J. Phys. Chem. 1996, 100, 8543-8550
8543
Inactivation of Ribulose-1,5-bisphosphate Carboxylase/Oxygenase during Catalysis. A Theoretical Study of Related Transition Structures O. Tapia* Department of Physical Chemistry, Uppsala UniVersity, Box 532, S-75121 Uppsala, Sweden
J. Andre´ s and V. S. Safont Department of Experimental Sciences, UniVersity Jaume I, Box 242, 12080 Castello´ , Spain ReceiVed: June 15, 1995; In Final Form: December 5, 1995X
Possible mechanistic paths for self-inhibition of rubisco have been theoretically characterized by using analytical gradients with both AM1 semiempirical and HF/3-21G level calculations. Starting from the framework of an enediol moiety previously obtained from characterizations of the saddle point of index 1 (SPi-1) for the carboxylation and oxygenation reactions, the formation of xylulose, 3-ketoribitol, and 3-ketoarabinitol inhibitors is made possible by following specific intramolecular hydrogen rearrangements. The xylulose is attained from the SPi-1 describing intramolecular enolization via an intermediate made by protonation of the hydroxyl group linked to the third carbon (C3) of the model substrate 3,4-dihydroxy-2-pentanone. One of these two hydrogens can migrate toward C3 with the correct stereochemistry to form xylulose inhibitor. 3-Ketoribitol and 3-ketoarabinitol inhibitors can be obtained after the enediol moiety is formed. Another minimum energy structure is found which is derived from the enediol via a SPi-1 corresponding to a retroenolization. This process finishes by forming a protonated hydroxyl group at C2. From this, and following the SPi-1, the 3-ketoribitol and the 3-ketoarabinitol inhibitors can be formed. The carbon and oxygen frameworks of the stationary geometries characterized in Vacuo fit well at the active site of rubisco, except perhaps for xylulose inhibitor. This geometric overlap with an experimentally determined transition state analog suggests that the active site can accommodate the interconversion chemistry found with the present approach which leads to self-inhibition. This is compatible with the hypothesis that the loss of activity is due to the products of substrate isomerization formed during catalysis.
1. Introduction D-Ribulose-1,5-bisphosphate carboxylase/oxygenase (rubisco, E.C.4.1.1.39) catalyzes the initial step in Calvin’s reductive pentose phosphate cycle, i.e. the photosynthetic fixation of atmospheric CO2 to the enzyme’s substrate D-ribulose-1,5bisphosphate. The enzyme also catalyzes a competing oxygenase reaction, thereby reducing the net efficiency of photosynthesis by up to 50% depending upon the relative concentration of CO2 and O2.1,2 Rubisco is not only bifunctional, since in Vitro and possibly in ViVo, the enzyme also suffers selfinhibition.2-9 Until now, no theoretical explanation has been found for this unusual behavior. This is the problem addressed in this paper. In spite of a certain catalytic inefficiency, which is manifested by a turnover number of 3 s-1, the abundancy of this enzyme ensures an annual fixation of 1011 tons of CO2 from the atmosphere to the biosphere. Genetic engineering techniques have been used to try the production of transgenic plants having enhanced CO2-fixation efficiency with rather disappointing results.1,2,10 To drive a successful genetic redesigning of this system, it is apparent that a thorough mechanistic knowledge would be required. In particular, one would like to find out whether bifunctionality and self-inhibition have common electronic structural origins. In recent papers11,12 theoretical studies were reported on a transition structure describing an intramolecular hydrogen transfer in molecular models representing D-ribulose-1,5-bisphosphate. There, a possible molecular mechanism was disX
Abstract published in AdVance ACS Abstracts, May 1, 1996.
