s2fieldsofstudy: Chemistry Biology

text:
NMR solution structure and function of the C-terminal domain of eukaryotic class 1 polypeptide chain release factor

Termination of translation in eukaryotes is triggered by two polypeptide chain release factors, eukaryotic class 1 polypeptide chain release factor (eRF1) and eukaryotic class 2 polypeptide chain release factor 3. eRF1 is a three-domain protein that interacts with eukaryotic class 2 polypeptide chain release factor 3 via its C-terminal domain (C-domain). The high-resolution NMR structure of the human C-domain (residues 277–437) has been determined in solution. The overall fold and the structure of the β-strand core of the protein in solution are similar to those found in the crystal structure. The structure of the minidomain (residues 329–372), which was ill-defined in the crystal structure, has been determined in solution. The protein backbone dynamics, studied using 15N-relaxation experiments, showed that the C-terminal tail 414–437 and the minidomain are the most flexible parts of the human C-domain. The minidomain exists in solution in two conformational states, slowly interconverting on the NMR timescale. Superposition of this NMR solution structure of the human C-domain onto the available crystal structure of full-length human eRF1 shows that the minidomain is close to the stop codon-recognizing N-terminal domain. Mutations in the tip of the minidomain were found to affect the stop codon specificity of the factor. The results provide new insights into the possible role of the C-domain in the process of translation termination.

Termination of translation in eukaryotes is triggered by two polypeptide chain release factors, eukaryotic class 1 polypeptide chain release factor (eRF1) and eukaryotic class 2 polypeptide chain release factor 3. eRF1 is a three-domain protein that interacts with eukaryotic class 2 polypeptide chain release factor 3 via its C-terminal domain (C-domain). The high-resolution NMR structure of the human C-domain (residues 277-437) has been determined in solution. The overall fold and the structure of the b-strand core of the protein in solution are similar to those found in the crystal structure. The structure of the minidomain (residues 329-372), which was ill-defined in the crystal structure, has been determined in solution. The protein backbone dynamics, studied using 15 N-relaxation experiments, showed that the C-terminal tail 414-437 and the minidomain are the most flexible parts of the human C-domain. The minidomain exists in solution in two conformational states, slowly interconverting on the NMR timescale. Superposition of this NMR solution structure of the human C-domain onto the available crystal structure of full-length human eRF1 shows that the minidomain is close to the stop codon-recognizing N-terminal domain. Mutations in the tip of the minidomain were found to affect the stop codon specificity of the factor. The results provide new insights into the possible role of the C-domain in the process of translation termination.

Introduction
Termination of translation in eukaryotes is governed by the cooperative action of two interacting polypeptide chain factors, eukaryotic class 1 polypeptide chain release factor (eRF1) and eukaryotic class 2 polypeptide chain release factor 3 (eRF3). The major functions of eRF1 include recognition of each of the three stop codons (UAA, UAG, or UGA) in the decoding center of the small ribosomal subunit and the subsequent peptidyl-tRNA hydrolysis. eRF3 is a ribosome-dependent and eRF1-dependent GTPase encoded by an essential gene that enhances the termination efficiency by stimulating the activity of eRF1 [1][2][3][4]. eRF1 contains three structurally separated domains, each of which can be assigned a specific function. The N-terminal domain (N-domain) is involved in the recognition of the stop codon [1,5,6]. The middle domain (M-domain) catalyzes the hydrolysis of the peptidyl-tRNA ester bond within the peptidyltransferase center of the 60S ribosome subunit [7,8]. The C-terminal domain (C-domain) binds to eRF3 [9][10][11][12], and this interaction increases the efficiency of translation termination [13,14]. However, in a simplified in vitro assay for the measurement of release factor (RF) activity, eRF1, deprived of the C-domain, still retains its RF activity [15]. The combination of the human M-domain and C-domain, in the absence of the N-domain, is able to bind to the mammalian ribosome and to induce the GTPase activity of eRF3 [16].
It has been found that eRF1 and eRF3 form ternary and quaternary complexes in solution with GTP and Mg 2+ (eRF1-eRF3-GTP and eRF1-eRF3-GTP-Mg 2+ ) [17]. Yeast two-hybrid and deletion analyses have revealed that residues 281-305 and 411-415 of human eRF1 are important for its binding to eRF3, but the last 22 residues (415-437) are not significant for this process [11]. In contrast, in the case of eRF1s from the budding and fission yeast, the last 19 residues of the C-terminal fragment are necessary for the eRF1-eRF3 interaction [9,12]. As residues 300-303 and 411-412 correspond to the b-sheets in the central hydrophobic core of the C-domain, it might be expected that truncation of these residues would lead to destabilization of the whole structure. This suggestion is in full agreement with recent studies on the yeast Y410S C-domain mutant [18].
The structure, dynamics and functions of the C-domain have been studied much less intensively than those of the M-domain or the N-domain. In the currently available crystal structure of human eRF1 [19], coordinates exist only for the atoms that belong to the main rigid core of the C-domain, and consequently the C-domain structure has extensive unresolved fragments in its mobile regions. More recently [20], the crystal structure of human eRF1 in a complex with the truncated form of eRF3 (residues 467-662) has been solved. In particular, it has been found that the two a-helices, a8 and a11, which belong to the main rigid core of the C-domain, together with Arg192 and Arg203 of the M-domain [21], form the interface with eRF3. However, all of the mobile regions that could not be seen in the crystal structure of human eRF1 [19] still remained undetermined in the structure of the eRF1-eRF3 complex [20].
We report here the high-resolution NMR structure of the human C-domain in solution, and present data on its dynamics. On the basis of the structural data, we have performed a mutational analysis of the C-domain and investigated the impact of the mutants on stop codon recognition.

Results
Resonance assignment 1 H, 13 C and 15 N chemical shifts were made for 99% of the protein backbone resonances of the isolated C-domain. Only Asn277, Asn325, and Gln397, whose amide group HN and 15 N signals could not be reliably determined because of signal overlap problems, were not assigned. More than 78% of all of the observed side chain 1 H, 13 C and 15 N chemical shifts were also determined.
The 1 H, 15 N-heteronuclear single quantum coherence (HSQC) spectra, measured over the temperature range 288-313 K, showed only a minor effect of temperature on the existence and line widths of the protein backbone resonances. This suggests the absence of multiple conformations that interconvert on the millisecond time scale. However, for several residues situated between positions 329 and 372 (in particular, residues 333-344, 351, and 357-370) a duplicated set of signals of approximately equal intensity was observed ( Fig. 1; Fig. S1). This clearly indicates the presence of two conformational states of residues 329-372 (minidomain) of eRF1, which is highly enriched in polar and charged residues.
Refolding of the C-domain leads to the presence of only one conformational state. The refolding was carried out by lowering the pH of the protein solution from 7.0 to 3.5, and then restoring the pH to its initial value. It is also worth noting that the relative populations of the two conformational states are affected by the components of different diluted liquid crystalline media. For example, in a solution of lipid bicelles [1,2- [22], a set of signals is observed that belongs to one conformation of the minidomain, whereas in the poly(ethylene glycol)-based system [23], another set of signals could be detected. Therefore, the sizes of the relative populations and possibly the rate of conformer interconversion are sensitive to the environment of the domain.
For the great majority of the residues in the minidomain, the differences between the chemical shifts of the two conformational states are sufficiently large to allow sequential assignments based on the use of 1 H, 13 C, 15 N triple-resonance experiments (3D experiment correlating the amide HN and the Ca signals, 3D experiment correlating the amide HN and the Ca signal of the preceding amino acid, 3D experiment correlating the amide NH with the Ca and Cb signals, 3D experiment correlating the amide NH with the Ca and Cb signals of the preceding amino acid, and 3D experiment correlating the amide NH with the C¢ signal of the preceding amino acid). Figure 2 presents the distribution of the chemical shift differences between the two protein conformers for the backbone amide proton, nitrogen and Ha signals for the minidomain. These differences are concentrated in regions 333-344 and 357-370, presumably reflecting differences in the structures in these regions. It should be noted that there are no detectable differences in chemical shifts for the remaining residues.

