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Faraday Discuss., 1992, 93, 239-248

Simulation Analysis of Triose Phosphate Isomerase: Conformational Transition and Catalysis Martin Karplus, Jeffrey D. Evanseck, Diane Joseph, Paul A. Bash? and Martin J. Field$ Department of Chemistry, Harvard University, Cambridge, M A 02138, USA

A theoretical approach is employed to study the catalysis of the dihydroxyacetone phosphate (DHAP) to D-glyceraldehyde 3-phosphate (GAP) reaction hy the enzyme triose phosphate isomerase (TIM). The conformational change in a loop involved in protecting the active site from solvent is examined by use of X-ray data and molecular dynamics simulations. A mixed quantum-mechanics and molecular mechanics potential is used to determine the energy surface along the reaction path. The calculations address the role of the enzyme in lowering the barrier to reaction and provide a decomposition into specific residue contributions. To obtain a clearer understanding of the electronic effects, the polarization of the substrate carbonyl group by the active site residues is examined and compared with FTIR measurements on the wild-type and mutant forms of the enzyme.

Although there have been many discussions of the factors contributing to rate enhancement by our understanding is limited by the lack of detailed information at the molecular level. An enzyme that has been the subject of intensive experimental studies is triose phosphate isomerase (TIM), which catalyses the interconversion of dihydroxyacetone phosphate (DHAP) and D-glyceraldehyde 3-phosphate (GAP), an essential step in the glycolytic pathway. A wide range of experiments, including kinetics,'-' X-ray nuclear magnetic infrared spectroscopy,'4915and site-specific m ~ t a g e n e s i s ' ~have ' ~ ~ been applied to TIM, but the role of individual amino acid residues in determining the energetics along the reaction path is not clear. Glu-165 has been implicated as the catalytic base and protonated His-95 has been thought to act as a generalized acid. To obtain a more detailed knowledge of the mechanism of TIM, theoretical approaches18y19 of the type now being widely applied to biomolecules can be used to supplement the experimental data. We report here an analysis of several aspects of the catalytic mechanism based on use of quantummechanical and molecular mechanics calculations. The nature of a con formational transition important for enzyme activity2' and the contribution of the specific enzyme residues to the energetics of the overall reaction path2' and to substrate polarization are determined.

The 'Lid' Transition Conformational change is often an essential part of enzyme mechanisms." In TIM an ll-residue loop region (residues 166-176) moves more than 7 A and closes over the active site when the substrate binds (Fi 1)."y20 Mutagenesis experiments have shown that the loop is essential for catalysis."*When the open and closed structures of TIM are superimposed by least-squares optimization of all a-carbons, the root-mean-square 1- Present address: Department of Chemistry, Florida State University, Tallahassee, FL 32301, USA. $ Present address: National Institutes of Health, Bethesda, MD 20892, USA.

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Fig. 1 Comparison of the closed and open structure of subunit 1; only a-carbons are shown. The two structures were superposed by least-squares optimization excluding the loop residues which are shown in thick black lines. Reproduced with permission from D. Joseph, G. A. Petsko and M. Karplus, Science, 1990,249, 1425. Copyright 1990 by the AAAS

