- Email: [email protected]
Dynamical analysis of tRNAGln–GlnRS complex using normal mode calculation
Chemical Physics Letters 372 (2003) 423–431 www.elsevier.com/locate/cplett
Dynamical analysis of tRNAGln –GlnRS complex using normal mode calculation Shugo Nakamura b
a,*
, Mitsunori Ikeguchi b, Kentaro Shimizu
a
a Department of Biotechnology, The University of Tokyo, Yayoi 1-1-1, Bunkyo-ku, Tokyo 113-8657, Japan Science of Biological Supermolecular Systems, Graduate School of Integrated Science, Yokohama City University, Suehirocho 1-7-29, Tsurumi, Yokohama, Kanagawa 230-0045, Japan
Received 5 December 2002; in final form 28 February 2003
Abstract We applied normal mode calculation in internal coordinates to a complex of glutamine transfer RNA (tRNAGln ) and glutaminyl-tRNA synthetase (GlnRS). Calculated deviations of atoms agreed well with those obtained from X-ray data. The differences of motions corresponding to low mode frequencies between the free state and the complex state were analyzed. For GlnRS, many motions in the free state were conserved in the complex state, while the dynamics of tRNAGln was largely affected by the complex formation. Superimposed images of the conserved and non-conserved motions of tRNAGln clearly indicated the restricted direction of motions in the complex. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction The functions of biomolecules in many cases are regulated by the dynamics of the molecules. Conformational changes are often caused by the complex formation, and analyzing the dynamics of biomolecules in their free state and in their complex state is very important to understand in detail the functions of the biomolecules. Transfer RNAs (tRNAs) play an essential role in the process of translating genetic codes into proteins. To avoid mistranslations of genetic codes, aminoacyl-tRNA synthetases (ARSs) need
*
Corresponding author. Fax: +81-3-5841-8002. E-mail address: [email protected] (S. Nakamura).
to discriminate their cognate tRNAs and charge the corresponding amino acid correctly. Most tRNAs are similarly shaped; a clover-like secondary structure consisting of four main parts called stems and arms, and a unique L-shaped tertiary structure (Fig. 1a). Therefore, an ARS must discriminate its cognate tRNA very accurately. A great deal of research has been done in an effort to elucidate the mechanism of this accurate molecular recognition. The structures of tRNA–ARS complexes have been solved for many amino acid systems of several eucaryotes and procaryotes, and these structures suggest the induced fit mechanism of this molecular recognition. Bullock et al. designed a mutant of E. coli tRNAGln that binds to GlnRS with 30-fold improved affinity compared to the wild type [1]. In this mutant, five bases in the
0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00425-1
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S. Nakamura et al. / Chemical Physics Letters 372 (2003) 423–431
Fig. 1. (a) The secondary (left) and the tertiary (right) structure of tRNAGln . Nucleotide number 17 in tRNAGln is skipped according to the conventional numbering rule of tRNAs (considering the correspondence of structures of various tRNA molecules). (b) The structure of the complex of tRNAGln and GlnRS (PDB code: 1GTR). The structure of tRNAGln was drawn by a wire frame model and that of GlnRS by a ribbon model using Molscript [17].
variable loop are replaced by four other bases, and the positions of these bases are apart from the region in contact with GlnRS. These facts suggest that the dynamics of the two molecules play an important role in the precise recognition of molecules. The dynamics of tRNAs in the free state have been analyzed using molecular dynamics simulation and normal mode calculation [2–5]. The number of atoms in a tRNA–ARS complex, however, is so large that computer simulation methods, such as molecular dynamics calculation, as well as biochemical analysis, such as NMR, have hardly been applied to the molecules. Tateno et al. built a static model structure of the tRNAGlu –GluRS complex, through considering
the conformational change of the molecules induced by complex formation, using molecular dynamics simulation and a molecular modeling method [6,7]. Bahar et al. analyzed the dynamics of the E. coli tRNAGln –GlnRS complex using a coarse-grained potential model called the ÔGaussian Network ModelÕ [8]. Their method could estimate the deviation of atoms that agreed with the X-ray data. However, to compare the dynamics of the molecules in the free state and in the complex state more precisely, a method of analysis that uses the potential function in atomic resolution is needed. Here, we present the results of an analysis of the dynamics of E. coli tRNAGln –GlnRS complex (PDB code: 1GTR [9], Fig. 1b) in internal coor-
S. Nakamura et al. / Chemical Physics Letters 372 (2003) 423–431
dinates using a normal mode calculation. Using internal coordinates, we can largely reduce the number of degrees of freedom of the molecules. The AMBER potential function was used. We previously reported the development of a parallel algorithm that quickly calculates the hessian matrix in internal coordinates [10]. This algorithm achieved about 33 times speedup with 60 processors for the hessian calculation of tRNAGln molecule. We used this algorithm for the normal mode calculations in the present research. Calculated normal modes corresponding to the low frequencies in the free state and in the complex state of the two molecules were compared. We found that the motions of the molecules were largely coupled in the low-frequency regions, and we estimated the effect of complex formation on the dynamics of tRNAGln and GlnRS molecules.
