Analysis of the kinetic mechanism of arginyl-tRNA synthetase

Biochimica et Biophysica Acta 1764 (2006) 307 – 319 http://www.elsevier.com/locate/bba

Analysis of the kinetic mechanism of arginyl-tRNA synthetase R. Kalervo Airas ⁎ Department of Biochemistry, University of Turku, FIN-20014 Turku, Finland Received 14 September 2005; received in revised form 19 November 2005; accepted 23 November 2005 Available online 22 December 2005

Abstract A kinetic analysis of the arginyl-tRNA synthetase (ArgRS) from Escherichia coli was accomplished with the goal of improving the rate equations so that they correspond more closely to the experimental results. 22 different steady-state kinetic two-ligand experiments were statistically analysed simultaneously. A mechanism and values for the ArgRS constants were found where the average error was only 6.2% and ranged from 2.5 to 11.2% in the different experiments. The mechanism included not only the normal activation and transfer reactions but also an additional step which may be a conformational change after the transfer reaction but before the dissociation of the product Arg-tRNA from the enzyme. The forward rate constants in these four steps were low, 8.3–27 s−1, but the reverse rate constants of the activation and transfer reactions were considerably higher (230 and 161 s−1). Therefore, in the presence of even low concentrations of PPi and AMP, the rate limitation occurs at the late steps of the total reaction. AMP increases the rate of the ATP-PPi exchange reaction due to the high reverse rate in the transfer reaction. The rate equation obtained was used to calculate the steady-state enzyme intermediate concentrations and rates between the intermediates. Three different Mg2+ binding sites were required to describe the Mg2+ dependence. One of them was the normal binding to ATP and the others to tRNA or enzyme. The measured Mg2+ dependence of the apparent equilibrium constant of the ArgRS reaction was consistent with the Mg2+ dependences of the reaction rates on the rate equation. Chloride inhibits the ArgRS reaction, 160 mM KCl caused a 50% inhibition if the ionic strength was kept constant with K-acetate. KCl strongly affected the Kapp m (tRNA) value. A difference was detected in the progress curves between the aminoacylation and ATP-PPi exchange rates. When all free tRNAArg had been used from the reaction mixture, the aminoacylation reaction stopped, but the ATP-PPi exchange continued at a lowered rate. © 2005 Elsevier B.V. All rights reserved. Keywords: Synthetase; tRNA; Arginyl-tRNA synthetase; Magnesium; Kinetic

1. Introduction The aminoacyl-tRNA synthetases are divided in two classes based on both structural and mechanistic features [1,2]. ArgRS belongs to class I, and it has close structural similarities with five aminoacyl-tRNA synthetases for neutral amino acids [3, 4]. The peculiar kinetic feature of ArgRS is the requirement of tRNAArg for the ATP-PPi exchange reaction [5]. ArgRS has previously been classified into the subclass Ic, together with the glutamyl- and glutaminyl-tRNA synthetases due to the similar requirements of the tRNA [6]. However, if structural properties are emphasized, it is rather placed into subclass Ia together with the aminoacyl-tRNA synthetases for neutral amino acids [3]. Abbreviation: ArgRS, arginyl-tRNA synthetase ⁎ Fax: +358 23336860. E-mail address: [email protected]. 1570-9639/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.bbapap.2005.11.020

Crystal structures have been obtained from yeast ArgRS with all three substrates separately [3,4,7], and conformational reorientations following the binding of the substrates have been elucidated. These are connected with the formation of the proper active site. ArgRS from E. coli has also been a target of some structural studies [8–11] but the exact structure is still lacking. Some other aminoacyl-tRNA synthetases from class Ia (isoleucyl-, valyl- and leucyl-tRNA synthetases) contain a separate domain and hydrolytic site to detect and hydrolyze oncognate amino acids from aa-tRNA·E in an editing reaction [12,13]. ArgRS does not have such a domain, and it is obscure whether editing reactions exist. In numerous kinetic studies on ArgRS, bisubstrate kinetics has been used to solve the binding order of the three substrates and in particular whether tRNA is required in formation of the correct binding site for arginine or ATP [14–19]. In ArgRS from E. coli and yeast, all three substrates can be bound separately to

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the enzyme, suggesting a random binding order. Another kinetic problem has been whether Arg-AMP is a normal intermediate or whether the enzyme follows a concerted mechanism where the activation and transfer occur simultaneously [20,21]. ArgRS is now rather considered to follow a similar mechanism to the other aminoacyl-tRNA synthetases in which the aminoacylAMP is first formed in the activation reaction and then the aminoacyl moiety is transferred to tRNA in the transfer reaction [3,4,14]. The structural similarity with other class I aminoacyltRNA synthetases supports this idea. In some previous studies, I have analysed the aminoacyltRNA synthetase reactions using total rate equations where the roles of substrates, products, magnesium ions and polyamines have been included [22–25]. The purpose has been that the same equation with the same constant values could describe the kinetic behaviour of the enzyme under different conditions. The reason to return to this subject is that in the previous analyses it became evident that the same experimental results could be satisfactorily fitted with several different mechanisms. The problem is more general and is met in all kinetic studies of the aminoacyl-tRNA synthetases, both in steady-state and fast kinetics. Interpretation of the measured results is always dependent on several parts of the complicated total reaction. Therefore a principal aim in the present work was to improve the accuracy by increasing the amount of experimental material. Another purpose was to avoid the inhibiting chloride ions in the experiments so as to better mimic conditions within the cell. A thorough kinetic analysis under the reaction conditions can supplement the information obtained, e.g., by crystallography.

The ATP/PPi exchange activities were measured in a similar reaction mixture to the aminoacylation, but 32PPi (200 000 cpm, 0.05–1 μM) was substituted for the radioactive amino acid, 20 μM non-radioactive PPi was added and Arg was 20 μM. To avoid the effect of the slight curvature in the rate curves, the initial rates were calculated using the integrated Michaelis–Menten equation containing product inhibition [27].

