Mg²⁺ ions show high initial mobility and occupy binding sites in good agreement with experimentally determined ones

Mg²⁺ ions have a strong influence on structure and stability of RNA [34,35]. However, modeling these ions in MD simulations is considered difficult [36] because Mg²⁺ ions show a slow exchange kinetics of first shell ligands [37] and display very slow diffusion rates [38,39]. Hence, given the length of our MD simulations of 550 ns, it was important to carefully place the Mg²⁺ ions in the simulation box to prevent poor sampling. To account for this, we placed the Mg²⁺ ions as hexahydrated complexes at electrostatically favorable positions along the RNA. For details about this placement procedure and its advantages over placing non-hydrated Mg²⁺, see ref. [33].

As a result, more than half of the Mg²⁺ ions showed a pronounced mobility during the first ~100 ns of the MD simulations (see Figure 2 in ref. [33]), and several ions remained mobile even after 500 ns. Additionally, we observed that several of the ions explore a large region around the aptamer in the MD simulations (shown exemplarily for three ions in S1 Fig). Furthermore, we occasionally observed that (temporarily) immobile hexahydrated Mg²⁺ ions swapped their positions during the MD simulations (Fig 1D). For other immobile Mg²⁺ ions, we observed that the ions lost water molecules from their first hydration shell and started to interact with the RNA (S2 Fig), despite the slow exchange kinetics. These observations are consistent with the known bias towards inner-shell binding of Mg²⁺ ions in RNA simulations using a non-polarizable force field [36,40,41]. S2 Fig also reveals that for both Gsw^apt and Gsw^loop with 12 Mg²⁺ and Gsw^apt with 20 Mg²⁺ the decrease in the number of hexahydrated Mg²⁺ is much slower in the second trajectory halves than the first, which suggests that these systems started to settle with respect to the binding of Mg²⁺ ions.

In order to investigate preferred occupation sites of Mg²⁺ ions in the MD simulations independent of their starting positions, an additional MD simulation was set up in which the Mg²⁺ ions were initially placed at least 10 Å from the RNA. As a result, preferred occupation sites between the RNA backbones were observed after 300 ns of MD simulations that are in very good agreement with binding sites of [Co(NH₃)₆]³⁺ in crystal structures of Gsw aptamers [8,18] (Fig 1E): Four out of six experimental binding sites in PDB ID 4FE5 were occupied between 25% to 74% of the simulation time of 550 ns; two additional binding sites from PDB ID 3RKF were occupied ~57% of the simulation time (S1 Table). Similar occupation rates were observed in the 18 MD simulations for which the Mg²⁺ ions had been placed at electrostatically favorable positions along the RNA (S1 Table). Likewise, nucleotides that show chemical shift changes upon Mg²⁺ titration to Gsw^loop in NMR experiments [18] were found in a distance < 5 Å to the preferred occupation sites of Mg²⁺ ions in our MD simulation (Fig 1E). Note that one cannot expect a perfect agreement of computed occupation sites with experimentally determined ones. On the one hand, this is partly due to the conformational dynamics of the RNA during the MD simulations, which can lead to a shift of an occupation site with respect to the (static) crystal structures. On the other hand, the occupation of sites in the two crystal structures already differs quantitatively (shift between red and orange spheres in Fig 1E) and qualitatively (occupation in one crystal structure but not the other; Fig 1E). Yet, when comparing the occupancies (S1 Table) in terms of ratios of mole fractions of an occupied versus unoccupied binding site between different MD trajectories (e.g., for binding site 1, Gsw^apt 12 Mg²⁺, and trajectories 1 and 2: (10/90) / (27 / 63)), for the overwhelming majority of the 96 cases (4 systems x 8 binding sites x 3 ratios), this ratio is close to one order of magnitude, and in only four cases it exceeds two orders of magnitude (the 16 cases where the occupancy was either 0 or 100% were not considered here); in our view, this observation displays an encouragingly high internal consistency of occupancies between different trajectories.

In summary, while these results do not prove convergence of the occupation of Mg²⁺ sites, they suggest that the respective systems sufficiently settled, and in a consistent manner, with respect to Mg²⁺ ion binding such that they can be compared to each other for investigating the influence of the concentration of Mg²⁺ ions on the structure and dynamics of Gsw^apt and Gsw^loop.