2. Methods 2.1. Theory of normal mode calculation We applied normal mode calculation to the tRNAGln –GlnRS complex. Assuming that the potential energy function EðqÞ (q: generalized coordinates) can be approximated as parabolic, then EðqÞ is expressed using the values of generalized coordinates at a local minimum q0 ¼ fq0j g as follows: EðqÞ ¼
1X Fij ðqi q0i Þðqj q0j Þ; 2 i;j
ð1Þ
where i and j are the numbers of generalized coordinates (ith and jth rotatable bonds in internal coordinates), and Fij is the second derivative of E by qi and qj , i.e., Fij ¼ o2 E=oqi oqj . The kinetic energy K can be expressed as follows: 1X K¼ Hij q_i q_j ; ð2Þ 2 i;j where X orl orl Hij ¼ ml ; oqi oqj l ml is the mass of atom l, and rl is the position vector of atom l. Using Eqs. (1) and (2), Lag-
425
rangeÕs equation of motion can be expressed as the generalized eigenvalue problem as follows: HAK ¼ FA;
AT HA ¼ dij ;
ð3Þ
where K is the diagonal matrix with its ði; jÞ element of Kij ¼ x2i dij (dij is the KroneckerÕs delta). A generalized coordinate qj can be expressed using coefficients Ajk and numbers of vibrations xk : X qj ¼ q0j þ Ajk Qk ; ð4Þ k
where Qk is kth normal mode and Qk ¼ ak cosðxk t þ bk Þ. The amplitude of each normal mode ak can be obtained using the equipartition law of energy as follows: sffiffiffiffiffiffiffiffi 2kT ak ¼ ; ð5Þ x2k where T is the temperature of the system, and k is the Boltzmann factor. For all the calculations of our present calculation, T is set to 300 K. Fluctuation vector of atom l of the kth mode (d kl ) can be calculates as follows: sffiffiffiffiffiffi X orl kT d kl ¼ Aik : ð6Þ x2k oqi i The square of thermal fluctuation of atom l can be obtained as the sum of the square of d kl over all normal modes. The forcefield parameters we used were those of AMBER4.0 [11,12] and the dielectric constant was set to a sigmoidal function between atoms [13]. For nucleotides, the rotatable bonds are a, b, c, d, and f along the phosphate backbone and v of the glycosyl bonds. For amino acids, / and w are considered to be rotatable. The number of degrees of freedom was 2621 for GlnRS, 441 for tRNAGln , and 3068 for the complex including the rotation and translation between the two molecules. 2.2. Building initial structures The structures of E. coli tRNAGln and GlnRS in the free states have not been identified up to now, thus we have to model the free-state structures of
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these molecules. Starting from the X-ray data of the complex, we applied the energy minimization in Cartesian coordinates to tRNAGln and GlnRS independently by 500-step conjugate gradient minimization of AMBER4.0 package. Then these structures were subjected to energy minimization in the internal coordinates using the combination of the steepest descent method and the Newton– Raphson method. For the initial structure of the complex, a process similar to minimization in Cartesian coordinates followed by the minimization in internal coordinates was applied to the structure determined by using X-ray analysis. After the minimization, all of the eigenvalues of the hessian matrix F in all cases became positive definite. The root-mean-square deviation (r.m.s.d.) for tRNAGln – after the minimization was 1.1 A Gln for tRNA , and 0.6 A for GlnRS complex, 1.6 A GlnRS (Ca atoms for GlnRS and phosphorus atoms for tRNAGln were considered).
3. Results and discussion 3.1. The lowest mode frequencies Using normal mode analysis, the thermal fluctuations of atoms can be divided into each normal mode having various mode frequencies. The lowest mode frequency for tRNAGln was 0.70 cm1 . This is similar to the lowest mode frequencies of other tRNA molecules [4]. The lowest mode frequency for GlnRS in the free state was 1.54 cm1 . The lowest mode frequency for tRNAGln –GlnRS complex slightly shifted from that for GlnRS in the free state to the lower value of 1.42 cm1 .
2.3. Correlation of the direction of motions between the free state and the complex state To compare the two normal modes in the free state and in the complex state, we define the similarity of the modes according to the directions of the fluctuation vectors of the atoms: N f X d im d cjm f N; Sij ¼ ð7Þ c m¼1 d im jjd jm where d fim shows the displacement vector of the mth atom of the ith mode in the free state, d cjm shows that of the mth atom of the jth mode in the complex state, and N is the number of atoms in the molecule. We focus on the direction rather than the phase of the atom fluctuations, hence we sum up the absolute values of dot products as the numerator of Eq. (7). The similarity is calculated after best fittings of the structures in both the free and complex states. If the directions of the displacement vectors are exactly the same for all atoms in the ith mode in the free state and in the jth mode in the complex state, the similarity Sij is equal to 1. If the directions of the displacement vectors are completely orthogonal for all atoms in both modes, Sij is equal to 0.