S0022-3654(95)01661-3 CCC: $12.00
cussed for the enolization step in rubisco. By accepting the intramolecular enolization mechanism, the complicated set of steps leading to enolization which are currently advocated in the literature were replaced by only one which leads to a more economic mechanistic description. The corresponding saddle point of index one (SPi-1) also gave some clues to understanding the slow inactivation of the enzyme during catalysis.11 In this paper, theoretical evidence is presented showing that the unusual inhibitory behavior of this enzyme in Vitro, and possibly in ViVo, can be qualitatively understood in terms of stereochemically incorrect intramolecular retroenolization processes. The paper is organized as follows: section 2 contains a short description of rubisco and its inhibitory modes. Section 3 includes a description of the methodology, molecular model, and computing method. AM1 and ab initio HF/3-21G results are reported in section 4 together with a description of SPi-1 and intermediates leading to the formation of xylulose 3-ketoribitol, and 3-ketoarabinitol inhibitors. In section 5 experimental and theoretical results are discussed. 2. Rubisco and Its Inhibitory Behavior Rubisco catalyzes the initial step in photosynthetic carbon reduction, i.e., the carboxylation of the natural substrate D-ribulose-1,5-bisphosphate (RuBP), and the initial step of the photorespiratory carbon oxidation cycle, i.e., the oxygenation of RuBP. The molecular mechanism begins with enolization leading to the enediol form of RuBP; this is sometimes considered the rate-limiting step. The enediol is subsequently attacked by a carbon dioxide molecule (CO2) at the C2 position, forming a carboxylated intermediate species. This intermediate © 1996 American Chemical Society
8544 J. Phys. Chem., Vol. 100, No. 20, 1996 has never been isolated outside the active site. The carboxylated intermediate is thereafter attacked by a water molecule at the C3 position, and the C2-C3 bond is cleaved, thereby yielding two molecules of D-phosphoglycerate. These are the experimentally detected products of the carboxylase activity of the enzyme.13 The mechanism for oxygenation shares the enolization step; thereafter an O2 molecule attacks the C2 center of the enediol. Further cleavage of the C2-C3 bond results in the formation of a molecule of D-phosphoglycerate and a molecule of phosphoglycolate. These are the products of the oxygenase activity of Rubisco.13 To obtain them, the critical step is the formation of enediol. At least two different mechanisms regulate the apparent specific activity of the enzyme:14 (i) the first one involves a reversible reaction of a lysine (Lys-201) with CO2 and Mg2+ to form a carbamate, which is essential for catalytic activity;15 this activation may be controlled by another chloroplast protein, ribulose-1,5-bisphosphate carboxylase activase;16,17 (ii) the second mechanism involves control of the concentration of an inhibitor of rubisco activity, 2-carboxyarabinitol 1-phosphate, which occupies the active center, thus preventing its occupation by the substrate and rendering the enzyme inactive.18-21 However, other possibilities have been proposed, because 2-carboxyarabinitol 1-phosphate is not the only inhibitor found in nature and plant species differ markedly in the mechanisms they use to regulate rubisco activity.14,19,22,23 When assayed in Vitro, purified rubisco from higher plants can be spontaneously activated by incubation with CO2 and Mg2+ at alkaline pH.6 Upon addition of the substrate to the rubisco so-activated, the catalytic rate decreases with a halftime of several minutes.3-9 This loss of activity (the term “fallover” is used to describe this phenomenon24) is not due to substrate exhaustion or product accumulation.3 Several explanations have been proposed for this behavior: (a) the substrate may bind more tightly to the uncarbamylated enzyme than to the carbamylated, metal-complexed form; this would promote decarbamylation with the subsequent loss of activity;4,5,25 (b) the substrate may bind to a regulatory site different from the active center;9 (c) inhibition is a consequence of the slow and tight binding of isomerization or degradation products which accumulate in substrate preparations during storage;26 (d) the products of substrate isomerization that inhibit rubisco are formed by the enzyme itself during catalysis.24,27-29 Whatever the mechanism might be, it seems that fallover does not occur in ViVo or, if it does, some repair mechanism exists to reverse the effect: an activase protein has been proposed to execute the task. In fact, experimental work indicates that ribulose1,5-bisphosphate carboxylase activase can both prevent and reverse in ViVo the observed in Vitro decline in rubisco activity and suggests that fallover results from the binding of a phosphorylated inhibitor to the active site of rubisco.7 Many experimental works have dealt with the problem of inactivation, but to our knowledge, no theoretical investigation has directly addressed this issue. In this paper, we examine the energy hypersurface around the saddle point of index 1 (or transition structure TS) describing the intramolecular enolization step, the objective being to identify other TSs for intramolecular hydrogen transfer which may be related with inhibitory species. 3. Methods, Models, and Computing Details 3.1. Methodology. The method has been described in previous reports from our group.11,12 Here, we summarize the essential points. For a system trapped at the active site of a given enzyme, a necessary condition to open a given interconversion pathway is the existence of surface complementarity