2.3. Equations The method of “rapid equilibrium segments” [28] was used in the derivation of the rate equations. Its use for the aminoacyl-tRNA synthetase reactions has been described previously [23,24]. The total reaction scheme was divided in 3–5 segments, depending on the mechanism to be tested. The segments were handled like single intermediates in the normal derivation of rate equations, and the rates between the segments (C terms) and the concentrations of intermediates within the segments (D terms) were used. The contents of the C and D terms depend on the details of the mechanism. The division into segments simplifies in particular the modification of the rate equations when the details of the mechanism are changed. It does not form a special feature of the reaction itself. A change in the mechanism normally causes changes in only two or three of these terms, the derivation of the whole rate equation is not necessary.

2.4. Best-fit analysis The analysis was based on the least-squares best-fit analysis between the measured and calculated rate values. The original rate values (v) were used in the analysis, not 1/v or s/v. The apparent variance of the fit was calculated for every experiment:
 1 ðmeanm =meanc Þv calculated
v measured 2 variance ¼ s2 ¼ ∑ n meanm meanm is the mean of the measured rate values and meanc of the calculated rate values in an individual experiment. By the relation (meanm/meanc ) the calculated rate values are adjusted to the same level as the measured rates (their means are set equal). The standard error (as percent of the mean) is: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ¼ 100* variance

2. Materials and methods 2.1. Materials ArgRS was purified from E. coli MRE600 by a procedure which included precipitation of nucleic acids with polyethylenimine, chromatography on DEAE-Sepharose CL-6B at pH 6 using a gradient of 0–300 mM NaCl, solubilization of the ammonium-sulphate-precipitated protein in a column of Sepharose CL-2B by a decreasing gradient of ammonium sulphate, gel filtration on Sephacryl S-300, and chromatography on hydroxylapatite (HA Calbiochem) using a gradient from 10 to 100 mM potassium phosphate pH 7. The ArgRS preparation was further purified by gel filtration through Superdex 200 (Amersham Pharmacia Biotech) in order to remove the remaining pyrophosphatase. The absence of pyrophosphatase was checked as in [26]. The specific activity of the preparation was 1.90 μmol min−1 mg−1. Unfractionated tRNA from E. coli MRE 600 (Boehringer) was used.

2.2. Enzyme assays The rates of the aminoacylation of the tRNA and the ATP/PPi exchange reactions were assayed as described previously [22] except that chloride was replaced by acetate. The standard reaction mixture (100 μl) for the aminoacylation contained 50 mM Hepes/25 mM KOH (pH 7.4 at 30 °C), 0.02% chicken egg albumin, 1 mg/ml of tRNA (0.96–1.35 μM tRNAArg), 2 mM ATP, about 50000 cpm of [14C] Arg (1 μM), 5 μM non-radioactive Arg, 3 mM Mg-(acetate)2 (1 mM excess Mg2+), 0.5 mM spermidine, 50 mM Kacetate, 1 mM dithiothreitol, and the enzyme. The reaction temperature was 30 °C.

the standard errors were calculated separately for each two-ligand experiment, and they are expressed in the figure legends. At the level of individual experiments an unweighted sum of the squared differences was used because the background values (mainly from the counting of the radioactivity) increase in particular the deviation of the lowest rate values. At the level of different experiments the variance values are weighted by division by meanm. Thereby the effects of different enzyme concentrations and activity levels in different experiments are corrected. In the best-fit analysis, the sum of the variances of the different experiments was minimized. The procedure of the Monte Carlo method was used [29]. The values of the rate and dissociation constants were randomly varied within a reasonable range. The sum of the variances was calculated for every set of the constants. (With the experimental material of the present work a 500 MHz computer calculates the variances and their sum in about one second. Hundreds or thousands of variance sum values must be calculated). When the fit became better, the ranges of the constants were narrowed and the number of the tested constants was lowered. Finally, every constant was optimized separately. The optimization was continued until any change, higher than 0.1% of the constant value, did not lower the sum of the variances. The process gives the best-fit values for the dissociation and rate constants. The optimization procedure must be repeated every time that changes are made in the mechanism. The deviations of the constants (at a 0.05 probability of difference in the F-statistics) were estimated using the ‘grid search method’ [29]. The deviations are not symmetrical, therefore both the lower and higher limits are given (in Table 1). The error percents of the separate experiments remain the same if all the rate constants in the equations are multiplied by the same number. The dissociation constants and the relative rates between the intermediates are

R.K. Airas / Biochimica et Biophysica Acta 1764 (2006) 307–319 Table 1 The best-fit values of the kinetic constants of the ArgRS reaction Constant

Definition

Unit

Value

K1M K1 KAM MgATP· EaatRNA K2 k+3 k−3 K4M K4MM K4 K5M K5 k+6 k−6 K71 K73 K74 k+8C k−8C k+8 k+8A k+8AMP KMR KSR KME KSE KME2 KSE2 KME3 KSE3 KME4 KSE4

MgATP·E free ATP·E μM

μM μM 783

577 2790 310–1463

Range 448–763 478–

amino acid·E activation pyrophosphorolysis s−1 MgPP·E Mg2PP·E free PPi ·E tRNA with Mg or spd tRNA without Mg transfer reverse transfer AMP·E in segment 1 AMP·E in segment 3 AMP·E in segment 4 conf. change reverse conf. ch. aa-tRNA from E aa-tRNA from EATP aa-tRNA from EAMP Mg·tRNA spd·tRNA Mg·EaatRNA spd·EaatRNA Mg·EaatRNA spd·EaatRNA Mg·EaatRNA spd·EaatRNA Mg·EaatRNA spd·EaatRNA

μM s−1 230 μM μM μM μM μM s−1 s−1 μM μM μM s−1 s−1 s−1 s−1 s−1 μM μM μM μM μM μM μM μM μM μM

5.68 26.9 206–254 59.1 240 8 0.312 0.482 20 161 25,000 1940 2075 8.3 0.12 1.29 19 0 753 256 4928 184 6655 3389 4506 159 1896 2080

3.88–8.39 20.9–35.0 53.5–65.8 14.9– – 0.206–0.457 0.308–0.822 18.1–22.2 109–231 504– 1380–2810 560– 6.0–11.6 −2.4 0.09–4.0 13.9–27.1 −13.3 331–1397 49–645 3375–7025 9–449 5513–8195 2633–4495 1193–11980 −879 1392–2718 578–

The kcat value of aminoacylation of tRNA at standard reaction conditions was 2.2 s−1.

not changed. Therefore, the differences in the specific activities of the enzyme preparations do not change the structure of the optimized mechanism.