Fig. 2. Deviation of atoms averaged over residues and nucleotides. Solid lines: deviations calculated by normal mode analysis. Dashed lines: deviations obtained from B-factors of X-ray data. (a) tRNAGln , (b) GlnRS.
S. Nakamura et al. / Chemical Physics Letters 372 (2003) 423–431
Fig. 2 shows the thermal fluctuations of the atoms of the complex. The solid line shows the fluctuations calculated by normal mode analysis averaged per residue and nucleotide. The broken line shows the fluctuations obtained from the B-factors of the X-ray data. Calculated fluctuations agreed well with the X-ray data. The correlation coefficient of these two lines was 0.97 for tRNAGln and 0.90 for GlnRS.
427
The amplitudes of the fluctuations of atoms in , both tRNAGln and GlnRS were mostly below 1 A which is rather smaller than those in the free state (data not shown). For tRNAGln , the fluctuations of atoms on the contacting surface with GlnRS, especially in the acceptor stem (U1-A7, U66-A76) and in the anticodon loop (U32-U38) were restricted. The fluctuations were not so restricted for atoms in the D loop (A13-A22) and the T loop
Fig. 3. (a) Atom fluctuations of the lowest frequency mode of tRNAGln –GlnRS complex. (Blue) tRNAGln . (Red) GlnRS. The mode frequency is 1.42 cm1 . The lengths of the arrows are magnified 15.0 times. The right figure is the side view of the left figure. (b) Domain motions of low-frequency modes (tRNAGln –GlnRS complex) analyzed by DynDom [15,16].
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(U54-U60). In the core region where the D arm meets the T arm (around U8-C16, A21-C27, G43C48, A59), deviations of the atoms were relatively small (except for U46 which flips to the outside of the molecule). That seemed to show the stabilization of this region. For GlnRS, large deviations were observed on residues Arg271, Met362, Glu427, and Asp485, which were on the surface of the molecule. The anticodon recognition domain (the bottom part of GlnRS in Fig. 1b) had relatively large deviations. Fig. 3a shows the displacement vectors of atoms corresponding to the lowest mode frequency. Arrows show the directions and the amplitudes of the displacement vectors of atoms. Blue arrows show the fluctuations of atoms in tRNAGln and red arrows show those of GlnRS. The lengths of the arrows are magnified 15 times. The right figure of Fig. 3a is the side view of the left figure. The main characteristics of the dynamics of the complex were highly coupled motions of tRNAGln and GlnRS. This is quite different from the case of globular protein complexes, such as the complex of subtilisin and eglin c [14], in which the lowest mode corresponds to the mostly relative motions between the two molecules and the internal motions of each molecule are relatively small. This difference may be caused by the unique L-shape of tRNAGln and the binding of the GlnRS to the inner side of tRNAGln having a large binding interface. The correlations between relative motions and internal motions had large negative values on the contacting surface of the two molecules (data not shown). This is similar to the complex of subtilisin and eglin c [14]. Fig. 3b shows the results of the analysis of the domain motions corresponding to the lowest frequency shown in Fig. 3a obtained by using DynDom [15,16]. In the figure, tRNAGln is represented by wireframe model and GlnRS is represented by a ribbon model. The regions in yellow, red, and blue are dynamic domain regions that can be considered to fluctuate as rigid bodies. The regions in green are inter-domain bending regions. The coupling of the motions of GlnRS and tRNAGln in this mode was clearly shown in Fig. 3b. The motions of the double helix of tRNAGln , which consists of the acceptor stem and the T arm, and those of the catalytic
domain of GlnRS were coupled (yellow region). The motions of the anticodon arm of tRNAGln and those of the anticodon recognition domain of GlnRS were also coupled (blue region). These
Fig. 4. Correlation of the motions between free state and complex state measured by the similarity measure of Sij . (a) tRNAðGlnÞ , (b) GlnRS.
S. Nakamura et al. / Chemical Physics Letters 372 (2003) 423–431
couplings are considered to indicate the tight binding of these parts of tRNAGln and GlnRS to enable accurate recognition of the anticodon and effective aminoacylation in the catalytic site. In the low-frequency modes, the major motions of GlnRS were bending motions between structural domains. The motions of tRNAGln were hinge bending between three parts, which were the acceptor stem, the anticodon arm, and the area around the core region of the molecule. This fact is considered to represent the characteristics of the dynamics of globular proteins and that of doublestranded nucleic acids. 3.2. Similarity of modes in the free state and in the complex state Fig. 4 shows the similarity of the fluctuations of atoms between the complex state and the free state of each normal mode, as defined by Eq. (7). In this section, one mode is assumed to correspond to the
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other mode if the directions of the atom fluctuations of these two modes are similar to each other. Fig. 4a is for tRNAGln and 4b for GlnRS. In both Figs. 4a and 4b, the vertical axis represents the mode numbers in the complex state and the horizontal axis represents those in the free state. Mode numbers are sorted in ascending order of the mode frequencies, therefore, Ômode 0Õ is the mode having the lowest frequency. For tRNAGln in the complex state, there are six modes that correspond to the modes in the free state (Sij P 0:65) out of 12 lowest modes (Fig. 4a). For example, mode 0 in the complex state corresponds to modes 2 and 8 in the free state, which means that the directions of the atom fluctuations of modes 2 and 8 in the free state are conserved in the complex formation. Modes 2, 6, and 8 have no corresponding modes in a free state, which means that these motions are induced by the complex formation. In Fig. 4a, the corresponding mode pairs (red and orange squares) are scattered on the matrix.
