Computational Modeling of the Catalytic Reaction in ...Computational Modeling of the Catalytic...

Computational Modeling of the Catalytic Reaction inTriosephosphate Isomerase

Victor Guallar1, Matt Jacobson2, Ann McDermott1 andRichard A. Friesner1*

1Department of ChemistryColumbia University, NewYork, NY 10027, USA

2Department of PharmaceuticalChemistry, University ofCalifornia at San FranciscoSan Francisco, CA 94143, USA

We present a comprehensive analysis of the catalytic cycle of the enzymetriosephosphate isomerase (TIM), including both the reactive chemistryand the catalytic loop and side-chain motions. Combining accuratemixed quantum mechanics/molecular mechanics (QM/MM) and proteinstructure prediction methods, we have modeled both the structural andchemical aspects of the reversible isomerization of dihydroxyacetonephosphate (DHAP) to D-glyceraldehyde 3-phosphate (GAP), for whichthere is a wealth of experimental data. The conjunction of this novel com-putational approach with the use of the recent near-atomic resolutionTIM-DHAP Michaelis complex PDB structure, 1NEY.pdb, has enabled usto obtain robust qualitative and, where available, quantitative agreementwith a wide range of experimental data. Among the principal conclusionsthat we are able to draw are the importance of the monoanionic (asopposed to dianioic) form of the substrate phosphate group in thecatalytic cycle, detailed positioning and energetics of the key catalyticresidues in the active-site, the flexible nature of Glu165, which favors itsdirect involvement in the formation of the enediol intermediate, energeticsof the open and closed form of the catalytic loop region in the presenceand absence of substrate, and quantitative reproduction of various experi-mentally measured reaction rates, typically to within ,1 kcal/mol. Ourresults are consistent with the available experimental data, and providean initial picture as to why loop opening when GAP is the product has ahigher barrier than when DHAP is the product.

q 2003 Elsevier Ltd. All rights reserved.

Keywords: enzymology; protein prediction; triosephosphate isomerase;loop conformations; catalysis*Corresponding author

Introduction

Triosephosphate isomerase (TIM) is one of themost extensively characterized enzymes in thechemical literature. TIM catalyses the reversibleisomerization of dihydroxyacetone phosphate(DHAP) to D-glyceraldehyde 3-phosphate (GAP)with exceptionally high efficiency, while suppres-

sing elimination of orthophosphate. To accomplishthis isomerization, TIM first extracts a pro-Rhydrogen from the C1 of DHAP and then stereo-specifically introduces a proton onto the C2 atom(Figure 1). A wealth of thermodynamic, spectro-scopic, kinetic, and structural studies have beencarried out, providing extensive experimental datawith which to compare theoretical calculations.Furthermore, the well-known large-scale catalyticloop motion in TIM (loop 6, residues 166–177),which alternates between open and closedpositions, poses a substantial challenge to compu-tational modeling efforts, one that is differentfrom modeling enzyme reactions with relativelysmall-scale structural changes in the protein overthe course of the catalytic cycle. The closed formof the loop is observed whenever the enzyme isligated, and is responsible for properly aligningactive-site residues fundamental to the catalytic

0022-2836/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.

Present address: V. Guallar, Department ofBiochemistry and Molecular Biophysics, WashingtonSchool of Medicine, 660 South Euclid Avenue, St. Louis,MO 63110, USA.

E-mail address of the corresponding author:[email protected]

Abbreviations used: TIM, triosephosphate isomerase;QM/MM, quantum mechanics/molecular mechanics;DHAP, dihydroxyacetone phosphate; GAP, D-glyceraldehyde 3-phosphate; ESP, electrostatic potential.

doi:10.1016/j.jmb.2003.11.016 J. Mol. Biol. (2004) 337, 227–239

process and for the stabilization of reactionintermediates.1

The conversion of DHAP to GAP, a thermo-dynamically unfavorable but biologicallysignificant reaction, occurs with a catalytic ratekcat ¼ 7:5ð^0:2 £ 102 s21 and a Michaelis constantKm ¼ 1:4ð^0:1Þ mM: The rate-limiting step appearsto be a slow conformational change as described bya variety of isotope data.2 In the reverse direction,with GAP as a substrate, kcat ¼ 8:7ð^0:3Þ £ 103s21;Km ¼ 0:055ð^0:004Þ mM; and the rate-limiting stepappears to be a proton transfer.3,4 Therefore, theopening of the loop on DHAP appears to be fasterthan 8 £ 103 s21, whereas on GAP it must be com-parable to 7 £ 102 s21. Recently, these kineticmeasurements have been complemented with avariety of spectroscopic kinetic probes of the loop-opening rates in the presence of a variety ofligands.5 – 7 Information on the chemical mechanismand the key players at the active-site has been pro-vided from a variety of enzymological, mutagenicand spectroscopic studies. Mutational changes ofLys128 and Glu1659 have important effects in bothKm and kcat; whereas the His95Q mutant reducesthe catalytic rate by 200-fold.10 – 11 A large collectionof crystal structures, including the recent TIM-DHAP Michaelis complex at near-atomicresolution, 1NEY.pdb,12 indicate a highly compactactive-site. Spectroscopic and X-ray crystallo-graphic data indicate that the substrate is primarilyin the form of the ketone DHAP in situ. Short-rangeinteractions to all three key residues, Glu165, His95and Lys12, are seen in the ground state orMichaelis complex. It is interesting, based on thishigh-resolution picture of the ground state, to askhow stabilization is provided for the key inter-mediates. This issue is best addressed through

computational studies, and must combinepredictions of quantum chemical pathways withpredictions of conformational freedom for keyresidues.