3. Results 3.1. Experiments for the analysis of the mechanism The experimental data for the statistical analysis were collected by doing different kinetic measurements for ArgRS, where either the ATP-PPi exchange rate (Fig. 1) or the tRNA aminoacylation rate (Fig. 2) was measured. The chosen plotting types in Figs. 1 and 2 were the Hanes plots (s/v vs. s) for the substrate concentration dependences and the Dixon plots (1/v vs. i) for the inhibitor concentration dependences. (In the ATPPPi exchange measurements also PPi behaves like a substrate.) The intersection points of the lines and the abscissa axes give app the apparent constants Km or Kiapp, and if straight lines are obtained, the rates follow the Michaelis–Menten hyperbola. The Mg2+ dependences were plotted as v vs. [Mg2+] due to their complexity. The free Mg2+ concentration at the half-height of these curves gives a rough estimate for the dissociation constant of the Mg2+ ion from the enzyme (or from tRNA). The various

309

approximate constant values can be used as starting values in the statistical optimization process. The statistical analysis was done using the v values and not 1/ v or s/v. Plotting as 1/v or s/v causes the relative deviation to look high at the lowest rate values although the absolute deviations would be low. The apparent systematic deviation e.g. in Figs. 1A, 1D and 2A may come from the inaccuracy of the measured background value, which affects in particular the lowest rate values. In Fig. 3, both the exchange and aminoacylation rates were measured at identical conditions and their relation was expressed. In addition to the experiments in Figs. 1–3, the material for the best-fit analysis included three more aminoacylation experiments, one of them was as shown in Fig. 2A but without spermidine and at 0.5 mM [Mg2+]free, and the two others were as in Fig. 2D, but without spermidine and at 1 mM [Mg2+]free or 8 mM [Mg2+]free. (The standard errors in these three experiments were 5.24, 2.52 and 3.53%, respectively.) 3.2. Direct observations from the experiments app The Km (Arg) values from Fig. 1 range from 1.6 μM to 2.7 μM, and from Fig. 2 from 1.6 to 4.2 μM. The values and their variation are similar in the aminoacylation and ATP-PPi app exchange experiments. The Km (ATP) values range from 0.26 app mM to 0.49 mM, and the Km (tRNA) from 0.13 μM to 0.22 μM. All the listed variations are due to the effects of the other substrates, as normally in the enzyme kinetics.At low Mg2+ app app concentrations, the Km (tRNA) values and also the Km (ATP) values are increased. Spermidine affects the ATP-PPi exchange rate (Fig. 1E), which is not the case in other aminoacyl-tRNA synthetases when tRNA is not involved in the activation reaction. An Scurve is obtained without spermidine showing that more than one Mg2+ ion is involved. In Figs. 1F and 2F ATP raises the highest rate values, suggesting a role not only in the activation but also in the dissociation of the completed Arg-tRNA from the enzyme. AMP strongly increases the ATP-PPi exchange activity (Fig. 1H and I). This is exceptional among the aminoacyltRNA synthetases, normally only slightly changed rate values are observed. AMP shifts the equilibrium of the intermediates so that the concentrations of the intermediates in the activation reaction are increased. In the aminoacylation reaction, AMP shows an uncompetitive inhibition pattern (Fig. 2D) which means that the inhibiting AMP is bound at the late steps of the total reaction and that the binding to the ATP site before the activation reaction does not cause significant inhibition.

3.3. Statistical analysis The main purpose of the present work has been to find a mechanism and rate equations which, with optimized constant values, fits well to all the experimental results and thus best corresponds to the real mechanism. The basic structure normally contained separate activation and transfer reactions,

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Fig. 1. ATP-PPi exchange rates at different conditions. The lines were calculated using Eqs. (1)–(15) and the optimized constant values from Table 1. The reaction conditions were as described in the methods, but in A and D [Mg2+] = [ATP] + [PPi] + 1 mM and in F, G and H no spermidine was present. The standard errors were in A, 4.95%; B, 5.79%; C, 6.49%; D, 7.25%; E, 8.09%; F, 6.45%; G, 4.94%; H, 3.33%; and I, 4.24%.

but also one model of the concerted mechanism was tested where the activation and transfer occur in the same reaction. The detailed problems in a mechanism included whether a ligand is bound or dissociated or whether conformational rearrangements occur at a given step of the total reaction. In the statistical best-

fit analysis the variances for the 22 different experiments were calculated and their sum was minimized. Some limitations in the explanation of the results must be mentioned. It is rather easy to reach better than 5% average error in most of the experiments separately, but this can be

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311

Fig. 2. Aminoacylation of tRNAArg at different conditions. The lines are as in Fig. 1. In A [Mg2+] = [ATP] + 0.5 mM, in B and D [Mg2+] = [ATP] + 1 mM, in C [Mg2+] = [PPi] + [ATP] + 1 mM and [spermidine] = 0.3 mM, in F no spermidine was present, in G [Mg2+] = [ATP] + expressed value, and in H and I [ATP] = 1 mM, [Mg2+] = [ATP] + [PPi] + expressed value and [spermidine] = 0.3 mM. The standard errors were in A, 9.59%; B, 4.98%; C, 10.58%; D, 5.48%; E, 9.55%; F, 8.46%; G, 6.06%; H, 2.88%; and I, 5.82%.

done with several mechanisms. Even when three experiments are analysed simultaneously, some variation exists in the mechanisms which can be chosen [24,25]. In such a complicated system a change in one constant can cause a

change in the values of some other constants. Therefore, the optimized constant values are valid only for the given mechanism and together with the given set of other constants.

