Kinetics and Thermodynamics of the Interaction of Elongation Factor Tu with Elongation Factor Ts, Guanine Nucleotides, and Aminoacyl-tRNA*

The exchange of elongation factor Tu (EF-Tu)-bound GTP in the presence and absence of elongation factor Ts (EF-Ts) was monitored by equilibrium exchange kinetic procedures. The kinetics of the exchange reaction were found to be consistent with the formation of a ternary complex EF-Tu . GTP. EF-Ts. The equilibrium association constants of EF-Ts to the EF-Tu. GTP complex and of GTP to EF-Tu-EF-Ts were calculated to be 7 X lo7 and 2 X 10’ M-’, respectively. The disso- ciation rate constant of GTP from the ternary complex was found to be 13 s-’. This is 500 times larger than the GTP dissociation rate constant from the EF-Tu. GTP complex (2.5 x lo-’ s-’). A procedure based on the observation that EF-Tu. GTP protects the aminoacyl-tRNA molecule from phosphodiesterase I-catalyzed hydrolysis was used to study the interactions of EF-Tu. GTP with Val-tRNAVd and Phe-tRNAPh”. Binding constants of Phe-tRNAPhe and Val-tRNAVd to EF-Tu-GTP of 4.8 X lo7 and 1.2 X lo7 M-’, respectively, were obtained. The exchange of bound GDP with GTP in solution in the presence of EF-Ts was also examined. The kinetics of the reaction were found to be consistent with a rapid equilibrium base-lines described apparent base-lines were observed in most of the experiments. experiments

initiated ribosome promoting the binding of aa-tRNA to the A site of the ribosome (1)(2)(3). The binding reaction is accompanied by hydrolysis of the GTP molecule (4)(5)(6). The resulting GDP is not released into solution, but remains bound to EF-Tu as a 1:l complex (5,6). EF-Tu.GDP dissociates from the ribosome and, in the presence of EF-Ts, GTP, and aa-tRNA, is rapidly reconverted into another EF-Tu. GTP. aa-tRNA complex which participates in the subsequent binding of a second aa-tRNA molecule (7).
The role of EF-Ts in the polypeptide elongation reaction is to accelerate the dissociation of the EF-Tu. GDP complex (8,9). In the absence of EF-Ts, the EF-Tu . GDP complex dissociates with a rate constant of about s-' (10). Since the in vivo rate of peptide synthesis is of the order of 10 amino acids/s/ribosome (ll), the spontaneous rate of dissociation of the EF-Tu GDP complex is much too slow to account for any significant fraction of EF-Tu recycling during peptide synthesis.
We have previously characterized the effect of EF-Ts on the dissociation of GDP (10). Kinetic analysis showed that EF-Tu. GDP, and EF-Ts participate in a rapidly fluctuating equilibrium according to the reaction scheme shown below: EF-Tu.GDP + EF-TS e EF-Tu. GDP. EF-TS Kl K2 EF-Tu.EF-Ts + GDP However, this equilibrium reaction represents only a partial reaction in the overall polypeptide elongation substrate supply mechanism. In this work, we describe the interactions of EF-Tu with GTP in the presence and absence of EF-TS and aa-tRNA. Our experiments show that the substrate supply reaction proceeds via the formation of several intermediates according to the reaction scheme shown below: EF-Tu.GDP + EF-TS e EF-TU. GDP.EF-Ts The equilibrium constants of Reactions 1 and 2 have been 6167 reported previously (10). In this work, we have determined the equilibrium constants of Reactions 3, 4, and 5. The rate constant k 3 was measured experimentally. A detailed mechanism for the overall reaction is discussed. EXPERIMENTAL

Materials
Escherichia coli K12 cells were obtained as frozen cell paste from Grain Processing Co., Muscatine, IA, and stored at -20 "C until use.

