Α3β3 Hexamer Research Articles

Structural and Biochemical Analysis Reveals a Distinct Catalytic Site of Salicylate 5-Monooxygenase NagGH from Rieske Dioxygenases.

Rieske nonheme iron oxygenases (ROs) catalyze the oxidation of a wide variety of substrates and play important roles in aromatic compound degradation and polycyclic aromatic hydrocarbon degradation. Those Rieske dioxygenases that usually act on hydrophobic substrates have been extensively studied and structurally characterized. Here, we report the crystal structure of a novel Rieske monooxygenase, NagGH, the oxygenase component of a salicylate 5-monooxygenase from Ralstonia sp. strain U2 that catalyzes the hydroxylation of a hydrophilic substrate salicylate (2-hydroxybenzoate), forming gentisate (2, 5-dihydroxybenzoate). The large subunit NagG and small subunit NagH share the same fold as that for their counterparts of Rieske dioxygenases and assemble the same α3β3 hexamer, despite that they share low (or no identity for NagH) sequence identities with these dioxygenase counterparts. A potential substrate-binding pocket was observed in the vicinity of the nonheme iron site. It featured a positively charged residue Arg323 that was surrounded by hydrophobic residues. The shift of nonheme iron atom caused by residue Leu228 disrupted the usual substrate pocket observed in other ROs. Residue Asn218 at the usual substrate pocket observed in other ROs was likewise involved in substrate binding and oxidation, yet residues Gln316 and Ser367, away from the usual substrate pocket of other ROs, were shown to play a more important role in substrate oxidation than Asn218. The unique binding pocket and unusual substrate-protein hydrophilic interaction provide new insights into Rieske monooxygenases.IMPORTANCE Rieske oxygenases are involved in the degradation of various aromatic compounds. These dioxygenases usually carry out hydroxylation of hydrophobic aromatic compounds and supply substrates with hydroxyl groups for extradiol/intradiol dioxygenases to cleave rings, and have been extensively studied. Salicylate 5-hydroxylase NagGH is a novel Rieske monooxygenase with high similarity to Rieske dioxygenases, and also shares reductase and ferredoxin similarity with a Rieske dioxygenase naphthalene 1,2-dioxygenase (NagAcAd) in Ralstonia sp. strain U2. The structure of NagGH, the oxygenase component of salicylate 5-monooxygenase, gives a representative of those monooxygenases and will help us understand the mechanism of their substrate binding and product regio-selectivity.

Heterologous expression and kinetic characterization of the α, β and αβ blend of the PPi-dependent phosphofructokinase from Citrus sinensis

This work reports the molecular cloning and heterologous expression of the genes coding for α and β subunits of pyrophosphate-dependent phosphofructokinase (PPi-PFK) from orange. When expressed individually, both recombinant subunits were produced as highly purified monomeric proteins able to phosphorylate fructose-6-phosphate at the expenses of PPi (specific activity of 0.075 and 0.017 units. mg−1 for α and β subunits, respectively). On the other hand, co-expression rendered a α3β3 hexamer with specific activity three orders of magnitude higher than the single subunits. All the conformations of the enzyme were characterized with respect to its kinetic properties and sensitivity to the regulator fructose-2,6-bisphosphate. A thorough review of current knowledge on the matter indicates that this is the first report of the recombinant production of active plant PPi-PFK and the characterization of its different conformations. This is a main contribution for future studies focused to better understand the enzyme properties and how it accomplishes its relevant role in plant metabolism.

Nucleus-Encoded Protein BFA1 Promotes Efficient Assembly of the Chloroplast ATP Synthase Coupling Factor 1

F-type ATP synthases produce nearly all of the ATP found in cells. The catalytic module F1 commonly comprises an α3β3 hexamer surrounding a γ/ε stalk. However, it is unclear how these subunits assemble to form a catalytic motor. In this work, we identified and characterized a chloroplast protein that interacts with the CF1β, γ, and ε subunits of the chloroplast ATP synthase and is required for assembly of its F1 module. We named this protein BIOGENESIS FACTOR REQUIRED FOR ATP SYNTHASE1 (BFA1) and determined its crystal structure at 2.8-Å resolution. BFA1 is comprised primarily of two interacting β-barrels that are oriented nearly perpendicularly to each other. The contact region between BFA1 and the CF1β and γ subunits was further mapped by yeast two-hybrid assays. An in silico molecular docking analysis was performed and revealed close fitting contact sites without steric conflicts between BFA1 and CF1β/γ. We propose that BFA1 acts mainly as a scaffold protein promoting the association of a CF1α/β heterodimer with CF1γ. The subsequent assembly of other CF1α/β heterodimers may shift the position of the CF1γ subunit to complete assembly of the CF1 module. This CF1 assembly process is likely to be valid for other F-type ATP synthases, as their structures are highly conserved.

