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J Biol Chem, Vol. 274, Issue 32, 22238-22242, August 6, 1999

An Iso-random Bi Bi Mechanism for Adenylate Kinase^*

Xiang Rong Sheng, Xia Li, and Xian Ming Pan

From the National Laboratory of Biomacromolecules, Institute of Biophysics, Academia Sinica, Beijing, 100101, China

	ABSTRACT

TOP ABSTRACT INTRODUCTION EXPERIMENTAL PROCEDURES RESULTS DISCUSSION REFERENCES

An iso-random Bi Bi mechanism has been proposed for adenylate kinase. In this mechanism, one of the enzyme forms can bind the substrates MgATP and AMP, whereas the other form can bind the products MgADP and ADP. In a catalytic cycle, the conformational changes of the free enzyme and the ternary complexes are the rate-limiting steps. The AP₅A inhibition equations derived from this mechanism show theoretically that AP₅A acts as a competitive inhibitor for the forward reaction and a mixed noncompetitive inhibitor for the backward reaction.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION EXPERIMENTAL PROCEDURES RESULTS DISCUSSION REFERENCES

Adenylate kinase (AK)¹ (EC 2.7.4.3) catalyzes the reaction MgATP + AMP  MgADP + ADP, which is essential for cell survival (1-8). This small kinase has also been considered as a "model kinase" in the study of the structure-function relationship of kinases (9). Although the catalytic kinetics of AK has been studied extensively (10-14), a full understanding mechanism is still lacking. The basic kinetic pattern is random Bi Bi (11), but whether the chemical step or the physical step(s) is rate-limiting is still controversial. Furthermore, it was reported in an early work of Kuby et al. (12) that the nature of the AP₅A inhibition changes qualitatively from competitive inhibition with respect to either substrate in the forward reaction (MgATP or AMP) to noncompetitive (mixed noncompetitive) in the backward reaction with either substrate (MgADP or ADP). There is still no convincing explanation for the inhibition nature of AP₅A.

In a series of previous studies in this laboratory, it was found that there are multiple native forms of AK in equilibrium in solution (15-18), which may help improve our understanding of the catalytic mechanism of AK. In this study, the catalysis and inhibition kinetics of AK was re-examined. An iso-random Bi Bi catalytic mechanism was proposed. The AP₅A inhibition equations derived from this mechanism show that AP₅A acts as a competitive inhibitor for the forward reaction and a mixed noncompetitive inhibitor for the backward reaction, agreeing well with experimental results.

	EXPERIMENTAL PROCEDURES

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Reagents-- Pyruvate kinase, lactate dehydrogenase, glucose-6-phosphate dehydrogenase, hexokinase, phosphoenolpyruvate, NADP, NADH, AMP, ADP, ATP, and AP₅A were Sigma products, and other reagents were local products of analytical grade.

Preparation and Activity Assay of Adenylate Kinase-- The enzyme was prepared essentially according to Zhang et al. (19) The yield was usually about 60 mg of pure enzyme per kilogram of rabbit muscle. The final preparation usually had a specific activity greater than 1,600 units/mg and showed only a single peak in SDS electrophoresis, gel filtration, and reversed-phase fast protein liquid chromatography. One unit is defined as 1 µmol of ADP (MgADP) generated per minute in forward reaction and 1 µmol of ATP generated per minute in backward reaction.

Methods-- UV absorbance at 340 nm was measured with either Cary 219 (Varian) or U-3000 (Hitachi, Japan) spectrophotometer.

The rate of the backward reaction (MgADP + ADP  MgATP + AMP) was measured by following the reduction of NADP at 340 nm in a coupled enzyme solution with hexokinase and glucose-6-phosphate dehydrogenase. The final assay mixture was: 50 mM Tris-HCl, pH 8.1, 2 mM -mercaptoethanol, 6.7 mM glucose, 0.67 mM NADP, 7.6 µM bovine serum albumin, 10 units/ml hexokinase, 10 units/ml glucose-6-phosphate dehydrogenase, varying and calculated concentrations of MgAc₂, and ADP.