Structure determination
The existence of two distinct sets of resonances for the minidomain allowed the determination of two families representing the two conformational states of the solution structure of the C-domain (shown as a stereo view in Fig. 3A). The structure determination was based on more than 2140 experimental restraints, using data obtained at 288 and 313 K (Table 1). This work made use of the standard double-resonance 15 N, 1 H-NMR and triple-resonance 15 N, 13 C, 1 H-NMR experiments applied to 13 C-labeled and ⁄ or 13 N-labeled samples of the human C-domain. For most of the protein residues, the number of NOE restraints per residue is between 15 and 25 (Fig. S2). However, the C-terminus and fragment 336-338 have significantly lower numbers of measured distance restraints. Therefore, extensive use of residual dipolar couplings (RDCs), measured in several alignment media, was important for the determination of the structures of the conformers of the C-domain. The dipolar couplings provided long-distance information on the global folding of both conformers.
The structure of the protein core (residues 277-328 and 373-413) in both conformers (Fig. 3B,C) is in good agreement with that of the corresponding part of the crystal structure [19]. Four b-strands (b1, 301-303; b2, 320-323; b6, 389-392; and b7, 409-412) form a b-sheet with three antiparallel strands (1, 2 and 7) and strand 6, which is parallel to strand 2. b-Strands are located between the four a-helices (a1, 278-294; a2, 305-313; a4, 374-381; and a5, 397-405), with two of the a-helices on one side of the b-sheet and two on the other side. The rmsd of the heavy atoms (Ca, C, and N) of the protein core, when the NMR structures of both conformers are superimposed on the crystal structure of human eRF1, is 1.58 ± 0.06 Å .

Two protein conformers
The main structural difference between the two protein conformers is in the orientation of a3 (residues 348-356), with respect to the b-structure of the minidomain and the corresponding tilt of the loop (residues 357-367) between a3 and b5 ( Fig. 3B,C). In one of the conformers (closed; Fig. 3C,E), the side chain of His356 is on the top of the a-helix and in closer contact with the negatively charged side chains of Glu365 and Glu367, whereas in the second conformer (open; Fig. 3B,D), His356 is closer to another charged side chain, that of Asp353, and the aromatic rings of Phe357 and Tyr331.
The two different orientations of the loops result from the substantial change in the backbone conformation around Phe357, which results in the proximity of Thr358 and Lys354 in the open conformer (Fig. 3B,D). The average backbone torsion angles of Phe357 in the ensemble of the open conformer are )60 ± 3°(/) and )38 ± 4°(w); these values fall within the range acceptable for an a-helical conformation. In the case of the closed conformer (Fig. 3C,E), these values are +57 ± 3°(/) and +6 ± 4°(w), which indicates the site of a break in the a-helix (residues 348-356).
The difference between the conformers is clear from the comparison of the intensities of the NOEs involving the HNs of Phe357 and Thr358 (Table S1). Such a twist in the protein backbone conformation between residues 354 and 358 causes a change in the protonproton distances and the intensities of the corresponding NOEs (Fig. 4). Thus, the NOE between the HN of Thr358 and the Ha of Ser355 could only be detected for the open conformer, whereas a crosspeak between the HN of Thr358 and the Ha of His356 could be seen in both conformers ( Fig. 4; Fig. S3). At the same time, the intensity of the NOE between the HN of Phe357 and the Ha of Lys354 in the open conformer is larger than in the closed conformer (Fig. S4). These observations are in full agreement with the structures of the two protein conformations (Fig. 3D,E), calculated with the extensive use of the RDCs for 1 D NH , which greatly helped with the accurate determination of the protein backbone orientation.
The structure of the protein backbone in the central part of loop 357-367 is similar for both conformers, which is in accord with the nearly identical sets of strong long-range, middle-range and intraresidue NOEs found for the two conformers (Fig. S2). There is also no significant change in the conformation of the polypeptide chain in region 365-372. The torsion angle w of Gln364 differs by 180°in the two protein conformers; however, this does not have a significant impact on the observed interatomic distances, partially owing to the high mobility of this protein region.

Temperature effects
Raising the temperature from 298 to 313 K leads to a significant decrease in the intensities of all the NOEs arising from the HN of Gly337 and all the sequential and medium-range NOEs arising from the HN atoms suggestion is supported by the existence of strong crosspeaks between the signal of the HN of Gly337 in the open conformer and the signal of the water protons. All of these observations indicate that the loop region of the open conformer has a higher degree of mobility than that in the closed protein conformer.

Testing the conformer stability
The HSQC spectra of samples of the human C-domain from different preparations showed slightly different relative populations of the two conformers. Therefore, the effects of pH, ionic strength of the solution and temperature on the populations of the two protein conformers were examined (see Experimental procedures). It was found that variation of pH in the range between 6.3 and 7.7, of ionic strength between 25 and 100 mm NaCl and of temperature between 278 and 313 K did not lead to any detectable change in the populations of the two conformers. However, as described earlier, refolding of the protein from a solution at pH 3.5 resulted in only the closed conformer being present in solution. Therefore, one hypothesis is that the protonation state of the His356 side chain could be crucial for protein folding and for the stabilization of the conformers. At pH values above its pK a , the imidazole ring of His is uncharged, and both conformers are stable. In attempts to experimentally detect any possible pH dependence of the populations of the two conformers, an NMR pH titration of the C-domain in solution was carried out. However, a significant amount of aggregated protein was detected at and below pH 6.0, which precluded the acquisition of this experimental evidence. The fact that protein expression gives equal populations of two protein conformations may also indicate that chaperones and ⁄ or cell translation machinery could facilitate the folding of the C-domain. The relative populations of the two protein conformations were found to be extremely sensitive to the nature of the alignment media used in the RDC experiments (see Experimental procedures). In n-alkylpoly(ethylene glycol) ⁄ n-alkyl alcohol medium [23], only the closed conformer could be detected. However, in media formed with phospholipid bicelles (DMPC ⁄ DHPC and DMPC ⁄ DHPC ⁄ SDS), the open conformer (90%) was mainly observed.

Backbone dynamics
Experimentally determined 15 N-relaxation parameters for the amide 15 N nuclei (R 1 , longitudinal relaxation rate; R 2 , transverse relaxation rate; and 15 N{ 1 H}-NOE values) measured at 298 K are shown in Fig. 5A-C. Figure 5D also shows the calculated values of the order parameter S 2 , which reflects the amplitude of picosecond-nanosecond amide bond vector dynamics, and Fig. 5E shows additional line broadening (R ex ) resulting from protein motions on the millisecond time scale. The best fitting of the relaxation parameters could only be obtained using a fully asymmetric tensor model for the molecular rotational diffusion motions.
Analysis of the relaxation data ( Fig. 5) shows that, ignoring the trivial case of the C-terminal tail of the protein, the most flexible region in the C-domain is loop 357-367 (Fig. S5). It is important to mention that no noticeable differences in the values of R 1 , R 2 and 15 N{ 1 H}-NOE for the two protein conformers, measured at 298 K, were detected. This indicates that the protein backbone mobility on the picosecond-nanosec-    (Fig. S6). A substantial contribution of chemical exchange, R ex , to the transverse relaxation rate, R 2 , was observed for residues 357-359 in the loop region (Fig. 5E). This result is in good agreement with the observed conformational changes between the open and the closed conformers, as Phe357 exhibits the most significant structural perturbation. Structural changes for residues 358 and 359 are smaller, but still detectable.

