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* Department of Biotechnology, Graduate School of Agricultural and Life Sciences, and
Agricultural Bioinformatics Research Unit, Graduate School of Agricultural and Life Sciences, The University of Tokyo, Tokyo, Japan
Correspondence: Address reprint requests to S. Nakamura, E-mail: shugo{at}bi.a.u-tokyo.ac.jp.
| ABSTRACT |
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| INTRODUCTION |
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Intermolecular interactions, especially ones in which identity elements are involved, are thus thought to be the most important in tRNA recognition. However, Bullock et al. (7
) reported an exceptional case in which the bases of tRNAGln far from the binding interface have a remarkable effect on the affinity to GlnRS. They studied the binding of wild-type tRNAGln and its derivatives, aptamer T1 and aptamer var-AGGU (Fig. 1), to GlnRS using a gel-shift assay and determined their dissociation constants (Kd) (7.1 nM for the wild-type, 0.13 nM for aptamer T1 and 0.27 nM for aptamer var-AGGU). As shown in Fig. 1, the nucleotide sequence for var-AGGU is different from the wild-type only in the variable loop. Var-AGGU has 26 times lower Kd than the wild-type, which corresponds to the difference in the binding free energy of
8 kJ mol1. Although aptamer T1 has additional mutations in the T and D loops, its Kd value is only approximately half that of var-AGGU. This suggests that the replacement of the CAUUC sequence in the variable loop of the wild-type tRNAGln with AGGU is essential for the high affinities of aptamers. Since the variable loop is located on the opposite side of the GlnRS-binding interface in the structure of the wild-type tRNAGln-GlnRS complex, they determined the crystal structure of the complex with var-AGGU (PDB ID: 1EXD). However, the difference between the complex structures was too small to explain the mechanism responsible for the high affinity from a comparison of the structures. Therefore, they hypothesized that the difference in affinity results from entropic factors.
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| METHODS |
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ions were added to the system (18
Calculation of free energies
The free energy can be expressed as the sum of gas-phase enthalpy, solvation free energy, and vibrational entropy. The gas-phase enthalpy and the solvation free energy for each state were calculated with the molecular mechanics-Poisson-Boltzmann/surface area (MM-PB/SA) method (26
28
), as average values calculated for snapshot structures recorded during the MD simulation. The nonpolar contribution to the solvation free energy was estimated by using an empirical relation (29
),
A + b, where A is the solvation-accessible surface area and
and b are empirical constants. Here, solvation-accessible surface area was estimated with the MolSurf program (30
) and the values of
and b were 0.0301 and 0.00 kJ mol1, respectively. The polar contribution was calculated by solving the Poisson-Boltzmann equation numerically with the Delphi program (31
).
The vibrational entropy was estimated from the covariance matrix in the Cartesian coordinate system calculated from the MD trajectory (32
) as
![]() | (1) |
= h/2
, and h is Planck's constant. The elements of the covariance matrix,
, are given by
![]() | (2) |
...
denotes the average over the simulation time. The preliminary entropy values were calculated for different simulation periods t (2, 3, 4, 5, and 6 ns for the free tRNAs, and 3, 4, 5, and 6 ns for complexes) and were plotted against 1/t. The value obtained by extrapolating the plot to infinite simulation times (i.e., 1/t = 0) was used as the entropy of the system. Due to limitations with computational resources, only the positions of non-hydrogen atoms were considered in the calculations.
Diagonalizing covariance matrix
yielded a set of eigenvectors and eigenvalues corresponding to the modes of the collective motion of the system and the squares of their amplitudes, respectively. This is well known as principal component analysis (PCA). We applied PCA to the ensemble of the backbone atoms of G4G29, C41G43, and C49C69 to analyze the dynamics of the tertiary core regions of tRNAs.
| RESULTS AND DISCUSSION |
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, N, C for ARSs, and P, O3', C3', C4', C5', O5' for tRNAs) from the initial structures during the simulations. The simulations of the complexes revealed small deviations, whereas the values from the simulations of the free tRNAs were large, indicating relaxation from the modeled structures. Since all the systems can be assumed to reach equilibria within 0.5 ns from these plots, we used the trajectories after 0.5 ns in further analyses. To confirm whether the simulation time is sufficiently long or not, we partitioned the 6-ns trajectory from each free tRNA simulation into two 3-ns blocks and compared the conformational distributions between the two blocks. The mean of RMSD values from the average structure calculated within each block ranged from 2.15 to 2.75 Å, whereas the RMSD values between the average structures were 1.102.31 Å. This indicates that the conformational distributions of the 3-ns blocks fairly overlap with each other and that the conformation spaces were sufficiently sampled during the 6-ns simulations.
