The melting profiles of Stem 1 for both structures are comparable in stability. Interestingly, close to its melting temperature Stem 1 exhibits a temporal increase in its melting profile (around 70 °C for the wild-type pseudoknot and around 74 °C for the DKC-mutated pseudoknot). We observe that this increase is attributed to the temporary stabilization of Stem 1 due to the formation of two UU base pairs, U99:U115 and U100:U114. These base pairs are observed in the hairpin form of the pseudoknot. We have conducted several high temperature simulations (360K, 380K, 390 K, 400K) and observed the formation of the same intermediate structure. This intermediate structure may be indicative of the possible transition from the pseudoknot to the hairpin form, thus, supporting the molecular switch.

Our scaled melting temperatures and profiles for both structures are in agreement with experimental observations (21) and calculated predictions (Table III). Albeit our theoretical melting calculations are approximate, they appear to give qualitatively the same peaks and shoulders and show similar relative stability in the melting profiles.

The Effects of DKC Mutations on the Hairpin

We have previously showed that the telomerase hairpin undergoes periodic structural flips represented by the opening of base pairs in the helix (27). The DKC mutations in the hairpin, which are located in the pentaloop, reduce the number of structural flips by 80%. The RMSD plot of the DKC-mutated pseudoknot shows one structural fluctuation per 20 ns (Figure 7a) to five structural fluctuations per 20 ns in the wild-type hairpin (Figure 7b). Figure 7c illustrates the change in the hairpin structure at the flip (point A). The structural changes at the flip include the loss of hydrogen bonds for the U100:U114, U101:U113, U102:C112, U103:A111 base pairs, the rotation of A111-U114 outside of the helix, and the shortening of the helical axis curvature by 15% (Figure 7c). To assess the bend during the flip we calculated the global curvature and axis shortening using the program CURVES5.1 (46). The global curvature is the angle between the local helical axes of the second and n-1 base pairs of the helical region. The axis shortening is defined as one minus the ratio between the end-to-end distance of the helix and the axis path length and is presented in percentage. In the average wild-type hairpin structure the global curvature is 23.4 degrees and the axis shortening is 36.3%. In the hairpin structure at the flip the global curvature is 66.1 degrees and the axis shortening is 51.7%. The numbers represent a significant overall helical bend during the flip.



Figure 7: RMSDs relative to the average structure of (a) the DKC-mutated hairpin structure and (b) the wild-type hairpin structure. Letters A, B, C, D, E, and F denote the approximate locations of the flips in the trajectory. (c) Superposition between the backbone atoms of residues 93-98 and 116-121 of the average wild-type hairpin structure (blue) and the structure at the 3.9 ns flip (red). Residues 111-114 are represented as sticks with U113-114 in yellow, C112 in magenta, and A111 in green. This represents the helical twist, opening of the base pairs, and the rotation of 112-114 onto the side of the structure.

We discovered earlier that the flips in the wild-type hairpin structure are directly related to the rotation of residue U105 (27). We also noticed that in the DKC-mutated hairpin U105 is hydrogen bonded with U109 or G108, consequently reducing the conformational freedom of U105 and reducing the number of structural flips. The U105:U109 base pair can adopt two alternative conformations and sporadically switch from one to another (27). The hydrogen bond occupancies in the first conformation are 48.5% for O4(U109)...H3(U105) and 43.8% for O2(U105)...H3(U109). The hydrogen bond occupancies for the second conformation are 11.4% for O4(U105)...H3(U109) and 10.8% for O2(U109)...H3(U105). The hydrogen bond occupancy for U105:G108 is about 10.7%. Therefore, the rotation of U105 that leads to a structural flip is significantly reduced by the DKC mutations, but is still possible during the switch from one base pair conformation to another.

The average structures of the wild-type and DKC-mutated hairpins are very similar, with an RMSD of 0.5 Å in the helix. The only visible change is in the pentaloop (Figure 8). This indicates that the only structural change that the DKC mutations induce on the hairpin structure is the change of the pentaloop structure and not the helix itself. Yet dynamically the DKC mutation brings more stability to the hairpin structure.


Figure 8: Superposition of the average wild-type (red) and the average DKC-mutated (grey) hairpins. Secondary structures with predicted tertiary interactions of (b) the wild-type pseudoknot and (c) the DKC-mutated hairpin.

Enthalpy of Folding

Free energy has two components, enthalpy and entropy. Entropy is a measure of disorder and enthalpy (ΔH) is the measure of the internal energy (ΔE) of a biological system. All biological reactions take place at constant pressure (P) and temperature. Therefore, ΔH = ΔE + PΔV. Since biological reactions occur in a large excess of liquid, volume changes (ΔV) are extremely small, hence, PΔV is very small as well. Therefore, enthalpy and internal energy values of biological reactions are approximately the same and are referred to as the energy change of a reaction. Since the energy change in a chemical reaction comes from making and breaking of bonds, the value of ΔH can be calculated from the energy of the bonds. Since in our case no breaking or making of covalent bonds occur, the enthalpy change depends heavily on noncovalent bond energies, such as hydrogen bonds and van der Waals contacts.