Effect of mutations in the minidomain on stop codon specificity
Superposition of the NMR structure of the human C-domain on the full-length crystal structure of eRF1 reveals that the minidomain is located close to or adjacent to the N-domain (see Discussion), which is responsible for the stop codon recognition (Fig. 6). One can assume that complex dynamic behavior of the minidomain may influence the state of the N-domain and may therefore modify the efficiency of the decoding process. To verify this hypothesis, we generated a series of mutant forms of eRF1 with the replacement of Tyr331, His334, His356, Phe357, Asp359, Gly363, Glu365, His366 and Glu370 by alanine. These point mutants were further assayed in a reconstituted in vitro eukaryotic translation system containing 60S and 40S ribosomal subunits, mRNA with different stop codons, aminoacylated tRNAs, and individual purified translation factors [13]. The efficiency of termination was estimated from the amount of released 35 S-labeled peptide at several time intervals. The mutations Y331A, H356A, F357A, D359A, G363A and E365A in the loop region were found to increase the termination efficiency of the ribosomal complex with the UAG stop codon, whereas the peptide release rate did not change significantly when UAA or UGA stop codons were used (Fig. 7). The maximum impact on the peptidyl-tRNA hydrolysis was found for the E365A and D359A mutants, in which negatively charged residues were replaced by alanine. One can speculate that the negative charges reduce the efficiency of the minidomain interaction with mRNA. It is also worth noting that the maximum impact was observed for mutations in the flexible loop 357-367. Replacement of His334, His366 and Glu370 did not change the peptide release rate, regardless of the stop codon used (Fig. S7).
In order to determine whether the observed effects of the mutations could be caused by changes in the efficiency of binding of eRF1 to eRF3, GTPase assays were performed. As eRF3 coupling with eRF1 and the ribosome results in activation of the eRF3 GTPase [4], GTP hydrolysis in such a ternary complex could be used to measure the efficiency of the eRF1-eRF3 interaction. All of the eRF1 mutants stimulated eRF3 GTPase activity nearly identically to that of the wildtype protein (Table S2). These results indicate that the C-domain is able to change the efficiency of stop codon recognition in a context-dependent manner.

Discussion
Comparison with crystal structure of human eRF1 The two reported crystal structures of human eRF1 (the protein itself, Protein Data Bank accession code 1DT9; and the complex of eRF1 with eRF3, Protein Data Bank accession code 3E1Y] contain the coordinates of the rigid protein core. However, these structures do not show the coordinates of the atoms in the minidomain, owing to the increased mobility of this protein fragment. The NMR structure of the human C-domain in solution reported here therefore represents the first view of this minidomain. Moreover, it was found that this minidomain exists in two conformations that undergo slow interconversion (on an NMR time scale). The lifetime of these conformational states is certainly longer than seconds, as no noticeable convergence of the two sets of signals was detected, even at 313 K.
Despite the rather simple topology of the minidomain (three antiparallel b-strands and one a-helix on top of the b-sheet), a search of the CATH database (http://www.cathdb.info) [24] provided no direct structural homologs. The closest cluster of structures has the fold found in the factor Xa inhibitor (CATH code 4.10.410). An additional manual search based on these results highlighted a structural homology between the minidomain and the zinc-binding domain of the zinc finger protein Ynr046w [25] (Fig. 8). The fit of the heavy atoms (Ca, C, and N) from three b-strands and the a-helices of both the closed and the open conformer onto a corresponding set of atoms of Ynr046w gives rmsd values of 3.7 and 4.1 Å , respectively. Smaller rmsd values of 1.9 and 2.4 Å are obtained when the b-core residues only are used for the superposition. Interestingly, this protein is a component of yeast eRF1 methyltransferase, which is involved in methylation of the Glu from the strictly conserved GGQ tripeptide, and therefore it also, like human eRF1, plays an important role in translation termination.
The superposition of the families of solution structures of the two conformers onto the crystal structure of human eRF1 (3E1Y) gives an rmsd for the heavy protein backbone atoms (N, Ca, and C¢) of 2.81 ± 0.13 Å for all residues of the C-domain except for the highly flexible C-terminal tail (residues 414-437). A superposition made using the same set of atoms from only the residues that belong to the main core of the protein gives a smaller rmsd of 1.58 ± 0.06 Å . Figure 6 shows a comparison of the structure of the protein core (residues 277-328 and 373-413) in solution and in the solid state, and indicates their similarity.
A superposition of the C-domain NMR structure on the crystal structure of the eRF1-eRF3 complex shows that the minidomain is in close proximity to the N-domain (Fig. 6). Recently, a molecular model of the complex of human eRF1 with mRNA and tRNA has been constructed [26]. Among the features of this complex, the authors noted that the C-domain was close to the mRNA stop codon region.

Stabilization of the two conformers
The two conformational states of the minidomain are almost equally populated, indicating that the energies of formation of these two states should be almost equal. The lifetime of each of the conformational states, and therefore the energy barrier between them, is relatively large. However, gel filtration experiments on the C-domain showed the presence of one peak only (Fig. S8). Therefore, the two protein conformers either have lifetimes of less than a few minutes or have similar physical properties. One can speculate that the two conformational states could be stabilized by the network of coulombic interactions between the charged side chains of the minidomain residues. The minidomain is indeed enriched in polar and charged residues, and the main structural difference between the two conformers is in the relative position of the side chain of His356 with respect to the negatively charged Asp353 and Glu367. The carboxyl groups of these two residues can form hydrogen bonds with the HN proton of the His356 imidazole ring, either directly or through a water molecule. His356 is near Asp353 in the open conformer and near Glu365 and Glu367 in the closed conformer, and these polar interactions may play an important role in the stabilization of the two conformers. The two His residues, His334 and His356, may both participate in stabilization of the polar interactions. Thus, His334, situated on the central b-strand, could interact with the Glu341 and Glu367. A stronger network of interactions between Glu341, His334 (Glu367 ⁄ Glu365) and His356 in the closed conformer may partially explain why the closed conformer is more rigid than the open one.
The structure of loop 357-367 in both conformers could also be stabilized by hydrogen bonds between the backbone carbonyl oxygen of Asp359 and the amide proton of Gly363 (Fig. S9). The distance between these atoms in the open conformer family is 1.70 ± 0.02 Å , and in the closed conformer it is 1.87 ± 0.10 Å . Additionally, the conformation of this loop could be partially stabilized by the interaction of the carbonyl oxygen of Asp359 with the amide proton of Thr362 (the distance in the open conformer family is 2.34 ± 0.01 Å , and in the closed conformer it is 2.56 ± 0.26 Å ) and possibly by the hydrophobic interactions of the methyl groups of Thr358 and Thr362 with a favorably oriented CH 2 group of Asp359, interactions that were confirmed by the corresponding set of NOEs.

Dynamic properties of the C-domain
The C-domain reveals a rather complex picture of the mobility of its protein backbone. Analysis of the 15 N-relaxation data shows that the protein core (residues 277-328 and 373-413) is rather rigid. This is in full agreement with the results of the crystallographic analysis of human eRF1 [19]. The minidomain, which was not resolved in the crystal structures, exists in two conformational states in solution. This is evidence for the existence of protein backbone conformational rearrangements occurring on a time scale of seconds or slower. However, the amplitudes of the motions of the minidomain backbone on the picosecond-nanosecond time scale are rather small, as shown by the large values of the order parameter S 2 , which are similar to the corresponding parameters of residues in the protein core region. The most flexible parts of the minidomain are loops 335-339 and 357-367. An accurate analysis of 15 N-relaxation measurements of residues 335-339 was not possible, owing to the overlapping of peaks in the 15 N, 1 H-correlation spectra, but the dynamics of loop 357-367 were analyzed. As seen in Fig. 5D, the relative amplitudes of the backbone motions of loop 357-367 were found to be larger than for all the other protein domains except for the C-terminal tail (residues 414-437). Several residues from loop 357-367 also exhibited conformational rearrangements occurring on the millisecond time scale (Fig. 5E). Overall, it seems that the slow conformational triggering is the most characteristic feature of the dynamics of the C-domain.