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Fig. 3. Relation of the rates of the ATP-PPi exchange and aminoacylation of tRNA. The line was calculated according to Eq. (17). The ATP-PPi exchange and aminoacylation rates were measured at identical conditions. ATP was 2 mM, Arg 5 μM, Mg2+free 1 mM and spermidine 0.5 mM. The tRNAArg concentrations were 0.23 (■), 0.46 (●), 0.69 (▴) or 1.15 μM (▾). The standard error between the calculated and measured values was 11.16%.

The simplest scheme for aminoacyl-tRNA synthetases is the three-segment mechanism, where the boundaries between the segments are at the activation and transfer reactions. It did not lead to a satisfactory fit. The required change to it was to add a reversible step after the transfer reaction by dividing the third segment in two separate segments. In the statistical analysis the rates between these segments became slow. Previously, it has been obscure whether there is an additional slow step between the activation and transfer reactions [24,30]. In most aminoacyl-tRNA synthetases, the substrate tRNA is required after the activation reaction, and then the additional step in the kinetic reaction model seems to be necessary. In ArgRS, the tRNA is required earlier, at the activation reaction. No doubt, also in ArgRS, some conformational reorientation occurs after the activation reaction when the complex is prepared for the transfer reaction. When the second segment in the scheme was divided into two separate segments, the rates between these segments became high, higher than any of the rate constants in the activation or transfer reactions. The statistical best-fit analysis of this five-segment mechanism led to similar, but not better, standard errors than the four-segment mechanism.

Due to its low kinetic importance, the additional reorientation step between the activation and transfer reactions was not included in the presented mechanism. In analysing the concerted model an additional intermediate was added after the activation-transfer reaction, where AMP remained bound. Otherwise the ATP-PPi exchange reaction would not have been possible. Even with that modification, such details of the mechanism could not be found which would have led to a satisfactory fit to the experimental results. The final best-fit model is shown in Scheme 1. It contains a random binding of substrates. The activation reaction runs only when tRNA is bound. In the transfer reaction PPi is not present. An additional step (k+8C, k−8C) divides the reactions after the transfer reaction in two segments. The nature of this additional step cannot be deduced from the kinetics, or more specified, it cannot be said whether the step is connected with a hydrolytic editing process after the transfer reaction. It has here been said a ‘conformational change’. The details of the mechanism are given by Eqs. (1)–(14), where the magnesium and polyamine dependences are also included. rf ¼ r0 =ð1 þ ½Spd=KSR þ ½Mg2þ  =KMR ½Mg2þ =KMR *½Spd=KSR Þ

ð1Þ

rr ¼ rf *ð½Mg2þ =KMR þ ½Spd=KSR þ ½Mg2þ =KMR *½Spd=KSR Þ r ¼ r0
rr

ð2Þ ð3Þ

C12 ¼ kþ3 *½Arg=K2 *½MgATP=K1M *ðr=K5 þ rr =K5M Þ *ð½Mg2 =KME þ ½Spd=KSE þ ½Mg2þ =KME *½Spd=KSE Þ ð4Þ C21 ¼ k
3 *ð½MgPPi =K4M Þ*ðr=K5 þ rr =K5M Þ*ð½Mg2þ Þ =KME2 þ ½Spd=KSE2 þ ½Mg2þ =KME2 *½Spd=KSE2 

ð5Þ

Scheme 1. Basic reaction mechanism of ArgRS. The frames show the four segments used in the derivation of rate equations. The three reactions between the segments are the activation, transfer and ‘conformational change’.

R.K. Airas / Biochimica et Biophysica Acta 1764 (2006) 307–319

C23 ¼ kþ6 *rr =K5M *ð1 þ ½Mg2þ =KME2 þ ½Spd=KSE2 þ ½Mg =KME2 *½Spd=KSE2 Þ

ð6Þ

2þ

C32 ¼ k
6 *½AMP=K73 *ð½Mg2þ =KME3 þ ½Spd=KSE3 Þ

ð7Þ

C34 ¼ kþ8C *ð1 þ ½Mg2þ =KME3 þ ½Spd=KSE3 Þ

ð8Þ

C43 ¼ k
8C *ð1 þ ½Mg =KME4 þ ½Spd=KSE4 Þ

ð9Þ

2þ

C41 ¼ ðkþ8 þ kþ8A *ð½ATPf =K1 þ ½MgATP=KAM Þ þ kþ8AMP *½AMP=K74 Þ

ð10Þ

D1 ¼ ð1 þ ½Arg=K2 Þ*ð1 þ r=K5 þ rr =K5M Þ*½1 þ ð½Mg2þ  =KME þ ½Spd=KSE þ ½Mg2þ =KME *½Spd=KSE Þ *ð1 þ ½MgATP=K1M þ ½ATP=K1 þ ½AMP=K71 Þ ð11Þ D2 ¼ ð1 þ r=K5 þ rr =K5M Þ*½1 þ ð½Mg2þ =KME2 þ ½Spd =KSE2 þ ½Mg2þ =KME2 *½Spd=KSE2 Þ*ð1 þ ½MgPPi  =K4M þ ½Mg2 PPi =K4MM þ ½PPi =K4 Þ ð12Þ D3 ¼ ð1 þ ½AMP=K73 Þ*ð1 þ ½Mg2þ =KME3 þ ½Spd=KSE3 Þ