The aptamer domain remains globally stable during the MD simulations but shows local structural changes

Data on structural deviations of Gsw^apt and Gsw^loop are given in Table 1 in terms of mean root mean-square deviations (RMSD) over three trajectories after root mean-square fitting of the conformations on the initial conformation, considering for fitting only those 80% of the nucleotides that show the lowest RMSF (S2 Table). All simulations show mean RMSD ≤ 3 Å for the whole aptamer structures (also exemplarily shown in S3 Fig as a function of simulation time for Gsw^apt), except for Gsw^loop in the absence of Mg²⁺ ions (4.2 Å). RMSD values of up to 3–4 Å have also been observed in other MD simulations of small riboswitches applying a similar simulation setup [42–44]. Accordingly, the comparison of the average conformation over the last 50 ns of MD simulations with the crystal structure shows only small overall structural deviations (S4 Fig). The ff99 force field used here has been reported to lead to irreversible transitions to unexpectedly open and under-twisted RNA structures resembling a ladder due to anti to high-anti shifts of the χ dihedral [43,45–47]. However, visual inspection of our MD trajectories neither revealed the formation of such ladder-like structures for Gsw^apt nor for Gsw^loop (S4 Fig). Furthermore, histograms of χ dihedrals using the ff99 force field on Gsw^apt and Gsw^loop in the presence of 20 Mg²⁺ ions are highly similar to those obtained for the ff10 force field, including the high-anti region (S5 Fig for the entire aptamer and S6 Fig for the P1 region only). We also note that some nucleotides in the bound crystal structures of Gsw^apt and Gsw^loop do occupy the χ high-anti region [33].

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Root mean square deviations of Gsw^apt and Gsw^loop as a whole and for substructures^[a].

https://doi.org/10.1371/journal.pone.0179271.t001

Mean RMSD for substructures of Gsw^apt and Gsw^loop were calculated after root mean-square fitting of those nucleotides showing the 80% smallest RMSF (“core nucleotides”) (Table 1, S2 Table). Together with small RMSD values observed for all substructures but J2/3 when fitting the respective substructure onto itself (S3 Table), these RMSD values thus mostly report on relative motions of the substructure with respect to the core nucleotides. The largest values were observed for the P1 region, up to 6 Å for MD simulations in the presence of Mg²⁺ and 7.6 Å (9.9 Å) for Gsw^apt (Gsw^loop) in the absence of Mg²⁺. Note, however, that these RMSD values result in part from the high mobility of the three terminal base pairs of P1. The P2 and P3 regions show overall the lowest mean RMSD values (≤ 2.8 Å, except for Gsw^loop in the absence of Mg²⁺ (3.0–3.7 Å)), as expected for paired regions in the center of the RNA. The larger structural deviations observed in the absence of Mg²⁺ result from relative motions of the P2 and P3 regions with respect to each other due to the lack of charge compensation by the ions. Regarding loops L2 and L3 of Gsw^apt, a similar trend is observed with mean RMSD values that are higher by about 1 Å in the absence of Mg²⁺ than in its presence; L2 and L3 of Gsw^loop show mean RMSD values that are yet higher by 1 Å than those of Gsw^apt. Finally, of the junction regions, J1/2 shows the lowest mean RMSD (~2 Å) in most simulations; the largest value (3.3 Å) is observed for Gsw^loop in the absence of Mg²⁺ ions. In contrast, the J2/3 region shows high mean RMSD values > 3 Å for all simulations as does the J3/1 region (~3 Å). Again, the only exception is Gsw^loop in the absence of Mg²⁺ ions where we observe mean RMSD values > 5 Å.

In summary, no gross conformational changes of the aptamer domain were observed during our MD simulations. On a local scale, the mutation in Gsw^loop induces local conformational rearrangements in the loop region as well as at the ligand binding site (J1/2, J2/3 and J3/1), manifested in higher RMSD values compared to the simulations of Gsw^apt.

The G37A/C61U mutation disturbs the native hydrogen bond network in the loop region

The tertiary interactions between the loops L2 and L3 are formed via a hydrogen bond network composed of two base quadruples. Each quadruple is formed by a canonical Watson-Crick base pair and a non-canonical base pair connected to it. The G37A/C61U mutation is located in the upper base quadruple, which is formed by the Watson-Crick base pair of nucleotides 37 and 61 and the two nucleotides 34 and 65 (Fig 1C). The lower base quadruple is identical in both Gsw variants and consists of the Watson-Crick base pair formed by nucleotides 38 and 60 and the two nucleotides 33 and 66 (S7 Fig).

We calculated average base pair occupancies for native base pairs in the loops L2 and L3 from the occupancies of the hydrogen bonds that are involved in the formation of the base pair (Table 2). For Gsw^apt in the absence of Mg²⁺ ions, almost all base pairs, except for A66-G38 from the lower base quadruple, are formed for > 50% of the time. The most stable base pairs are the Watson-Crick base pairs C61-G37 (99%) and C60-G38 (98%), which are also described as the most crucial components of the tertiary interaction [20]. The presence of Mg²⁺ ions in the simulations of Gsw^apt results in a stabilization of almost all hydrogen-bonded base pairs and in occupancies for the hydrogen bonds of at least 78% except for the base pair A66-G38 (61%). The occupancies in the presence of Mg²⁺ ions are up to 44% higher than in the absence of Mg²⁺ ions.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Hydrogen bond occupancy in the L2/L3 loop region of Gsw^apt and Gsw^{loop [a]}.