Tapia et al. between geometry associated with the saddle point of index 1 and the active site. This complementarity can be checked via a geometric superposition of the calculated stationary structures with transition state analogs and slow substrates whose X-ray structure is known. Insofar as rubisco is concerned, some points have already been established. First, one should note that productive substrate binding implies a large deformation of the keto-form. This is experimentally elicited by X-ray diffraction data.1,30,31 Second, there exists an important result concerning the geometry of the C-framework obtained from theoretical characterizations of a number of saddle points of index 1.32 For the intramolecular enolization, the theoretically calculated SPi-1 and the experimental structure of the substrate have geometric frameworks which almost overlap. Moreover, the geometric framework of the carboxylation reaction SPi-112,33 also overlaps with a transition state analog (2′-CABP)1 as well as with the SPi-1 for the oxygenation reaction and, to a lesser extent, with the C-framework of the SPi-1 for intramolecular enolization.11,12 Third, the substrate bound to the enzyme appears to be strained when its geometry is compared with the ground state geometry in Vacuo. We noticed that under these circumstances the acid-base properties of a given molecule may be modified. Thus, even if the strain is counteracted by protein-substrate interactions, the pKa of the carbo-acid at C3 can be seen as sensibly changed when the substrate is bound to rubisco. Following a similar line of reasoning, the carbonyl basic strength can also be modified. The result would be that the intramolecular hydrogen transfer, which under normal conditions is most unlikely, is to be prompted by the molding effect of the protein on the substrate.11 This sort of mechanism has sometimes been used to explain unexpected acidity of carbon acids in enzymecatalyzed reactions.34 The existence of saddle point structures matching the active site is not always sufficient to activate a mechanistic step. Whether a given pathway is used or not would depend upon the energetics and fluctuation properties of the reacting system. At the present stage, we will concentrate on the geometric characterization of saddle points that may account for selfinhibition and check if they have a conformation compatible with the experimental and theoretical data. 3.2. Model and Computing Details. The tautomeric pair 3,4-dihydroxy-2-pentanone/2,3,4-trihydroxy-2-pentene is selected as a model to represent the real substrate, D-ribulose 1,5bisphosphate. Compared to the real substrate, only the two phosphates attached to carbon atoms 1 and 5 (see Figure 1 for the atom numbering) are not present, so that our model is in fact the D-ribulose. The phosphates are assumed to mediate the specific binding of the substrate to the active site. For all reactive species found in this work, we assume that this binding is not modified. Saddle points of index 1 have been characterized. These structures describe theoretically well-defined geometric rearrangements. Atomic displacements along the directions defined by the transition vector (TV)35 should correspond to a zero-order representation of the particular interconversion. Those saddle points describing the chemical interconversion processes would correspond to the standard transition structures whose changes may be related with the experimentally based molecular mechanism.36-38 The hypothesis that intermolecular effects will not change the nature of the transition structure, insofar as geometry and reaction vector fluctuation are concerned, underlies the approach used here.32 Thus, the existence of SPi-1’s geometrically compatible with the active site would activate corresponding reactive channels.
Ribulose-1,5-bisphosphate Carboxylase/Oxygenase
Figure 1. 3,4-Dihydroxy-2-pentanone, the keto form of the molecule used here as a model of D-ribulose-1,5-bisphosphate. The numbering of the atoms is shown. The hydrogen atom H3 is transferred to the oxygen atom O2 in the enolization step. The hydrogen atom H(O3) is transferred to the carbon atom C2 in the retroenolization step. The conformation of the carbon skeleton of our model is taken mimicking the one experimentally obtained by means of X-ray spectroscopy for the transition structure analog 2-carboxyarabinitol-1,5-bisphosphate (2′CABP).
The present study was done first with the semiempirical AM139 method. Thereafter, all saddle points were recalculated at an HF/3-21G basis set level to check for geometry invariances. At each point, the Berny analytical gradient optimization routines were used for the optimization.40,41 The requested convergence on the density matrix was 10-9 au; the threshold value of maximum displacement was 0.0018 Å and that of maximum force was 0.00045 hartree/bohr. The nature of each stationary point was established by calculating analytically and diagonalizing the Hessian matrix (force constant matrix). All calculations were carried out using the GAUSSIAN 92 program.42 The geometric result is fairly independent of the methodology used. The correlation energy would be likely to affect the value of the total energy and the detailed charge distribution, but it is not likely that the main geometric parameters would be affected.43 We have calculated a number of cases related to transition structures where the model system is increased in size; the invariance of the stationary point has been numerically established either with respect to models or on some other occasions with respect to the level of computing.44-48 Similar results have been recently obtained by Teleman et al.49 In particular, we have carried out calculations with ab initio methods with different basis sets (3-21G, 4-31G, 6-31G**). The results are similar to AM1 semiempirical: the geometry of the stationary points and the components of transition vectors associated with TSs are rather robust entities. These results can justify a more exhaustive analysis of the potential energy surface associated with inhibitory processes in Rubisco enzyme at the AM1 semiempirical level. 4. TSs and Reactive Channels The enolization SPi-1 occupies a central position in the following discussion. A thorough description has been given elsewhere.11 Since the actual substrate is trapped by the protein in a cavity isolated from the solvent, we assume that those atoms representing the phosphate positions are fluctuating around restricted positions in space. This result follows from X-ray measurements. The structure of the SPi-1 in Vacuo when fitted at the active site has no steric hindrances; the phosphates help constrain the substrate into a deformed conformation. A priori, a fine-tuned fitting of the SPi-1 is actually not expected since there is no reason to find an almost perfect geometric overlap between stationary points obtained in Vacuo and structures