Possible functional role of the minidomain
There are several proteins that bind to eRF1. It has been shown by deletion analysis that the catalytic subunit of protein phosphatase 2A (PP2A) binds to region 338-381 of eRF1 [27]. This region substantially overlaps with the minidomain. It is not known whether eRF1 is phosphorylated in vivo and whether the interaction of eRF1 with PP2A influences the termination of translation [27]. The eRF1-PP2A interaction may be important for another closely related process, nonsense-mediated decay (NMD). Upf1p, a protein that plays a key role in NMD [28,29], binds to an unknown region of eRF1 [30]. Such an interaction halts translation termination and facilitates the degradation of mRNA [30,31]. It should be noted that the ribonucleoprotein complex, formed during NMD and containing subunits of PP2A, plays a regulatory role in Upf1p phosphorylation.
For termination of translation, eRF3 is one of the most important interaction partners of eRF1. It has been shown previously that both the M-domain [21] and the C-domain [10,11,32] interact with eRF3. Recently, it was also shown that the eRF1 interaction interface with eRF3 is formed by two Arg residues, Arg192 and Arg203, in the M-domain [21] and by a cluster of hydrophobic residues, Phe291, Ile294, Tyr301, Phe303, and Phe406, in the C-domain [20]. Residues 329-372 are situated on the opposite side of the C-domain, and therefore do not participate directly in the interaction with eRF3. This conclusion was also confirmed by the results of the GTPase assays, which showed that mutations in the minidomain of eRF1 did not change the GTPase activity of eRF3.
The minidomain in the crystal structure is near the N-terminal domain, which plays a key role in stop codon recognition. The ability of the minidomain to act as a conformational switch and its probable proximity to the stop codon recognition site in the termination complex hint at its possible functional role. The termination efficiencies of several eRF1 mutants were examined. The residues for mutation were selected from those that appeared to be important for stabilization of the two protein conformers, i.e. those in loop 357-367 and several neighboring residues. The observed impact of the mutations at Tyr331, His356, Phe357, Asp359, Gly363 and Glu365 on the termination efficiency of eRF1 with regard to UAG stop codon recognition are in accord with the hypothesis that the C-domain could be involved in the regulation of translation termination. As Asp359 and Gly363 are important for stabilization of both conformations of loop 357-367, it is possible that stop codon specificity is regulated by the conformation of this flexible part of the C-domain. His334, His366 and Glu370 are located outside this loop, and this may explain the absence of an effect of their replacement by Ala on termination efficiency. Although the effects of the mutations on peptide release are relatively modest, the increase in efficiency (rather than a decrease) is nevertheless an important observation, and makes it more likely that the phenomenon is caused by a direct interaction related to the UAG stop codon recognition process.
It has also been reported that mutations in eRF3 that reduce its GTPase activity also decrease the efficiency of translation termination for some, but not other, stop codons [14]. Thus, a 17-fold reduction in termination efficiency was observed for the UGAC stop signal, whereas much weaker effects were detected in the case of other termination signals. The authors suggested that the GTPase activity of eRF3 acts to couple the recognition of translation termination signals by eRF1 to efficient polypeptide chain release. Genetic screening experiments also identified mutants with changes in the C-terminal tail of yeast eRF1 that were unable to recognize one of the three stop codons [5]. Two of the mutations (Q415X and E428Q) are situated near the eRF3-binding motif, and could therefore influence the efficiency of the eRF1-eRF3 functional interaction [9,12]. The mutations in the minidomain reported here have no impact on the eRF1-eRF3 interaction, and are more likely to control termination efficiency through a direct interaction with the stop codon recognition sites.
It should be noted that loop 357-367 is one of the most variable regions in the sequence of class 1 eukaryotic release factors [33] (Fig. S10). The majority of eukaryotes utilize all three stop codons. However, the frequencies of UAA, UAG and UGA in the coding sequences of mRNAs differ between species [34]. It is possible that the variable residue composition of loop 357-367 may contribute to the modulation of the affinity of eRF1 for different stop codons according to the most abundant termination signal in the transcriptome. Indeed, UAG is a rare stop codon in the Homo sapiens transcriptome [34], and is therefore a relatively weak signal for human eRF1. Mutations in loop 357-367 that increase the efficiency of eRF1 recognition of the UAG codon are in agreement with this hypothesis.

Sample preparation
The DNA fragment encoding the C-domain (residues 277-437) with a C-terminal His 6 -tag fusion was cloned into the pET23b(+) vector (Novagen) under the phage T7 RNA polymerase promoter. The C-domain was overproduced in Escherichia coli BL21(DE3), in M9 minimal medium, and isolated using Ni 2+ -nitrilotriacetic acid resin (Qiagen). The protein was further purified by cation exchange chromatography, using HiTrap SP columns (GE Healthcare). For 13 C and ⁄ or 15 N labeling, [ 13 C 6 ]d-glucose and ⁄ or 15 NH 4 Cl (Cambridge Isotope Laboratories) were used as the isotope sources in M9 minimal medium. The samples for NMR (protein concentration of 1 mm) were prepared in either 95% H 2 O ⁄ 5% D 2 O or 100% D 2 O and 10 mm potassium phosphate and 50 mm KCl (pH 7.0). b-Mercaptoethanol ( 2 mm) was added to the final solution in order to prevent oxidation of the free Cys residues Cys302 and Cys335. Shigemi microcell NMR tubes, containing 330-380 lL, were used in the recording of the NMR spectra.

Cloning and mutagenesis of human eRF1
Plasmids with mutant eRF1 genes were obtained by sitedirected mutagenesis, using the PCR-based 'megaprimer' method as described previously [6]. The resulting PCR products were inserted into the XhoI-Bst98I sites of the pERF4b plasmid. The sequences of the PCR primers used for the generation of the eRF1 mutants are available upon request.

Expression and purification of human RFs
Wild-type human eRF1, its mutants and eRF3c containing His 6 -tags at the C-termini were produced in E. coli BL21(DE3), and purified as described previously [6,13,35].
mRNA transcripts mRNA was transcribed by T7 RNA polymerase on MVHL-stop plasmids, encoding a T7 promoter, four CAA repeats, the b-globin 5¢-UTR, the MVHL tetrapeptide followed by one of three stop codons (UAA, UAG, or UGA) and the 3¢-UTR, comprising the rest of the natural b-globin coding sequence. The MVHL-stop plasmids (containing UAA, UAG and UGA stop codons) were prepared as described previously [39]. For run-off transcription, all plasmids were linearized with XhoI.

Peptide release assays
These were performed as described previously [12], with some minor modifications. Aliquots containing 0.1 pmol of pretermination complexes, formed in the presence of [ 35 S]Met-tRNA, and with an activity of about 10 000 c.p.m., were incubated at 37°C with 2.5 pmol of eRF1 for 0-15 min. Ribosomes and tRNA were pelleted with ice-cold 5% trichloroacetic acid, supplemented with 0.75% casamino acids, and centrifuged at 4°C and 14 000 g. The amount of released [ 35 S]Met-containing tetrapeptide, which indicated the efficiency of peptidyl-tRNA hydrolysis, was determined by scintillation counting of the supernatants using an Intertechnique SL-30 liquid scintillation spectrometer.

GTPase activity assays
These were based on the measurement of the accumulation of [ 32 P]P i , using a modified charcoal precipitation method [7]. The incubation mixture (12.5 lL) contained 20 mm Tris ⁄ HCl (pH 7.5), 30 mm NH 4 Cl, 15 mm MgCl 2 , 0.16 lm ribosomes, 0.16 lm human eRF3c, and 0.5 lm [ 32 P]GTP[cP] (10 000 c.p.m. ⁄ pmol); human wild-type eRF1 or mutant eRF1s were added to give 0.04, 0.08, 0.12 and 0.16 lm final concentrations. The reactions were run at 30°C for 20 min, and terminated by mixing with 0.5 mL of a 5% activated charcoal suspension in 50 mm NaH 2 PO 4 , cooled on ice. The mixture was vortexed and centrifuged at 16 000 g for 10 min at 4°C. Aliquots of the supernatants (0.375 mL) were counted on a scintillation counter. Values of eRF3 GTPase activity and corresponding error limits were estimated from five experiments carried out for each eRF1 mutant.