ð13Þ

D4 ¼ ð1 þ ½Mg2þ =KME4 þ ½Spd=KSE4 Þ *ð1 þ ½AMP=K74 þ ½MgATP=KAM þ ½ATP=K1 Þ: ð14Þ In the list, r0 is the total concentration of tRNA, rf the free tRNA and rr the “reactive tRNA” (MgtRNA or SpdtRNA). Spd is the free spermidine. The concentrations of the different complexes of ATP, PPi, Spd and Mg were calculated using their Kd values as described in [24]. The D-terms in Eqs. (11)–(14) express the total intermediate concentrations within a segment (=[Ei]*Di) and the C-terms in Eqs. (4)–(10) mean the rates between the segments: rate = [Ei] *Ci,j where Ei is the central (simplest) intermediate within a segment. Ei is free E, EArgAMP, *EArgtRNA, or EArgtRNA in segments 1–4, respectively. The C and D terms are used in the rate Eqs. (15)–(17). Eq. (15) gives the rate of the ATP/PPi exchange reaction: vexch ¼ C21 *½C32 =C23 *ðC43 þ C41 Þ=C34 þ C41 =C23  =½D1 *fC21 =C12 *½C32 =C23 *ðC43 =C34 þ C41 =C34 Þ þC41 =C23  þ C41 =C12 gþD2 *fC32 =C23 *½ðC43 þ C41 Þ =C34  þ C41 =C23 gþD3 *ðC43 þ C41 Þ=C34 þ D4  ð15Þ Eq. (16) gives the rate of the aminoacylation of tRNA: vacyl ¼ C41 =½D1 *fC21 =C12 *½C32 =C23 *ðC43 =C34 þ C41 =C34 Þ þC41 =C23  þ C41 =C12 gþD2 *fC32 =C23 *½ðC43 þ C41 Þ =C34  þ C41 =C23 gþD3 *ðC43 þ C41 Þ=C34 þ D4 : ð16Þ The simple relation of the exchange and aminoacylation rates from Eqs. (15) and (16) is given in Eq. (17): vexch =vacyl ¼ ðC21 =C23 Þ*ðC34 þ C32 Þ=C34

ð17Þ

313

The best-fit values of the constants are given in Table 1, and the lines in Figs. 1–3 are calculated using these equations and the constant values from Table 1. The average standard error (sy.x) of the 22 experiments is as good as 6.2%. The weakest values are slightly above 10% for two experiments (Figs. 3 and 2C). These suggest that especially between the activation and transfer reactions, in segment 2, the relation between PPi and tRNA may be more complicated than in the equations. 3.4. Calculated enzyme intermediate concentrations and rates between the intermediates The real rates between the enzyme intermediates do not depend only on the rate constants but they are affected by the intermediate concentrations, too. These steady-state concentrations (at a given set of ligand concentrations) can be calculated using the constant values from Table 1 and the kinetic equations. The expressions of the C and D terms in Eqs. (1)– (14) remarkably help the calculations. Fig. 4 shows the PPi dependences of the calculated enzyme intermediate concentrations and the rates between them. The ligand concentrations were chosen to mimic the conditions in growing E. coli cells. In Fig. 4A the highest PPi concentration (500 μM) is the value measured from E. coli cells [31], but which probably cannot totally be in contact with the aminoacyl-tRNA synthetases. The proportion of the intermediates in segment 1, before the activation reaction, is dominating at 500 μM PPi, and therefore the rate of the aminoacylation of tRNA is only 11% of the rate without PPi. Below 50 μM PPi this dominating amount diminishes, the enzyme is divided to all segments, and the inhibition is less than 50%. At steady-state conditions the difference forward rate − reverse rate is equal at different steps (Fig. 4B). The reverse 'conformational change' between segments 3 and 4 is slow (b0.06 s−1), therefore the rates of the 'conformational change' and the dissociation of the product are about equal. Within a segment the intermediates are in equilibrium. Therefore the relative change of each intermediate concentration in a segment (as function of the PPi concentration) is similar to the total concentration change in that segment. (Segment 2 is an exception due to the binding of PPi itself.) Fig. 4C shows the concentrations of some key intermediates. The four highest curves represent the intermediates preceding the key reactions: activation, transfer, ‘conformational change’ or product dissociation. At 30 μM PPi three of these concentrations are equal. 3.5. Different progress curves in the exchange and aminoacylation reactions In Fig. 5, the reactions are “run to the end” or until all tRNAArg has been used. The aminoacylation reaction behaves as expected. The product level reaches a constant value and the reaction rate is lowered close to zero. According to Eq. (17) the relation of the ATP-PPi exchange and aminoacylation reaction rates should remain constant, or the exchange reaction should behave almost identically. However, in Fig. 5A, the ATP-PPi exchange reaction continues under the same conditions at about

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exchange reaction (at a slower rate). This would require a conformation of the-CCA-Arg end which does not cause total steric hindrance for the new arginine. Another possibility could be a fast hydrolysis of the Arg-tRNA, either spontaneously or enzymatically at the assay conditions. This would lead to extra consumption of ATP, which has not been found in other studies [15]. Initial velocities were measured and the integrated Michaelis equation was used in the calculations in the normal kinetic experiments of the present work. Therefore the effect of the difference in the rate curves should be minimal. 3.6. Magnesium dependence of the measured equilibrium constant Further support for the Mg dependence of the total aminoacylation reaction is obtained from equilibrium measurements. It is known that metal binding to a substrate or product changes the measured equilibrium constant of an enzyme reaction [32]. Since the Mg2+ ion is bound to ATP, PPi, AMP, tRNA and aa-tRNA, the equilibrium constant of aminoacyltRNA synthetase reactions is a complicated function of the Mg2+ concentration. The first dissociation constants of Mg2+ from ATP and PPi, Kd (MgATP) = 60 μM [33] and Kd (MgPPi) = 55 μM [34], are so low that the uncomplexed species do not practically exist at normal measurement conditions of the aminoacyl-tRNA synthetase reactions. Therefore these dissociations can be omitted from the equations. The second dissociation constant for PPi, Kd (Mg2PPi) = 2.6 mM at pH 7.4 [34], is high enough to allow the existence of both MgPPi and Mg2PPi when [Mg2+free] is in the millimolar range. The reacting form of PPi in the class I aminoacyl-tRNA synthetases is MgPPi [35]. Formation of Mg2PPi is the main factor causing the Mg2+ dependence of the measured equilibrium constant. At higher magnesium concentrations AMP is also in a magnesium complex, Kd (MgAMP) = 14 mM [33]. ATP, apparently, does not bind a second Mg2+ ion [33]. As mentioned above, the reacting tRNA is as a Mg2+ complex but in Arg-tRNA the Mg2+ ion is not bound. Eq. (18) shows the real equilibrium constant of ArgRS Fig. 4. Calculated PPi dependences of the enzyme intermediate concentrations and rates between the intermediates in the ArgRS reaction. The optimized constant values were used and the ligand concentrations were 2 mM ATP, 10 μM Arg, 50 μM PPi, 0.2 mM AMP, 1 mM free Mg2+, and 0.3 mM free spermidine. (A) Division of the total enzyme in the four segments of Scheme 1. (B) Calculated forward and backward rates in the activation, transfer, and putative conformational change steps. (C) Concentrations of the enzyme intermediates which are involved in the activation, transfer, conformational change and product dissociation steps.