Fig. 5. Superimposed images of the atom fluctuations of conserved modes (modes 1, 2, 4, 6, 8, and 9; green) and non-conserved modes (modes 0, 3, 5, and 7; magenta) of tRNAGln in the free state.
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This means that the mode frequencies of the corresponding modes were not conserved before and after the complex formation. For GlnRS in the complex state, there are 10 modes that have corresponding modes in the free state out of twelve lowest modes (Fig. 4b). The corresponding mode pairs are in the diagonal region on the matrix. The frequencies of the corresponding modes were mostly conserved. This means that the dynamics of GlnRS molecule was not affected by the binding of tRNAGln and that this result is in contrast with the case of tRNAGln . Fig. 5 shows the superposition of conserved (modes 1, 2, 4, 6, 8, and 9) and non-conserved (modes 0, 3, 5, and 7) modes up to the 10 lowest modes for tRNAGln in the free state. The conserved motions are represented by green arrows and non-conserved motions are represented by magenta arrows. The right figure is the side view of the left figure. The lengths of the arrows are magnified seven times. It is clearly shown that the motions along with the Ôopen and closeÕ of the L-shape are restricted and thus disappear in the complex, while the swings of both the anticodon arm and the acceptor arm perpendicular to the open/close direction are conserved. Most tRNAs have similar L-shape structures, but the structures of ARSs and the binding modes of tRNAs and ARSs of different amino acids and different species are quite diverse. Conserved and non-conserved motions of tRNAs and ARSs are likely to represent the dynamical aspects of the characteristics of the molecular recognition mechanism for each tRNA–ARS complex. Now we are working on analyzing the dynamics of other types of tRNA–ARS complexes in the complex and free states by using normal mode calculation and molecular dynamics simulation.
4. Conclusion We analyzed the dynamical aspects of the E. coli tRNAGln –GlnRS complex by using normal mode calculation. The estimated deviation of atoms agreed well with that obtained from X-ray data.
Atom fluctuations that corresponded to modes having a low-frequency region revealed the largely coupled motion of tRNAGln and GlnRS, especially around the active site and the anticodon region. We analyzed the similarity of atom fluctuations between in the complex state and in the free state. For GlnRS, low-frequency motions are almost conserved, while for tRNAGln the dynamics are largely affected by the complex formation. Superimposed images of the conserved and non-conserved motions of tRNAGln revealed the restricted directions in the complex. The comparison of these dynamical characteristics may provide clues to elucidate the mechanism of tRNA–ARS recognition in each amino acid system.
Acknowledgements This work was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Encouragement of Young Scientists.
References [1] T.L. Bullock, L.D. Sherlin, J.J. Perona, Nature Struct. Biol. 6 (2000) 497. [2] S.C. Harvey, M. Prabhakaran, J.A. McCammon, Biopolymers 24 (1985) 1169. [3] M. Prabhakaran, S.C. Harvey, J.A. McCammon, Biopolymers 24 (1985) 1189. [4] S. Nakamura, J. Doi, Nucleic Acids Res. 22 (1994) 514. [5] A. Matsumoto, M. Tomimoto, N. G o, Eur. Biophys. J. Biophys. Lett. 28 (1999) 369. [6] M. Tateno, O. Nureki, K. Yura, K. Morikawa, T. Noguti, S. Yokoyama, M. Go, Prot. Eng. 8 (1995) 47. [7] M. Tateno, O. Nureki, S. Sekine, K. Kaneda, M. Go, S. Yokoyama, FEBS Lett. 377 (1985) 77. [8] I. Bahar, R.L. Jernigan, J. Mol. Biol. 281 (1998) 871. [9] M.A. Rould, J.J. Perona, T.A. Steitz, Nature 352 (1991) 213. [10] S. Nakamura, M. Ikeguchi, K. Shimizu, J. Comput. Chem. 19 (1998) 1716. [11] S.J. Weiner, P.A. Kollman, D.A. Case, U.C. Singh, C. Ghio, G. Alagona, P. Weiner, J. Am. Chem. Soc. 106 (1984) 765. [12] S.J. Weiner, P.A. Kollman, D.T. Nguyen, D.A. Case, J. Comput. Chem. 7 (1986) 230. [13] B.E. Hingerty, R.H. Ritchie, T.L. Ferrell, J.E. Turner, Biophys. J. 24 (1985) 427.
S. Nakamura et al. / Chemical Physics Letters 372 (2003) 423–431 [14] H. Ishida, Y. Jochi, A. Kidera, Proteins 32 (1998) 324. [15] S. Hayward, A. Kitao, H.J.C. Berendsen, Proteins 27 (1997) 425.