Measurements of the velocity of the forward reaction (MgATP + AMP  MgADP + ADP) was performed by monitoring the oxidation of NADH at 340 nm coupling with pyruvate kinase and lactate dehydrogenase. The final assay mixture was: 50 mM Tris-HCl, pH 7.5, 2 mM -mercaptoethanol, 75 mM KCl, 4 mM phosphoenolpyruvate, 1.0 mM of MgAc₂ as free Mg²⁺, 0.2 mM NADH, 10 units/ml pyruvate kinase, 20 units/ml lactate dehydrogenase, 7.6 µM bovine serum albumin, plus varying and calculated amounts of MgAc₂, ATP, and AMP.

Iso-random Bi Bi Mechanism-- The catalysis and inhibition mechanism of adenylate kinase is suggested as shown Scheme 1.

View larger version (18K): [in this window] [in a new window]   Scheme 1.

Using the combined equilibrium and steady-state treatment developed by Cha (20) and described by Huang (21), Scheme 1 can be reduced to Scheme 2 and Eq. 1.

Here E₁ and E₂ denote two native forms of enzyme, one form (E₁) can bind with AMP (M) and MgATP (T), and the other one with ADP (D₁) and MgADP (D₂). Both interconversions of the ternary complexes and free enzymes are rate-limiting steps. This mechanism is, in principle, a random Bi Bi type, similar to that proposed by an earlier study (11), but with the major modification that two native forms of enzyme are introduced. This mechanism is based on the fact that AK undergoes large domain movements upon substrate binding (22). After aligning 17 known structures of nucleoside monophosphate kinases, Vonrhein et al. (23) gave movies to demonstrate the catalytic cycle of AK, which showed that the conformation of ternary complex of enzyme binding with AMP and ATP is different from that of enzyme binding with two ADP. That is to say, AK undergoes at least two steps of conformational changes. One step is the change of a ternary complex with bound substrates to one with bound products during the reaction, and the other is the change of the free enzyme in different forms. These conformational changes should be the rate-limiting steps in the catalytic cycle of AK, whereas the binding of substrates to and the release of products from the enzyme are quickly equilibrated. AP₅A is composed of ATP and AMP connected by a fifth phosphate, and mimics both substrates (24). It was assumed that AP₅A (I) can only bind to E₁ and the binding reaction of E₁ with AP₅A is rapid with an equilibrium constant of K_I. We have also assumed that the affinities for substrates of free enzyme and binary complexes, ME₁ and E₁T, as well as D₁E₂ and E₂D₁, are the same.

(Eq. 1)

In the forward reaction, one binding site is specific for AMP, whereas the other less specific one is for MgATP (25), so the reaction system consists of free enzymes E₁ and E₂, binary complexes ME₁, E₁M, and E₁T and ternary complexes ME₁T and ME₁M. The products, D₁ and D₂, are rapidly removed by the coupled enzymes, so that the concentration of ternary complex D₁E₁D₂ approaches zero.

In the absence of AP₅A, we have Eq. 2.

(Eq. 2)

Here a factor of two is introduced, because the forward reaction produces two ADP molecules.

In the presence of AP₅A, we have Eq. 3.

(Eq. 3)

Eq. 3 shows that AP₅A acts as a competitive inhibitor for the forward reaction.

In the backward reaction, one binding site is specific for ADP, and the other less specific one for MgADP (25), so the reaction system consists of free enzymes E₁ and E₂, binary complexes D₁E₂, E₂D₁, and E₂D₂, as well as ternary complexes D₁E₂D₂ and D₁E₂D₁. The product ATP is rapidly removed by coupled enzymes, so that the concentration of ternary complex ME₁T approaches zero. The product conversion was controlled under 10%, and the concentration of binary complex ME₁ could be considered as zero.

In the absence of AP₅A, we have Eq. 4.

(Eq. 4)

The free concentrations of ADP ([D₁]) and MgADP ([D₂]) can be calculated from the total concentrations of ADP ([D₁]₀)and Mg ([Mg]₀) by Eqs. 5 and 6.

(Eq. 5)

(Eq. 6)

The stability constant K_Mg = 2,500 M¹ was used in the calculation (26).

In the presence of AP₅A, we have Eq. 7.

(Eq. 7)

Eq. 7 shows that AP₅A acts as a mixed noncompetitive inhibitor for backward reaction.