Free energy and enthalpy calculations by molecular dynamics simulations can provide direct feedback between our findings on change in structural interactions and macroscopic thermodynamics. Moreover, free energy and enthalpy can also be measured experimentally. Furthermore, MM-PB(GB)SA calculations of binding free energy, absolute free energy, entropy, and enthalpy have been shown to correlate well with experimental observation for a number of molecular complexes (57, 58, 59, 60, 61). The entropy calculations are very computationally expensive for our system?s size and, therefore, were omitted in our results. We computed the enthalpy of folding (ΔH) for all four molecules, the wild-type hairpin and pseudoknot, and the DKC-mutated hairpin and pseudoknot. The folding process generally involves going from an RNA coil conformation to a folded structure. We have thus calculated the energetic differences between the folded structure and coiled sequence as described in the Methods section and compared it to the enthalpy obtained from the optical melting data analysis (21) and the enthalpy obtained from the efn server (62) (Table III). Since the efn server can not calculate the energy of the pseudoknot, pseudoknot structures were separated into Stem 1 (residues 93-121) and Stem 2 (residues 107-184). The Efn server 2.3 energy rules provide the free energy, entropy, enthalpy, and melting temperature values. First, we will discuss the hairpin structures followed by the pseudoknot structures.

For the hairpin structures, the secondary structure free energy calculations (62), which are based on the stability of the helix and loop size (independent of loop context), obtained identical thermodynamic parameters as expected. The experimentally observed enthalpy favors the DKC-mutated hairpin structure by 7 kcal/mol (21). Our MM-GBSA calculations show a similar enthalpy value for the hairpin with or without the DKC mutations.

For the pseudoknot structures, secondary structure free energy calculations, experimental results, and our simulation analysis agree that the DKC mutation significantly destabilizes the pseudoknot structure. Secondary structure free energy calculations (efn server) show an increase in the enthalpy due to the DKC mutations in the pseudoknot by 21 kcal/mol, which is attributed to the loss of two base pairs in Stem 2. Thermal denaturation experiments and our simulations show enthalpy gains of 41 to 51 kcal/mol, which indicate that there is a significant disruption of the bonding in the P3 helix involving more than two base pairs. Moreover, the difference between our simulated enthalpy and the experimentally determined enthalpy is reasonably small, with our values being slightly lower than the experimentally determined ones. The enthalpy agreement indicates that the noncovalent bonds, including H-bonds and van der Waals contacts in our predicted pseudoknot structures are within a reasonable proximity of the experimental structures.

Experimental Observations

The pseudoknot structure of the telomerase RNA is important for the catalytic activity of telomerase and TERT binding. Experimental studies of a two base mutation in DKC (GC107/108 → AG107/108) show significant reduction of telomerase activity and possible structural changes. Comolli et al. (20) showed that the DKC-mutations abrogated in vitro telomerase activity and hyperstabilized the hairpin conformation, blocking pseudoknot formation. Moreover, nondenaturating gel electrophoresis confirmed by NMR indicates that the DKC-mutations prevent formation of the P3 helix (20), in agreement with our results. Theimer et al. (21, 23, 26) reached similar conclusions about the effect of the DKC-mutation on telomerase and indicated that the DKC mutations significantly destabilized the pseudoknot conformation, resulting in the favorability of the hairpin structure and a reduction of activity by 93%. DKC mutations destabilize the pseudoknot by 6.6 kcal/mol and lower the tertiary melting temperature by 12-14 °C. Fu and Collins (22) found that the DKC-mutation and mutations in the P3 helix of the pseudoknot domain led to a strong decrease in telomerase activity in vivo and in vitro. Cerone et al. (24) showed that the DKC-mutated telomerase produced a weakly active telomerase enzyme defective in telomere elongation. Our results agree with the experiments that the DKC-mutations overstabilize the hairpin structure and disfavor pseudoknot formation. Moreover, we have suggested potential structural implications in the formation of the pseudoknot and its binding to hTERT, which can explain the reason for abrogated functionality.

Conclusions

In this paper, detailed analyses of the effects of the DKC mutations on the wild-type pseudoknot structure and dynamics were carried out. The DKC-mutated pseudoknot structure was predicted using molecular modeling. We show that DKC-mutations abolish the formation of the P3 helix, change the global orientation and appearance of the pseudoknot, and overall destabilize the structure. Energetic analysis reveals that the lower free energy and the higher stability of the wild-type telomerase pseudoknot are associated with a favorable electrostatic energy. The 3D prediction of the wild-type and the DKC-mutated pseudoknot structures is reinforced by comparison of the enthalpy of folding calculations.

In the hairpin form, the DKC mutations significantly improve stability and reduce the number of structural flips by roughly 80%. These flips were previously suggested to represent a nucleation point for pseudoknot formation or initiation of a molecular switch. Thus, we presume that the DKC mutations reduce the probability of a molecular switch by at least 80%.

We also conducted melting experiments that exhibit good agreement with UV denaturation experiments. Melting profiles show a temporary stabilization of Stem 1 just below the melting temperature due to the formation of U99:U115 and U100:U114 base pairs, as is found in the hairpin form of the pseudoknot telomerase RNA domain.

Overall, our study shows that the DKC mutations stabilize the hairpin form by extra non-Watson-Crick interactions in the pentaloop and destabilize the pseudoknot form by preventing the stable formation of the P3 helix. Our results are consistent with experimental observations and support published biochemical data. A potential drug can be designed to suppress the wild-type telomerase activity in cancerous cells by attacking the same bases that participate in the DKC mutation.

The predicted pseudoknot structure in this study was determined purely by molecular modeling. The accuracy of this structure is heavily dependent on accuracy of the force field, efficient conformational sampling, and the global energy minimum. Since the wild-type and the DKC-mutated pseudoknot structures have not been experimentally determined, presumably due to their complexity and lack of stability, our method shows a possible way to predict the main features of tertiary structures from a known secondary structure via molecular modeling and to examine the structural effects of mutations. The predicted structures can then be fitted into NMR NOESY data to determine their compatibility.

Acknowledgments

This research was supported by the Intramural Research Program of the NIH, National Cancer Institute, Center for Cancer Research. The computational support was partly provided by the National Cancer Institute?s Advanced Biomedical Computing Center.

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