Several theoretical studies, using semiempiricaland DFT-based QM/MM methods to study TIMcatalysis, have provided an initial atomic-levelpicture of the various reaction steps.13 – 17 However,these studies were not able to utilize the recentTIM-DHAP crystal structure discussed above as astarting point. The resulting structural uncertain-ties, in conjunction with issues concerning theaccuracy of the computational technologyemployed in the calculations, made it difficult toconfidently draw quantitative conclusions.Furthermore, no investigation of the catalytic side-chains or loop motion was carried out. Thus, acomplete, robust theoretical picture of TIMcatalysis has not been produced.

Here, we use a combination of QM/MM andprotein structure modeling techniques to providea comprehensive, and quantitatively reliable,description of the TIM catalytic cycle. Our QM/MM methods enable routine treatment of quantumregions of the active-site as large as 150–200 atoms,for which full DFT geometry optimizations can becarried out with sufficiently large basis sets toguarantee accurate structures. The QM/MM inter-face parameterization that we employ has beentested extensively in a wide range of priorcalculations on small model systems andproteins;18,19 we have demonstrated that the errorsarising from the interface are less than 1 kcal/molð1 cal ¼ 4:184 JÞ: Furthermore, the overall accuracyin calculating free energies of intermediates andtransition states for enzymatic reactions appears tobe of the order of 2–3 kcal/mol. This technology

Figure 1. DHAP to GAP catalytic pathway in TIM. The first step, DHAP ! I1, involves the transfer of a proton fromC1 of DHAP to the catalytic base, Glu165. The different alternative paths between the two intermediates I1 and I2 areshown in the lower-right square panel. A ball-and-stick representation is used for the atoms involved directly in eachstep and curved arrows indicate the primary proton transfers. Path C requires a rotation of the carboxylate group ofthe Glu side-chain and a second proton transfer from HO1 to Glu165 (not shown). The final catalytic step, I2 ! GAP,involves a proton transfer from Glu165 to C2. For all structures, E ¼ Glu165, K ¼ Lys12 and H ¼ His95.

228 Triosephosphate Isomerase Catalytic Modeling

represents a significant improvement in accuracywhen compared with models and methods usedin previous theoretical studies, thus enablingreliable quantitative conclusions to be drawnconcerning barrier heights, protonation states, andother details of the reaction. As discussed below,the protonation state of the phosphate group onthe ligand is of particular importance, and wehave invested considerable effort in consideringthe alternatives and assessing them according tototal energies obtained.

We investigate the catalytic loop motion in TIMusing methods for loop and side-chainprediction,20–23 based on a protein molecularmechanics force-field and a surface GeneralizedBorn (SGB) continuum solvation model that wehave developed several years ago.24 The methodshave been validated through an extensive series oftests in predicting loop and side-chain structures inthe PDB, and have been shown to yield a remarkablyhigh level of accuracy, even for relatively large loops(the catalytic TIM loop is 11 residues, which is withinthe validation range of our test suite). QM/MMcalculations are used to generate charges for theligand, which is likely to be a substantial improve-ment over using generic force-field parameters,particularly for the charged phosphate group.

The structural prediction methods are able tosuccessfully generate open and closed forms ofthe loop, with and without the ligand present,with thermodynamics that are consistent with theentire range of experimental data. These calcu-lations provide an initial atomic level picture ofthe loop opening with the ligand present, whichhas been proposed as the rate-determining step inthe TIM catalytic cycle.

Models for TIM catalysis

The specific reaction catalyzed by TIM thatwe have chosen to study is given below in

Equation (1):

E þ DHAP $ EDHAP $ EGAP $ E þ GAP ð1Þ

The thermodynamic stability of the product andreactant in aqueous solution has been measuredexperimentally, and yields a DG of 1.9 kcal/mol.25

Thus, the products are somewhat less stable thanthe reactants. In vivo, the product is essential foroptimal throughput in the glycolytic pathway.Depletion of product continues to drive transform-ation of the reactants. Without catalysis, the reac-tion rate in solution is ,1027 s21,26 which wouldbe inadequate to serve the relevant biological func-tion. TIM accelerates the rate by about nine ordersof magnitude.

The key residues involved in the catalysis arebelieved to be Glu165, His95, and Lys12 (Figure 1).It is widely accepted that the first step involves thetransfer of a proton from C1 of DHAP to thecatalytic base, Glu165 (atom notation can befollowed with Figures 1 and 2). From this point,three different paths have been proposed and dis-cussed by several experimental and theoreticalgroups. Paths A and C involve the formation of anenediol intermediate by transfer of a proton fromHis95 (path A) or Glu165 (path C) to the substrateO2 atom. The enediol intermediate then formsenediolate by the transfer of a proton from O1 toHis95 (path A) or Glu165 (path C). Path A, the“classical” mechanism, was proposed by Knowleset al.4 and has been accepted widely. Path C hasbeen supported recently by NMR experiments,27

and by ab initio active-site theoretical models.17

Path B13 forms an enediolate intermediate directlyby internal proton transfer from O1 to O2. Thefinal catalytic step, common to all paths, involvesa proton transfer from Glu165 to C2 to form theproduct GAP. The proposed steps for the reactionshould account for central experimental evidence:the substantial isotope washout when 2H and 3Hare used as substrate.28

Figure 2. QM/MM DHAP-binding complex. The left panel shows a cartoon superposition of the QM/MM and thecrystallographic structure, 1NEY.pdb. On the right, main hydrogen bond distances in the active site: QM/MM/X-ray.Distances are in A.