(rms) deviation of the a-carbons is only 0.42A, whereas that for the loop residues is 4.8 A. The a-carbon of Thr-172, which is at the centre of the loop, is shifted by 7.1 A, while the ends of the loop change little; for example, the distance from a-carbon 166 to a-carbon 176 is 7.3 A in the open structure and 7.5 A in the closed structure. Most important is the striking similarity between the internal structure of the loop in the open and closed forms; that is, when residues 166-176 in the initial and final states are superposed, the rms deviation for all loop atoms is only 0.73 A. These structural results suggest that a rigid-body, hinge-type motion takes place when the loop closes over the substrate in the active site; i.e. the so-called ‘loop’ moves more like a ‘lid’. To identify the hinge regions, a-carbon pseudo-dihedral angle and main-chain dihedral angle differences between the open and closed loop were plotted against residue number. From the a-carbon plots in Fig. 2A, it is evident that there are two hinges. One of these involves the angles 166-167 and 167-168, and the other the angles 174-175, 175-176, 176-177. Changing only these angles from their values in the closed structure to their values in the open structure yields an ‘open’ loop with an a-carbon rms difference of 1.9 I$ from the open structure when non-loop a-carbons are superimposed; if the dihedral 164-165 is also rotated, the rms difference is reduced to 1.1 A. This rather simple picture contrasts with that obtained from the dihedral angles (b and (Fig. 2B). It is evident from the dihedral angle difference plots that motion occurs in the region of residues 174 and 175, but it is less evident that there is also a significant change in the region of residues 166 and 167. Analysis of the van der Waals packing and hydrogen-bonding interactions within the lid provides an explanation for its rigid-body motion and the presence of two hinges. To obtain information about the lid motion, several MI) simulations were performed. High temperatures were used to decrease the time required for a conformational change. All simulations began with the closed form since an open structure with increased entropy was expected to be favoured at high temperatures, even in vacuum. At 298 K,

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Plots of closed minus open loop structure dihedral angle differences for subunit 1 and for subunit 2. A, The a-carbon pseudo-dihedral angle differences and B main-chain dihedral angle differences vs. residue number. In A the number i corresponds to angle i, i + 1; in B circles Reproduced with permission from D. Joseph, G. A. represent relative 4 and squares relative Petsko and M. Karplus, Science, 1990,249, 1425. Copyright 1990 by the A A A S

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the loop oscillated about the closed position, whereas during the 1000 K MD simulation the loop opened and closed repeatedly. The 500 K MD simulation was the most interesting; the loop oscillated about the closed position until 29 ps when it flipped to a more open position; the Thr-172 a-carbon difference from the closed form was cu. 5 . 5 & somewhat less than the value of 7.1 A found experimentally. Plots of the dihedral angle differences between the MD structure at 29 ps and the closed and open structures show the largest changes between residues 174 and 175. This suggests that the loop starts to open in the region of 174 and 175. The analysis,20which demonstrates that the TIM conformational change involves a rigid lid rather than a flexible loop, suggests that similar behaviour will be found in other enzymes that have 'loop' regions involved in substrate binding. In fact, 'lid' behaviour has been identified recently in lactate dehydrogenase.22

Reaction Path in TIM To examine the energetics of the TIM reaction path, a simulation method2' was employed that is suitable for the study of reactions in solution or in an enzyme. To determine changes in the electronic structure of the reacting species (bond making and bond breaking), a semiempirical quantum-mechanical (QM) method23is used for the subset of atoms directly involved in the reaction. The remainder of the system (other protein atoms and/or solvent) is treated by molecular mechanics (MM)24and the two subsystems are coupled by electrostatic and van der Waals interactions. Initial atomic coordinates for the simulations were obtained from the refined X-ray crystal structurego of TIM complexed with the substrate analogue phosphoglycolohydroxamate (PGH) with the amide NH group of the PGH replaced by a CH, methylene group in a tetrahedral configuration to form the DHAP substrate. A 16A spherical