	RESULTS

TOP ABSTRACT INTRODUCTION EXPERIMENTAL PROCEDURES RESULTS DISCUSSION REFERENCES

Catalytic Patterns-- Fig. 1, A and B, shows the catalytic pattern when AMP and ATP were used as substrates of the forward reaction with the concentration of magnesium ion kept constant at 1 mM. Fig. 1A shows AMP as the variable substrate, whereas Fig. 1B shows MgATP as the variable substrate. With MgATP concentration lower than 0.1 mM, the specific activity increases initially then decreases with increasing concentration of AMP, implying that AMP can bind to the MgATP site (Fig. 1A).

View larger version (16K): [in this window] [in a new window]   Fig. 1.   Catalytic pattern of adenylate kinase at pH 7.4 in the forward reaction. The free magnesium ion concentration was kept constant at 1 mM. A, AMP as variable substrate at various fixed MgATP concentrations as indicated; B, MgATP as variable substrate at various fixed AMP concentrations as indicated. In all experiments, the final concentration of adenylate kinase was 2.3 nM unless otherwise specified.

In the backward reaction, the concentrations of ADP and MgADP are dependent on the concentration of magnesium ion. The kinetic measurements were carried out under either varied concentrations of magnesium ion with constant ADP (Fig. 2A) or varied concentrations of ADP with constant magnesium ion (Fig. 2B). Fig. 2A shows that when ADP concentration is lower than 0.5 mM, the specific activity increases first then decreases with the increasing concentration of magnesium ion, because the concentration of MgADP increases with the increasing of magnesium ion concentration, whereas that of ADP decreases. Fig. 2B shows that with magnesium ion concentration lower than 0.5 mM, the specific activity increases first then decreases with increasing ADP concentrations, implying that ADP can bind to the MgADP site.

View larger version (16K): [in this window] [in a new window]   Fig. 2.   Catalytic pattern of adenylate kinase at pH 8.1 in the backward reaction. A, magnesium ion as variable substrate at various fixed ADP concentrations as indicated; B, ADP as variable substrate at various fixed magnesium ion concentrations as indicated.

The full set of data in Figs. 1 and 2 was fitted to Eqs. 2 and 4 to calculate kinetic parameters by a computer program. The best fit kinetic parameters are summarized in Table I and were used to draw the solid lines in Figs. 1 and 2, which are in good agreement with the experimental results.

AP₅A Inhibition Patterns-- It has been reported by Kuby et al. (12) that AP₅A acts as a competitive inhibitor for the forward reaction and a noncompetitive inhibitor (the origin figures show a mixed noncompetitive) for the backward reaction, here the AP₅A inhibition patterns were re-examined.

Because the affinities of AMP to MgATP site as well as ADP to MgADP site are relatively smaller, Eqs. 10 and 12 can be treated as linear. Fig. 3, A and B, shows the AP₅A inhibition patterns in the forward reaction with varied AMP (Fig. 3A) and MgATP (Fig. 3B) concentrations, respectively, indicating that AP₅A acts as a competitive inhibitor for the forward reaction.

View larger version (18K): [in this window] [in a new window]   Fig. 3.   Inhibition pattern of AP5A in the forward reaction. A, the MgATP concentration was kept constant at 0.05 mM, and AMP as variable substrate at various fixed AP5A concentrations as indicated; B, the AMP concentration was kept at 0.1 mM, and MgATP as variable substrate at various fixed AP5A concentrations as indicated.

Fig. 4, A and B, shows the AP₅A inhibition patterns in the backward reaction with varied ADP (Fig. 4A) and MgADP (Fig. 4B) concentrations calculated according to Eqs. 3 and 7, respectively, exhibiting that AP₅A acts as a mixed noncompetitive inhibitor for the backward reaction.

View larger version (19K): [in this window] [in a new window]   Fig. 4.   Inhibition pattern of AP5A in the backward reaction. A, the MgADP concentration was kept at 0.1 mM, and ADP as variable substrate at various fixed AP5A concentrations as indicated; B, the ADP concentration was kept at 0.03 mM, and ADP as variable substrate at various fixed AP5A concentrations as indicated.