https://doi.org/10.1371/journal.pone.0179271.t002

For Gsw^loop, the loss of two hydrogen bonds in the upper base quadruple (Fig 1C) results in an overall destabilized hydrogen bond network in our MD simulations, manifested in lower occupancies for the hydrogen bonds in the loop region. In the absence of Mg²⁺ ions, the base pair between the nucleotides 61 and 65 in the upper base quadruple shows hydrogen bond occupancy of only ~5%, i.e., ~50% lower than for Gsw^apt in the absence of Mg²⁺. The mutated Watson-Crick base pair A37-U61 yields a value of 86% in the absence of Mg²⁺, ~10% lower than for the G37-C61 base pair in Gsw^apt. The last base pair in the upper base quadruple (A65-U34) also shows a reduced occupancy in the case of Gsw^loop compared to Gsw^apt. The lower base quadruple is influenced by the mutation as well. Here, the G38-C60 Watson-Crick base pair is again the most stable base pair from this quadruple (70%), whereas the other two base pairs show occupancies of 22% and 28% in the absence of Mg²⁺ ions. As in Gsw^apt, the presence of Mg²⁺ ions in simulations of Gsw^loop results in higher occupancy values for the hydrogen bonds of the hydrogen bond network, except for the interactions between the nucleotides 37 and 61.

In summary, we observe that the hydrogen bond network in the loop region of Gsw^apt is more stable than the network in Gsw^loop, as expected by the introduction of the G37A/C61U mutation in Gsw^loop. The G37A/C61U mutation does not only decrease the stability of the upper base quadruple in which the mutation is located, but also destabilizes the lower base quadruple. Furthermore, we found that the presence of Mg²⁺ ions results in more stable tertiary interactions for both Gsw^apt and Gsw^loop, in agreement with experimental findings [15,31].

The presence of Mg²⁺ ions maintains a more compact structure

In order to investigate the influence of Mg²⁺ ions and the G37A/C61U mutation on the compactness of the aptamer domain of Gsw, we calculated the radius of gyration (R_g) of the RNA molecules (Table 3). In the presence of Mg²⁺ ions, the mean R_g of both Gsw^apt (16.2 ± 0.3 Å) and Gsw^loop (16.4 ± 0.4 Å) agree with the value calculated for the ligand-bound crystal structures (16.1 Å and 16.3 Å, respectively), which contain [Co(NH₃)₆]³⁺ ions in addition. Only minor differences were observed when comparing the mean R_g from MD simulations with 12 and 20 Mg²⁺ ions. The mean R_g in the absence of Mg²⁺ ions is increased by ~1 Å for both Gsw^apt and Gsw^loop. The more compact structure in the presence of Mg²⁺ ions is maintained due to the ions compensating the negative charges of the RNA backbone. For all three Mg²⁺ ion concentrations, the differences in mean R_g between Gsw^apt and Gsw^loop are only marginal (≤ 0.2 Å), indicating only a minor influence of the mutation on the compactness of the structure.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 3. Radius of gyration of Gsw^apt and Gsw^{loop [a]}.

https://doi.org/10.1371/journal.pone.0179271.t003

In summary, we observe that the G37A/C61U mutation does not have an influence on the structural compactness of the RNA. The absence of Mg²⁺ ions in the MD simulations results in a less compact structure than when Mg²⁺ is present and in the ligand-bound crystal structures.

The G37A/C61U mutation increases, whereas Mg²⁺ ions decrease the structural dynamics of the aptamer

In order to gain insights into the influence of Mg²⁺ ions and the G37A/C61U mutation on the dynamics of the RNA, we calculated atomic root mean-square fluctuations (RMSF) and averaged them per nucleotide (Fig 2A and 2B). For all simulations, the stem regions P2 and P3 are the least mobile, while the terminal P1 region shows high RMSF. The low mobility of the P2 and P3 regions is in line with SHAPE experiments of the unbound state of a purine riboswitch characterizing these regions among the most stable ones [16].

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Atomic fluctuations calculated from MD simulations.

A, B: Mean (± SEM) atomic fluctuations (RMSF) on a per nucleotide level for Gsw^apt (A) and Gsw^loop (B) over the three simulations for each system setup. Secondary structure regions are depicted above the plots and colored according to Fig 1A. Red: simulations in the absence of Mg²⁺ ions; green: simulations with 12 Mg²⁺ ions per RNA molecule; blue: simulations with 20 Mg²⁺ ions per RNA molecule. C, D, E: Differences in atomic fluctuations projected onto the RNA structure. Larger differences are colored red, smaller differences blue. Nucleotides responsible for ligand binding are shown as sticks. C: Difference in atomic fluctuations for Gsw^apt of 0 Mg²⁺—20 Mg²⁺ ions per RNA molecule. D: Difference in atomic fluctuations in the absence of Mg²⁺ for Gsw^loop—Gsw^apt. E: Difference in atomic fluctuations for Gsw^loop of 0 Mg²⁺—20 Mg²⁺ ions per RNA molecule.