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[16] S. Hayward, H.J.C. Berendsen, Proteins 30 (1998) 144. [17] P.J. Kraulis, J. Appl. Crystallogr. 24 (1991) 946.
Dynamical analysis of tRNAGln –GlnRS complex using normal mode calculation Shugo Nakamura b
a,*
, Mitsunori Ikeguchi b, Kentaro Shimizu
a
a Department of Biotechnology, The University of Tokyo, Yayoi 1-1-1, Bunkyo-ku, Tokyo 113-8657, Japan Science of Biological Supermolecular Systems, Graduate School of Integrated Science, Yokohama City University, Suehirocho 1-7-29, Tsurumi, Yokohama, Kanagawa 230-0045, Japan
Received 5 December 2002; in final form 28 February 2003
Abstract We applied normal mode calculation in internal coordinates to a complex of glutamine transfer RNA (tRNAGln ) and glutaminyl-tRNA synthetase (GlnRS). Calculated deviations of atoms agreed well with those obtained from X-ray data. The differences of motions corresponding to low mode frequencies between the free state and the complex state were analyzed. For GlnRS, many motions in the free state were conserved in the complex state, while the dynamics of tRNAGln was largely affected by the complex formation. Superimposed images of the conserved and non-conserved motions of tRNAGln clearly indicated the restricted direction of motions in the complex. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction The functions of biomolecules in many cases are regulated by the dynamics of the molecules. Conformational changes are often caused by the complex formation, and analyzing the dynamics of biomolecules in their free state and in their complex state is very important to understand in detail the functions of the biomolecules. Transfer RNAs (tRNAs) play an essential role in the process of translating genetic codes into proteins. To avoid mistranslations of genetic codes, aminoacyl-tRNA synthetases (ARSs) need
*
Corresponding author. Fax: +81-3-5841-8002. E-mail address: [email protected] (S. Nakamura).
to discriminate their cognate tRNAs and charge the corresponding amino acid correctly. Most tRNAs are similarly shaped; a clover-like secondary structure consisting of four main parts called stems and arms, and a unique L-shaped tertiary structure (Fig. 1a). Therefore, an ARS must discriminate its cognate tRNA very accurately. A great deal of research has been done in an effort to elucidate the mechanism of this accurate molecular recognition. The structures of tRNA–ARS complexes have been solved for many amino acid systems of several eucaryotes and procaryotes, and these structures suggest the induced fit mechanism of this molecular recognition. Bullock et al. designed a mutant of E. coli tRNAGln that binds to GlnRS with 30-fold improved affinity compared to the wild type [1]. In this mutant, five bases in the
0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00425-1
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S. Nakamura et al. / Chemical Physics Letters 372 (2003) 423–431
Fig. 1. (a) The secondary (left) and the tertiary (right) structure of tRNAGln . Nucleotide number 17 in tRNAGln is skipped according to the conventional numbering rule of tRNAs (considering the correspondence of structures of various tRNA molecules). (b) The structure of the complex of tRNAGln and GlnRS (PDB code: 1GTR). The structure of tRNAGln was drawn by a wire frame model and that of GlnRS by a ribbon model using Molscript [17].
variable loop are replaced by four other bases, and the positions of these bases are apart from the region in contact with GlnRS. These facts suggest that the dynamics of the two molecules play an important role in the precise recognition of molecules. The dynamics of tRNAs in the free state have been analyzed using molecular dynamics simulation and normal mode calculation [2–5]. The number of atoms in a tRNA–ARS complex, however, is so large that computer simulation methods, such as molecular dynamics calculation, as well as biochemical analysis, such as NMR, have hardly been applied to the molecules. Tateno et al. built a static model structure of the tRNAGlu –GluRS complex, through considering
the conformational change of the molecules induced by complex formation, using molecular dynamics simulation and a molecular modeling method [6,7]. Bahar et al. analyzed the dynamics of the E. coli tRNAGln –GlnRS complex using a coarse-grained potential model called the ÔGaussian Network ModelÕ [8]. Their method could estimate the deviation of atoms that agreed with the X-ray data. However, to compare the dynamics of the molecules in the free state and in the complex state more precisely, a method of analysis that uses the potential function in atomic resolution is needed. Here, we present the results of an analysis of the dynamics of E. coli tRNAGln –GlnRS complex (PDB code: 1GTR [9], Fig. 1b) in internal coor-
S. Nakamura et al. / Chemical Physics Letters 372 (2003) 423–431
dinates using a normal mode calculation. Using internal coordinates, we can largely reduce the number of degrees of freedom of the molecules. The AMBER potential function was used. We previously reported the development of a parallel algorithm that quickly calculates the hessian matrix in internal coordinates [10]. This algorithm achieved about 33 times speedup with 60 processors for the hessian calculation of tRNAGln molecule. We used this algorithm for the normal mode calculations in the present research. Calculated normal modes corresponding to the low frequencies in the free state and in the complex state of the two molecules were compared. We found that the motions of the molecules were largely coupled in the low-frequency regions, and we estimated the effect of complex formation on the dynamics of tRNAGln and GlnRS molecules.