Triosephosphate Isomerase Catalytic Modeling 229

In previous theoretical studies, the enzymaticcycle was studied using the dianionic (D state)form of the ligand phosphate group. This is thethermodynamically most stable form of the ligandin neutral solution, as the second pKa of the phos-phate group is ,6.5. However, the free energydifference between the singly (monoanionic, Mstate) and doubly charged species would be lessthan 1 kcal/mol; furthermore, partial burial of thephosphate group in the enzyme active-site wouldtend to favor the protonated species, as the outershell Born energy of the dianion (substantiallylarger than that of a single charged species) wouldbe diminished. Thus, a pKa shift from the solutionvalue is expected. In what follows, we study theabove reactions using both the singly (M) anddoubly (D) charged forms of the phosphate group.We did briefly investigate the neutral species aswell, which produce a substantial reduction in acti-vation barrier; however, the pKa of this last protonis extremely low, ,2–3, making it highly unlikelythat this species contributes substantially to thereaction mechanism. Note that even if the effect ofthe protein on pKa is negligibly small and the dia-nion substrate is the major bound complex,29 thesingly charged form can still dominate the opti-mum reaction pathway; all that is required is thatthe overall activation free energy of this pathwayis lower than that achieved by going through thedoubly charged species exclusively. In formulatingthis argument, we assume that protonation is diffu-sion-controlled, so that the kinetic barrier to form-ing the monoanion from the dianion at pH 7would be significantly lower than that observedfor the overall reaction.

Results

We first introduce the QM/MM study of thecatalytic chemistry and discuss the differentproposed paths. We then describe our predictionsof the opening and closing of the catalytic loop forseveral different enzymatic structures, in theabsence of substrate and in the presence of DHAPand GAP.

QM/MM modeling of the catalytic chemistry

DHAP protein–ligand complex

Figure 2 compares the important interatomicdistances of the QM/MM-optimized and X-ray(1NEY.pdb) structures in the active-site of theDHAP protein–ligand complex. The Ca RMSDbetween the two structures is 0.6 A, which istypical of the level of agreement that we have seenin previous work. The core structure of the activesite is maintained, although there are minordifferences in the hydrogen bond network betweenthe main catalytic residues and the substrate.Specifically, the QM/MM refinement of the crystalstructure reveals a closer interaction of Glu165

with the substrate protons, H1 and HO1. One ofthe main differences between our QM/MM modeland previous theoretical studies16 is the position ofLys12. In previous studies, based on a substrateanalogue crystal structure, Lys12 forms a tighthydrogen bond with the phosphate oxygen O3,with a considerably longer O2-Lys12 distance. Therecent high-resolution TIM-DHAP crystal structurereveals a well-defined position for Lys12, in acloser hydrogen bond with the substrate O2 and acrystallographic water molecule. Furthermore, asalt-bridge of Lys12 with Glu97 helps to anchorthis important residue in the catalytic cycle. Thisdifference in the hydrogen bond pattern is signifi-cant in quantitatively computing the energetics ofthe various states in the catalytic cycle.

DHAP-I1

As was discussed above, we have studied theDHAP ! GAP process employing both the D andM protonation states of the ligand phosphategroup. Abstraction of a proton from Glu165requires 21.2 kcal/mol and 16.8 kcal/mol for theD and M states, respectively. If we consider zero-point correction energies, these energy barriers arereduced to 18.6 kcal/mol and 14.1 kcal/mol. Thezero-point energy corrections were obtained byrunning quantum mechanical frequency calcu-lations on a reduced subsystem obtained directlyfrom the QM region in the QM/MM system. Ourzero-point values are almost identical with that ofa previous theoretical study using a semiempiricalapproach on a 450 atom model.30 The relativeenergies of DHAP and I1 are 14.9 kcal/mol and11.4 kcal/mol for the D and M state, respectively,indicating that this initial step is endothermic.Thus, the energy profile for the proton abstractionresembles that of a highly asymmetric double-well, where quantum mechanical tunneling effectswill be negligible, in agreement with the modestapparent isotope effect for removal of the H1proton.31 The neutral species, where the phosphategroup is doubly protonated, results in a substantialreduction of the activation barrier and endo-thermicity, 10 kcal/mol and 5 kcal/mol, respect-ively. However, as was pointed out above, whenthe activation free energy required to convert thephosphate group to a neutral species is taken intoaccount, this pathway is not competitive, and weshall not consider it further.

The main geometry difference between the pro-ton abstraction for the D and M states is a closerO2-Lys12 interaction in the M state. Our resultsindicate a decrease in electron density on O2 as thephosphate group is successively protonated. Thisdecrease is more important in the reactant DHAPspecies than in the proton abstraction product, I1,which translates into a larger O2-Lys12 electrostaticstabilization in I1 as the substrate is neutralized.Specifically, an electrostatic potential (ESP) chargefitting indicates a 248 ! 2 36 reduction of theO2 charges in DHAP when neutralizing from D to


M, compared to only a 261 ! 255 reduction forthe I1 proton abstraction product. This chargevariation on the substrate is quantitatively repro-duced in a gas phase calculation.