Gel filtration analysis of the C-domain
This was performed on Superose 12 in a buffer containing 20 mm Tris ⁄ HCl (pH 7.5), 100 mm KCl, 2 mm dithiothreitol, and 5% glycerol. Only one peak was observed, indicating that the two conformational states could not be separated by this method.

NMR spectroscopy
All spectra were acquired on Varian INOVA 600 and 800 MHz and Bruker AVANCE 600 and 700 MHz spectrometers equipped with triple-resonance z-gradient probes. The 700 and 800 MHz spectrometers were equipped with cryoprobes. Spectra were processed by nmrpipe, and analyzed using sparky (from Goddard and Kneller; http:// www.cgl.ucsf.edu/home/sparky) and autoassign [40]. Sequential backbone assignments [41] and side chains assignments were obtained using 3D spectra obtained from 3D experiments correlating the amide NH with the C¢ signal of the preceding amino acid, correlating the amide HN and the Ca signals, correlating the amide HN and the Ca signal of the preceding amino acid, correlating the amide NH with the Ca and Cb signals, correlating the amide NH with the Ca and Cb signals of the preceding amino acid, a threedimensional experiment correlating amide HN with Ha and Hb signals (HNHAHB), three-dimensional experiment correlating amide HN with Ha and Hb signals of preceding residue via carbonyl carbon (HBHA(CO)NH) and threedimensional experiment correlating amide HN and Ha signals (HNHA) [42], measured at 298 K, and three-dimensional experiment correlating side-chain protons via 13 C-13 C correlations (HCCH)-TOCSY, measured at 313 K. Additional side chain assignments and NOE distance restraints were extracted from the 1 H, 13 C-NOESY and 1 H, 15 N-NO-ESY spectra measured at 298 and 313 K with 100 ms mixing time. Assignments were obtained for more than 99% of the 1 H, 13 C and 15 N atoms of the protein backbone, and for more than 78% of the side chain atoms.
The main set of backbone u and w dihedral angles was calculated from the chemical shift values of backbone atoms 13 Ca, 13 Cb, 13 C¢, 1 Ha, 1 HN, and 15 N, using talos software [43]. Additional dihedral angles for those residues with no agreement in talos were obtained by the anglesearch program [44].
RDC constants were measured using partially oriented diluted liquid crystalline media: 5% (v ⁄ w) C12E5 ⁄ hexanol [23] and DHPC ⁄ DMPC bicelles [22]. In this series of experiments, alternative orientations of the alignment ten-sor were achieved by modifying the DHPC ⁄ DMPC bicelles with SDS. Sixty-nine RDCs were measured in C12E5 ⁄ hexanol, and 90 in DHPC ⁄ DMPC ⁄ SDS, at 311 K. Neutral 5% (v ⁄ w) DHPC ⁄ DMPC bicelles were also used. However, none of these measured RDCs was used in the subsequent calculations, because of the very weak alignment of the protein in this medium (maximum dipolar interactions did not exceed 5 Hz). The RDC values were calculated from the 1 DJ NH and 1 J NH constants, extracted from the inphase antiphase (IPAP)-HSQC spectra [45], acquired in anisotropic and isotropic conditions respectively.
Spectra for the measurement of 15 N longitudinal relaxation rates (R 1 ), transverse relaxation rates (R 2 ) and 15 N{ 1 H} heteronuclear NOE values were collected on a 1 mm 15 N-labeled C-domain sample at 298 K with a Varian INOVA 600 MHz NMR spectrometer, using pulse sequences modified from those described by Kay et al. [46] to compensate for cross-correlation effects [47].

Structure calculation and refinement
The initial structure was generated in cns, using a set of manually unambiguously assigned NOEs. The structure was then submitted to aria, and further assigned NOEs were obtained by an iterative procedure [48] using aria-cns [49]. NOE peak intensities were used for distance estimation, instead of volumes, because of significant crosspeak overlapping. All of the measured proton-proton distances were divided into ranges, with upper limits of 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5 and 6.0 Å . The structure calculations and refinement were performed by a simulated annealing protocol carried out in Cartesian coordinate space using cns [50] and the slightly modified script anneal.inp. The calculations were performed in an iterative manner. Database values of conformational torsion angle pseudopotentials [51] were introduced at the final stages of refinement. The final force constants were as follows: NOE restraints, 75 kcalAEmol )1 AEÅ 2 ; dihedral angle restraints, 200 kcalAEmol )1 AErad 2 ; RDCs, 50 kcalAEmol )1 AEHz 2 ; and a scale factor for conformational database restraints [10,51]. The weighting for the RDC potential was scaled from 0.01 to 50. The restraint violations were monitored after each cycle of refinement by the inhouse program nmrest or the cns script accept.inp. Violated restraints were checked and corrected or declined. One thousand eight hundred and fifty-seven NOE-derived distance restraints, 216 dihedral angles and 90 RDCs were used in the calculation of the final ensemble ( Table 1). The structure quality was analyzed with aqua and procheck-nmr software [52] (Fig. S11) and by using the nmrest program. The best 24 structures out of 100 (with respect to the minimum restraints violation value criterion) were accepted as the final ensemble for each protein conformer.
Structure visualization and analysis were carried out using the insightii software package (Accelrys Software Inc.) and pymol (DeLano Scientific LLC).  15 N-heteronuclear NOE experiments was 4.0 s. Spectra were processed using nmrpipe [53]. The nonlinear fitting of the integrated peak volumes in the pseudo-3D spectra of the relaxation rate experiments and the calculation of standard deviations were accomplished using the nlinls procedure. The values of R 1 and R 2 were then calculated from the table of relative peak intensities, produced by nmrpipe and nlinls, using relaxfit, which was written in-house [54]. The standard deviations of the 15 N{ 1 H}-NOE values were calculated using the rmsd noise of the background regions [55], and were further checked and corrected by using two independently collected experimental datasets.

NMR dynamics analysis
The analysis of the R 1 , R 2 and 1 H, 15 N-NOE values was carried out using a model-free formalism, with tensor 2.0 [56]. To determine the rotational diffusion tensor, all of the isotropic, axially symmetric and fully asymmetric molecular tumbling models were tested. Parameters of the tensors for fully anisotropic diffusion of the open and closed conformers are presented in Table 2. The values of the diffusion tensor axis were then used to fit models of internal motions for the backbone HN vectors of the amino acids. Five models were tested during the calculation: (a) a rigid body model (using the very fast internal motions, t c < 20 ps) (model 1); (b) the model-free Lipari-Szabo model [57]  Typically, most of the residues of the protein rigid core could be successfully fitted using models 1 and 2. For a few residues of the minidomain (330-332, at the beginning of the central b-strand) and residues 343 and 351, model 1 was selected as the best. For residues 357-359 of the minidomain and for several other residues, a significant contribution of chemical exchange was observed, and model 3 had to be used to fit the relaxation data. For the other residues of the minidomain, model 2 was selected. Model 5 was applied only to fit the relaxation data obtained for the residues from the flexible C-terminal tail. 0.125 ± 0.003 0.128 ± 0.002 D zz = 10 8 (s )1 ) 0.140 ± 0.003 0.139 ± 0.002 s 1 = (4D xx + D yy + D zz ) )1 (ns) 14.86 ± 0. 18 14.90 ± 0.27 s 2 = (D xx + 4D yy + D zz ) )1 (ns) 13.48 ± 0. 22 13.30 ± 0.21 s 3 = (D xx + D yy + 4D zz ) )1 (ns) 12.71 ± 0. 19 12.74 ± 0.19

Supporting information
The following supplementary material is available: Fig. S1. A region of the 1 H, 15 N-HSQC spectrum of the C-terminal domain of human eRF1 illustrating the presence of two conformational states of the protein.   Fig. S5. A cylindrical ribbon representation of the backbone of the C-terminal domain of human eRF1. Fig. S6. The order parameter, S 2 , calculated separately for the open and closed conformers of the C-terminal domain of human eRF1 using a model-free analysis with an assumption of fully asymmetric molecular motions and tensors. Fig. S7. The rate of peptidyl-tRNA hydrolysis in response to human eRF1, with mutations in the minidomain (H334A, H366A, and E370A). Fig. S8. Results of the gel filtration and SDS ⁄ PAGE (8% acrylamide) of the C-terminal domain of human eRF1. Fig. S9. The stabilization of the loop (residues 358-363) by a network of hydrogen bonds.  Table S1. Differences in the experimental restraints used for the structural determination of the two conformers of the C-terminal domain of human eRF1 in solution. Table S2. Impact of mutations of human eRF1 on the GTPase activity of eRF3 in its ternary complex with the ribosome. This supplementary material can be found in the online version of this article.
Please note: As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer-reviewed and may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.