2. Methods 2.1. Theory of normal mode calculation We applied normal mode calculation to the tRNAGln –GlnRS complex. Assuming that the potential energy function EðqÞ (q: generalized coordinates) can be approximated as parabolic, then EðqÞ is expressed using the values of generalized coordinates at a local minimum q0 ¼ fq0j g as follows: EðqÞ ¼
1X Fij ðqi q0i Þðqj q0j Þ; 2 i;j
ð1Þ
where i and j are the numbers of generalized coordinates (ith and jth rotatable bonds in internal coordinates), and Fij is the second derivative of E by qi and qj , i.e., Fij ¼ o2 E=oqi oqj . The kinetic energy K can be expressed as follows: 1X K¼ Hij q_i q_j ; ð2Þ 2 i;j where X orl orl Hij ¼ ml ; oqi oqj l ml is the mass of atom l, and rl is the position vector of atom l. Using Eqs. (1) and (2), Lag-
425
rangeÕs equation of motion can be expressed as the generalized eigenvalue problem as follows: HAK ¼ FA;
AT HA ¼ dij ;
ð3Þ
where K is the diagonal matrix with its ði; jÞ element of Kij ¼ x2i dij (dij is the KroneckerÕs delta). A generalized coordinate qj can be expressed using coefficients Ajk and numbers of vibrations xk : X qj ¼ q0j þ Ajk Qk ; ð4Þ k
where Qk is kth normal mode and Qk ¼ ak cosðxk t þ bk Þ. The amplitude of each normal mode ak can be obtained using the equipartition law of energy as follows: sffiffiffiffiffiffiffiffi 2kT ak ¼ ; ð5Þ x2k where T is the temperature of the system, and k is the Boltzmann factor. For all the calculations of our present calculation, T is set to 300 K. Fluctuation vector of atom l of the kth mode (d kl ) can be calculates as follows: sffiffiffiffiffiffi X orl kT d kl ¼ Aik : ð6Þ x2k oqi i The square of thermal fluctuation of atom l can be obtained as the sum of the square of d kl over all normal modes. The forcefield parameters we used were those of AMBER4.0 [11,12] and the dielectric constant was set to a sigmoidal function between atoms [13]. For nucleotides, the rotatable bonds are a, b, c, d, and f along the phosphate backbone and v of the glycosyl bonds. For amino acids, / and w are considered to be rotatable. The number of degrees of freedom was 2621 for GlnRS, 441 for tRNAGln , and 3068 for the complex including the rotation and translation between the two molecules. 2.2. Building initial structures The structures of E. coli tRNAGln and GlnRS in the free states have not been identified up to now, thus we have to model the free-state structures of
426
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these molecules. Starting from the X-ray data of the complex, we applied the energy minimization in Cartesian coordinates to tRNAGln and GlnRS independently by 500-step conjugate gradient minimization of AMBER4.0 package. Then these structures were subjected to energy minimization in the internal coordinates using the combination of the steepest descent method and the Newton– Raphson method. For the initial structure of the complex, a process similar to minimization in Cartesian coordinates followed by the minimization in internal coordinates was applied to the structure determined by using X-ray analysis. After the minimization, all of the eigenvalues of the hessian matrix F in all cases became positive definite. The root-mean-square deviation (r.m.s.d.) for tRNAGln – after the minimization was 1.1 A Gln for tRNA , and 0.6 A for GlnRS complex, 1.6 A GlnRS (Ca atoms for GlnRS and phosphorus atoms for tRNAGln were considered).
3. Results and discussion 3.1. The lowest mode frequencies Using normal mode analysis, the thermal fluctuations of atoms can be divided into each normal mode having various mode frequencies. The lowest mode frequency for tRNAGln was 0.70 cm1 . This is similar to the lowest mode frequencies of other tRNA molecules [4]. The lowest mode frequency for GlnRS in the free state was 1.54 cm1 . The lowest mode frequency for tRNAGln –GlnRS complex slightly shifted from that for GlnRS in the free state to the lower value of 1.42 cm1 .
2.3. Correlation of the direction of motions between the free state and the complex state To compare the two normal modes in the free state and in the complex state, we define the similarity of the modes according to the directions of the fluctuation vectors of the atoms: N f X d im d cjm f N; Sij ¼ ð7Þ c m¼1 d im jjd jm where d fim shows the displacement vector of the mth atom of the ith mode in the free state, d cjm shows that of the mth atom of the jth mode in the complex state, and N is the number of atoms in the molecule. We focus on the direction rather than the phase of the atom fluctuations, hence we sum up the absolute values of dot products as the numerator of Eq. (7). The similarity is calculated after best fittings of the structures in both the free and complex states. If the directions of the displacement vectors are exactly the same for all atoms in the ith mode in the free state and in the jth mode in the complex state, the similarity Sij is equal to 1. If the directions of the displacement vectors are completely orthogonal for all atoms in both modes, Sij is equal to 0.