I1 ! I2. A, B or C competitive pathways

The I1 ! I2 energy profiles, for all of the variouspathways, are less sensitive to the substrate ionicstate than the initial proton abstraction. Path B, anintramolecular proton transfer between the sub-strate O1 and O2, involves a substantially largerenergy barrier, 16 kcal/mol, than the differentsteps along paths A and C. His95, as pointed outin previous studies,16 introduces a steric andelectrostatic repulsive interaction with the intra-molecular proton transfer. The protonation state ofHis95 has been the subject of an active experi-mental and theoretical discussion.13,16 NMR studiesdemonstrated that the imidazole group is neutralat physiological pH values.32 In the TIM-DHAPMichaelis crystal structure at near-atomicresolution, 1NEY.pdb, the imino Nd forms a hydro-gen bond with an amidic NH backbone group, andN1 is tightly hydrogen bonding the substrate O1and O2, accounting for the repulsive interactionobserved in this and previous studies. Therefore,we do not believe that this pathway can contributesignificantly to the observed reaction mechanism,and we do not consider it further in what follows.

Paths A and C involve the formation of anenediol intermediate. In path A, the enediol inter-mediate is obtained via a proton transfer fromHis95 to the substrate O2 atom. This processexhibits activation barriers of 5.2 kcal/mol and4.5 kcal/mol, and is 0.9 kcal/mol and 0.4 kcal/molexothermic, for the D and M protonation states,respectively. In order to obtain I2, the histidine pro-ton is restored from the substrate HO1; this processdisplays activation barriers of 4.2 kcal/mol and3.7 kcal/mol, and overall exothermicities of3.9 kcal/moland 3.1 kcal/mol, for the D and Mstates, respectively. In path C, the enediol inter-mediate is obtained after insertion of H1 into O2.Thus, the Glu165 side-chain has to rotate andtranslate slightly in order to position H1 in anorientation that enables efficient transfer to O2.Due to the difference in energy profile for theinitial catalytic step between the D and M states(strongly favoring the M state, as is discussed

below), and due to the similarities observed forthe two protonation states along path A, we havestudied path C only for the M ionic state. Figure 3shows the result of the Glu165 side-chain samplingsearch after abstraction of H1. This sampling step,where everything but Glu165 is kept frozen,searches for an initial set of reasonable side-chainconformations. The results indicate clearly theexistence of only two possible clusters of confor-mations, which correspond to structures involveddirectly in paths A and C. All conformations inFigure 3 are within 10 kcal/mol of each other.Interestingly, there are more different local minimacorresponding to a path C conformation, althoughthe absolute minimum corresponds to a path Aconformation, which is equivalent to the inter-mediate I1. The lowest-energy path Cconformation lies within 3.2 kcal/mol of the low-est-energy path A conformation. This initialGlu165 sampling is followed by a QM/MM refine-ment step, where all different accessible confor-mations (within 10 kcal/mol) are minimized andwhere the entire system is free to move. After theQM/MM refinement, the path C conformationbecomes 2 kcal/mol more stable than I1, duemainly to a substrate reorientation that produces acloser H1–O2 interaction. Transfer of H1 fromGlu165 into O2 requires 3.5 kcal/mol in activationenergy, is 0.2 kcal/mol exothermic, and producesan enediol intermediate (Figure 3) that is 1.8 kcal/mol more stable than that derived from path A,and only 9.2 kcal/mol above the DHAP reactantspecies. Protonation from H01 to Glu165 forms thesecond intermediate common to all paths, I2. Thistransfer requires 4.7 kcal/mol in activation energyand is 7.0 kcal/mol exothermic.

In considering whether path C is a realisticpossibility, we must also analyze the barrier tointerconversion between the two clusters of confor-mation states for Glu165. This issue turned out tobe difficult to address with a simple reaction pathanalysis; instead, we employ molecular dynamicssimulations, using the same molecular mechanicsforce-field and solvation model employed in ourloop and side-chain modeling efforts, and derivingcharges for the ligand from the QM/MMcalculations. Figure 4 introduces the H1–O2 (blue)and H1–C1 (black) distances for the I1 inter-mediate along four independent moleculardynamic trajectories. For each trajectory, I1 is

Figure 3. Left: Glu165 side-chainsampling. Glu165 lies behind thesubstrate (only partly shown).Conformations within 10 kcal/molare included. Right: enediol inter-mediate for the path C includingseveral water molecules in thevicinity of Glu165.


heated to 300 K in five steps of 2 ps each, for a totalof 10 ps. Then, a constant-temperature moleculardynamics trajectory is integrated for another 25 ps.Only atoms within 10 A around Glu165 areallowed to move. Interconversion consistently isobserved on a picosecond timescale, demonstrat-ing that this process is not a significant hindranceto the adoption of path C which, as discussedbelow, is otherwise energetically competitive.

The presence of the path C conformation signifi-cantly hinders path A. In particular, we havestudied the path A energy barrier for the I1 !enediol process in the presence of the Glu165 Cside-chain conformation. The results indicate thatthe electrostatic stabilization of O2 by H1 increasesthe energy barrier for this step by 5 kcal/mol.Therefore the A side-chain conformation isrequired in order to effectively follow the A path.

The possible implication of Lys12 in a direct pro-tonation of O2 has been investigated. All attemptsto obtain a stable enediol intermediate wereunsuccessful, and the proton is transferred spon-taneously back to Lys12. The results indicate a12 kcal/mol uphill protonation energy profile.