Amputation of a C-terminal helix of the γ subunit increases ATP-hydrolysis activity of cyanobacterial F1 ATP synthase

F1 is a soluble part of FoF1-ATP synthase and performs a catalytic process of ATP hydrolysis and synthesis. The γ subunit, which is the rotary shaft of F1 motor, is composed of N-terminal and C-terminal helices domains, and a protruding Rossman-fold domain located between the two major helices parts. The N-terminal and C-terminal helices domains of γ assemble into an antiparallel coiled-coil structure, and are almost embedded into the stator ring composed of α3β3 hexamer of the F1 molecule. Cyanobacterial and chloroplast γ subunits harbor an inserted sequence of 30 or 39 amino acids length within the Rossman-fold domain in comparison with bacterial or mitochondrial γ. To understand the structure–function relationship of the γ subunit, we prepared a mutant F1-ATP synthase of a thermophilic cyanobacterium, Thermosynechococcus elongatus BP-1, in which the γ subunit is split into N-terminal α-helix along with the inserted sequence and the remaining C-terminal part. The obtained mutant showed higher ATP-hydrolysis activities than those containing the wild-type γ. Contrary to our expectation, the complexes containing the split γ subunits were mostly devoid of the C-terminal helix. We further investigated the effect of post-assembly cleavage of the γ subunit. We demonstrate that insertion of the nick between two helices of the γ subunit imparts resistance to ADP inhibition, and the C-terminal α-helix is dispensable for ATP-hydrolysis activity and plays a crucial role in the assembly of F1-ATP synthase.

Direct Measurement of Single-Molecule Adenosine Triphosphatase Hydrolysis Dynamics

F1-ATPase (F1) is a bidirectional molecular motor that hydrolyzes nearly all ATPs to fuel the cellular processes. Optical observation of labeled F1 rotation against the α3β3 hexamer ring revealed the sequential mechanical rotation steps corresponding to ATP binding/ADP release and ATP hydrolysis/Pi release. These substeps originate from the F1 rotation but with heavy load on the γ shaft due to fluorescent labeling and the photophysical limitation of an optical microscope, which hampers better understanding of the intrinsic kinetic behavior of ATP hydrolysis. In this work, we present a method capable of electrically monitoring ATP hydrolysis of a single label-free F1 in real time by using a high-gain silicon nanowire-based field-effect transistor circuit. We reproducibly observe the regular current signal fluctuations with two distinct levels, which are induced by the binding dwell and the catalytic dwell, respectively, in both concentration- and temperature-dependent experiments. In comparison with labeled F1, the hydrolysis rate of nonlabeled F1 used in this study is 1 order of magnitude faster (1.69 × 108 M-1 s-1 at 20 °C), and the differences between two sequential catalytic rates are clearer, demonstrating the ability of nanowire nanocircuits to directly probe the intrinsic dynamic processes of the biological activities with single-molecule/single-event sensitivity. This approach is complementary to traditional optical methods, offering endless opportunities to unravel molecular mechanisms of a variety of dynamic biosystems under realistic physiological conditions.

Rotation triggers nucleotide-independent conformational transition of the empty β subunit of F₁-ATPase.

F1-ATPase (F1) is the catalytic portion of ATP synthase, a rotary motor protein that couples proton gradients to ATP synthesis. Driven by a proton flux, the F1 asymmetric γ subunit undergoes a stepwise rotation inside the α3β3 headpiece and causes the β subunits' binding sites to cycle between states of different affinity for nucleotides. These concerted transitions drive the synthesis of ATP from ADP and phosphate. Here, we study the coupling between the mechanical progression of γ and the conformations of α3β3. Using molecular dynamics simulations, we show that the nucleotide-free β subunit, initially in the open, low-affinity state, undergoes a spontaneous closing transition to the half-open state in response to the γ rotation in the synthesis direction. We estimate the kinetics of this spontaneous conformational change and analyze its mechanism and driving forces. By computing free energy profiles, we find that the isolated empty β subunit preferentially adopts the half-open conformation and that the transition to this conformation from the fully open state is accompanied by well-defined changes in the structure and interactions of the active site region. These results suggest that ADP binding to F1 occurs via conformational selection and is preceded by the transition of the active site to the half-open conformation, driven by the intrinsic elasticity of β. Our results also indicate that opening of the nucleotide-free β during hydrolysis is not spontaneous, as previously assumed. Rather, the fully open conformation observed in the F1 X-ray structure is enforced sterically by the γ subunit whose orientation is stabilized by interactions with the two other β subunits in the completely closed state. This finding supports the notion that γ acts by coupling the extreme conformational states of β subunits within the α3β3 hexamer and therefore is responsible for high efficiency of the coordinated catalysis.