Fig. 2. Deviation of atoms averaged over residues and nucleotides. Solid lines: deviations calculated by normal mode analysis. Dashed lines: deviations obtained from B-factors of X-ray data. (a) tRNAGln , (b) GlnRS.
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Fig. 2 shows the thermal fluctuations of the atoms of the complex. The solid line shows the fluctuations calculated by normal mode analysis averaged per residue and nucleotide. The broken line shows the fluctuations obtained from the B-factors of the X-ray data. Calculated fluctuations agreed well with the X-ray data. The correlation coefficient of these two lines was 0.97 for tRNAGln and 0.90 for GlnRS.
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The amplitudes of the fluctuations of atoms in , both tRNAGln and GlnRS were mostly below 1 A which is rather smaller than those in the free state (data not shown). For tRNAGln , the fluctuations of atoms on the contacting surface with GlnRS, especially in the acceptor stem (U1-A7, U66-A76) and in the anticodon loop (U32-U38) were restricted. The fluctuations were not so restricted for atoms in the D loop (A13-A22) and the T loop
Fig. 3. (a) Atom fluctuations of the lowest frequency mode of tRNAGln –GlnRS complex. (Blue) tRNAGln . (Red) GlnRS. The mode frequency is 1.42 cm1 . The lengths of the arrows are magnified 15.0 times. The right figure is the side view of the left figure. (b) Domain motions of low-frequency modes (tRNAGln –GlnRS complex) analyzed by DynDom [15,16].
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(U54-U60). In the core region where the D arm meets the T arm (around U8-C16, A21-C27, G43C48, A59), deviations of the atoms were relatively small (except for U46 which flips to the outside of the molecule). That seemed to show the stabilization of this region. For GlnRS, large deviations were observed on residues Arg271, Met362, Glu427, and Asp485, which were on the surface of the molecule. The anticodon recognition domain (the bottom part of GlnRS in Fig. 1b) had relatively large deviations. Fig. 3a shows the displacement vectors of atoms corresponding to the lowest mode frequency. Arrows show the directions and the amplitudes of the displacement vectors of atoms. Blue arrows show the fluctuations of atoms in tRNAGln and red arrows show those of GlnRS. The lengths of the arrows are magnified 15 times. The right figure of Fig. 3a is the side view of the left figure. The main characteristics of the dynamics of the complex were highly coupled motions of tRNAGln and GlnRS. This is quite different from the case of globular protein complexes, such as the complex of subtilisin and eglin c [14], in which the lowest mode corresponds to the mostly relative motions between the two molecules and the internal motions of each molecule are relatively small. This difference may be caused by the unique L-shape of tRNAGln and the binding of the GlnRS to the inner side of tRNAGln having a large binding interface. The correlations between relative motions and internal motions had large negative values on the contacting surface of the two molecules (data not shown). This is similar to the complex of subtilisin and eglin c [14]. Fig. 3b shows the results of the analysis of the domain motions corresponding to the lowest frequency shown in Fig. 3a obtained by using DynDom [15,16]. In the figure, tRNAGln is represented by wireframe model and GlnRS is represented by a ribbon model. The regions in yellow, red, and blue are dynamic domain regions that can be considered to fluctuate as rigid bodies. The regions in green are inter-domain bending regions. The coupling of the motions of GlnRS and tRNAGln in this mode was clearly shown in Fig. 3b. The motions of the double helix of tRNAGln , which consists of the acceptor stem and the T arm, and those of the catalytic
domain of GlnRS were coupled (yellow region). The motions of the anticodon arm of tRNAGln and those of the anticodon recognition domain of GlnRS were also coupled (blue region). These
Fig. 4. Correlation of the motions between free state and complex state measured by the similarity measure of Sij . (a) tRNAðGlnÞ , (b) GlnRS.
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couplings are considered to indicate the tight binding of these parts of tRNAGln and GlnRS to enable accurate recognition of the anticodon and effective aminoacylation in the catalytic site. In the low-frequency modes, the major motions of GlnRS were bending motions between structural domains. The motions of tRNAGln were hinge bending between three parts, which were the acceptor stem, the anticodon arm, and the area around the core region of the molecule. This fact is considered to represent the characteristics of the dynamics of globular proteins and that of doublestranded nucleic acids. 3.2. Similarity of modes in the free state and in the complex state Fig. 4 shows the similarity of the fluctuations of atoms between the complex state and the free state of each normal mode, as defined by Eq. (7). In this section, one mode is assumed to correspond to the
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other mode if the directions of the atom fluctuations of these two modes are similar to each other. Fig. 4a is for tRNAGln and 4b for GlnRS. In both Figs. 4a and 4b, the vertical axis represents the mode numbers in the complex state and the horizontal axis represents those in the free state. Mode numbers are sorted in ascending order of the mode frequencies, therefore, Ômode 0Õ is the mode having the lowest frequency. For tRNAGln in the complex state, there are six modes that correspond to the modes in the free state (Sij P 0:65) out of 12 lowest modes (Fig. 4a). For example, mode 0 in the complex state corresponds to modes 2 and 8 in the free state, which means that the directions of the atom fluctuations of modes 2 and 8 in the free state are conserved in the complex formation. Modes 2, 6, and 8 have no corresponding modes in a free state, which means that these motions are induced by the complex formation. In Fig. 4a, the corresponding mode pairs (red and orange squares) are scattered on the matrix.