I2 ! GAP protein–ligand complex

Transferring a proton from Glu165 to the sub-strate C2 results in the catalytic product GAP. Thisproton transfer requires the lowest energy barrierin the enzymatic cycle, 2.0 kcal/mol and 1.5 kcal/mol for the D and M states, respectively. The pro-cess is 8.8 kcal/mol and 4.2 kcal/mol exothermicfor the D and M states, which translates into a rela-tive DHAP/GAP energy difference of 2.3 kcal/moland 2.7 kcal/mol. Thus, the protonation state doesnot modify the ratio of DHAP/GAP-bound sub-strate significantly. As in the DHAP ! I1 step, theI2 intermediate is less endothermic with respect toGAP (and DHAP) in the M state. Our resultsagain indicate a closer interaction between O2 andLys12 in the M state as a result of a relativeincrease in O2 electronic density in I2 when thesubstrate is partially neutralized.

Figure 5 summarizes the main energies involvedalong the A and C enzymatic paths.

Opening and closing of the catalytic loop

Prediction of the catalytic loop region in theabsence of substrate

We first describe conformational sampling ofloop 6 in the absence of substrate. The native con-formation of the loop is obtained from the 1YPIcrystal structure33 after addition and optimizationof hydrogen atoms. To investigate the potentialrole of crystal packing forces in determining theobserved loop conformations, we perform looppredictions both on a single protein and in thecrystal packing environment. For the crystalsimulations, we explicitly reconstruct the unit cell,arbitrarily choose one asymmetric unit to simulate,but include all atoms from other surrounding

Figure 4. H1–O2 (blue) and H1–C1 (black) distancesobtained from four independent molecular dynamicstrajectories for the I1 structure.

Figure 5. Main energies along the A and C enzymatic paths. For the A path, as well as for the common structures,DHAP, I1, I2 and GAP, energies for both the M (top) and D (bottom) ionic states are shown. For path C, only theenergies corresponding to the M state have been computed. Energies are in kcal/mol. Zero-point corrections are notincluded.


asymmetric units that are within 20 A. Table 1summarizes the loop prediction results in bothenvironments. Both simulations generate openloop conformations, shown in green, that are veryclose to the experimentally observed conformationin the absence of substrate. The native-like confor-mation in the crystal environment is somewhatcloser to experiment, 0.43 A versus 0.93 A Ca

RMSD. However, in the absence of crystal packingforces, the native-like loop conformation is not thelowest in energy. Rather, a significantly different“closed” conformation (.5 A RMSD from theopen conformation), shown in red, is lowest inenergy, albeit by a small amount (,1 kcal/mol). Asimilar conformation has significantly higherenergy (than the native-like conformation) whencrystal packing is taken into account. These resultssuggest that, in the absence of ligand, crystal pack-ing forces play a significant role in determining theobserved conformation of the loop in crystal struc-tures. In solution, the loop appears to be “floppy”,with several local minima potentially populated,and the crystal packing forces stabilize one of themembers of this “ensemble” to the preference ofthe others. It should be noted that the samplingenergies do not include entropic contributions ofthe protein degrees of freedom (solvation entropyis incorporated into the continuum solvationmodel), which could contribute favorably to thefree energy of the open conformation.

Prediction of the loop region in the presenceof substrate

The native conformations for the loop in bothDHAP and GAP-bound complexes have beenderived from the minimized QM/MM structures,since only the DHAP complex is available experi-mentally (1NEY.pdb). The substrate charges areobtained from ESP charge fitting for the dianionicphosphate protonation state. Since the QM/MMmethodology does not at present handle the pre-

sence of a crystal environment, the loop samplingwith substrate present has been only with a singleprotein chain (no crystal packing). Table 2 summar-izes the loop prediction results for both the DHAPand GAP complexes. As in the case where no sub-strate was present, the ab initio loop samplingreproduces accurately both the DHAP and theGAP native structures, 0.86 A and 0.98 A RMSD,respectively (green ribbon in Table 2). A ball-and-stick representation of the substrate and Gly171aids visualization of the structures of the native-like (closed) and open predicted structures of theloop. In both the DHAP and GAP complexes, thenative-like predicted structure forms a hydrogenbond between the substrate and Gly171, in agree-ment with the observed closed loop conformationin the TIM-DHAP crystal structure. The predictednative-like conformation and the first two openconformations, which are represented by blue andred ribbons, are nearly identical for both sub-strates. The two TIM-DHAP open loops, however,are significantly closer in energy to the native-likeclosed structure than the GAP open loops, by2–3 kcal/mol. The stabilization of the lowestenergy open conformations in the DHAP case isdue to more favorable electrostatics (23.4 kcal/mol) and solvation (22.7 kcal/mol), which ispartially offset by less favorable Lennard–Jones(þ2.1 kcal/mol) and covalent (þ1.4 kcal/mol)energy terms. The potential functional significanceof this observation is considered in Discussion.

Discussion

QM/MM modeling of the catalytic chemistry

We first discuss the effects of QM/MM geometryoptimization of the crystal structure. These calcu-lations reveal a closer interaction between Glu165and the substrate than that observed in the crystalstructure, positioning the carboxylate group of

Table 1. Low-energy conformations of loop 6 for the substrate-free TIM enzyme with (right) and without (left) crystalpacking included in the predictions

No crystal packing Crystal packing

Green (native-like)(0.93/0.0)

Green (native-like(0.43/0.0)

Yellow (2.13/0.5) Blue (2.58/4.5)Blue (2.51/1.0) Red (5.75/6.0)Red (5.28/21.0)

For each low-energy loop conformation, we provide the relative energies (in kcal/mol) and RMSD for the Ca atoms in the loop(residues 166–177), using the format (RMSD/energy).