Methods
Preparation of Radiolabeled EF-Tu. Nucleotide Compbxes-EF-Tu was purified as described previously (10). EF-Tu. ['HIGDP was prepared by incubation of EF-Tu.GDP with tritiated GDP as described elsewhere (10). [y''P]GTP was prepared by a method described by Johnson and Walseth (12). Radiolabeled EF-Tu. GTP was prepared by incubation of EF-Tu.GDP with [3H]GDP and ["PIGTP in the presence of phosphoenolpyruvate (2 mM) and pyruvate kinase (10 pg/ml) in 0.02 M phosphate buffer (pH 7.2), 0.1 M NaCl, 0.01 M MgCl', and 1 mM dithiothreitol (reaction buffer). The phosphorylation of the nucleotide diphosphate was monitored by measuring the amount of radioactive material retained on nitrocellulose filters. The reaction was continued until the ratio of filter-bound tritiated to filter-bound "P-labeled material reached a constant value. This material was further examined by thin layer chromatography in polyethyleneimine-cellulose. The filter-bound material was extracted either by dissolution of the filter in 0.5 ml of 2-methoxyethanol or by addition of 0.5 ml of 5% trichloroacetic acid. 10-pl aliquots were spotted on plastic polyethyleneimine-cellulose TLC plates and dried in air. After two to three applications, the TLC plates were developed with 0.3 M ammonium sulfate, dried in air, and cut into 0.5-cm strips. The migration of the radioactive material was determined by scintillation counting of the strips. In general, over 90% of the bound nucleotide was identified as GTP.
Preparation of Val-tRNAvd and Phe-tRNAPk-Valine-specific amonoacyl-tRNA synthetase was obtained as a side-product of the purification of EF-Tu. The enzyme copurifies with EF-Tu.GDP during most of the preparation. It was separated by hydroxylapatite chromatography, concentrated, and then dialyzed against 0.02 M phosphate (pH 6.8) containing 0.1 M NaCl and 1 mM dithiothreitol. The enzyme is about 90% pure at this step and can be stored in 10% glycerol for long periods of time. Phenylalanine-specific aminoacyl-tRNA synthetase was prepared from E. coli K12 by the procedure described by Littauer (13).
Val-tRNA""' and Phe-tRNAPhe were prepared by incubation of unfractionated or purified valine-or phenylalanine-specific tRNAs with the appropriate tritiated amino acid and the specific enzyme in the presence of ATP according to the procedure described by Littauer (13). The aminoacylated tRNA5 were ethanol-precipitated, dissolved in acetate buffer, and lyophilized. The aminoacylated tRNA5 cannot be stored over long periods of time and thus were used within 48 h after their preparation.
Exchange Kinetics-Radiolabeled EF-Tu. nucleotide complexes were used to study the kinetics of the exchange of bound nucleotide with nucleotide free in the solution. Three different types of exchange experiments were performed (a) the exchange of bound radioactive GTP with free unlabeled GTP under equilibrium conditions (10); (b) the exchange of bound GDP with free GTP; and ( c ) the exchange of bound GTP with free GDP. All experiments were performed at 21 'C in 20 mM phosphate (pH 7.2) containing 0.1 M NaC1, 10 mM M&~z, and 1 mM dithiothreitol using a rapid filtration apparatus as described elsewhere (10).
Hydrolysis of au-tRNA by Snake Venom Phosphodiesterase-A EF-Tu was developed. The method was based on the observation that rapid, simple procedure to study the interactions of aa-tRNA and the observed rate of hydrolysis of aa-tRNA by C. adamanteus phosphodiesterase I decreases by at least 2 orders of magnitude when the nucleic acid is bound to EF-Tu.GTP (15khe Tritiated Val-tRNA""' and Phe-tRNA were incubated at 21 "C with varying amounts of EF-Tu.GTP in 0.02 M phosphate buffer (pH 7.2), 0.1 M NaCl, 0.01 M MgClP, 1 mM dithiothreitol, and 1 mM GTP. The hydrolysis reaction was started by addition of phosphodiesterase to a final concentration of 0.3 unit/ml. After 5 min of incubation, 2 0 4 aliquots of the reaction mixture were absorbed onto Whatman No. 3 filter paper and immersed into ice-cold trichloroacetic acid. The filters were subsequently washed with 5% cold trichloroacetic acid (twice), ethanol, ethanol-ether, and ether. The amount of radioactive material bound to the filter was determined by scintillation counting. Analysis of the Kinetic Data-The data were analyzed by a twoparameter fit of the observed time course of the exchange reactions to the appropriate rate equations. Equilibrium exchange experiments were fit to a single exponential function by simultaneous adjustment of the observed rate constants and the apparent base-lines as described previously (10). Relatively high apparent base-lines were observed in most of the experiments. This effect was generally observed when the experiments were carried out in the rapid filtration apparatus and is attributed to nonspecific binding of the EF-Tu. GTP complex to the filter membrane during the incubation period. In the mathematical analysis procedure, this effect was incorporated as a constant. Some of the exchange experiments were found not to follow first order kinetics and were fit to theoretical curves obtained from the numerical integration of the respective rate equations. In these cases, the rate equations describing the kinetic processes were solved simultaneously by a modified Runge-Kutta algorithm (14), and the adjustable parameters were varied to obtain the best fit of the theoretical curve to the data.