Fig. 5. Superimposed images of the atom fluctuations of conserved modes (modes 1, 2, 4, 6, 8, and 9; green) and non-conserved modes (modes 0, 3, 5, and 7; magenta) of tRNAGln in the free state.
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This means that the mode frequencies of the corresponding modes were not conserved before and after the complex formation. For GlnRS in the complex state, there are 10 modes that have corresponding modes in the free state out of twelve lowest modes (Fig. 4b). The corresponding mode pairs are in the diagonal region on the matrix. The frequencies of the corresponding modes were mostly conserved. This means that the dynamics of GlnRS molecule was not affected by the binding of tRNAGln and that this result is in contrast with the case of tRNAGln . Fig. 5 shows the superposition of conserved (modes 1, 2, 4, 6, 8, and 9) and non-conserved (modes 0, 3, 5, and 7) modes up to the 10 lowest modes for tRNAGln in the free state. The conserved motions are represented by green arrows and non-conserved motions are represented by magenta arrows. The right figure is the side view of the left figure. The lengths of the arrows are magnified seven times. It is clearly shown that the motions along with the Ôopen and closeÕ of the L-shape are restricted and thus disappear in the complex, while the swings of both the anticodon arm and the acceptor arm perpendicular to the open/close direction are conserved. Most tRNAs have similar L-shape structures, but the structures of ARSs and the binding modes of tRNAs and ARSs of different amino acids and different species are quite diverse. Conserved and non-conserved motions of tRNAs and ARSs are likely to represent the dynamical aspects of the characteristics of the molecular recognition mechanism for each tRNA–ARS complex. Now we are working on analyzing the dynamics of other types of tRNA–ARS complexes in the complex and free states by using normal mode calculation and molecular dynamics simulation.
4. Conclusion We analyzed the dynamical aspects of the E. coli tRNAGln –GlnRS complex by using normal mode calculation. The estimated deviation of atoms agreed well with that obtained from X-ray data.
Atom fluctuations that corresponded to modes having a low-frequency region revealed the largely coupled motion of tRNAGln and GlnRS, especially around the active site and the anticodon region. We analyzed the similarity of atom fluctuations between in the complex state and in the free state. For GlnRS, low-frequency motions are almost conserved, while for tRNAGln the dynamics are largely affected by the complex formation. Superimposed images of the conserved and non-conserved motions of tRNAGln revealed the restricted directions in the complex. The comparison of these dynamical characteristics may provide clues to elucidate the mechanism of tRNA–ARS recognition in each amino acid system.
Acknowledgements This work was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Encouragement of Young Scientists.
References [1] T.L. Bullock, L.D. Sherlin, J.J. Perona, Nature Struct. Biol. 6 (2000) 497. [2] S.C. Harvey, M. Prabhakaran, J.A. McCammon, Biopolymers 24 (1985) 1169. [3] M. Prabhakaran, S.C. Harvey, J.A. McCammon, Biopolymers 24 (1985) 1189. [4] S. Nakamura, J. Doi, Nucleic Acids Res. 22 (1994) 514. [5] A. Matsumoto, M. Tomimoto, N. G o, Eur. Biophys. J. Biophys. Lett. 28 (1999) 369. [6] M. Tateno, O. Nureki, K. Yura, K. Morikawa, T. Noguti, S. Yokoyama, M. Go, Prot. Eng. 8 (1995) 47. [7] M. Tateno, O. Nureki, S. Sekine, K. Kaneda, M. Go, S. Yokoyama, FEBS Lett. 377 (1985) 77. [8] I. Bahar, R.L. Jernigan, J. Mol. Biol. 281 (1998) 871. [9] M.A. Rould, J.J. Perona, T.A. Steitz, Nature 352 (1991) 213. [10] S. Nakamura, M. Ikeguchi, K. Shimizu, J. Comput. Chem. 19 (1998) 1716. [11] S.J. Weiner, P.A. Kollman, D.A. Case, U.C. Singh, C. Ghio, G. Alagona, P. Weiner, J. Am. Chem. Soc. 106 (1984) 765. [12] S.J. Weiner, P.A. Kollman, D.T. Nguyen, D.A. Case, J. Comput. Chem. 7 (1986) 230. [13] B.E. Hingerty, R.H. Ritchie, T.L. Ferrell, J.E. Turner, Biophys. J. 24 (1985) 427.
S. Nakamura et al. / Chemical Physics Letters 372 (2003) 423–431 [14] H. Ishida, Y. Jochi, A. Kidera, Proteins 32 (1998) 324. [15] S. Hayward, A. Kitao, H.J.C. Berendsen, Proteins 27 (1997) 425.
431
[16] S. Hayward, H.J.C. Berendsen, Proteins 30 (1998) 144. [17] P.J. Kraulis, J. Appl. Crystallogr. 24 (1991) 946.