https://doi.org/10.1371/journal.pone.0179271.g002

In all MD simulations, the J2/3 region shows a pronounced mobility in agreement with experiments [16] and the assumption that the J2/3 region acts as an entry gate to the ligand binding site [9]. The fluctuations of nucleotides in the J1/2 and J3/1 regions are similar in magnitude to those in the P2 and P3 regions in all MD simulations, except for Gsw^loop in the absence of Mg²⁺ ions. Here, nucleotide 74 in the J3/1 region shows RMSF values that are ~2 Å higher than those of the other simulations. Pronounced fluctuations can also be observed in the L2 and L3 regions. In general, Gsw^loop shows a higher mobility than Gsw^apt, as seen from mean RMSF values calculated over the 80% least fluctuating nucleotides (S2 Table) that are up to ~0.6 Å higher in the former case (S4 Table). The presence of 20 Mg²⁺ ions results in mean RMSF values that are lower by ~0.5 Å (~0.8 Å) for Gsw^apt (Gsw^loop) than in the absence of Mg²⁺ ions.

In Fig 2C, 2D and 2E, differences in mean RMSF on a per-nucleotide level are projected onto the aptamer structure. Comparing the mean RMSF of Gsw^apt in the absence and presence of 20 Mg²⁺ ions (Fig 2C), we observe differences ≤ 1 Å at the ends of the terminal P1 region and in the loop region, which points to a subtle Mg²⁺-induced decrease in structural dynamics of the loop region and the adjacent P3 region. Addressing the influence of the G37A/C61U mutation on the aptamer mobility surprisingly reveals that the largest differences in RMSF between Gsw^loop and Gsw^apt in the absence of Mg²⁺ ions (Fig 2D) are not found at the mutation site in the loop region, but at the ligand binding site ~30 Å away and at the even farther end of the terminal P1 region. At the ligand binding site, particularly J2/3 and J3/1 show higher mobility in Gsw^loop, with the largest difference calculated for nucleotide 74 (2.4 Å). These results provide the first evidence at the atomistic level that the G37A/C61U mutation has a long range effect in terms of increasing the structural dynamics at the ligand binding site, as has been inferred from the influence on the ligand binding ability of Gsw^loop [15,18], and the P1 region, which has not been considered so far.

As for Gsw^apt but much more marked, we observe a Mg²⁺-induced decrease in structural dynamics of the aptamer for Gsw^loop: The Mg²⁺ ions now decrease the structural dynamics across the entire aptamer domain (Fig 2E). Large differences (> 2 Å) are found for the ends of the terminal P1 region (between 2.2 and 4 Å) and for the nucleotides in J3/1. Especially nucleotide 74 shows a large decrease in mobility in the presence of Mg²⁺ ions (2.2 Å). In addition, the L3 loop, the P3 region, and the joining J2/3 region are affected by the Mg²⁺-induced decrease in structural dynamics. Finally, the differences in RMSF between Gsw^loop and Gsw^apt in the presence of 20 Mg²⁺ ions (S8 Fig) are mostly small, with the largest difference (1.2 Å) found for nucleotide 63, which is part of the L3 loop, and other differences (< 1 Å) observed in the loop region.

In summary, we find that the G37A/C61U mutation results in increased structural dynamics of the aptamer domain of Gsw^loop compared to Gsw^apt. This is not only the case in the loop region where the mutation in Gsw^loop is located, but interestingly also at the distant ligand binding site and the P1 region. Mg²⁺ ions decrease the structural dynamics of the aptamer domains of both Gsw^apt and Gsw^loop. The Mg²⁺-induced decrease of the structural dynamics is much more pronounced in the case of Gsw^loop, however, such that Gsw^apt and Gsw^loop behave similarly in terms of atomic mobility in the presence of 20 Mg²⁺ per RNA.

Particularly in the presence of Mg²⁺, information on ligand binding is channeled to the P1 region

In order to gain further insights into the interplay of the L2-L3 region, the ligand binding core, and the P1 region as a function of ligand binding, we applied a graph-based rigidity analysis as implemented in the FIRST software [48]. The approach converts structural information of an input structure into a constraint network, where vertices represent atoms and edges (constraints) represent covalent and noncovalent interactions (hydrogen bonds, salt bridges, and hydrophobic interactions). Subsequently, the pebble game algorithm [49,50] is applied on the constraint network, which results in a decomposition into rigid regions and flexible links in between. Rigidity analyses have been successfully applied to investigate static properties (flexibility and rigidity characteristics) of proteins [48,51–54], also including analyses on the effect of ligand binding [52,55]. As to RNA, the approach was applied to the large ribosomal subunit [56–58] as well as smaller RNAs [59]. To do so, an RNA-specific parameterization of the constraint network has been developed [59], which is applied here. As suggested earlier [52,60,61], we applied the rigidity analysis to an ensemble of structures in order to improve the robustness of the results.