Glu165 in an optimal geometry for the abstractionof H1. The experimental structure indicated awell-defined electron density, with a low DebyeWaller factor for both Lys12 and His95, in agree-ment with the minor adjustment of both residuesin the QM/MM-optimized DHAP complex.Glu165, with a larger QM/MM reorganization,presents a higher X-ray temperature factor, ,20for the glutamate group (1NEY.pdb).

Abstraction of H1 by Glu165 depends stronglyon the protonation state of the substrate phosphategroup. Obviously, abstraction of a proton from aless anionic species should be more favorable.Furthermore, gas phase calculations on DHAPand I1 indicate a relative increase of electronic den-sity on O2 when abstracting the proton in the Mstate. In the protein–ligand complex, the presenceof a positive residue in hydrogen bond contactwith O2, Lys12 (and, to a lesser extent, His95),translates this increase of electronic density into asignificant electrostatic stabilization. Lys12 hasbeen proposed as a critical residue involved inTIM enzymatic functionalization. Extensive theor-etical calculations on the D state at the QM/MMand QM (reduced models) levels16 have pointedout the role of Lys12 in lowering the H1 abstractionbarrier, which is ,30 kcal/mol in gas phase. Theseprevious studies, however, overestimated theLys12 interaction, because they developed modelsbased on a crystal structure in which the positionof the lysine residue was not well defined. Specifi-cally, along with the proton abstraction by Glu165,Lys12 moved towards O2 by almost 0.7 A, stabiliz-ing I1 and the proton abstraction barrier by almost11 kcal/mol. In the recent DHAP-complex crystalstructure, 1NEY.pdb, a tight active-site and thesalt-bridge between Lys12 and Glu97 preventlarge motions of Lys12. Therefore, their I1 relativeenergy, 6 kcal/mol endothermic with respect toDHAP, and the abstraction barrier, 11.3 kcal/mol,are in quantitative disagreement with our resultsfor the D state, 14.9 kcal/mol and 21.2 kcal/mol,

respectively. Our results present clear evidencethat the monoanionic phosphate protonation stateplays the major role in the enzymatic catalysis.The enzymatic barrier of the M state, 14.1 kcal/mol, is almost 4.5 kcal/mol lower than the barrierin the D state, and agrees exceptionally well withthe experimentally determined estimate of thebarrier height, 13 kcal/mol.4 Hence, accuratemodeling of the phosphate protonation state isessential for reproducing the experimentallyobserved barrier height. As we pointed out pre-viously, even if the effect of the protein on pKa issmall, and the dianionic species is the most stableDHAP complex (presumably by ,0.5 kcal/mol),the singly charged form can still dominate theoptimal reaction pathway. A very similar argument(including the dominance of the monoanion proto-nation state) can be presented for the reverse initialstep GAP ! I2. The energy barrier, however, issubstantially lower, a result observed in gas phase,solution and enzyme model calculations.16

The protonation state does not significantlyaffect the DHAP/GAP population ratio. Interest-ingly, the calculated relative energies of theenzyme with DHAP and GAP, 2.3–2.7 kcal/mol,are quite similar to the experimental DG value insolution (1.9 kcal/mol), and agree quite well withrecent solution and solid-state NMR data that indi-cates that DHAP is the major form present in theenzyme (with ,1% population of GAP or GAPhydrate).12 If we compare the I1 and I2 energyprofiles in Figure 5, it is clear that I1 has the longerlifetime. Adding zero-point corrections to theI2 ! GAP process, would convert this step into aspontaneous transfer. Thus, the first stable inter-mediate in the GAP ! DHAP direction is theenediol species, whereas in the DHAP ! GAPreaction it is I1. The barriers involved to reachboth intermediates differ significantly, 12.0–11.2 kcal/mol (A–C enediol, as obtained fromFigure 5) and 16.8 kcal/mol, respectively. Obtain-ing the enediol intermediate from GAP, however,

Table 2. Low-energy loop 6 conformations for the DHAP and GAP TIM complexes

DHAP conformations (RMSD/energy) GAP conformations (RMSD/energy)

Green (native-like) (0.86/0.0) Green (native-like) (0.98/0.0)Blue (1.41/7.4) Blue (1.48/10.0)Red (2.02/13.0) Red (2.11/16.0)

Energies are in kcal/mol. RMSD is for the Ca atoms in the loop (residues 166–177).


involves a large nuclear reorganization in an uphilldirection, which should affect the kinetics of thisprocess considerably.

Consistent with previous studies, our resultsappear to exclude the intramolecular pathway,path B. Steric and electrostatic repulsive inter-actions by His95 increase the energy barrier forthe intramolecular proton transfer. The energyprofiles for paths A and C indicate that the enediolintermediate is 1.8 kcal/mol more stable in path Cthan in path A. This result represents the firstquantitative measurement of the enediol speciesfor path A and C. The molecular dynamicstrajectories of I1 indicate clearly the existence ofonly two possible conformations for the Glu165side-chain, the path C conformation being morestable. Furthermore, most of the trajectories rotatethe glutamic carboxylic group in the annealing pro-cess, at lower temperatures. Thus, the lifetime of I1in the path A conformation appears to be ,1–2 psat room temperature. These results point to thedominance of path C in the wild-type enzymaticprocess.