Towards the low temperature growth of uniform diameter multi walled carbon nanotubes by catalytic chemical vapour deposition technique

1Department of Chemistry, Anna University Chennai, Chennai-25, India 2Department of Chemical Engineering, University of Massachusetts, Amherst, USA *Corresponding author. E-mail address: soma_nano@yahoo.co.in (T. Somanathan) Towards the low temperature growth of uniform diameter multi walled carbon nanotubes by catalytic chemical vapour deposition technique Thirunavukkarasu Somanathan1,* and Arumugam Pandurangan1,2

the electrical properties of multiwalled CNT bundles grown by chemical vapor deposition (CVD) have been intensively investigated for interconnect applications [1][2][3][4]. Lowtemperature growth of CNTs is one of the most fundamental issues to be resolved for development of CNT based on interconnects technology compatible with LSI manufacturing processes.
Generally, carbon nanotubes have been synthesized by three different techniques: arc discharge between two graphite electrodes [5], laser evaporation of carbon target [6] and chemical vapour deposition (CVD) [7]. The major drawback of arc discharge and laser evaporation methods is that they are extremely uncontrolled in terms of process parameters, resulting in CNTs that contains significant fractions of unwanted material and that are difficult to manipulate and assemble in specific designs. CVD method is based on the thermal decomposition of hydrocarbon compounds over transition metal catalyst particles.
It appears to be a simple and economic technique to synthesize this kind of material at a low temperature, ambient pressure and it represents the best hope for large scale production.
To date, all the metal-catalyzed CNT growth studies have mainly focused on transition metals. Curiously, f-block transition elements also referred to as inner transition elements have still not been well explored. One reason could be that inner transition elements are not known to be highly catalytic as the transition elements. It has also been suggested that lanthanoids such as gadolinium and europium exhibit insufficient carbon solubility, slow carbon diffusion, and limited carbide formation to catalyze CNT growth [8]. Recently, gadolinium and europium were used as catalyzed to synthesize single walled carbon nanotubes [9].
Gd (III) ion exchanged NaY zeolite has been reported as a gastrointestinal contrast agent [10]. However, Y zeolite has a pore size of around 1

Characterization of Catalysts and Carbon nanotubes
The powder XRD diffraction patterns for the calcined

Physico-chemical characteristics of Gd incorporated MCM-41 materials
The physico-chemical characteristics of the Gd incoporated MCM-41 materials that were used for the synthesis of carbon nanotubes were investigated by means of XRD, N 2 sorption studies, TGA, SEM, TEM and EPR analysis.

XRD of the catalysts
In order to aware about the periodic and porous nature of the materials, the XRD analysis was performed. The XRD patterns of Gd-MCM-41 (Si/Gd = 50, 75 and 100) are shown in

N 2 sorption studies
The N 2 sorption analysis was employed for Gd-MCM-41 materials and their data are presented in Table 1. The N 2 sorption studies were typical for type IV, with a hysteresis loop characteristic of mesoporous materials (see Fig. 2). The isotherms exhibited three stages. The first stage is due to monolayer adsorption of nitrogen to the walls of the mesopores at a low relative pressure (P/P 0 < 0.25). The second stage is characterized by a steep increase in adsorption (P/P 0 > 0.25). As the relative pressure increases, the isotherm exhibits a sharp inflection characteristic of capillary condensation within the uniform mesopores. The P/P 0 at the inflection is related to the diameter of the mesopore [15]    Gd-MCM-41 (100) catalysts are presented in Fig. 3. The initial weight loss up to 120C is due to desorption of physically adsorbed water and the weight loss from 120C to 350C are attributed to the organic template. The oxidative desorption of the organic template takes place at 180C and the minute quantity of weight loss above 350C to 550C is related to water loss from the condensation of adjacent Si-OH groups to form siloxane bond [11,17].

SEM and TEM analysis for the catalyst
The particle size and morphology of Gd-MCM-41 (100) sample was determined by SEM analysis and shown in Fig. 4.

EPR analysis
Gadolinium (III) ions are often used in paramagnetic complexes due to their good paramagnetism. The EPR spectrum with three and more absorption signals is usually assigned to isolated Gd 3+ ions, while a single broad absorption signal encompassing g = 2 is assigned to the group of Gd 3+ ions [19].
After crystallization the EPR spectra mainly consist of relative large line with g = 2.0 suggesting that the surrounding of Gd 3+ ions are experiencing weak crystal fields resulting from structural relaxation [20] which is shown in Fig. 6.  When the deposition temperature is higher than 550°C, the yield of CNTs is decreased up to 68.45 %. At higher temperature, the decomposition of C 2 H 2 promotes and consequently increases the concentration of carbon atoms, which can result in a dissolution rate that is higher than the rates for diffusion and precipitation. In that case carbon atoms will accumulate on the surface of the catalyst to form a carbon shell [22]. The catalyst particles then lose their activity and it retards the growth of CNTs.
Moreover, when the temperature is too high, a chemical reaction may take place between the carbon and the metal, leading to the formation of metal carbide, which is passivity the catalyst and then started dropping at approximately 600°C. At too high temperatures, the catalyst become highly mobile and quickly agglomerates into metal particles that are too large particles to initiate CNTs nucleation. These sintered large particles are rapidly encapsulated by carbon deposits and become inactive.
Hence 550°C was found to be optimum low growth temperature to achieve the very high yield and hollow structure of good respectively which may be ascribed to its greater ability to decompose unsaturated hydrocarbons. If the metal catalyst is exposed to acetylene, metal particles can easily diffuse on the surface to form larger particles, leading to MWCNT growth. The percentage of carbon yield for above mention catalysts are presented in Table 2, it can be clearly understood that support plays a prominent role in determining the dispersion and hence the catalytic activity of the metals in the production of CNTs.
Though Gd 3+ ion is toxic and when it is sequestered by chelation or encapsulation with another material, it reduced is toxicity therefore we utilized nanosized mesoporous siliceous material as a chelating agent in order to reduce the toxicity of gadolinium ion. Since, in our present study, we have used porous silica material to reduce the toxicity of metal and it would be an excellent carrier for the metal because of its porous nature.  bonding), since carbon nanotubes are known to be good transporters of water [23] and protons [24], whereas the active centers in gadofullerenes do not have this access. From a practical point of view, the rate of proton exchange is especially important since it contributes to the proton relativity [25]. These gadolinium carbon nanotubes are the contrast agent materials where superparamagnetic metal centers have access to many coordinated or exchanging water molecules per Gd 3+ ion. These Gd 3+ nanotubes species are linear superparamagnetic molecular magnets with MRI efficacies are more than any Gd 3+ based contrast agent in future clinical use. Figure 8 shows the XRD pattern of Gd containing

Characterization of carbon nanotubes XRD
MWCNTs synthesized at temperature of 550°C. The highest sharp peak at 2θ = 25.8° can be assigned to graphite (002), indicating that graphite layers are regularly stacked. While the other peaks at 44.3° (101) correspond to the remaining graphitic particles, a similar trend was observed by previous reporters [26]. Figure 9 shows the synthesized MWCNTs characterized by TGA in air. The weight loss is due to the combustion of carbon with oxygen and therefore, corresponds to the carbon content in the sample. The major mass loss observed in the temperature range of 375585°C due to the oxidation of carbon nanotubes, which is consistent with previous report [27].