From the rigid cluster decomposition, we calculated the probability for each nucleotide to be in the largest rigid cluster (p_lrc(i), Eq 1), as done previously [52], and averaged these results over the MD-derived ensembles of Gsw^apt and Gsw^loop apo structures. In order to simulate the presence of guanine in the binding site of Gsw, we added additional constraints to the network connecting the nucleotides U47, C74, and U51, which bind guanine in the crystal structure (Fig 3A and 3B). According to ref. [59], the number and distribution of constraints will result in the nucleobases of U47, C74, and U51 forming one rigid unit. To probe how this local rigidification will percolate through the aptamer domain, we also calculated p_lrc(i) per nucleotide in the presence of the ligand constraints and, finally, the difference Δp_lrc(i) = p_lrc(i)_lig − p_lrc(i)_apo (S9 Fig, Fig 3C, 3D, 3E and 3F). The results yield insights into the influence of ligand binding on the location of the largest rigid cluster in the aptamer domain. Note that by construction, any influence due to conformational changes of the RNA between apo and ligand-bound state is excluded.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Rigidity analyses.

A: Nucleotides involved in binding guanine in the binding site of the aptamer domain of Gsw (PDB ID 1Y27 [26]). Black dashed lines indicate hydrogen bonds. B: Constraints (black lines) added to conformations of the apo aptamer domain of Gsw to model the presence of guanine in the binding site for rigidity analyses. C, D, E, F: Nucleotide-wise differences in the probability to be in the largest rigid cluster (Δp_lrc(i), Eq 1, E_HB = −0.6 kcal/mol for the rigidity analyses) between the ligand being present or absent in the aptamer domain, projected onto the aptamer domain of Gsw^apt (C, E) and Gsw^loop (D, F) in the absence of Mg²⁺ ions (C, D) and in the presence of 20 Mg²⁺ ions (E, F).

https://doi.org/10.1371/journal.pone.0179271.g003

In the absence of Mg²⁺ ions in the MD simulations (Fig 3C and 3D), the presence of the ligand constraints results in an increase of p_lrc(i) for nucleotides in the J1/2, J2/3 and J3/1 regions, which is not surprising. Similarly, nucleotides in P1, P2, and P3 adjacent to the ligand binding site show an increased p_lrc(i) in the presence of the ligand constraints, including nucleotides in the “P2 tune box” [17]. These results reveal a stabilization of the ligand binding site and its environment “above and below” due to the presence of ligand constraints.

In the presence of 20 Mg²⁺ ions (Fig 3E and 3F), we observe that the presence of the ligand constraints has only little effect on p_lrc(i) of nucleotides in the P2, P3, L2, and L3 regions (|Δp_lrc (i)|≤1%). In contrast, the presence of the ligand constraints result in a much larger increase in p_lrc(i) for nucleotides in the J2/3 region (up to 42%) and in the J3/1 region (up to 20%). As for the absence of Mg²⁺ ions, we again observe an increase in p_lrc(i) for all nucleotides in the P1 region by the presence of the ligand constraints, even though the values are higher in the absence of Mg²⁺ ions. Thus, in the presence of 20 Mg²⁺ ions, the stabilizing effect of ligand constraints is more local and channeled towards the P1 region.

The detailed comparison of Δp_lrc(i) between Gsw^apt and Gsw^loop in the absence of Mg²⁺ ions (Fig 3C and 3D) shows that the influence of the ligand constraints is similar by and large for the two variants, although differences up to ~5% in Δp_lrc(i) are found. Nucleotides in the binding region show a stronger influence of the ligand constraints in Gsw^loop. This is likely due to the larger flexibility observed for Gsw^loop in the binding region in the apo state, which becomes more restricted by the presence of the ligand constraints. In contrast, the presence of the ligand constraints has a slightly larger influence on nucleotides in the P1 region for Gsw^apt (up to 3%) than for Gsw^loop. In the presence of 20 Mg²⁺ ions, the stabilizing effect of the ligand constraints towards the terminal ends in the P1 region is more pronounced for Gsw^apt, which shows Δp_lrc(i) values for this region 2 to 7% higher than for Gsw^loop, with the higher values being closer to the ligand binding site.

In summary, we observe an increase in p_lrc(i) in the presence of ligand constraints for nucleotides at the ligand binding site and in its environment. In Gsw^apt and when 20 Mg²⁺ ions are present, the rigidifying effect towards the terminal ends of P1 is largest. Considering that the tertiary loop interactions are already preformed in the unbound state of Gsw^apt even in the absence of Mg²⁺ ions [31,32], yet are further strengthened in the presence of Mg²⁺ [31,62], this finding suggests that both the L2-L3 region and ligand binding cooperatively stabilize the P1 region.