Kinetics of the GTP Exchange Reaction
When a solution containing EF-Tu. [3H]GTP or EF-Tu.
[r3'P]GTP is mixed with a large excess of unlabeled GTP, the bound ligand exchanges very rapidly with the free nucleotide (Fig. 1). The addition of 1.25 nM EF-Ts accelerates the reaction significantly. The time course of the reaction follows first order kinetics whether or not EF-Ts is present in the reaction mixture (Fig. 2). The observed first order rate constants of the GTP exchange reactions were found to be 0.025 and 0.102 s" in the absence and presence of EF-Ts (1.25 nM), respectively.
The observed kinetic behavior of the GTP exchange reactions is analogous to the GDP exchange reaction previously studied in this laboratory (10). It is, therefore, susceptible to a detailed analysis under equilibrium exchange assumptions. Since the EF-Tu concentration in the experiments shown in Fig. 2 is 100-fold in excess over the EF-Ts concentration, the effect of the latter must be catalytic and the increment in the observed exchange rate demonstrates the formation of a ternary complex involving EF-Tu, EF-Ts, and GTP.
Accordingly, EF-Tu, GTP, and EF-Ts participate in a multiple equilibrium as shown below. The observed rate of exchange of bound GTP in the presence of EF-Ts is the result of two independent reactions: ( a ) the spontaneous dissociation of the radiolabeled ligand from the EF-Tu-GTP complex, and ( b ) the dissociation of GTP from the EF-Tu. GTP. EF-Ts ternary complex. Therefore, the observed rate of exchange can be written as: where GTP* represents the radiolabeled nucleotide species, k-GTp is defined as the dissociation rate constant of EF-Tu.
GTP, and kat is either k-3 or k",l (as defined above), depending on the rate-limiting step of the EF-Ts-mediated reaction. The uncertainty in the assignment of kcat arises from the fact that EF-Ts must be recycled during the reaction.
At equilibrium, the exchange reaction follows first order kinetics. The first order rate constant of the reaction is a function of the equilibrium concentration of the components and can be written as: (7) where the subscript T denotes the total concentration of the components. K4 is the association equilibrium constant of EF-Ts with the EF-Tu GTP complex.
According to Equation 7, kb should be a linear function of the concentration of EF-Ts. This is indeed the case, as shown in Fig. 3. In these experiments, the concentration of EF-Ts was varied between 0.2 and 1.5 nM while the concentrations of EF-Tu GTP and GTP were kept constant at 200 nM and 1 mM, respectively. They intercept of Fig. 3 is the dissociation rate constant of GTP from the EF-Tu. GTP complex. k-GTp, calculated from these data, was found to be 0.023 s-l, which compares very well with the value obtained by measuring directly the EF-Tu. GTP dissociation rate in the absence of EF-Ts (Fig. 1).
Equation 7 can be transformed into