J. Phys. Chem., Vol. 100, No. 20, 1996 8545 embedded in real protein environments. However, such fitting is a theoretical result which has been found on several occassions.32,45,50 We assume that a SPi-1 (in Vacuo) geometrically compatible with the active site is a necessary condition to open the corresponding reactive channel32 in the enzyme. In Figure 2, a schematic representation is depicted of the different reaction pathways obtained with the present model. They give a plausible mechanistic description of self-inhibition. A schematic energy diagram is depicted in Figure 3 for the different stationary points: enediol, intermediates, and different TSs. Four types of transition structures were identified on the potential energy surface relating the enediol structure, considered as the central element of this mechanism, to the substrate ribulose and the xylulose, 3-ketoribitol, and 3-ketoarabinitol inhibitors. The carboxylation and oxygenation transition structures are not depicted, as they have already been described.12,33 In Figure 2, the thick arrows underline the computational fact that from the TS the corresponding structures can be attained with energy minimization techniques. The dotted arrows indicate an absence of a direct adiabatic pathway between the structures. The results do not depend upon the level of theory used to characterize them. The general features can be summarized as follows. (1) The TS e corresponds to the intramolecular enolization process and connects the substrate (Ribulose) with the enediol intermediate. From this TS e, a pathway to the xylulose inhibitor can be suggested by means of a stereochemically different retroenolization via the intermediate I 1. (2) The intermediate I 1 has two outgoing channels. One, via the TS 1, will come back to the starting substrate. If really present, this dead-end path would work against the efficiency of this enzyme. The other channel presents a connection with the TS 2 which links this intermediate with the xylulose inhibitor. (3) The TS r is the key point in the transformation from the enediol to the I 2 intermediate and opens the way to the formation of the 3-ketoribitol and 3-ketoarabinitol inhibitors. (4) TS 3 relates the intermediate I 2 with the 3-ketoribitol inhibitor, and TS 4 links the same intermediate with the 3-ketoarabinitol inhibitor. The geometry, force constants (for those selected geometric parameters defined with the Z-matrix), TV, energy, imaginary frequency, and Hessian’s unique negative eigenvalue for these TSs are given in Tables 1-4. The TV provides the essentials of the chemical process under study. The internal variables used for intramolecular hydrogen transfer describe distances and bond and dihedral angles. The distances χ-, χ+, and F are defined in Figure 4. For TS e, TS 1, and TS 2, the variable F measures the distance of the hydrogen atom being transferred in each case (H3) to the base line formed by the C3-O2 interatomic distance (χ+); χ- corresponds to the distance X-O2. For TS r, TS 3, and TS 4, the variable F measures the distance of the hydrogen atom being transferred in each case (H(O3)) to the base line formed by the C2-O3 interatomic distance (χ+); χ- corresponds to the distance X-O3. The negative eigenvalue of different TSs results from the cross terms in the force constant matrix. Negative force constants appear at ab initio level for TS 2 and TS 3, corresponding to O3-C3-C2-O2 and C2-C3-O2-C1 dihedral angles and O2-C2-C3-O3 dihedral angle, respectively. The eigenvector describes a collective fluctuation if we bear in mind the quantum nature of the interconversion (cf. section 5). The normal mode analysis of these structures yields relatively
8546 J. Phys. Chem., Vol. 100, No. 20, 1996
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Figure 2. Schematic representation of the structures and reactive channels: (a) thick arrows, connecting ribulose, TS e, enediol structures, and carboxylation or oxygenation exit, represent the chemical processes catalyzed by rubisco; (b) thin arrows, from the enediol structure to 3-ketoarabinitol or 3-ketoribitol compounds via TS r, I 2, and TS 4 or TS r, I 2, and TS 3, respectively, correspond to the inhibitory processes; (c) thin arrows, from the enediol structure to xylulose, via TS e, I 1, and TS 2 correspond to the main inhibitory process experimentally claimed; (d) thin arrows from the enediol intermediate to ribulose are associated with the backward reaction; (e) dashed arrows connecting TS e and xylulose or TS r and 3-ketoribitol or 3-ketoarabinitol indicate an absence of a direct pathway between the stationary structures. The intermediate structures are obtained with the dihedral angle O2-C2-C3-O3 frozen at the value obtained for the saddle point TS e (I1) and TS r (I2), respectively, and all other variables are reoptimized.
Figure 3. Energetic diagram showing different stationary points. Relative to the enediol energy (heat of formation ) -0.144 125 au), Erel is given in kcal/mol.