30% of the rate of the initial velocity. It is well known that ArgRS (like GluRS and GlnRS) requires the cognate tRNA for the activation reaction. There is a discrepancy between this general rule and the results in Fig. 5, but this was not further analysed in this study. One possible explanation would be that the product Arg-tRNAArg could replace the tRNAArg in the

Keq ¼

½MgPPi ½AMP½ArgtRNA½Mg2þ  ½MgATP½Arg½MgtRNA

ð18Þ

The apparent equilibrium constant from a measurement is given by Eq. (19): app Keq ¼

½PPi;tot ½AMPtot ½ArgtRNAtot  ½MgATP½Arg½tRNAtot 

ð19Þ

In Eq. (20) the dissociations of the Mg–ligand complexes are taken into account.


 ½Mg2þ  ½Mg2þ  1 app Keq ¼ Keq 1 þ 1þ : KM2PP KMAMP KMR þ ½Mg2þ  ð20Þ

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Fig. 5. Progress curves of the ATP-PPi exchange and aminoacylation reactions. The measurements in A and B were done at the same conditions: 2 mM ATP, 20 μM Arg, 20 μM PPi, 3 mM Mg2+, and 0.5 mM spermidine.

Fig. 6 shows the measured equilibrium constant values as a function of the free Mg2+ concentration. The values range from 1 to 2 and slightly different values are obtained in the presence of spermidine. The best-fit analysis of the data in Fig. 6 with Eq. (20) gives values for KMR = 2.36 mM and Keq = 2.54. The value app of Keq at 1 mM [Mg2+] is 1.13. If the binding of Mg2+ to ArgtRNA was included in the best fit analysis, its dissociation constant value became high, the higher the better fit. It means that Mg2+ is not bound to Arg-tRNA (in a way that could prevent its binding to the enzyme). There is thus a difference between the Mg2+ binding to tRNA and Arg-tRNA which is consistent with the reaction-rate-based analysis above. In the reaction model where Arg-tRNA is also as a magnesium complex when dissociating from the enzyme, the calculated Mg2+ dependence does not even approximately fit to the measured. In that model the slopes in Fig. 6 would be higher and the plots curved upwards. The value of KMR in Table 1 (0.75 mM) is lower than the value calculated from Fig. 6 (2.36 mM). However, the second Arg-AMP binding of Mg2+ to the complex EtRNA should also be taken into account in the comparison. Then the value pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KME2 *KMR = 2.24 mM is close to the value from the equilibrium measurements. 3.7. Chloride inhibition KCl inhibits the ArgRS reaction (Fig. 7). TyrRS has previously been analysed for chloride inhibition [25], and the

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inhibition of ArgRS shows many features in common with it. Kacetate does not inhibit at lower than 200 mM concentrations where KCl inhibits. A salt concentration of about 50 mM (KCl or K-acetate) is required for full activity, but above that the inhibition by KCl is evident. KCl affects the binding of tRNA to app (tRNA) value is 0.27, 0.48, 0.94 and 1.91 the enzyme. The Km μM at 0, 50, 100 and 150 mM KCl, respectively. High Mg2+ concentrations (10 mM) weaken the chloride inhibition in TyrRS. In ArgRS the effect is weaker because the dissociation constants for Mg2+ are generally higher in the ArgRS system. Sulphate also inhibits ArgRS like TyrRS: 45 mM K2SO4 inhibits as efficiently as 100 mM KCl when the ionic strength is kept constant with K-acetate. The requirement of tRNA for the activation reaction in ArgRS causes a difference in the chloride inhibition: chloride inhibits the ATP-PPi exchange reaction in ArgRS but not in TyrRS. The effect of KCl on the PPi inhibition and AMP inhibition of ArgRS resemble the same inhibition seen with TyrRS [25]. The Kiapp (AMP) values are not much changed but the order of the lines in the Dixon plots at different Mg2+ concentrations are the opposite at 150 mM KCl compared with 0 mM KCl. KCl causes almost no change in the relation exchange/ acylation, which means according to Eq. (17) that chloride does not affect the reaction steps in segment 2, between the activation and transfer reactions. The best-fit analysis of the chloride effects was done for three types of experiments simultaneously, but for 50 mM and 150 mM KCl concentrations separately. The types of experiments were the Km determination for tRNA, Mg2+ dependence of the AMP inhibition and Mg2+ dependence of the PPi inhibition (as for TyrRS in [25]). The analysis, however, did not give only a single set of values for the constants. KCl changed the values of the constants which were connected to the formation of the reactive complex of the activation reaction (K5M, K5, KMR, KSR, K1M, KME, and KSE ), but low error percents were obtained with different combinations of these constant values. The best set showed, at 50 mM KCl, a threefold increase in K5M and K5 and a twofold increase in K1M and KME2 compared to the values in Table 1. At 150 mM KCl the changes were sevenfold increases in K5M, K5 and KME2, and tenfold increase in K1M.

Fig. 6. Magnesium dependence of the measured equilibrium constant. The start conditions were 2 mM ATP, 6 μM Arg, 1.15 μM tRNAArg, 0.5 mM PPi, and 0.25 mM AMP. The spermidine concentration was 0 (■) or 1 mM (●), and the free magnesium concentration as indicated.

