that the tunnel expands and becomes more circular as the ion moves to bind the phosphate oxygen (Fig. S3), which ultimately allows the ion to pass through the tunnel. As the ion reaches loop B (Fig. 4 d), it binds to O2P at A_8B for ∼100 ps, then gets further dehydrated due to shared binding between N7@G_8A and O2P@A_8B. During this shared binding mode, the G_8A residue extends toward A_8B, which results in an acute kink at loop A. The ion then shifts completely toward N7@G_8A and stays there for the next 100 ps. Again, a shared binding of Na⁺ with O6@G_8A and N7@G_8A dehydrates the ion. In general, Na⁺ sheds water molecules in the event of shared direct binding and regains its hydration shell in the case of a single binding event.

Figure 4.

(a) Hydration profiles of the longest resident Na⁺ ion inside the ColE1 loop-loop region for 19–20.5 ns time period. The inlets (b–d) represent the simulation snapshots of the Na⁺ ion passing through the tunnel.

We observed that Na⁺ ion hydration dynamics is correlated with its mobility inside this RNA tunnel. Fig. 5 represents a plot of mean-square displacement (MSD) versus number of waters in the first hydration shell (hydration states) for the same Na⁺ ion inside ColE1 during a 4-ns trajectory (17–21 ns) as in Fig. 4. The first hydration shell of Na⁺ in the RNA loop-loop region fluctuates from 2 to 11 water molecules. Our observations of hydration states and number of ions in the TAR-TAR^∗ KL region agrees with a previous simulation study (25). The presence of such diverse hydration states of Na⁺ indicates a reasonable amount of conformational sampling. An ion in the loop-loop region exhibits a characteristic reduction in MSD for intermediate states of hydration, typically between four and five water molecules in the first hydration shell. For all KL motifs, the most probable hydration states had five to six water molecules around the Na⁺ ion. In the event of direct binding, there is either a loss of a water molecule or a distortion of the hydration shell. It can be seen from Fig. 5 that higher MSDs at lower hydration states occur rapidly to restore a thermodynamically favorable state. However, when the ion had more than six waters in the first hydration shell, water molecules would screen Na⁺ from the electronegative charges of RNA. Once shielded with water molecules, the electrostatic forces on the Na⁺ ion became consequently weaker, so the hydrated ion could displace faster inside the loop-loop region. Similar trends were observed for all sampled KLs (Fig. S6). It is interesting that the MSD of a hydrated ion follows the trend of purine distribution in the sampled KLs. The lowest MSDs observed for ions were inside Mo-MuL, followed by TAR-TAR^∗, HM KL, and HIV1-DIS, with the highest MSDs observed for ColE1.

Figure 5.

Mean-square displacements of a Na⁺ inside the KL region of the ColE1 complex in relation to its hydration states during a 4-ns trajectory (17–21 ns). (Insets) Snapshots of the distorted hydration shell.

Conclusions

Our simulations suggest that KL complexes have ionic tunnels that attract, retain, and exchange cations. The dynamics of ions inside a KL complex is distinctly different from that of the counterion cloud surrounding helical RNA and depends on a number of basepairs, sequence symmetry, and the presence of unpaired flanking nucleotides. Cations interact strongly and exhibit some degree of direct binding with the KL complexes. However, sodium ions do not stay bound to RNA all the time and can pass through the tunnel while retaining most of their first hydration-shell waters. Our results indicate that cations in the ionic tunnels show strong preferential distribution around purines. KL complexes can uptake a certain number of cations, which depends on the number of basepairs between the loops. Water-shell dynamics show that the mobility of Na⁺ ions inside the KL are correlated to the number of water molecules in the first hydration shell and the number of basepairs between loops.

We observed that KLs that are involved in similar functions also exhibit similar cationic dynamics. The Mo-MuL and HIV-1 DIS KL complexes are both involved in dimerization initiation. Each of these KL complexes shows high fluctuations in tunnel structural profiles, small minimum average tunnel diameters, and a low probability of cationic specific binding to RNA atoms inside their KLs despite differences in their sequence and number of basepairs between loops. Two other KL complexes, HIV TAR-TAR^∗ and ColE1, can be recognized by a ROM (RNA one modulator) protein that binds specifically to the KL complexes and stabilizes their association (55). It has been shown that a ROM protein can bind the TAR-TAR^∗ KL complex with an affinity similar to that of the ColE1 KL complex (12). Our simulations indicate that both KL complexes (TAR-TAR^∗ and ColE1 KL) exhibit high cation localization near the purine stretches, long specific cationic binding, lower structural fluctuations in the tunnel, and higher diffusion coefficients, as compared to Mo-MuL and HIV-1 DIS KLs. The HM KL, which mediates contacts with the adjacent stem loop of 23S rRNA (27), has strong cationic binding but high structural fluctuations. It is interesting that the cationic dynamics in DIS-related KL complexes (Mo-MuL and HIV-1 DIS) is significantly different from the cationic dynamics in ROM-recognized KL complexes (TAR-TAR^∗ and ColE1) or KL complex from the ribosomal subunit (HM).