Heterogeneous Exchange Reactions
The experiments described above show that EF-Tu, EF-Ts, and GTP interact in a rapid equilibrium system similar to the equilibrium established with the nucleoside diphosphate GDP described previously (10). However, there are two important questions that the equilibrium exchange experiments cannot answer per se. First, the value of the rate constant kat cannot be unequivocally established by the equilibrium exchange technique; and second, it is necessary to show that bound GDP can be exchanged with GTP free in solution in order to determine whether or not the set of reactions studied are relevant to the mechanism of EF-Tu turnover during peptide elongation. Therefore, studies of the exchange of bound GDP with free GTP in the solution and the exchange of bound GTP with free GDP were initiated.
The Exchange of Bound GDP with GTP-When EF-Tu.
[3H]GDP (60 nM) is incubated with 1 mM in the absence of EF-Ts, the bound GDP exchanges with a first-order rate constant of 1.8 X s-' (Fig. 5, upper curue). The exchange reaction in the presence of EF-Ts did not follow first order kinetics and appeared to be a biphasic process. A fraction of the bound GDP exchanges initially very rapidly, as shown in Fig. 5 (lower curue). The remaining GDP exchanges at a much slower rate. This observation can be explained in terms of the relative affinity of EF-Ts to EF-Tu.GTP and EF-Tu.GDP. As shown above, EF-Ts binds to EF-Tu + GTP with a binding constant of 7.2 X lo7 M-', whereas the binding constant of EF-Ts to EF-Tu.GDP is about 400 times smaller (Kl = 1.8 X IO5 M" (10)). Thus, a comparison of these constants indicates that the EF-Tu. GTP complex formed as a result of the exchange reaction will behave as a strong inhibitor of the EF-Ts-catalyzed GDP exchange reaction.
Additional evidence of this "product inhibition" was obtained by incubating a mixture of EF-Tu-[3H]GDP and EF- The material retained on the filter after filtration of the reaction mixture and subsequent washing was extracted with 5% trichloroacetic acid and examined by thin layer chromatography in polyethyleneimine-cellulose developed with 0.3 M ammonium sulfate. The TLC plastic sheet was cut in 0.5-cm strips, and the migration of the radioactive material was determined by scintillation counting of the strips. Fig. 6 shows that under the experimental conditions used, over 90% of the bound GTP was exchanged within 30 s, whereas essentially all the GDP remained bound to EF-Tu. These results show that, under the experimental conditions used, GTP alone cannot displace EF-Tu-bound GDP at a rate consistent with the velocity of polypeptide elongation. As will be shown below, aa-tRNA is required for complete displacement of the bound GDP.
The exchange of bound GDP with GTP can be represented by the following equilibrium scheme:

EF-Tu. GTP + EF-Ts
The data shown in Fig. 5 can be fit to an equation describing a rapid equilibrium mechanism. The rate equation in this case is: can be numerically integrated and fit to the data shown in Fig. 5 by adjustment of the value of k-2. The best fit of the data was obtained with k-2 = 1200 s-' . This is shown in the lower curue in Fig. 5 . This result is in excellent agreement with the estimated value of k 2 reported previously (10) and demonstrates that the rapid equilibrium assumption is consistent with the time course of the exchange reaction.
The Exchange of Bound GTP with GDP- Fig. 7 shows  Fig. 7 demonstrates that when bound GTP is exchanged with GDP, the reaction is essentially linear until completion and does not follow first order kinetics.
Assuming rapid equilibrium mechanisms, the rate equation that describes this process can be written as:

k -n R IEF-TU. I Y -~~P~G T P~ IEF-TslT (14)
with k-3 = 15 s-' (Fig. 7, solid lint?, lower curue). As above, the rapid equilibrium assumption is consistant with the kinetics of the exchange reaction. As shown above, kcat, the rate constant of the rate-limiting step of the GTP equilibrium exchange reaction (see Equation 9) was estimated to be 12.8 s-' . This value is in close agreement with the value of k-3 as calculated above and shows that the dissociation of GTP of the ternary complex EF-Tu . GTP. EF-Ts is the rate-limiting step of the GTP equilibrium exchange reaction. This result also yields a lower estimate for L r , the rate constant of dissociation of EF-Ts from the ternary complex EF-Tu. GTP. EF-Ts. As shown previously, equilibrium exchange experiments failed to identify the rate-limiting step of the reaction. The identification of k-3 as the rate-limiting step of the equilibrium exchange reaction indicates that k-4 must be larger than k-3 = 13 s-'. The

Ib = 1 + KG[EF-Tu.GTP]
where K5 is the equilibrium association constant of sa-tRNA to EF-Tu . GTP( K6 = k5/k-5). The free EF-Tu. GTP concentration was calculated from mass conservation equations of the system. The values obtained for K5 were 4.8 X lo7 and 1.2 X lo7 M-' for Phe-tRNAPh" and Val-tRNAva', respectively. These values are in close agreement with previously published results (16).

The Effect of aa-tRNA on the Rate of Exchange of EF-Tubound GDP with GTP
We have shown above that when EF-Tu. GDP is incubated with excess GTP in the presence of EF-Ts the observed rate of dissociation of the bound nucleotide decreases with time as the reaction proceeds. This decrease of the nucleotide dissociation rate occurs because of the higher binding constant of EF-Ts to the EF-Tu. GTP complex which is formed during the exchange reaction. However, when Val-tRNAva' is included in these exchange experiments, essentially all the bound GDP exchanges at a very fast rate. Fig. 9 shows the rate of exchange of EF-Tu-bound GDP (60 nM) in the presence of EF-Ts (0.625 nM) and GTP (1 mM), with (open circles) and without (closed circles) 90 PM Val-tRNAVa'. Both solid lines were obtained by numerical integration of Equation 13. These data were analyzed according to a model which assumed that the binding of aa-tRNA to EF-Tu.GTP was not rate-limiting. The results of this analysis lead to the conclusion that the EF-Tu. GDP complex can be recycled rapidly during the polypeptide elongation reaction only when the concentration of aa-tRNA is sufficiently high to drive the reaction in the direction of the formation of the EF-Tu. GTP. aa-tRNA ternary complex.