low imaginary frequencies: they are fairly invariant, with values ranging from 1562i to 1851i cm-1, which reflect the fact that the hydrogen motions are strongly coupled with the heavy atom motions as well. Although quite obvious, the keto-enol interconversion is an intramolecular redox process, and its description cannot be reduced to the simple picture of a hydrogen atom displacement. The precursor and successor structures are obtained via a displacement of the atoms following the interconversion coor-
dinate χ-, while the C-frame is kept frozen to mimic the effect of substrate binding at the active site. The saddle is the stationary point. Differences are detected from the TV components associated with the different TSs. For TS e there are three dominant contributions appearing in both TSs: F, χ-, and O3-C3 bond distances, as shown by a perusal of the amplitudes of the TV. For TS 1 and TS 4 the major components are F and the dihedral angle associated with internal rotation around the C2-C3 bond,
Ribulose-1,5-bisphosphate Carboxylase/Oxygenase
J. Phys. Chem., Vol. 100, No. 20, 1996 8547
TABLE 1: (a) AM1 Calculated Heat of Formation (au), Hessian Unique Negative Eigenvalue (au), Imaginary Frequency (cm-1) Obtained from a Normal-Mode Analysis in Cartesian Coordinates, Main Geometric Parameters (G, Distances in Å and Angles and Dihedrals in deg), Force Constants (F, au), and Corresponding Eigenvector Components (C) for the Transition Structure TS e. (b) SCF/3-21G Results a energy (AM1) negative eigenvalue imaginary frequency χχ+ F C2-C3 O3-C3 C2-C3-O2 O3-C3-C2-O2 C2-C3-O2-C1
G
F
C
0.04 0.71 0.03 0.74 0.40 7.77 0.59 1.10
-0.67 0.05 -0.72 -0.08 -0.10 0.04 -0.02 0.09
b
χχ+ F C2-C3 O3-C3 C2-C3-O2 O3-C3-C2-O2 C2-C3-O2-C1
a -0.118 525 -0.110 50 1561.91i
0.712 2.269 1.289 1.415 1.452 31.85 2.40 12.76
energy (HF/32-1G) negative eigenvalue imaginary frequency
TABLE 2: (a) AM1 Calculated Heat of Formation (au), Hessian Unique Negative Eigenvalue (au), Imaginary Frequency (cm-1) Obtained from a Normal-Mode Analysis in Cartesian Coordinates, Main Geometric Parameters (G, Distances in Å and Angles and Dihedrals in deg), Force Constants (F, au), and Corresponding Eigenvector Components (C) for the Transition Structure TS 1 and TS 2. (b) SCF/3-21G Results
energy (AM1) negative eigenvalue imaginary frequency χχ+ F C2-C3 O3-C3 C2-C3-O2 O3-C3-C2-O2 C2-C3-O2-C1
TS 1
TS 2
-0.109 146 -0.647 51 1777.70i
-0.099 734 -0.586 70 1624.87i
G
F
C
G
F
C
2.606 2.359 1.427 1.474 1.476 27.22 8.89 3.84
0.04 0.90 0.10 0.73 0.33 7.95 0.19 0.86
-0.12 -0.10 -0.56 0.06 0.03 0.03 -0.33 -0.05
2.728 2.383 1.463 1.484 1.464 26.02 126.51 -1.48
0.02 0.85 0.15 0.77 0.34 8.00 0.28 0.69
0.20 -0.19 0.60 -0.06 -0.07 0.05 -0.29 -0.13
-417.291 372 -0.089 45 563.86i
b
G
F
C
0.749 2.299 1.241 1.405 1.543 29.32 -3.60 9.97
0.18 0.73 0.07 0.61 0.26 8.12 0.81 1.17
-0.59 0.06 -0.77 -0.09 -0.13 0.05 -0.03 0.12
i.e., the O3-C3-C2-O2 dihedral angle. For TS 2 and TS 3 subtle differences between semiempirical and ab initio methods are detected for the geometry and TV: χ- and O3-C3-C2O2 dihedral angles are larger at the AM1 level than with the ab initio method. The TV dominant components are F and, to a lesser extent, the dihedral angle associated with internal rotation around the C2-C3 bond at the semiempirical level and basically this dihedral angle at the ab initio level. For TS r, the geometric parameters χ- and F are slightly dependent on the methodology used, being larger for the ab initio method than at the AM1 level (1.412-0.682 and 1.952-1.289 Å, respectively). The TV dominant components are χ- and F (AM1 result) and χ- and the two dihedral angles (ab initio result). It is important to note the high value of the force constants, ranging from 6.3 to 8.1 au, associated with the C2-C3-O2 bond angle for TS e, TS 1, and TS 2. From the TS for the enolization process (TS e), a precursor complex I 1 was identified at ca. 4 kcal/mol below the energy of the SPi-1, while an enediol structure representing a successor structure was found at ca. 16 kcal/mol below the SPi-1. The intermediate I 1 corresponds to an alcohol protonated at O3. From this, the hydrogen can be transferred stereochemically to the same position of ribulose (H below the plane C2-C3O3) through