Analysis of the Open and Closed Conformations of the β Subunits in Thermophilic F1-ATPase by Solution NMR

F(1)-ATPase, composed of alpha, beta, gamma, delta, and epsilon subunits, is a unique enzyme in terms of its rotational catalytic activity. The smallest unit showing this function is the alpha(3)beta(3)gamma complex. We have investigated the alpha(3)beta(3)gamma epsilon(Delta C) (epsilon(Delta C), truncated epsilon) complex from thermophilic Bacillus PS3 (TF(1)', 360 kDa) in the solution state by using the combination of extensive deuteration, segmental-labeling, and CRINEPT (cross-correlated relaxation-enhanced polarization transfer) NMR. Well-resolved CRINEPT-HMQC (heteronuclear multiple-quantum correlation) spectra of partially (15)N-labeled TF(1)' were obtained for this huge and asymmetric protein complex. The spectrum of the C-terminal domain of the beta subunit revealed that the open form of the beta subunit in the TF(1)' complex is similar to that of the free beta monomer. The open beta subunit in the TF(1)' complex does not exhibit high affinity for nucleotides unlike the monomer, but this is in agreement with the results of single-molecule analysis of TF(1)alpha(3)beta(3)gamma. On the other hand, the closed form of the beta subunit in the TF(1)' complex was shown to be distinct from that of the nucleotide-bound beta monomer. This is consistent with a previous report that the closed form of the TF(1)beta monomer could be a catalytically activated state. The loop between the N-terminal beta-barrel and the central domain is highly flexible in the TF(1)' complex, in contrast to that in the alpha(3)beta(3) hexamer, suggesting that it is affected by the presence of the gamma subunit in this area.

Temperature Dependence of Single Molecule Rotation of the Escherichia coli ATP Synthase F1 Sector Reveals the Importance of γ-β Subunit Interactions in the Catalytic Dwell

The temperature-dependent rotation of F1-ATPase gamma subunit was observed in V(max) conditions at low viscous drag using a 60-nm gold bead (Nakanishi-Matsui, M., Kashiwagi, S., Hosokawa, H., Cipriano, D. J., Dunn, S. D., Wada, Y., and Futai, M. (2006) J. Biol. Chem. 281, 4126-4131). The Arrhenius slopes of the speed of the individual 120 degrees steps and reciprocal of the pause length between rotation steps were very similar, indicating a flat energy pathway followed by the rotationally coupled catalytic cycle. In contrast, the Arrhenius slope of the reciprocal pause length of the gammaM23K mutant F1 was significantly increased, whereas that of the rotation rate was similar to wild type. The effects of the rotor gammaM23K substitution and the counteracting effects of betaE381D mutation in the interacting stator subunits demonstrate that the rotor-stator interactions play critical roles in the utilization of stored elastic energy. The gammaM23K enzyme must overcome an abrupt activation energy barrier, forcing it onto a less favored pathway that results in uncoupling catalysis from rotation.

Structure Analysis of F1-ATPase via Molecular Dynamics

F1-ATPase is comprised of five different subunits (α to e). The α3β3 hexamer contains nucleotide binding sites and γ rotates sequentially by a cooperative binding change mechanism for ATP synthesis and hydrolysis. The structures of β subunits, undergoing large conformational changes during the binding change mechanism, can be classified as tight (βDP), loose (βTP) or empty (βE). To elucidate the relationship between intrinsic dynamics of F1-ATPase and its function, we have carried out a equilibrium molecular dynamics simulation for a F1-ATPase crystal structure (PDB cord: 2JDI) for 30 ns. The structural features of each subunit and their inter-subunit interactions were analyzed by the residue fluctuations and correlation. Previous studies revealed that the catalytically active βDP subunit interacts strongly with αDP. However, we found that the non-catalytic pair, βDPαE also interacts strongly. This suggests that sandwiched βDP can efficiently transmit some structural change caused by the chemical reaction to the adjacent subunits. Furthermore, structural fluctuation of the γ subunit was correlated mainly with βDP. This result suggests that the chemical reaction on βDP can affect not only the conformational change for the other α, β subunits but also the γ-subunit rotation.