Tertiary interactions in the loop region and ligand interactions cooperatively stabilize the terminal nucleotides in the P1 region

In order to verify that the tertiary loop-loop interactions and the presence of the ligand constraints rigidify the terminal nucleotides in the P1 region cooperatively, we computed the cooperative effect Coop(i) on the stabilization of nucleotides i in the P1 region from respective p_lrc(i) values according to Eq 2. If Coop(i) > 0, interactions at both sites together have a larger effect on nucleotide i than the sum of the effects of the separate interactions.

For the terminal nucleotides in the absence of Mg²⁺ ions, almost all of the nucleotides in the five terminal base pairs show Coop(i) values that are not significantly different from zero (Table 4), demonstrating that in this case the L2-L3 region and the ligand binding do not act cooperatively on P1. The only exception is nucleotide 77, which is close to the ligand binding site. In contrast, in the presence of 20 Mg²⁺ ions, all nucleotides in the five terminal base pairs show Coop(i) values that are positive and significantly or even highly significantly different from zero (Table 4, Fig 4A), demonstrating that with a structurally more stable aptamer domain, the L2-L3 region and the ligand binding act cooperatively on P1.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 4. Coop(i) values for the terminal nucleotides in the P1 region^[a].

https://doi.org/10.1371/journal.pone.0179271.t004

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. Cooperative influence on the P1 region.

A: Coop(i) values mapped onto the aptamer. The values were calculated according to Eq 2 for the systems in the presence of 20 Mg²⁺ ions (see also Table 4). Grey nucleotides show Coop(i) values that are not significantly different from zero (p > 0.05). B, C: Model for the influence of tertiary interactions and ligand binding on the stability of the P1 region. The tweezer represents the aptamer domain of the guanine-sensing riboswitch. The secondary structure elements are indicated by colors as in Fig 1A. The tertiary interactions are shown as dotted lines at the top of the tweezers and are encircled. The flexibility of the P1 region is indicated by the differently sized arrows at the bottom. B: The ligand-unbound state; C: The ligand (purple) has a stabilizing influence on the P1 region, but more so if the tertiary interactions are present.

https://doi.org/10.1371/journal.pone.0179271.g004

In summary, the stabilization of the L2-L3 region by tertiary interactions and the ligand binding site by ligand binding cooperatively influences the structural stability of the terminal base pairs in the P1 region in the presence of Mg²⁺ ions.

Molecular dynamics simulations

The setup of the molecular dynamics (MD) simulations in the present study is similar to that in our previous work [33]. However, the MD simulations performed here are 2.5 times longer than before. In detail: MD simulations were performed with the Amber 11 suite of programs [84,85] and the force field ff99 [86]. The starting structures for the MD simulations were obtained from ligand bound crystal structures. The ligands were removed from these, and the sequence of the wild type structure (PDB ID: 4FE5 [17]) was adapted to match the sequence of the G37A/C61U mutant (PDB ID: 3RKF [18]). For this, the coordinates of the bases of the mutant were copied after superimposing the wild type structure. As a result, wild type and mutant only differed in nucleotides 37 and 61. The modified wild type will be referred to as Gsw^apt, and the G37A/C61U mutant will be referred to as Gsw^loop, as introduced by Schwalbe et al. [18]. For both structures, three simulation systems with different Mg²⁺ concentrations (0, 12 and 20 Mg²⁺ ions per RNA molecule) were set up according to experimental findings on the Mg²⁺ dependence of Gsw^loop properties [15,18,31]. Due to slow exchange times of first shell ligands of the Mg²⁺ ions [37], the Mg²⁺ ions were added to the RNA system with a first hydration shell of six water molecules. This was done to prevent an early “sticking” of the Mg²⁺ ions to the RNA during the equilibration phase. To prevent clashes between the hydration shell and the RNA during the placement step, dummy ions with equal charge but larger radius of 4 Å, which is close to the radius of a hexahydrated Mg²⁺ ion [87], were placed first at electrostatically favorable locations with leap of Amber 11; these dummy ions were then replaced with a hexahydrated Mg²⁺ ion [69]. For details about the influence of the initial placement and the choice of the Mg²⁺ parameters see [33]. The system was afterwards placed in an octahedral box of TIP3P water molecules [88]. The distance between the edge of the water box and the closest RNA atom was at least 11 Å. Na⁺ ions [89] were added to neutralize the system net charge, resulting in a final system size of ~50,000 atoms.