the TS 1, or the other way around, H above the C2-C3-O3 plane through the TS 2. The latter opens a plan leading to the xylulose-related structure. The enediol structure is obtained from the intramolecular enolization SPi-1. This is the precursor moiety in both the carboxylation and oxygenation channels. It is most interesting that there is another SPi-1 at about 9 kcal/mol above the enediol, and consequently it is located about 6 kcal/mol below the TS e. This new stationary point corresponds to a retroenolization process (TS r) that connects with another intermediate (I 2) which is only 1 kcal/mol above the enediol structure. This new
energy (HF/32-1G) negative eigenvalue imaginary frequency G χ2.475 χ+ 2.359 F 1.324 C2-C3 1.471 O3-C3 1.670 C2-C3-O2 26.24 O3-C3-C2-O2 -1.11 C2-C3-O2-C1 3.55
TS 1
TS 2
-417.268 329 -1.328 17 1841.30i
-417.205 737 -4.316 39 2071.4i
F 0.06 0.75 0.05 0.61 0.19 6.94 0.62 1.33
C
G
F
C
0.16 1.874 0.09 -0.01 -0.03 2.357 0.73 -0.01 -0.52 1.201 0.06 0.14 0.10 1.461 0.60 -0.06 0.03 1.624 0.21 -0.07 0.03 26.17 6.31 0.13 -0.30 20.38 -0.42 -0.55 -0.17 9.43 -0.11 -0.46
intermediate corresponds to an alcohol protonated at O2 and opens two possible channels: the hydrogen can be transferred to the C2 through either the TS 3 or the TS 4; this would lead, respectively, to 3-ketoribitol or to 3-ketoarabinitol inhibitors. From the intermediate I 2 the system may return to the deformed enediol via the TS r used to transfer the hydrogen. It is not difficult to see that the hydroxyl hydrogen at the O3 atom can be used to transfer it toward C2 following a direct retroenolization pathway. Depending on the position of this hydrogen with respect to the plane formed by C2-C3-O3, the final stereochemistry at C2 would lead to 3-ketoribitol or 3-ketoarabinitol inhibitors. It is interesting to note that formation of xylulose inhibitor would entail a conformational change by moving H from below to above the plane C2-C3-O3. Xylulose would then be deformed when comparison is made with the in Vacuo molecule without constraints. 5. Discussion The multifaceted behavior of Rubisco raises important mechanistic questions. In previous studies, carboxylation and oxygenation reactions have been discussed.11,12,33,50 The key transition structure opening the interconversion between the keto to an enediol forms was recently identified as an intramolecular hydrogen rearrangement.11 Such a mechanism can be understood if the substrates are molded into geometries that look like the transition structure determined with quantum chemical methods. In the present paper, a more realistic molecular model has been used to identify the stationary points. The model used in our previous work12 was subjected to ab initio MO studies
8548 J. Phys. Chem., Vol. 100, No. 20, 1996
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TABLE 3: (a) AM1 Calculated Heat of Formation (au), Hessian Unique Negative Eigenvalue (au), Imaginary Frequency (cm-1) Obtained from a Normal-Mode Analysis in Cartesian Coordinates, Main Geometric Parameters (G, Distances in Å and Angles and Dihedrals in deg), Force Constants (F, au), and Corresponding Eigenvector Components (C) for the Transition Structure TS r. (b) SCF/3-21G Results a
-0.129 340 -0.122 30 1592.53i
energy (AM1) negative eigenvalue imaginary frequency χχ+ F O3-C3 O2-C2-C3 O2-C2-C3-O3 C1-C2-C3-O3
G
F
C
0.682 2.272 1.289 1.301 103.98 -0.92 229.28
0.04 0.84 0.02 1.09 1.75 0.60 0.21
0.68 -0.09 0.71 -0.12 -0.04 -0.02 0.09
b
-417.290 135 -0.050 16 462.46i
energy (HF/32-1G) negative eigenvalue imaginary frequency χχ+ F O3-C3 O2-C2-C3 O2-C2-C3-O3 C1-C2-C3-O3
G
F
C
1.412 2.309 1.952 1.260 101.86 -4.12 239.54
0.13 0.70 0.20 0.93 1.80 4.33 0.34
0.56 -0.04 0.19 0.02 -0.05 -0.32 -0.21
TABLE 4: (a) AM1 Calculated Heat of Formation (au), Hessian Unique Negative Eigenvalue (au), Imaginary Frequency (cm-1) Obtained from a Normal-Mode Analysis in Cartesian Coordinates, Main Geometric Parameters (G, Distances in Å and Angles and Dihedrals in deg), Force Constants (F, au), and Corresponding Eigenvector Components (C) for the Transition Structure TS 3 and TS 4. (b) SCF/3-21G Results
Figure 4. Definition of internal coordinates used to identify SPi-1: (a) TS e, TS 1, and TS 2; (b0 TS r, TS 3, and TS 4.