Besides the stability of path C, it is important tonotice the substantial mobility of the carboxylategroup, which is in agreement with the moderatelyhigh experimental Glu165 temperature factors. Asobserved in Figure 3, the enediol intermediate forpath C is surrounded by crystallographic watermolecules that are within hydrogen bonding dis-tance of the substrate and the glutamate oxygenatoms. The high mobility of Glu165 might befacilitated by the mobility of these watermolecules, which can stabilize transient hydrogenbond networks. The presence of crystallographicwater molecules in the vicinity of the catalyticbase, sequestered from solution by the binding ofthe substrate, has been proposed by Knowles et al.as a possible explanation for the rapid exchange ofH1 into solution.28 We should note here that theexchange of H1 could affect both path A and pathC. Therefore, even if we used the notation of H1along the enzymatic pathway, it could be moreexact to refer to H1 as the glutamate hydrogenatom after its abstraction by Glu165.

Opening and closing of the catalytic loop

The loop prediction algorithm does an excellentjob of reproducing the observed conformations ofthe catalytic loop both with and without boundsubstrate (,1 A Ca RMSD). We investigated therole of crystal packing forces in determining theloop conformation in substrate-free TIM and con-clude that: (1) crystal packing forces contributesignificantly to the particular “open” loop confor-mation observed in the unligated crystal structure;and (2) the removal of the crystal packing forces islikely to result in multiple loop conformationsbeing populated, including several open confor-mations as well as one closed conformation similarto that observed in structures of TIM with DHAPbound. The crystal packing results are in agreement

with all known X-ray structures as well as thesolid-state NMR data. In the absence of crystalpacking, the energy difference between the closedloops and the open loop is much smaller, suchthat a relative ranking is not clear. While existingdata do suggest that the open form is dominantfor unligated enzymes, both in solution and crystalenvironments, partial occupancy of the closedunligated loop cannot be ruled out on the basis ofkinetic, diffraction or NMR data.

Finally, we note that the closed structures pre-dicted in the absence of substrate, which are simi-lar in both the crystal environment and solution,are qualitatively close in structure to the closedloop conformation obtained experimentally andtheoretically in the presence of substrate. This com-parison is depicted in Figure 6. The principaldifference between the closed structure in thepresence and in the absence of substrate is in theregion that, in the substrate bound complex, ishydrogen bond to the phosphate group. The phos-phate group pulls over a flexible section of theloop so as to form a hydrogen bond with Gly171.The significance of this observation is that itdemonstrates that the closed form of the loop isalready at a low (if not the lowest) free energywithout substrate; addition of substrate makes theclosed form the dominant one, as is discussedfurther below. Thus, evolution has designed thecatalytic TIM loop so that the open form is juststable enough to enable effective substrate distri-bution, but no more. Indeed, the fact that the openform, which is displaced substantially from thebody of the protein in a fashion not typically seenin normal loop structures, is even competitive infree energy with the closed form in solution, indi-cates an unusual, highly optimized structure ofthe loop itself, and of the surrounding proteinenvironment, which in some fashion makes it diffi-cult to form a compact alternative packing in theabsence of substrate.

The loop sampling in the presence of DHAP andGAP indicates two important results. There is aremarkable similarity between the open and closedloop conformations for both substrates. The twoTIM-DHAP open loops, however, are significantlyless endothermic than the GAP open loops. Thesmall differences between the different terms ofthe potential energy do not allow us to drawquantitative conclusions. However, a qualitativeanalysis indicates that both electrostatic and sol-vation terms are central in the opening of the loop.

The difference in relative energies between theopen and closed loops in DHAP and GAP, inaddition to the previous kinetic analysis of theDHAP ! I1 and GAP ! I2 enzymatic steps, arequalitatively consistent with the experimentalresults obtained by Knowles et al. with regard tothe rate-determining processes in each of the twodirections of TIM catalysis. In the DHAP ! GAPdirection, the rate-limiting step appears to be aslow conformational transition (presumed to beopening of the loop and escape of the substrate),


whereas in the GAP ! DHAP direction, the rate-limiting step has been shown to be a proton trans-fer, presumably (based on the results in Figure 5)the final transfer to produce DHAP.

The low-energy open loop conformations thatwe discussed above are not themselves transitionstates, and hence we cannot directly compute rateconstants from them. However, to the extent thatthe transition state resembles the product (likelyin the present case), the energy gap manifestedbetween the open loops is likely to be reproducedin the transition state. From the experimental data,we can estimate the free energy of activation ofloop opening when GAP is bound to be,13.7 kcal/mol, based on converting the rate con-stant quoted above, 7 £ 102 s21, into a barrier viasimple transition state theory (T ¼ 300 K; Equation(2)). This is larger than the experimental rate con-stant for the initial proton abstraction from DHAP(the rate-limiting step in the reactive chemistry inthis direction, as shown in Figure 5), which is con-sistent with the experimental observations:

k ¼kBT

he2DG#=RT ð2Þ

In the GAP ! DHAP direction, the experimentaloverall rate of reactive chemistry can be estimatedto be ,12.2 kcal/mol (from a kcat ¼ 8:7 £ 103 s21Þ:This is consistent with our result, 11.4 kcal/mol,obtained from the DHAP ! GAP barrier,14.1 kcal/mol, and subtracting their relativeenergy (considering zero point contributions to beequivalent for both substrates). The barrier to loopopening must be smaller than this value in orderto explain the experimental results that protontransfer is rate-determining. If we subtract thedifference between low-energy loops in DHAPand GAP (2.6 kcal/mol) from the estimate of thefree energy barrier to loop opening in GAP, weobtain a value of 10.9 kcal/mol, which is againconsistent with the experimental results. Whilethis estimate clearly cannot be viewed as quanti-tatively rigorous, it suggests that the basic physics

of the different behaviors in the two directionshave been captured qualitatively in our variouscalculations. An interesting point to note is justhow close the loop-opening and proton-transferbarriers are, undoubtedly a consequence of evol-utionary optimization in which the structural andreactive chemistry aspects of the problem havebeen balanced exquisitely; there would not bemuch point in lowering the reactive chemistrybarrier to, say, 5 kcal/mol, if the barrier to loopopening remained at 13 kcal/mol.