A value of K_I = 2 ± 0.5 × 10⁶ mM was obtained from the full set of data in Figs. 3 and 4.

	DISCUSSION

TOP ABSTRACT INTRODUCTION EXPERIMENTAL PROCEDURES RESULTS DISCUSSION REFERENCES

There are two nucleotide-binding sites of AK, one for the magnesium complexes and the other for uncomplexed nucleotides. X-ray and NMR studies suggested that the latter substrate site is more specific, whereas the former can bind uncomplexed substrates to some extent (24). The above experiments demonstrate that AMP or ADP shows substrate inhibition in the forward or the backward reaction, respectively. This result, which was also observed in bakers' yeast AK by Russell and co-workers (25), is in agreement with the x-ray and NMR findings.

The equilibrium concentrations of E₁ and E₂ in the absence of substrates should be different from those at steady state, so a lag (or burst) phase should occur in the beginning of the catalytic reaction. However, because the activity of AK was assayed with a coupled enzyme system, the initial process is too complicated to follow.

The fact that AP₅A acts as a competitive inhibitor for the forward reaction and a mixed noncompetitive inhibitor for the backward reaction cannot be explained by the normal random Bi Bi mechanism. However, these inhibition patterns are consistent with an iso-random Bi Bi mechanism in which the substrates can bind to one isoform while the products bind to another isoform of the enzyme. This strongly supports the suggestion that two native forms of AK might be involved in the catalytic reactions.

The rate of enzyme conformational changes is on the order of 10² s¹ in the catalytic reactions, which is much higher than that determined by ANS fluorescence probe (about 10² s¹, see Ref. 15). This perhaps can be explained that substrates decrease whereas ANS increases the activation energy of enzyme conformational changes. It was indeed observed that ANS inhibits the folding of AK, whereas AMP, ADP, and ATP can accelerate the folding (16). Another possibility is that the two native forms involved in the catalytic cycle are different from those distinguished by ANS probe, and AK might exist in more native forms in equilibrium. The current experimental results provide no information to distinguish the above possibilities.

It has been reported that some proteins may exist in more than one distinct folded form in equilibrium. Evidence for distinguishing multiple native forms of staphylococcal nuclease has come from electrophoresis and NMR studies (27-32). For calbindin D_9K, the evidence of multiple forms has come from not only NMR studies but also from x-ray crystal structures (33, 34). These results shed light on the understanding of the protein folding problem but give little information on the biological role of the multiple native forms. Is the multiple native forms are necessary for protein to perform its biological functions or only the results of protein folding? Our results suggest that the multiple native forms are necessary for AK to perform its catalytic function. AK, a small nucleoside monophosphate kinase, undergoes large domain movements during catalysis (23), because it has to shield its active center from water to avoid ATP hydrolysis. Because the folded forms of AK must be flexible, multiple native forms with small free energy difference can exist in equilibrium in the absence of substrates.

In summary, two rate-limiting steps are involved in the catalytic cycle of AK. Only one form (E₁) of AK can bind with AP₅A, so AP₅A acts as a competitive inhibitor for the forward reaction and a noncompetitive inhibitor for the backward reaction.

	ACKNOWLEDGEMENTS

We express our sincere thanks to Prof. C. L. Tsou of this institution for reading the manuscript.

	FOOTNOTES

^* This work was supported in part by Grants 39625008 and 39670157 from the National Natural Science Foundation of China and the Pandeng Project of the China Commission for Science and Technology.The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

To whom correspondence should be addressed: National Laboratory of Biomacromolecules, Institute of Biophysics, Academia Sinica, 15 Datun Rd., Beijing 100101, China. Tel.: 86-10-6488-8497; Fax: 86-10-6487-2026; E-mail: xmpan@sun5.ibp.ac.cn.

	ABBREVIATIONS

The abbreviations used are: AK, adenylate kinase; ANS, 1-anilino-8-naphthalenesulfonate.

	REFERENCES

TOP ABSTRACT INTRODUCTION EXPERIMENTAL PROCEDURES RESULTS DISCUSSION REFERENCES

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Sheng, X. R. Articles by Pan, X. M. Search for Related Content PubMed PubMed Citation Articles by Sheng, X. R. Articles by Pan, X. M. Social Bookmarking                      What's this?