a energy (AM1) negative eigenvalue imaginary frequency G χ2.744 χ+ 2.387 F 1.454 O3-C3 1.233 O2-C2-C3 114.09 O2-C2-C3-O3 125.43 C1-C2-C3-O3 255.82
TS 3
TS 4
-0.096 268 -0.437 86 1645.60i
-0.111 505 -0.756 90 1850.90
F
C
G
0.01 -0.24 2.548 0.41 0.19 2.353 0.15 -0.61 1.431 1.25 0.00 1.247 0.43 -0.12 112.20 0.27 0.39 10.73 0.26 0.15 -117.60
F
C
0.03 0.48 0.11 1.16 0.52 0.05 0.25
0.09 -0.07 -0.48 -0.03 -0.17 -0.54 -0.11
b energy (HF/32-1G) negative eigenvalue imaginary frequency G
TS 3
TS 4
-417.200 966 -1.971 99 2120.34i
-417.262 820 -1.044 83 1891.62
F
χ1.832 0.08 χ+ 2.336 0.44 F 1.178 0.09 O3-C3 1.237 0.85 O2-C2-C3 109.26 0.52 O2-C2-C3-O3 19.04 -0.48 C1-C2-C3-O3 232.88 0.19
C
G
-0.08 2.427 -0.06 2.346 0.19 1.350 0.15 1.233 -0.22 103.42 -0.73 1.24 0.06 -115.54
F
C
0.05 0.45 0.07 0.96 0.84 0.63 0.33
0.16 -0.05 -0.43 -0.04 -0.12 -0.54 -0.11
that produced the same results as the one reported here. For the sake of completeness, in Tables 1b-4b the results obtained with the ab initio method at the 3-31G level for the different
TSs, TS e, TS 1, TS 2, TS r, TS 3, and TS 4, are summarized. Similar geometric parameters and transition vectors have been found for AM1 and 3-21G calculations. The hypothesis behind the present study is based on the idea that substrate molding to a catalytically apt complex can open the channels for other intramolecular hydrogen rearrangements. The identification of a number of SPi-1’s relating the deformed substrate to xylulose, 3-ketoarabinitol, and 3-ketoribitol with consistent barriers shows that the molding hypothesis would give at least a unified view of the ensemble of reactions related with this rather unique enzyme. The real substrate has two phosphate groups. They are essential, together with magnesium, to correctly orient the substrate and would likely contribute to the work required to mold the substrate and protein into their catalytically appropriate conformation. In this respect, the role of 2-carboxyarabinitol 1-phosphate (CA1P) is significant.2 CA1P has preferential binding to the carbamylated form of rubisco with a dissociation constant Kd ≈ 1 nM. It is a competitive inhibitor. The absence of the phosphate at position 5 may be seen as a reason preventing the enzyme from working against the intramolecular force field and activating the molecule, as can be the case with the real substrate RuBP. This would explain why the MichaelisMenten51 Km is larger than Kd for this particular case. Experimentally, it is well documented that the formation of D-xylulose-1,5-bisphosphate (XuBP) occurs about once per 400 turnovers. Hartmann and Harpel call this process a misprotonation at C3.2 A close look at the crystal structure does not show
Ribulose-1,5-bisphosphate Carboxylase/Oxygenase any residue that could be accomplishing such misprotonation. On the contrary, from the intramolecular hydrogen transferr perspective one can figure out a simple epimerization mechanism. In fact, besides the pathway indicated in Figure 2 (i.e. TS e-I 1-TS 2-xylulose), which rather hints at the low rate of XuBP carboxylation, there is another mechanism leading to a deformed xylulose. This would depend upon a change in fluctuation pattern of the activated complex represented by TS e, the I 1 complex, and back to a TS e′ (not shown), where the transfered hydrogen is just coming from the oposite side. Here, the dihedral angle O2-C2-C3-O3 would be slightly out of plane and trans. This TS e′ would then relax to a xylulose tightly bound structure (this is suggested by the broken line in Figure 2). The enediol structure being more stable than I 1 by 11 kcal/mol, one would expect a larger population of the former structure. Experimentally, XuBP is carboxylated at approximately 0.03% the rate of the normal substrate by the spinach and displays a Km similar to RuBP. Rubisco from Rhodospirillum rubrum does not present fallover and catalyzes the carboxylation of XuBP at approximately 0.2% of the RuBP carboxylation rate.2 The lost in catalytic efficiency of XuBP can be understood in simple terms. Assuming that XuBP and RuBP (similar Km) have similar binding energies and that the species of Figure 2 correctly represent the interconverting events, the reaction would proceed extremely slow for the xylulose-related system when compared with dienol formation. Assuming that the xylulose uses a deformed trans enediol intermediate TS e′, such a structure would have lost part of its stabilization due to a weaker Mg-O3 bond compared to the cis-like conformer. This difference may contribute to the low performance of rubisco with this substrate. The differences found between R. rubrum and spinach would have to do with differences in the binding site that cannot be assessed with the present study. Still, to avoid fallover it would be sufficient to destabilize the intermediate I 1. The binding of XuBP by R. rubrum rubisco would simply proceed via a TS e′ structure to form the deformed translike dienol. In Figure 2, the formation of 3-ketoribitol and 3-ketoarabinitol depends upon the formation of the dienol intermediate. According to the in Vacuo energy profile, if the dienol is formed, it would cost more activation energy to form the 3-ketoribitol than the 