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4. Discussion 4.1. Details of the reaction

Fig. 7. Chloride effect on the aminoacylation reaction. (A) KCl inhibition compared with K-acetate. In (▴) the concentrations [KCl] + [K-acetate] were kept constant at 200 mM and [KCl] was plotted. (B) KCl effect on the Mg2+ dependence of the ArgRS reaction. (C) Hanes plots for the Km (tRNA) determination at different KCl concentrations.

The KCl inhibition seems not to be caused by the ionic strength but is more specific to the Cl− ion. If the ionic strength is kept constant with K-acetate, the chloride inhibition remains strong. The non-specific ionic strength effects on the tRNA binding [36,37] may become evident at higher than 200 mM salt concentrations. The chloride concentration in the E. coli cells is low, a few mM [38] and therefore the inhibition by chloride, but not by organic ions, may be of biological importance. It resembles the chloride effect on some other protein–nucleic acid interactions [25,39]. Due to the inhibiting effect of chloride and sulphate ions they should be avoided in the aminoacyl-tRNA synthetase assays. In particular the use of MgCl2 or MgSO4 in the measurements of the Mg dependence can lead to erroneous results.

The forward rate constants of the total acylation reaction from Table 1, k+3, k+6, and k+8 are of the same order of magnitude with each other (27, 20 and 19 s−1), but k+ 8C is lower (8 s−1). The reverse rates at the activation and transfer steps are high (k−3 = 230 s−1, k−6 = 161 s−1 ). The values show that in the absence of PPi and AMP the rate limitation does not occur in one single step but is divided in four steps. At natural conditions, in the presence of low concentrations of PPi and AMP, the rate limitation occurs at the late steps of the total reaction. Previous pre-steady-state and steady-state measurements of the rates in ArgRS from yeast [14] have given some rate values which are reasonably related to the values of the present work: activation (k+3) 47 s−1, charging of tRNA (k+6) 33 s−1, and deacylation of Arg-tRNA (k−8C) 0.1 s−1, when the steady-state rate has been 2.78 s−1. The higher rate of charging of tRNA compared to the steady-state rate was interpreted by a slow conformational change step on the dissociation of the product Arg-tRNA from the enzyme. This was supported by a burst in the pre-steady-state kinetics of charging of tRNA. These similarities to the present work show that a statistical ‘globaltype’ analysis can lead to correct mechanism and to values of constants which are correctly related with each other. The rate-limiting step in many aminoacyl-tRNA synthetases has been shown to be at the dissociation of the product aminoacyl-tRNA [24,40]. Among others, the class I enzymes IleRS, TyrRS and GlnRS show this feature [41,42]. ArgRS seems to follow this model. The high values of k−3 and k−6 enable strong PPi and AMP inhibitions. The AMP-caused increase in the ATP-PPi exchange rate, mentioned above, is also due to the high k−6 value. Preliminary data from some other aminoacyl-tRNA synthetases [24] show that, generally, the pyrophosphorolysis (k−3) seems to be much faster than the activation (k+ 3), which means that the PPi inhibition tends to be strong. In the transfer reaction, k−6 is not generally higher than k+6 although in ArgRS it is much higher. Therefore in most aminoacyl-tRNA synthetases AMP does not increase the ATP-PPi exchange rate. The kinetic analysis gives the minimum amount of Mg2+ bindings affecting the reaction at different steps. In the best-fit equations the Mg2+ dependence of the total reaction is described by eight dissociation constants (KMA, KMP, KM2P, KMR, KME, KME2, KME3, KME4). The binding to ATP and PPi are well known and do not need any estimation in the analysis [33,34]. KME and KME2 are assumed to describe the same binding of Mg2+ to the enzyme at different steps. In addition, KMR, KME3 and KME4 may be from the same binding to the tRNA and Arg–tRNA·E complex. Thus the minimum requirement according to the statistical analysis would be three Mg2+ ions. In the activation reaction two Mg2+ ions must be present (KMA and KME) and the third (KMR ) can be present but is not obligatory. In the transfer reaction one Mg2+ must be present (KMR ) and the second (KME2) is not obligatory, and

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MgPPi is not present. In the dissociation of Arg–tRNA from the enzyme the Mg2+ ion is not bound (KME4). Even in the simple cases of the activation kinetics it is not always possible to say whether an activator is bound to the enzyme or to the substrate, since both cases give similar curves [43]. The same limitation concerns also the aminoacyl-tRNA synthetase reaction: it is not self-evident whether Mg2+ is bound to the tRNA or to the enzyme, although the binding efficiency can be different at different steps of the total reaction. Several Mg2+ ions are known to be bound to tRNA [44] but only a few of them are of functional importance. Despite the uncertainty of the binding site, the number of functionally efficient ligands and the binding efficiency can be analysed. Spermidine can replace the Mg2+ ions in other bindings but not in ATP. In the best-fit model the spermidines and Mg2+ ions are written to be bound to different sites. In segment 2 the binding of spermidine (KSE2) is weak. The role of spermidine and other polyamines may be decisive in vivo. They are natural compounds in cells, and they lower the required magnesium concentration especially in the class I aminoacyl-tRNA synthetases [24]. At least in some cases they improve the selection of correct tRNA [45]. In several aminoacyl-tRNA synthetases the Mg2+ requirement of the tRNA can be explained by one or two tRNAbound Mg2+ ions, and these can be replaced by polyamines [24]. It also seems to be a general feature that the dissociation of the product aminoacyl-tRNA from the enzyme is essentially slower if the Mg2+ is bound at that step, and that the presence of high concentration of ATP improves the dissociation. It is not yet clear whether the tRNA-bound Mg2+ ions or polyamines affect the conformation of the CCA end or if the site is somewhere else in the tRNA. The same question concerns the chloride inhibition which also seems to be a general feature and which has opposite effects to the Mg2+ ion effects. Previous kinetic and structural studies have shown that the class I aminoacyl-tRNA synthetases require one Mg2+ ion in the activation reaction (ATP-bound) [46]. The requirement of tRNA makes ArgRS more complicated since the correct binding of tRNA requires Mg2+ ions or polyamines. There is no reason to believe that the transition state structure in the activation reaction would be essentially different from the other class Ia enzymes. The additional obligatory Mg2+ ions are replaceable by spermidine, which would not be probable in the strictly organized transition state. The real role of spermidine can be explained only after structural studies when the binding sites of the Mg2+ and spermidine ions have been identified. The concentration of free Mg2+ ions in E. coli cells is 0.5–2 mM [47]. It has been suggested that the formation of a citrate– Mg complex (Kd = 0.6 mM) would serve as a control system [48] as changes in the citrate concentration in the cell would affect the free Mg2+ concentration. According to the present results ArgRS would also be sensitive to such a Mgconcentration-based control mechanism.