DISCUSSION
When the ternary complex EF-Tu . GTP. aa-tRNA interacts with the ribosome to induce binding of aa-tRNA to the ribosomal A site, EF-Tu. GDP is released as a product of the reaction (4,5). Since the intracellular concentration of EF-Tu is about 10-fold greater than that of the ribosomes (20,21), the overall rate of the reaction that enables EF-Tu GDP to dissociate and reform the EF-Tu. GTP e aa-tRNA complex must be at least 1/10 the rate of protein synthesis. The in vivo rate of protein synthesis has been estimated to be about 10 amino acids/s (11). Therefore, the in uiuo half-life of the formation of the ternary complex EF-Tu. GTP. aa-tRNA from EF-Tu. GDP must be less than 1 s. However, the rate constant for dissociation of GDP from the EF-Tu. GDP complex is only about 1.7 X s-', which is equivalent to a halflife of about 400 s (10). Thus, the elongation factor Ts is required to accelerate GDP dissociation to within limits consistent with the rate requirements of the elongation process.
We have previously demonstrated that the EF-Ts-catalyzed dissociation of EF-Tu. GDP proceeds via the formation of a ternary complex EF-Tu. GDP. EF-Ts which dissociates rapidly into GDP and EF-Tu. EF-Ts (10). In this report, we have examined the remaining reactions of the EF-Tu turnover reaction using equilibrium and kinetic experimental procedures and analyses.
A quantitative description of the interactions of EF-Tu. GTP and EF-Ts has been obtained. We have shown that EF-Tu. GTP and EF-TS participate in the formation of a ternary complex EF-Tu. GTP-EF-Ts, which exists in rapid equilibrium with its components as shown below: The interactions of EF-Tu. GTP and aa-tRNA were studied using a procedure based on the C. adamanteus phosphodiesterase I-catalyzed hydrolysis of aa-tRNA. The procedure was based on the observation that EF-Tu. GTP decreased the apparent rate of hydrolysis of aa-tRNA by 2 orders of magnitude. The equilibrium association constants of Phe-tRNAPh" and Val-tRNA""' were found to be 4.8 X lo7 and 1.2 X lo7 M-', respectively. We also attempted to use this procedure to study the interaction of EF-Tu. GDP with aa-tRNA, but at the EF-Tu. GDP concentrations employed, we were unable to detect any significant changes in the rate of phosphodiesterase-catalyzed aa-tRNA hydrolysis.
The rate of dissociation of aa-tRNA from the ternary complex EF-Tu. GTP a aa-tRNA cannot be unequivocally determined from hydrolysis protection experiments such as those described in this paper as well as in others (16,17). This is due to the fact that these procedures fail to distinguish between the hydrolysis of EF-Tu. GTP-bound aa-tRNA and the dissociation of the nucleic acid followed by hydrolysis of the free aa-tRNA. However, the rate of dissociation of the aa-tRNA from the ternary complex cannot be much faster than the rate of hydrolysis measured during protection experiments. Since the rate of hydrolysis decreases by at least 50fold in the presence of EF-Tu. GTP, the rate-limiting step of the hydrolysis reaction is either the dissociation of aa-tRNA or the hydrolysis of the bound aa-tRNA, whichever is faster. Thus, an upper limit of k-5, the dissociation rate constant of aa-tRNA from the ternary complex, can be calculated from hydrolysis experiments. These values vary from 8 X to 6 X lo-' s " for different species of aa-tRNA (16,17). Table I summarizes the thermodynamic and kinetic parameters for the interactions among EF-Tu, guanine nucleotides, EF-Ts, and aminoacyl-tRNA. Although further information is required, a general description of the mechanism of the  complexes EF-Tu GDP EF-Ts and EF-Tu. GTP. EF-Ts involves about the same Gibbs energy change. In the next step of the reaction, the EF-Tu.GTP.EF-Ts complex dissociates into EF-Tu. GTP and EF-Ts and, in the presence of aa-tRNA, the ternary complex EF-Tu-GTP .aa-tRNA is formed. The latter complex exhibits thermodynamic stability similar to the two previously described complexes. The latter complex is, however, extremely long lived ( tH > 2 h) in the absence of active, initiated ribosomes.
The complete reaction appears to be kinetically controlled by the presence of aa-tRNA. Although GTP can displace EF-Tu-bound GDP under equilibrium conditions when GTP is in large excess, the exchange reaction does not proceed at a rate consistent with the rate of protein elongation unless a sufficient amount of aa-tRNA is present in the system. This is because of the high affinity of EF-Tu GTP to EF-Ts, which results in the depletion of free EF-Ts with a consequent deceleration of the GDP exchange reaction.
A report of the binding of aa-tRNA to EF-Tu. GDP has been published (22). This finding suggests an additional role of aa-tRNA in the substrate supply reaction, namely the acceleration of GDP dissociation in a manner analogous to that proposed for EF-Ts. We investigated this possibility by incubating EF-Tu.
[3H]GDP with up to M Val-tRNAVaL in the presence of 1 mM GDP, but were unable to detect any effect on the kinetics of the GDP exchange reaction. This result rules out this possibility, at least within the concentrations of aa-tRNA used in this study. The mechanism discussed herein thus remains the most likely pathway of the polypeptide elongation substrate supply reaction.