3-ketoarabinitol. However, there is a distinct possibility of forming a TS r′ (not shown) structure by letting the system fluctuate back and forth with the I 2 complex structure. This TS r′ can be related to 3-ketoribitol; on the other hand, the TS r without further change can be related to 3-ketoarabinitol. In terms of probabilities, the latter compound may appear more often than the former. The chemical promiscuity may be traced back to the accessibility of different reactive fluctuations opened by substrate binding into a deformed conformation. Site-directed mutagenesis results are of interest here. The mutant Glu48Gln (E48Q) in R. rubrum is severely impaired catalytically. The mutant shows a side reaction, not detected with wild-type enzyme, leading to xylulose bisphosphate that proceeds as rapidly as carboxylation of D-ribulose-1,5-bisphosphate by the mutant.2,10 In wild-type R. rubrum, Glu48 contributes to form the active site via its interaction with Lys329. The positioning of this residue is essential for carboxylation,52 and a displacement of Lys329 due to the absence of Glu48 in E48Q mutant may help break the surface complementarity for carboxylation.12,32,33 Oxygenation will be much less affected, as the SPi-1 indicates no possible close contact with lysine.11,12,23 With the carboxylation reaction impaired, the lifetime of the
J. Phys. Chem., Vol. 100, No. 20, 1996 8549 species related to xylulose formation may consequently increase, and the probability for this reaction to proceed increases. Harpel and Hartman have observed in mutants lacking this key lysyl group (Lys329Ala (K329A) and Lys329Cys mutants) that xylulose 1,5-bisphosphate and 3-ketoarabinitol 1,5-bisphosphate transiently accumulate to low levels during turnover of RuBP by K329A. These compounds eventually react with oxygen.52 Lee et al.10 have shown the production of arabinitol 1,5bisphosphate after treatment of the intermediates with sodium borohydride. No report yet of 3-ketoribitol is known to the present authors. Although rather conjecturally at this stage, the promiscuity properties of rubisco enzyme could be related to the presence of SPi-1s associated with intramolecular retroenolization processes. All these interconversion channels have finite lifetimes, with the consequent possibility of losing memory. Other properties, such as those revealed by chemical rescue by exogenous amines of a site-directed mutant of rubisco lacking the key lysyl residue,52 may well be related to the coupling of the dynamical fluctuations of the enzyme’s active site wall with the characteristic fluctuations of the precursor-successor complex related to carboxylation. As pointed out by Harpel and Hartman,52 the surrogate for the lysyl side chain must not only mimic the catalytic roles of Lys329 but also stabilize the closed conformation of loop 6 at the appropriate stage of the reaction coordinate. This stabilization would ensure the closing-off the active site, prompting the coupling between the protein and active site fluctuations. Moreover, Larimer et al. have shown the role of the protein ligands involved in “tethering” the P1 phosphate to avoid β-elimination of phosphate from the dienol intermediate.53 In other words, subtle changes in ligand binding may control reactive fluctuations, thereby avoiding some types of reactions and opening the channel for others. These dynamical factors can be incorporated in a theoretical perspective where a reaction is not seen as a simple wandering over a hypersurface even with recrossings but as quantum mechanical processes.54,55 Acknowledgment. We thank Dr. M. R. Harpel for invaluable comments and reprints of their work on Rubisco, and we hope the theoretical study is up to the challenge conveyed by this enigmatic enzyme. This work received support from the Conselleria d’Educacio´ i Cie`ncia, Generalitat Valenciana (Project GV-1142/93 and equipment special funds), and by the DGICYT (Project PB93-0661). The authors are grateful to the Centre de Processament de Dades de la Universitat Jaume I for providing them with CPU time on the cluster of Hewlett-Packard 9000/730 workstations. O.T. thanks, NFR for financial support. References and Notes (1) Schneider, G.; Lindqvist, Y.; Bra¨nde´n, C.-I. Annu. ReV. Biophys. Biomol. Struct. 1992, 21, 119-143. (2) Hartman, F. C.; Harpel, M. R. Annu. ReV. Biochem. 1994, 63, 197234. (3) Andrews, T. J.; Hatch, M. D. Biochem. J. 1969, 114, 117-125. (4) Laing, W. A.; Christeller, J. T. Biochem. J. 1976, 159, 563-570. (5) McCurry, S. D.; Pierce, J.; Tolbert, N. E.; Orme-Johnson, W. H. J. Biol. Chem. 1981, 249, 6623-6628. (6) Mott, K. A.; Berry, J. A. Plant Physiol. 1986, 82, 77-82. (7) Robinson, S. P.; Portis, A. R., Jr. Plant Physiol. 1989, 90, 968971. (8) Sicher, R. C.; Hatch, A. L.; Stumpf, D. K.; Jensen, R. G. Plant Physiol. 1981, 68, 252-255. (9) Yokota, A.; Kitaoka, S. Plant Cell Physiol. 1989, 30, 183-191. (10) Lee, E. H.; Harpel, M. R.; Chen, Y.-R.; Hartman, F. C. J. Biol. Chem. 1993, 268, 26583-26591. (11) Tapia, O.; Andre´s, J.; Safont, V. S. J. Phys. Chem. 1994, 98, 48214830. (12) Tapia, O.; Andre´s, J.; Safont, V. S. J. Chem. Soc., Faraday Trans. 1994, 90, 2365-2374.
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