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4.2. Editing reactions and the effects of PPi The discrimination of non-cognate amino acids by the aminoacyl-tRNA synthetases has been an object of interest during the whole span of time that these enzymes have been known [49–52]. At least three steps in the improvement of accuracy can be separated. In the initial discrimination the binding of substrates includes steps of ‘induced fit’-like conformational reorientations of the enzyme and tRNA, but non-cognate substrates do not cause proper reorientations. In the pre-transfer editing the formed non-cognate aminoacylAMP is hydrolysed or it is returned back to the substrates in the reverse pyrophosphorolysis reaction which must then be faster for the non-cognate than for cognate amino acids. In the third type of discrimination, post-transfer editing, the wrong aminoacyl-tRNA is hydrolysed. Some details of the initial discrimination in ArgRS from yeast have been solved from crystal structures [4, 7]. The binding of tRNA modifies the ATP binding site to a reactive conformation, and the binding of arginine causes a correct positioning of the CCA end of tRNAArg . In GlnRS the cognate tRNAGln is required to modify the correct structure of the active site, and thereby the affinity for glutamine is increased [42,53]. The non-cognate glutamate inhibits the correct binding of tRNAGln. Three enzymes (IleRS, ValRS and LeuRS) from subclass Ia possess a separate domain for the hydrolytic post-transfer editing reaction [12,13]. The editing site is located about 30 Å from the aminoacylation site. Although from class Ia, ArgRS does not have such a domain, and therefore the post-transfer editing must follow a different mechanism, if any. In a kinetic study of the discrimination of 19 non-cognate amino acids by ArgRS Freist et al. [54] did not find high posttransfer editing activity against any of them. Some pre-transfer editing activity was detected, e.g. for lysine. The discrimination was weakest against tryptophan, cysteine and lysine. The presence of PPi in E. coli may, however, change the role of the pre-transfer editing in vivo. As well, the interpretation of the discrimination results may change if the assumed reaction mechanism is changed. The PPi concentration in E. coli cells has been repeatedly measured as about 0.5 mM [31], which is much higher than the measured Kiapp values for PPi (80–190 μM) or the K4M value of 59 μM for ArgRS. Although it seems not possible that such a high PPi concentration could be in contact with ArgRS (or aminoacyl-tRNA synthetases in general) due to the strong inhibition, probably a part of it is. Fig. 4 shows that the concentrations of the important enzyme intermediates and the forward rates in the key steps of the ArgRS reaction are at a reasonable level if the PPi concentration is 20–50 μM. Previously, it was estimated for the isoleucyl-tRNA synthetase reaction that an efficient kinetic proofreading requires the presence of about 50 μM PP i [30]. A moderate PP i concentration thus may be necessary for the optimal accuracy of the aminoacyl-tRNA synthetases although it causes some inhibition.

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In a previous paper I have pointed out that the benefit of the pretransfer proofreading is lost if free PPi is present in the cell and if there is no slow step before the transfer reaction to separate the proofreading-corrected species from the uncorrected [30]. Since the k−3 value in the ArgRS is high and the above analysis did not allow a slow step between the activation and transfer reactions, there cannot exist an efficient pretransfer proofreading system in ArgRS in vivo. Furthermore, the transfer reaction is also reversible with a high k−6 value (161 s−1). Therefore the inefficiency of the editing reactions is expanded also to segment 3. In well-growing E. coli cells the AMP concentration is about 0.1–0.2 mM [55,56] which is high enough to enable a fast reversible reaction, as shown by Fig. 4B. The low value of k−8C between segments 3 and 4 means that from segment 4 the possibly edited Arg-tRNA does not return to the earlier steps of the total reaction. If there is higher than 20 μM concentration of PPi in contact with ArgRS, according to the analysis the only place for an efficient editing process would be between the segments 3 and 4 (k+8C). In all, the kinetic results emphasize the importance of the initial discrimination of noncognate amino acids in ArgRS, instead of editing processes later in the total reaction. 4.3. Concluding remarks The present study shows that it is possible to improve the accuracy of the kinetic analysis of aminoacyl-tRNA synthetase reactions by using a great amount of experimental material and a ‘global analysis’, where the optimization is done simultaneously on the whole material and using the same equations. Once a general rate equation has been optimized, it can be used to describe many different features of the reaction. The rate equation of ArgRS was used to calculate the rates of the partial reactions and intermediate concentrations, to draw conclusions about the proofreading systems, and to interpret the equilibria and chloride inhibitions. Such a kinetic model can never include all possible details of the reaction, but it can show which are the most important. Although many features of the reaction can be deduced directly from the experiments, finding of some important details remains problematic and resembles ‘trial and error’. In particular the role of the Mg2+ ions at different steps of the total reaction is the cause of some uncertainty. The quality of the experimental material is decisive in this kind of study. The experiments must cover all parts of the total reaction. For example, the AMP inhibition describes mainly the events after the transfer reaction, PPi inhibition between the activation and transfer, and substrate binding before the activation reaction. It is useful to do a part of the assays without polyamines to analyse the dissociation constants of Mg2+. The crystal structure analyses of ArgRS have revealed conformational rearrangements on binding of the arginine and tRNA substrates [4,7]. The present kinetic analyses do not efficiently show such rearrangements if these are faster than the total aminoacylation reaction. The existence or non-existence of ES complexes decide the mechanism in a kinetic analysis, and

therefore a 'random binding of substrates' is obtained for ArgRS although the real events may be much more complicated.

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