Each system was then prepared based on a protocol described earlier [90]. In detail, each system was minimized by 200 steps of steepest descent minimization, followed by 50 steps of conjugate gradient minimization. The particle mesh Ewald method [91] was used to treat long range electrostatic interactions, and the SHAKE algorithm [92] was used to constrain bond lengths involving bonds to hydrogen atoms. The time step for all MD simulations was 2 fs, with a direct-space nonbonded cutoff of 9 Å. We carried out canonical ensemble (NVT)-MD simulations for 50 ps, during which the system was heated from 100 to 300K. During this step, harmonic restraints with force constants of 5 kcal mol^-1 Å^-2 to all solute atoms were applied. In addition, harmonic restraints were applied to the Mg²⁺ ions and the water molecules in their first hydration shell. Subsequently, isothermal isobaric ensemble (NPT)-MD simulations were used for 50 ps to adjust the solvent density. Finally, the force constants of the harmonic restraints on positions of RNA, Mg²⁺, and first hydration shell waters were gradually reduced to 1 kcal mol^-1 Å^-2 during 250 ps of NVT-MD simulations. This was followed by 50 ps of NVT-MD simulations without applying positional restraints. From the following 550 ns of NVT-MD simulations at 300 K performed by the GPU version of pmemd [93], conformations were extracted every 20 ps.

For each of the six system setups (Gsw^apt and Gsw^loop with three Mg²⁺ concentrations each), three independent MD simulations of 550 ns length each were performed summing up to a total simulation time of ~10 μs.

Trajectory analyses

The MD simulations were analyzed using cpptraj [94] of the AmberTools 13 program suite [95]. The initial 50 ns of each trajectory were discarded because the largest increase in overall RMSD was observed during this period (S3 Fig). The radius of gyration (ROG), a measure of the compactness of a structure, was calculated omitting the P1 region. This was done for conformations generated by MD simulations as well as for the crystal structures. Prior to the calculation of root mean-square atomic fluctuations (RMSF), global translational and rotational differences between the structures along the trajectory need to be removed by least-squares fitting. In order to reduce the influence of very mobile regions on the picture of internal motions [52,96–98], conformations were root mean-square fitted on those 80% of the nucleotides with the lowest fluctuations (S2 Table). These 54 nucleotides were chosen from an initial calculation of the mean RMSF over the three simulations of Gsw^apt in the absence of Mg²⁺ ions. These nucleotides were also used in the case of Gsw^loop then. Root mean-square deviations (RMSD) of atomic positions were calculated as a measure for structural similarity with respect to the initial structures. The RMSD was calculated after aligning the conformations onto the initial structure, using those 80% of the nucleotides with the lowest RMSF. The RMSD was then calculated for all atoms of the RNA as well as for all atoms of substructural parts of the aptamer (S5 Table). In order to investigate the change within a substructural part of the aptamer, RMSD values in S3 Table were calculated for the substructural parts after root mean-square fitting on the respective part in the initial conformation. Mean values were calculated over all three MD trajectories. Preferred Mg²⁺ ion occupancy sites were determined by the cpptraj program using the grid command using a grid spacing of 0.4 Å. The occupancy for hydrogen bonds between bases in the L2/L3 base quadruples were determined using default geometrical parameters (distance: 3.5 Å; angle: 120°). Block averaging over blocks of 10 ns length was used to determine the statistical uncertainty within one trajectory. The values reported in Table 2 were averaged over all hydrogen bonds between a pair of bases. The hexahydration of Mg²⁺ ions was determined by “following” the hydration shell around the ions over the simulation. Here, “following” means that we calculated the number of water molecules around each Mg²⁺ ion within a distance of 3.5 Å. Changes in the number of water molecules in the first hydration shell were subsequently confirmed by visual inspection. Furthermore, the direct chelation of Mg²⁺ ions to the RNA was determined by calculating the distance of each Mg²⁺ ion to the RNA. We considered a distance below 3.5 Å between a Mg²⁺ ion and an RNA atom indicative that the hydration shell of this Mg²⁺ ion is incomplete. The direct chelation was then confirmed by visual inspection of the trajectory.

We assessed the convergence of our simulations in two ways: First, we performed a principal component analysis for the phosphorus atoms of the aptamer over all trajectories. Then, we projected each trajectory onto the combinations of principal components (PC) PC1/PC2, PC1/PC3, and PC2/PC3. As shown in S10–S12 Figs exemplarily for Gsw^apt in the presence of 20 Mg²⁺ ions and Gsw^loop in the absence of Mg²⁺, all projections markedly overlap when comparing MD simulations of the same system, and when comparing the first and the second half of the trajectories. For Gsw^loop in the absence of Mg²⁺ ions, the projections onto PC1 show a larger spread between the MD simulations; however, the projections onto PC2 and PC3 overlap well. These results demonstrate that the three independent MD simulations per system sample similar regions in PC space, and the sampling agrees between the first and second halves of the trajectories. Additionally, we calculated the RMSD average correlation (RAC) [94,99] as implemented in cpptraj [94]. The RAC is a measure for the time scales on which structural changes happen in MD simulations. The RAC curves for all our simulations are shown in S13 Fig. From the bumps in the curves, we can estimate that structural changes happen on time scales of ~50–100 ns for Gsw^loop in the absence of Mg²⁺ ions (S13B Fig), whereas for the other systems, such bumps are found at shorter time intervals. For time intervals > 300 ns, the curves appear smooth, which suggests that there are no large structural changes happening on these time scales. Note that we calculated the RAC with respect to the first structure omitting the first 50 ns of each MD trajectory. As an alternative, the RAC can be calculated with respect to the average structure of an MD trajectory, which would result in smaller values [99]. Overall, these analyses are indicative to what extent the conformational ensembles of sampled aptamer structures are converged.