Role of the Asymmetry of the Homodimeric b2 Stator Stalk in the Interaction with the F1 Sector of Escherichia coli ATP Synthase

The b subunit dimer in the peripheral stator stalk of Escherichia coli ATP synthase is essential for enzyme assembly and the rotational catalytic mechanism. Recent protein chemical evidence revealed the dimerization domain of b to contain a novel two-stranded right-handed coiled coil with offset helices. Here, the existence of this structure in more complete constructs of b containing the C-terminal domain, and therefore capable of binding to the peripheral F1-ATPase, was supported by the more efficient formation of intersubunit disulfide bonds between cysteine residues that are proximal only in the offset arrangement and by the greater thermal stabilities of cross-linked heterodimers trapped in the offset configuration as opposed to homodimers with the helices trapped in-register. F1-ATPase binding analyses revealed the offset heterodimers to bind F1 more tightly than in-register homodimers. Mutations near the C terminus of b were incorporated specifically into either the N-terminally or the C-terminally shifted polypeptide, bN or bC, respectively, to determine the contribution of each position to F1 binding. Deletion of the last four residues of bN substantially weakened F1 binding, whereas the effect of the deletion in bC was modest. Similarly, benzophenone maleimide introduced at the C terminus of bN, but not bC, mediated cross-linking to the delta subunit of F1. These results imply that the polypeptide in the bN position is more important for F1 binding than the one in the bC position and illustrate the significance of the asymmetry of the b dimer in the enzyme.

Numerical study of the coupling between F 0 with varied numbers of c -subunits and F 1 in an ATP synthase

ATP synthase is a rotary motor which is composed of two portions: the `rotor' F0, consisting of a c-ring and the `stator' F1, consisting of an α3β3 hexamer. In different species, the number ofc-subunits which form the c-ring is varied from 10 to 14, whereas the α3β3 hexamer is fixed to be 3-fold symmetrical. We have numerically studied the rotational coupling between F0 with varied number ofc-subunits and F1. It is found that, for any number of c-subunits, the rotor F0 advances 3 steps per revolution on average, which is determined by the period of F1, whereas the exact angular pausing positions are determined by the period of F0. When the symmetry of thec-ring of F0 is matched with the 3-fold symmetry of F1, the three steps have equivalent sizes. If not matched, the three steps become nonequivalent: both the step size and average dwell time are different for these steps.

Both Rotor and Stator Subunits Are Necessary for Efficient Binding of F1 to F0 in Functionally Assembled Escherichia coli ATP Synthase

In F1F0-ATP synthase, the subunit b2delta complex comprises the peripheral stator bound to subunit a in F0 and to the alpha3beta3 hexamer of F1. During catalysis, ATP turnover is coupled via an elastic rotary mechanism to proton translocation. Thus, the stator has to withstand the generated rotor torque, which implies tight interactions of the stator and rotor subunits. To quantitatively characterize the contribution of the F0 subunits to the binding of F1 within the assembled holoenzyme, the isolated subunit b dimer, ab2 subcomplex, and fully assembled F0 complex were specifically labeled with tetramethylrhodamine-5-maleimide at bCys64 and functionally reconstituted into liposomes. Proteoliposomes were then titrated with increasing amounts of Cy5-maleimide-labeled F1 (at gammaCys106 and analyzed by single-molecule fluorescence resonance energy transfer. The data revealed F1 dissociation constants of 2.7 nm for the binding of F0 and 9-10 nm for both the ab2 subcomplex and subunit b dimer. This indicates that both rotor and stator components of F0 contribute to F1 binding affinity in the assembled holoenzyme. The subunit c ring plays a crucial role in the binding of F1 to F0, whereas subunit a does not contribute significantly.