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region centred on atom OE2of Glu-165 was selected as the model system for the simulations. Explicit water molecules were introduced to solvate the active site of the enzyme and stochastic boundary conditions were applied.25 The system was energyminimized using the QM/MM hybrid method with the substrate and the side chains of Glu-165 and His-95 treated quantum-mechanically and all other atoms treated by a molecular mechanics potential. To verify that the simulation system is well behaved, the resulting structure was compared with the original TIM-PGH X-ray structure. The rms deviation between the structures was 0.504 A (0.636 A) for main-chain (all) protein atoms included in the system. This is comparable to the rms difference of 0.39 A for the C a atoms of the two monomers of the TIM dimer." More important, the relative positions of key groups (e.g.His-95, Glu-165, Lys-12 and DHAP) after the minimization are very similar to those in the X-ray structure. The reaction profile for the reaction steps depicted in Fig. 3A is shown in Fig. 3B, which presents the results with His-95 initially singly or doubly protonated. For the first step [Fig. 3A ( a ) + ( b ) ] ,the distance between OE2of Glu-165 and C of CH2 of DHAP in the minimized structures is in the range 2.6-3.3 A during the transfer. This result is in accord with the model compound calculations of Alagona et a2.T who showed the barrier is very sensitive to the donor-acceptor distance. Interestingly, His-95 has only a small (ca. 3 kcal mol-') effect on the transition-state energy for this step. The transfer of the proton from O2 to 0' of the enediolate [Fig. 3A ( b )-+( d ) ] is thou ht to involve His-95 either as an electrostatic catalyst or as a generalized base and acidf7 The calculations (see Fig. 3B) suggest that the N' of a neutral His-95 can transfer a proton to O2 of the enediolate to form the imidazolate and an enediol with an energy barrier for the proton transfer of the order of the experimental estimate (ca. 13 kcalm ~ l - ' ) .A ~ ~corresponding calculation has been made for doubly protonated His-95. When this simulation is carried out, His-95 reorients from its position in the crystal structure" so as to move its NS hydrogen away from the amide hydrogen of residue 97. This leads to a very different reaction profile with a deep well for the state involving the enediol and neutral histidine. There is no evidence for such a stable enediol intermediate,27 whose existence would hinder the reaction. The novel possibility21,28 that a neutral His-95 acts as a generalized acid is reinforced by a comparison of pKa values. The second pK, of His (His- His-+Hf) is ca. 14 in aqueous Although the conditions in the enzyme are different from those in solution, this suggests the possibility of a balance between the pK,s of a neutral His and the enediol; the pKa of an enediol has not been measured, but values for enols are ca. ll.30This contrasts with the apparent imbalance between the pK, of a protonated His and the enediol, which the calculations indicate results in a thermodynamic 'trap' for the intermediate. Recent NMR studies of "N-labelled His-95 in the TIM-PGH complex show that a neutral imidazole is p r e ~ e n t . ' ~ By use of a perturbation technique (see caption of Fig. 4), the effects of individual amino acids on the energy difference between Glu- + DHAP and Glu H + enediolate [Fig. 4A; step ( a )to (6) in Fig. 3A] and that between enediolate + His and enediol + His[Fig. 4B; step (6) to ( c ) in Fig. 3A] were determined. Lys-12 has the largest effect on both steps of the reaction. The protonated amino group of Lys-12 is close to O2 of the inhibitor in the TIM-PGH crystal structure and remains there during the simulations of the reactions (the N5 of Lys-12 to O2 distance is 3.0-3.1 A). The protonated amino group stabilizes the enediolate by 20.1 kcal mol-' relative to DHAP because O2 is more negative after removal of the methylene proton (the Mulliken charges are -0.32 and -0.65, respectively). On the other hand, the protonated O2 [Fig. 3A( c ) ] is less negative than the ionized 02,so that there is a destabilizing interaction of 11.5 kcal mol-' with Lys-12 in the transfer step [( b ) ( c )in Fig. 3A]. Other residues make smaller contributions, but their cumulative effect is important; also there are a number of residues far from the active site (e.g. Lys-237) that have a significant effect on catalysis.

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Fig. 3 A, Putative mechanism for the isomerization of dihydroxyacetone phosphate (DHAP) to D-glyceraldehyde3-phosphate (GAP) with residues Glu-165 and His-95 of TIM acting as acid/base catalysts. B, Energy profile for the proton-transfer steps depicted in Fig. 3A. The ordinate is E Q M / M M normalized to the ground-state energy for the enzyme-substrate complex. The reaction coordinates for the various steps are indicated along the abscissa; for each step the distance measures that of the transferred proton from the heavy atom to which it is bonded in the reactant. Reprinted with permission from P. A. Bash, M. J. Field, R. C. Davenport, G. A. Petsko, D. Ringe and M.Karplus, Biochemistry, 1991,30, 5826. 'Copyright 1991 American Chemical Society