SEM and TEM analysis
SEM image of CNTs prepared by Gd-MCM-41 (100) catalyst with an optimized condition of flow rate of acetylene and temperature were 40 ml/min and 550°C respectively, is shown in Fig. 10. The image clearly shows thinner nanotubes with metal particles at the tip of the tubes, and it also in agreement with TEM observations.
The TEM image (see Fig. 11a) indicates that CNTs grown are multiwalled and bamboo shaped. The structure shows that the CNTs grow with layers of graphite deposited on the surface of Gd catalyst were separated from the catalyst surface resulting in the growth of CNT with closed end (see Fig. 11b). However, if the deposition on Gd catalyst is too fast due to higher

Raman spectroscopy
Raman Spectroscopy is an important tool for investigating CNTs, which provides information about the crystalline nature of the sample. Figure 13 shows Furthermore, pyrolytic carbon particles deposited on nanotubes also contributed to the D-band intensity [33,34]. In the present system, G band is at higher intensity, indicating that the CNTs are graphitized, which is in agreement with the result of TEM observation.


s2fieldsofstudy: Chemistry Physics

text:
A theoretical scheme for generation of Gazeau-Klauder coherent states via intensity-dependent degenerate Raman interaction

A theoretical scheme is presented for generating Gazeau-Klauder coherent states(GKCSs) via the generalization of degenerate Raman interaction with coupling constant to intensity-dependent coupling. Firstly, we prove that in the intensity-dependent degenerate Raman interaction, under particular conditions, the modified efective Hamiltonian can be used instead of Hamiltonian in the interaction picture, for describing the atom-field interaction. We suppose that the cavity field is initially prepared in a nonlinear CS, which is not temporally stable. As we will observe, after the occurrence of the interaction between atom and field, the generated state involves a superposition of GKCSs which are temporally stable and initial nonlinear CS. Under specific conditions which may be prepared, the generated state just includes GKCS. So, in this way we produced the GKCS, successfully.

Introduction
Coherent states (CSs) defined as the right eigenstates of the harmonic oscillator annihilation operator, i.e., a|α = α|α play an important role in quantum optics and modern physics [1]. Along the generalization of these states, nonlinear CSs [2] or f -CSs [3] have been introduced. According to this formalism f -deformed annihilation and creation operators, respectively defined as A = af (n) and A † = f † (n)a † where a, a † and n = a † a are bosonic annihilation, creation and number operators, respectively. The intensitydependent function f (n) is responsible for the nonlinearity of the states. Nonlinear CSs |z, f are then defined as the right eigenstates of f -deformed annihilation operator, The Fock space representation of these states is explicitly given by where [f (n)]! = f (1)f (2)...f (n) and by convention [f (0)]! . = 1. Note that we have confined ourselves to the special case of real valued function f (n).
Roknizadeh et al derived a Hamiltonian associated to a nonlinear system based on action identity requirement of nonlinear coherent states as H = A † A = nf 2 (n) [4]. So, the eigenvalue equation for any one dimensional physical system with known discrete eigenvalues may be given by H|n = e n |n = nf 2 (n)|n , where 0 = e 0 < e 1 < e 2 < ... < e n < e n+1 < ... . Accordingly, one simply has f (n) = e n /n associated to solvable quantum systems. In this way the nonlinear CSs may be deduced corresponding to any solvable quantum system as [5]: But it is remarkable that these states are not temporally stable like the original nonlinear CSs in (2). Moreover, an analytical representation of Gazeau-Klauder CSs (GKCSs) corresponding to any Hamiltonian with discrete (nondegenerate) eigenvalues is defined as [6,7,8] where N (|z| 2 ) is a normalization constant. These states satisfy the following requirements: (i) continuity of label, (ii) resolution of the identity, (iii) temporal stability and (iv) action identity. The last condition requires ρ(n) = [e n ]!. So the state in (4) can be written as It is also established in [7] that GKCSs are a class of nonlinear CSs with nonlinearity function f GK (α, n) = en n e iα(en−e n−1 ) , which are temporally stable, i.e., Along this work, Gazeau-Klauder squeezed states associated to solvable quantum systems have been introduced by one of us [9]. On the other hand, recently there has been much interest in the superpositions of CSs [10]. Due to the quantum interference between the coherent components, such superposition states may exhibit various nonclassical properties such as squeezing and sub-Poissonian statics. Nonclassical states of light are central to quantum optics. Their importance comes from potential applications on advanced optics, as teleportation [11], quantum computation [12], quantum communication [13], quantum cryptography [14], quantum lithography [15], etc. A number of schemes have been proposed for generating such states [16]. Among them, a method has been presented for generating superpositions of CSs of a cavity field via degenerate Raman interaction [17,18]. In this paper, we have followed the same approach and suggested a theoretical scheme for generating the GKCSs which are temporally stable, via the intensity-dependent degenerate Raman interaction. It is worth to mention that, we have used the intensity-dependent modified effective Hamiltonian which describes appropriately the dynamics of the interaction between atom and field. This is while, to the best of our knowledge, no scheme for generation of GKCSs may be found in the earlier literature.

Degenerate Raman interaction and modified effective Hamiltonian
The degenerate Raman interaction describes the interaction between a degenerate Λ-type three-level atom (as shown in Fig. 1) and a single-mode radiation field characterized by bosonic operators a, a † . Various properties of this system have been previously discussed [19,20]. The Hamiltonian for such a system in the interaction picture is given by: where we have set ≡ 1, |e and |g are the two degenerate lower states and |i is the upper state of the atom, the coupling constant of the transition between |i and |g (|e ) with the cavity field is denoted by g 1 (g 2 ), △ = (ω i − ω 0 ) − ω f is detuning, where ω f is the cavity field frequency, ω 0 is the energy of the two lower states and ω i is the energy for the upper level of the atom. On the other side, to describe the degenerate Raman interaction, an effective Hamiltonian was derived by Agarwal in [21], when the atomic transition between the upper and lower levels is far from the frequency of the field mode. Indeed, after adiabatically eliminating the upper level, the author introduced the effective Hamiltonian as: where λ = g 1 g 2 /△ indicates the effective atom-field coupling constant. In fact, in the effective Hamiltonian approach, the two lower levels are coupled with a single-mode field through a virtual upper level. As a result, the degenerate Raman interaction is reduced to an effective two-level system. Also, the effective Hamiltonian given in (8) leads to the elimination of time-dependent phase factors in (7). These factors are related to the ac Stark shifts of energy levels [22]. The Hamiltonian that represents the Stark shifts of energy levels is given by: where λ 1 = g 2 1 /∆ (λ 2 = g 2 2 /∆) describes the Stark shift of the state |g (|e ). Hence, one may modify the effective Hamiltonian given in (8), so that it includes the ac Stark effects represented in (9). In this way, for the modified effective Hamiltonian, one has then [23] Inserting H e and H s respectively from (8) and (9) in (10), the modified effective Hamiltonian can be written as follows: It is found that, the modified effective Hamiltonian H ef f is more suitable than the wellknown effective Hamiltonian H e in studying the time evolution of the systems. Xu and Zhang in [23] showed that, in the degenerate Raman interaction, far off-resonant (enough large value of ∆), the modified effective Hamiltonian has been given in (11), can be applied instead of the Hamiltonian in the interaction picture in (7). In fact, starting from a unique state vector at t = 0, both of the Hamiltonians lead to the same state vector of atom-field system at any time t. Altogether, several other mathematical physics methods were suggested to obtain the modified effective Hamiltonian in [24,25].