Fluorescence resonance energy transfer between coumarin-derived mitochondrial F1-ATPase γ subunit and pyrenylmaleimide-labelled fragments of IF1 and c subunit

We introduced a reporting group into a critical position of the mitochondrial F1-ATPase in order to gain structural information about enzyme—ligand complexes. Incubation of 7-diethylamino-3-(4′-maleimidylphenyl)-4-methylcoumarin (CPM) with bovine heart mitochondrial F1-ATPase pretreated with 1mM sodium arsenite modified the only cysteine residue in the γ subunit (γ-Cys78), resulting in an enzyme—CPM fluorescent complex (CPM—F1) with an ATPase activity similar to that of the native enzyme. Transferred fluorescence of F1-bound CPM occurred when different peptide fragments of naturally binding polypeptides carrying a pyrenylmaleimide (PM) moiety were bound to the enzyme. Fluorescence resonance energy transfer (RET) from PM bound to cysteine residues associated with Glu40, Lys47 and Lys58 of fragments of the inhibitor protein (IF1) with CPM—F1 occurred with an efficiency of approx. 20, 21 and 3% respectively. The distance at which the efficiency of energy transfer was 50%, R0, for the CPM and PM donor/acceptor pair was 4.1nm, indicating that the three IF1 fragments must be within 6.7nm of γ-Cys78. RET from the PM-bound hydrophilic fragment of c subunit (residues 37–42) of the F1F0-ATPase complex and CPM-bound γ-Cys78 occurred with an efficiency of approx. 30%, indicating a distance of 4.7nm between the two fluorophores. Based on previous observations and on the present RET measurements, the hydrophilic loop of c subunit was located at the base of the F1 foot, and the N-terminal region of IF1 was located on the surface of F1 in the lower part of the α3β3 hexamer ring.

Fe(III) Binding to Bacillus PS3 F1ATPase, αβ Subcomplexes and Isolated α- and β-Subunits

Isolated α- and β-subunits of Thermophilic Bacillus PS3 F1ATPase (TF1) bind about 1 Fe(III) equivalent. Upon reassembling in the symmetric α3β3 hexamer, Fe(III) binding capacity decreases, as this complex binds about three Fe(III) equivalents. In accordance, when the hexamer is dissociated in the α1β1 heterodimer, each heterodimer binds about one Fe(III) equivalent. On the contrary, native TF1 exhibits a single Fe(III) site. CD spectra in far UV indicate that upon Fe(III) binding both the whole complex and the isolated β-subunit undergo structural modifications accompanied by decrease of α-helix content, while α-subunit doesn't. As in α3β3 and in the whole enzyme the number of bound Fe(III) equivalents is consistent with the number of β-subunits in the “empty” conformation, it is inferred that the single Fe(III) site in TF1 is probably located in βE.

Lengthening the Second Stalk of F1F0 ATP Synthase in Escherichia coli

In Escherichia coli F(1)F(0) ATP synthase, the two b subunits dimerize forming the peripheral second stalk linking the membrane F(0) sector to F(1). Previously, we have demonstrated that the enzyme could accommodate relatively large deletions in the b subunits while retaining function (Sorgen, P. L., Caviston, T. L., Perry, R. C., and Cain, B. D. (1998) J. Biol. Chem. 273, 27873-27878). The manipulations of b subunit length have been extended by construction of insertion mutations into the uncF(b) gene adding amino acids to the second stalk. Mutants with insertions of seven amino acids were essentially identical to wild type strains, and mutants with insertions of up to 14 amino acids retained biologically significant levels of activity. Membranes prepared from these strains had readily detectable levels of F(1)F(0)-ATPase activity and proton pumping activity. However, the larger insertions resulted in decreasing levels of activity, and immunoblot analysis indicated that these reductions in activity correlated with reduced levels of b subunit in the membranes. Addition of 18 amino acids was sufficient to result in the loss of F(1)F(0) ATP synthase function. Assuming the predicted alpha-helical structure for this area of the b subunit, the 14-amino acid insertion would result in the addition of enough material to lengthen the b subunit by as much as 20 A. The results of both insertion and deletion experiments support a model in which the second stalk is a flexible feature of the enzyme rather than a rigid rod-like structure.

Coupling H+ transport and ATP synthesis in F1F0-ATP synthases: glimpses of interacting parts in a dynamic molecular machine.