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Fig. 4 First-order perturbation estimate of residue contributions to the energy along reaction pathway. A, Plot of the EQM/MM energy difference (due to the electrostatic potential of specific residues) between states (b) and ( a ) of Fig. 3A as a function of the fraction of the protein included in the calculations. The abscissa represents an ordering of amino acid residues by the distance from their centre of mass (COM) to that of the substrate. The points on the curve were obtained by setting the MM charges to zero on residues in order from the furthest to the closest COM distance. His-95 is in a single protonated state for these calculations. B, The same as A for states (e) and ( 6 ) of Fig. 3A. 'Vacuum' in the figures refers to the energy difference calculated when the charges on all amino acids, other than those treated as QM atoms, were set to zero. Reprinted with permission from P. A. Bash, M. J. Field, R. C. Davenport, G. A. Petsko, D. Ringe and M. Karplus, Biochemistry, 1991, 30, 5826. Copyright 1991 American Chemical Society

Substrate Polarization The unusual behaviour of His-95 ( i e . that a neutral histidine acts as a generalized acid) suggests that further investigation concerning its proposed role in the reaction would be fruitful. Fourier-transform infrared (FTIR)spectroscopy has been used by Knowles and c o - ~ o r k e r s ' ~ to*show ~ ~ that the carbonyl stretching frequency of DHAP bound to TIM is red-shifted by ca. 19 cm-' relative to solution; the observed spectrum is rather broad so that the quantitative shift is difficult to determine. This has been interpreted as an electronic distortion of the carbonyl moiety by which the enzyme-substrate complex

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destabilizes the ground state of DHAP relative to the transition-state structure for deprotonation of C' [ ( a ) to ( b ) in Fig. 3A]. Based on the X-ray structure of the TIM-PGH complex," His-95 is thought to have the predominant role in the polarization of DHAP. This conclusions appears to be confirmed by the demonstration of a reduced red shift in the mutants H95Q and H95N.I5 We describe here the results of a theoretical analysis of the origin of the observed shifts in the carbonyl frequency of DHAP bound to wild-type TIM and to the mutants H95Q and E165D. To determine the vibrational frequency of the carbonyl group of DHAP, quantum-mechanical calculations with ab initio31and semiempirical methods23 were performed. Initial atomic coordinates were obtained from X-ray crystal structures of yeast wild-type TIM-PGH," yeast H95Q TIM-PGH16 and chicken E165D TIM-PGH (Sugio and Ringe, personal communication). Active-site residues that are implicated in catalysing the abstraction of a proton from DHAP (see above) were examined. The residues are Asn-10, Lys-12, HislGln-95, Ser-96, Glu-97 and Glul Asp-165, all of which are conserved in 13 TIM sequences."720 To simplify the calculations, the sidechains of Asn or Gln, Lys, His, Ser and Glu or Asp were modelled by acetamide, ammonium or methylammonium, imidazole, ethanol and formate or acetate, respectively; the protein backbone was modelled by acetamide and the essential portion of DHAP was modelled by acetone; neglect of the phosphate group of DHAP has been shown to have a small effect on the carbonyl stretching frequency. Since the full active site was not included in the calculation and the main purpose of the study was to determine the contribution of individual amino acid residues to substrate polarization, it was necessary to introduce constraints to preserve the geometry corresponding to the X-ray structures. The constraints were applied to appropriately chosen intermolecular distances, angles and dihedral angles. The internal degrees of freedom of the substrate and amino acid model were minimized in the presence of the geometric constraints. Because of the isolated position of the carbonyl stretching frequency in the vibrational spectrum, the error due to the presence of the constraints is expected to be small; test studies indicate the effect is

Simulation analysis of triose phosphate isomerase: conformational transition and catalysis.

A theoretical approach is employed to study the catalysis of the dihydroxyacetone phosphate (DHAP) to D-glyceraldehyde 3-phosphate (GAP) reaction by t...
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