Rigidity analyses

In order to investigate the influence of the presence of a ligand in the binding site on the rigidity characteristics of the aptamer domain, we applied the FIRST software (version 6.2) [48]. FIRST converts structural information of an input structure into a constraint network representation, where vertices represent the atoms and edges represent interatomic interactions, e.g. covalent bonds, hydrogen bonds, or hydrophobic interactions. FIRST then uses the pebble game algorithm [49,50] to decompose the network into rigid regions and flexible links.

FIRST has not only been successfully applied to protein structures, but also proved successful in investigating and predicting flexibility and rigidity characteristics of RNA structures [56–59]. Here, we use an RNA-specific set of parameters developed by Fulle et al. [59] for modeling constraints due to non-covalent interactions, using -0.6 kcal mol^-1 as an energy cutoff E_cut for hydrogen bonds (Fig 3C, 3D, 3E and 3F; S9 Fig). A value of E_cut = −1.0 kcal/mol yielded very similar results (S14 Fig), as found earlier [59].

From the rigid cluster decomposition, we calculate the probability p_lrc(i) that atom i belongs to the largest rigid cluster according to , where n₁(i) is the number of occurrences of atom i as part of the largest rigid cluster, determined over all N snapshots extracted from the trajectory [52]. p_lrc(i) was calculated in the absence (apo) and presence (lig) of a ligand, as was the difference (1)

The average of Δp_lrc(i) over the three independent MD simulations for each of the six system setups is shown in S9 Fig, and projected onto the aptamer domain in Fig 3C, 3D, 3E and 3F. For the visualization, the value calculated for the N1 atom of each nucleotide's base is projected onto the whole nucleotide.

Averaging over an ensemble of snapshots from an MD simulation increases the robustness of the results compared to using a single input structure only [52,60,61]. Snapshots were extracted from the MD trajectories, considering the RNA and, if present, Mg²⁺ ions and their first hydration shell water molecules as proposed by Fulle et al. [59]. In detail, interactions between Mg²⁺ ions and their first hydration shell water molecules, or Mg²⁺ ions and the RNA, were modeled as covalent bonds, whereas interactions between water and RNA were modeled as hydrogen bonds. These snapshots were subsequently converted using the ambpdb program from the AmberTools suite of programs to FIRSTdataset files. In order to model the presence of the ligand guanine for the rigidity analyses by FIRST, we added constraints to the FIRSTdataset file connecting nucleotides U47, C74, and U51 in a pair-wise manner; these nucleotides interact with the ligand in the crystal structure (Fig 3A and 3B). To validate that the added constraints represent the bound ligand in the binding site, we additionally performed the rigidity analysis on the minimized X-ray structure of Gsw^loop (i) without a ligand in the binding site, (ii) with guanine at the position of the original ligand, and (iii) with the added constraints representing the ligand, and investigated the rigid cluster decomposition of the binding nucleotides (U47, U51, and C74) (S15 Fig). Without guanine or the ligand-representing constraints, the binding nucleotides do not belong to one rigid cluster (S15A Fig). The presence of guanine at the ligand binding site results in a rigid cluster that comprises all three binding nucleobases (S15B Fig). Similarly, when adding the ligand-representing constraints to the network, all three binding nucleobases are part of one rigid cluster (S15C Fig). The difference in the spread of the rigid cluster visible between S15B and S15C Fig relates to using a “weak” coupling scheme for the ligand-representing constraints, as discussed above.

In order to investigate the interplay between the presence of tertiary interactions in the loop region and the presence of a ligand in the binding site, we evaluate cooperative effects on the P1 region. To do so, we computed p_lrc(i) values for the aptamer domain without ligand constraints ( and for Gsw^apt and Gsw^loop, respectively) and with ligand constraints ( and for Gsw^apt and Gsw^loop, respectively). was chosen as the reference because it lacks interactions at both the loop region and the binding site. From this, we calculated the cooperative effect on the stabilization of the P1 region due to interactions at the two sites according to (2) where the term (3) describes the influence of the tertiary interactions together with the ligand, (4) describes the influence of the tertiary interactions alone, and (5) describes the influence of the ligand alone.

If Coop(i) > 0, interactions at both sites together have a larger effect on nucleotide i than the sum of the effects of the separate interactions. We are mainly interested in the effect on the terminal nucleotides in the P1 region, and thus in Coop(i) for i ∈ {15, 16, 17, 18, 19, 77, 78, 79, 80, 81}.