Reversible, F1F0-type ATPases (also termed F-ATP synthases) catalyze the synthesis of ATP during oxidative phosphorylation. In animal cells, the enzyme traverses the inner mitochondrial membrane and uses the energy of an H+ electrochemical gradient, generated by electron transport, in coupling H+ translocation to ATP formation. Closely related enzymes are found in the plasma membrane of bacteria such as Escherichia coli, where the enzymes function reversibly depending upon nutritional circumstance. The F1F0-type enzymes are more distantly related to a second family of H(+)-translocating ATPases, the vacuolar-type or V-ATPases. Recent structural information has provided important hints as to how these enzymes couple H+ transport to the chemical work of ATP synthesis. The simplest F1F0-type enzymes, e.g. as in E. coli, are composed of eight types of subunits in an unusual stoichiometry of alpha 3 beta 3 gamma delta epsilon (F1) and a1b2c12 (F0). F1 extends from the membrane, with the alpha and beta subunits alternating around a central subunit gamma. ATP synthesis occurs alternately in different beta subunits, the cooperative tight binding of ADP + Pi at one catalytic site being coupled to ATP release at a second. The differences in binding affinities appear to be caused by rotation of the gamma subunit in the center of the alpha 3 beta 3 hexamer. The gamma subunit traverses a 4.5 nm stalk connecting the catalytic subunits to the membrane-traversing F0 sector. Subunit c is the H(+)-translocating subunit of F0. Protonation/deprotonation of Asp61 in the center of the membrane is coupled to structural changes in an extramembranous loop of subunit c which interacts with both the gamma and epsilon subunits. Subunits gamma and epsilon appear to move from one subunit c to another as ATP is synthesized. The torque of such movement is proposed to cause the rotation of gamma within the alpha 3 beta 3 complex. Four protons are translocated for each ATP synthesized. The movement of gamma and epsilon therefore probably involves a unit of four c subunits. The organization of subunits in F0 remains a mystery; it will have to be understood if we are to understand the mechanism of torque generation.

The photosynthetic F1-?3?3 and ?1?1 catalytic core complexes

Minimal photosynthetic catalytic F1(αβ) core complexes, containing equimolar ratios of the α and β subunits, were isolated from membrane-bound spinach chloroplast CF1 and Rhodospirillum rubrum chromatophore RrF1. A CF1-α3β3 hexamer and RrF1-α1β1 dimer, which were purified from the respective F1(αβ) complexes, exhibit lower rates and different properties from their parent F1-ATPases. Most interesting is their complete resistance to inhibition by the general F1 inhibitor azide and the specific CF1 inhibitor tentoxin. These inhibitors were earlier reported to inhibit multisite, but not unisite, catalysis in all sensitive F1-ATPases and were therefore suggested to block catalytic site cooperativity. The absence of this typical property of all F1-ATPases in the α1β1 dimer is consistant with the view that the dimer contains only a single catalytic site. The α3β3 hexamer contains however all F1 catalytic sites. Therefore the observation that CF1-α3β3 can bind tentoxin and is stimulated by it suggests that the F1γ subunit, which is required for obtaining inhibition by tentoxin as well as azide, plays an important role in the cooperative interactions between the F1-catalytic sites.

ATP-Hydrolyzing Excitation State of the Reconstituted α3β3 Complex of ATP Synthase from the Thermophilic Bacterium PS3: Structural Characteristics Shown by Time-Resolved Small-Angle X-Ray Scattering with Synchrotron Radiation1

The ATP-hydrolyzing excitation state of the alpha 3 beta 3 complex of the ATP synthase from the thermophilic bacterium PS3 was investigated using time-resolved small-angle X-ray scattering with synchrotron radiation. The results showed the presence of the alpha 3 beta 3 complex at a steady state during ATP hydrolysis when the alpha 3 beta 3 hexamer reacted with Mg-ATP. The radius of gyration of the complex in the steady state was significantly larger than that of the Mg-AMP-PNP-hexamer complex, indicating a conformational change to an expanded structure during catalysis. This alpha 3 beta 3 complex dissociated into alpha 1 beta 1 heterodimers with apparent first-order reaction kinetics after all the ATPs were converted to ADPs. In contrast, when the alpha 3 beta 3 complex reacted with Mg-ADP, the complex dissociated into dimers with apparent first-order reaction kinetics without showing the steady state of the complex. The dimers, however, re-associated into the hexamer when Mg-ATP was added. The results were well-explained by a computer simulation based on non-linear chemical dynamics, in which a reaction mechanism that incorporates the dynamic structure of the hexamer in the steady state was considered.