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Htot =
Htot(wild-type)
Htot(var-AGGU)) was 162 ± 12.8 kJ mol1. Note that the enthalpy and solvation free energy of ARS alone were canceled out in this calculation. The negative sign indicates that the binding of the wild-type tRNA to GlnRS was more preferable than that of the var-AGGU tRNA with respect to these terms. Therefore, the replacement of the nucleotide sequence of the variable loop did not increase the binding affinity enthalpically. Of the electrostatic (Hele + Gpol), nonpolar (Hvdw + Gnp), and internal (Hint) energy terms, the electrostatic term made the largest contribution to 
H. When the changes due to the replacement of the variable-loop sequence were calculated as the value of the wild-type minus that of var-AGGU, the change in the electrostatic contribution was larger in the complex state [
(Hele+Gpol)(complex) = 1324 kJ mol1] than in the free state [
(Hele+Gpol)(free) = 1146 kJ mol1].
To examine the electrostatic interactions more precisely, we counted the number of intermolecular and intramolecular hydrogen bonds that were formed during >30% of the entire simulation time (Table 2). In the MD simulations, the wild-type had more intermolecular hydrogen bonds than var-AGGU. Although the numbers of hydrogen bonds in which identity elements (6
) were involved were almost the same, the numbers of intermolecular hydrogen bonds outside the identity elements were considerably different. This same tendency was observed in the crystal structures. Changes in the intramolecular hydrogen bonds due to the replacement of the variable-loop sequence, on the other hand, were almost the same in the free and complex states. Therefore, the sequence replacement in the variable loop had an adverse effect on the binding free energy to ARS through the decrease in the number of intermolecular hydrogen bonds in the region outside the identity elements.
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TS =
TS(wild-type)
TS(var-AGGU)) was 106.4 ± 109.1 kJ mol1. Note that the entropy term of ARS is canceled out in the calculation. The negative sign of the average value indicates that the binding of var-AGGU to GlnRS is more preferable than that of the wild-type with respect to entropy. The difference between the entropies of the two complexes was very small (16 kJ mol1 from Table 3). This may be because the dynamics of the complex state is strongly predominated by GlnRS dynamics (34
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8 kJ mol1 (7The larger entropy of the wild-type tRNA in the free state implies greater internal mobility or wider conformational distribution in the molecule. To examine the conformational distributions of the tRNAs in free states, we analyzed the principal components of the covariance matrix used in calculating entropy. However, we could not find specific modes that could explain the difference in entropy. This was probably because the large bending motion inherent in the free tRNA obscured relatively small differences in entropy. Therefore, we only examined the conformational distributions of the backbone atoms of G4G29, C41G43, and C49C69 composed of spatial neighbors of the variable loop instead of whole structures, because this region is located in the center of the L-shaped tRNA structure and is not affected by bending motion. Note that this region includes the part of the tertiary core region common to wild-type and var-AGGU tRNAs.
Fig. 6 plots the contribution of each principal mode, converted into entropy, calculated from the conformational distributions for these regions of free tRNAs. The first two principal modes had large differences between wild-type and var-AGGU. Fig. 7 shows projections for the conformational distributions onto planes made by the first and the second principal axes. The distribution for the wild-type is broader than that for var-AGGU, and three well-separated conformational clusters can be identified. The distribution for var-AGGU is narrow and is composed of only one conformational cluster. To clarify the cause of multiplicity in the backbone structure for the wild-type in this region, we analyzed the hydrogen bonds bridging this region and the variable loop (Table 4). The hydrogen bonds for which stabilities were different between clusters are shown in Fig. 8. Clusters 1 and 3 had a similar pattern for the hydrogen-bond network. Although the non-Watson-Crick hydrogen bond between C44 and A26 observed in the crystal structure was not maintained well during the simulations, C44 formed hydrogen bonds with G24 and C25 in clusters 1 and 3 instead, whereas the base of C44 did not form stable hydrogen bonds in cluster 2. Clusters 1 and 3 were significantly different in the interaction between the N3 of U47 and the phosphate group of A21. In cluster 1, they formed a tight hydrogen bond as in the crystal structure, but the interaction was weak in clusters 2 and 3. In addition, the conformation of U46 in cluster 3, which was exposed to solvent, was quite different from those of clusters 1 and 2, as shown in Fig. 8. Conformational exchange between the structures of clusters 1 and 3 was observed during the first run of the simulations. Although most structures for the second and third runs were included in clusters 2 and 1, respectively, transitions to the structures of the other clusters were observed during the simulations. In this way, the tertiary core region of the wild-type tRNA adopted multiple stable conformations with a dynamic rearrangement of the hydrogen-bond network, whereas rearrangement was not observed during the simulations of free var-AGGU or of the complexes with ARS. It is reasonable to attribute the difference in the internal mobility in this region to the difference in the length and sequence of the variable loop between the wild-type and var-AGGU. Since the internal mobility of the tertiary core region probably has an influence on the mobility of the whole structure, we concluded that the larger entropy of the wild-type tRNA in the free state arises from the greater mobility in the tertiary core region. NMR studies in combination with hydrogen-deuterium exchange experiments are probably useful to verify the internal mobility of the tertiary core region, since they can quantify the strength of the hydrogen bonds and can determine the structure of the hydrogen-bond network in exchange equilibrium.
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| CONCLUSION |
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| ACKNOWLEDGEMENTS |
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Submitted on July 21, 2006; accepted for publication September 15, 2006.
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