Generalizing the degenerate Raman interaction to intensity-dependent interactions
Generalization of the single-mode to two-mode degenerate Raman process has been recently done in [26]. But, to achieve our aim of the paper, we should generalize the single-mode degenerate Raman interaction in a rather different way. Indeed, following the path of Knight in [27] and specifically Zheng in [28], we replace the bosonic operators a, a † in (11) , the generalized f -deformed ladder operator. This type of generalization may be arisen from the same procedure of degenerate Raman interaction, briefly illustrated in the previous section, with the difference that the interaction between the same Λ-type atom and a single-mode radiation field is now considered to be intensity-dependent. Henceforth, analogously to (7) one may suggest the following form for the Hamiltonian of such a system in the interaction picture In the same way, analogously to (11), for the intensity-dependent modified effective Hamiltonian we suggest Clearly, inserting f (n) = 1 in (12) and (13) recovers the usual degenerate Raman interaction (intensity independent coupling) introduced in (7) and (11), respectively. This type of generalization (of degenerate Raman interaction) to intensity-dependent interaction can be frequently found in the literature, for instance, whenever one imposes nonlinearity on the standard JCM [29]. Before we proceed, to establish the above formal approach more explicitly, the following discussion may be offered. As mentioned, when ∆ is enough large, the equivalence of the introduced Hamiltonian in (7) and (11) are demonstrated in [23]. Our aim at this stage is to prove that, in the nonlinear degenerate Raman interaction, under particular conditions, the nonlinear modified effective Hamiltonian in (13) can be applied appropriately instead of the nonlinear Hamiltonian in the interaction picture introduced in (12). To investigate the validity of our proposal, we will obtain the time evolution of the state vector of the atom-field system by using (12) and (13), and continue with showing that for enough large value of ∆, these two state vectors are equal. For this purpose, we suppose that the atom is initially in a superposition of |g and |e : and the field is in the arbitrary state: where q n determines the initial state of the field. The state of the atom-field system at t = 0 is thus given by: The time evolution of the state of the atom-field system, governed by H I introduced in (12), is the solution of: where |Φ s,I (t) , denotes the state of the atom-field system after time t. The following general solution may be considered as: |Φ s,I (t) = ∞ n=• q n C n g (t)|g, n + C n i (t)|i, n − 1 + C n e (t)|e, n .
The problem is now determining the time dependent coefficients which may be obtained by lengthy but straightforward calculations with the following final results: where we have set B n 1 (t) = e i∆t/2 −i B n 2 (t) = e i∆t/2 −i with the following definitions: On the other side, if we use H ef f introduced in (13) for obtaining the time evolution of the state of the atom-field, we have to solve the equation where |Φ s,ef f (t) denotes the state of the atom-field system after time t. The general solution may be given by |Φ s,ef f (t) = ∞ n=0 q n C n g (t)|g, n + C n e (t)|e, n C n e (t) = D n 2 (t)C g (0) + D n 3 (t)C e (0).
Here we have set When 4nf 2 (n) ≪ ∆ 2 /G namely ∆ be enough large and (nf 2 (n)) 2 G 2 t/δ 3 ≪ π which means that evolving time is not too long, one has: Therefore, by using the two above approximations we have: and consequently, As it is observed, we established that in the nonlinear degenerate Raman interaction, whenever ∆ be enough large, the state vectors given in (18) and (30) will be equal. Therefore, in the nonlinear degenerate Raman interaction, when ∆ be enough large, the nonlinear modified effective Hamiltonian is equivalent to the nonlinear Hamiltonian in the interaction picture.

Generating of GKCSs via the intensity-dependent degenerate Raman interaction
Now, in the remainder of the paper, we want to present our theoretical scheme for generating temporal stable GKCSs via the introduced intensity-dependent degenerate Raman interaction, while the atom-field interaction is described by the modified effective Hamiltonian given in (13). It is worth to notice that, without loss of generality, g 1 = g 2 = g is assumed in (13) for continuing the calculational works, thus one has λ 1 = λ 2 = λ = g 2 /△. So, one arrives at the modified effective Hamiltonian as follows: Using the expression of A, A † , it may be readily seen that the effective Hamiltonian in (41) can be explicitly re-written as: Inserting λ 1 = λ 2 = λ in (11) and then comparing the recasted relation with (42), the above development can be, in a sense, considered simply as generalizing λ to λf 2 (n). This result may be viewed as intensity-dependent atom-field coupling. Now, suppose that the cavity field is initially prepared in the nonlinear CS introduced in (2). Also, the flux of the atoms injected into the cavity is such a low that there exists at most one atom at a time inside the cavity. If the first atom be initially in a superposition of |e and |g , such that the state of the atom-field system at t = 0 is thus given by: Using the time evolution of the state of atom-field described by: with H ef f in (42) and the initial state in (44), the state of the atom-field system after time t is given by: The atomic velocities can be controlled such that every atom interacts for a fixed time τ , with the radiation field inside the cavity. Suppose that the atom which is exiting the cavity is detected in the state |e , so the cavity field certainly collapses to |Ψ (1) where N 1 is an appropriate normalization factor that may be determined. Inserting C n from (2) in (47) one can rewrite the field state as It is worth mentioning the fact that the normalization coefficient N (|z| 2 ) for both nonlinear CS and GKCS is exactly the same. Noticing that nf 2 (n) = e n , at last the state in (48) can be written as where |z, α 1 is a GKCS introduced in (5) with α 1 ≡ −2λτ . It is clear from (49) that we have arrived at a superposition of GKCS and initial nonlinear CS. Now, if one prepares the atom in the initial state (43) with ε 1 = 1, namely the probabilities of the presence of the atom in |e and |g are equal, the cavity field will collapse to |z, α 1 . So, we have successfully generated a temporal stable state from initial nonlinear CS |z, f that is not temporally stable. Now, assume that the second atom is injected into the cavity, while it is initially in the state described by If the second atom also interacts for a time τ , with the cavity field which is described by (47) and then, it is detected in the state |e , the cavity field collapses to where again N 2 is a normalization constant. Similar to the procedures we followed in (47)-(49), the state in (51) can be re-written as where we have set α 2 ≡ −4λτ . Now, once again when the first and second atoms are initially prepared in 1 √ 2 (|e + |g ), i.e., ε 1 , ε 2 = 1, the cavity field would be in |z, α 2 , i.e., in the GKCS.
By further iteration of the above procedure it is easy to show that if the mth atom is initially in the state and we enter N atoms into the cavity, one by one, we can generate a superposition of N temporally stable GKCSs and the initial state of the cavity field |z, f that is not temporally stable. When all of N atoms that are exiting one by one from the cavity are detected in the state |e , the state of the cavity field is given by where N N is an appropriate normalization constant and α m ≡ −2 m λτ . Again, if ε 1 , ε 2 , ..., ε N = 1, then C 0 = 0 and {C m } N −1 m=1 = 0. As a result, the cavity field would be in |z, α N which is exactly in the GKCSs family.
We end this section with noticing that, the initial state of the cavity, i.e., nonlinear CS may be generated experimentally. As an evidence recall that the generation of photonadded coherent states as a well-known class of nonlinear CSs reported by Zavatta et al in [30]. Also, a theoretical scheme for generation of any class of nonlinear CSs in a micromaser using the intensity-dependent Jaynes-Cummings model was introduced in [31].

Summary and concluding remarks
In summary, using the intensity-dependent degenerate Raman interaction procedure has been introduced in the present paper and assuming the cavity field to be initially in the nonlinear CS (which is not temporally stable), the atoms that are in a superposition of the states |g and |e are sent inside the cavity, one by one. The atomic velocity can be controlled such that every atom interacts with the cavity field for a specific time interval τ . If each of the atoms, which is exiting from the cavity is detected in the state |e , the cavity field collapses to a superposition of GKCSs and initial nonlinear CS. If N atoms are sent inside the cavity, superposition of N GKCSs and the initial state of the cavity will be generated. Preparing the initial state of the atom, such that the probabilities of being every atom in states |g and |e are equal, then the generated states reduce to a GKCS. In fact, we have generated temporally stable GKCS from a nonlinear CS which does not have this property. In addition to these, we have found a more deep insight to the physical foundation of GKCSs, where we observed that according to our proposal, the parameter α in the phase factor of GKCSs in (5) explicitly depends on λ (the effective coupling constant of the atom-field) and τ (the time of the interaction between atom and field). Altogether, our proposal may be considered as the first step in producing the GKCSs. We hope that the proposed theoretical scheme will stimulate further better approaches to study the GKCSs, experimentally.