Conclusions

We have presented a comprehensive picture ofTIM-mediated catalysis of the substrates DHAPand GAP at an atomic level of detail. Excellentagreement with the experimental data is obtainedat both a qualitative and (when available) quanti-tative level. Among the key new findings of thiswork are: (1) the identification of the monoanionicform of the substrate phosphate group as the prin-cipal channel for abstraction of the initial protonfrom DHAP; (2) an energy-based description ofthe opening and closing of the catalytic loop in thepresence and in the absence of substrate (as wellas crystal packing effects), which is consistentwith several experimental observations; (3)detailed elucidation of all of the steps in the cataly-tic cycle in a fashion that can readily explain theisotope washout data reported by Knowles andco-workers.28 The fact that accurate free energiesare obtained for a variety of barriers and inter-mediates, while preserving fidelity to the availablecrystallographic data, constitutes strong confirm-ation that the picture presented here is correct inits detail as well as in broad outline.

While the above results constitute significantprogress in the understanding as to how TIM func-tions, additional work is necessary to provide atruly complete description and to further test thereliability of the QM/MM and protein structure

Figure 6. Comparison of the closed (left panel) and open (right panel) loop predictions for the TIM free substrate(red), with the experimental TIM-DHAP bind complex (yellow).


prediction methodologies. Logical extensions ofthe present efforts along these lines are as follows.

(1) Calculation of the transition state of theloop opening/product release steps for bothDHAP and GAP. This will require adding tran-sition state optimization capabilities to the algor-ithms in our protein structure prediction code.

(2) Prediction of the structures and reactiveenergetics of TIM mutants. A substantial numberof mutant enzymes have been produced, some ofwhich have crystal structures, and kinetic andthermodynamic studies have been carried outfor many of these mutants. The ability of thecomputational methods to reproduce theseresults quantitatively would provide anadditional level of confidence with regard to therobustness of the methodologies.

(3) Calculations predicting the effects of novelmutations, and of catalysis with other substrates.The use of computation in a predictive, asopposed to postdictive, mode, constitutes theultimate test of its validity.

Efforts in these various directions are currentlyin progress in our laboratories.

We have presented the first attempt to combinetwo different techniques, protein predictionsampling methods with QM/MM active-sitechemistry calculations, to obtain a comprehensivedescription of TIM’s complex mechanism of cataly-sis. The combination of these techniques representsa promising new tool for describing both short andlong timescale motion in enzymatic reactions.

Materials and Methods

QM/MM protocol

The QM/MM model has been derived from the recentexperimental structure, 1NEY.pdb.12 The full protein, adimer, has been included in the calculations, althoughonly the active-site of the B chain has been treated at theQM level. The total system contains approximately 8000atoms. All crystallographic water molecules within 20 Aof the substrate are incorporated into the QM/MMsystem. Both the dianionic and the monoanionic, D andM, states are obtained initially after a 20 ps moleculardynamics annealing (to 300 K) of the crystallographicwater molecules. Surface polar amino acid residues,Lys, Arg, Glu and Asp, are neutralized if they do notform a salt-bridge, which yields a zero net charge of theoverall system. Their position is then fixed during allsubsequent optimizations. Such a protocol introducesapproximate solvation effects (i.e. screening of ionizedgroups on the protein surface by high dielectric water).The QM region for all calculations is shown in Figure 1,top left panel. It includes the substrate, Glu165, Lys12and His95. Geometry optimizations are carried outusing the B3LYP function in combination with the6-31G* basis set. All QM calculations have been per-formed with the Jaguar suite of ab initio electronic struc-ture programs. The QM/MM calculations are carriedout with the QSite program,34 which was developed viaa close coupling of Jaguar and the IMPACT35 protein

modeling program of Levy and co-workers. The QM/MM methodology and protocol, as well as extensive vali-dation studies demonstrating excellent agreement withfully QM calculations for peptides and protein active-sites, have been described extensively elsewhere.36,37

These studies suggest that the errors in the QM/MMmethodology are typically less than 1–2 kcal/mol, likelya smaller contributor to the error than uncertainties inrelative energies obtained with the DFT protocol(estimated for metal-containing systems to be of theorder of 2–3 kcal/mol, and probably less in the presentcase). The results obtained above, when compared withexperiment, are consistent with these accuracy estimates,which are derived from our previous QM and QM/MMmodeling efforts for a number of systems.

Methods for high-resolution protein structureprediction and refinement

We have developed methods for high-resolutionprotein structural prediction and refinement based onthe use of an accurate protein molecular mechanicsforce-fields and a surface-generalized Born continuumsolvent model.24 For the molecular mechanics potentialenergy function, we used a recently updated version ofthe OPLS-AA parameterization (OPLS2001), which hasbeen fit to high-level ab initio quantum chemical data formore than 200 rotamer states of the various amino aciddipeptides. This refitting reduced the RMSD of relativerotamer state energy as compared to quantum chemicalcalculations by a factor of ,2, modifications of thetorsional parameters were also made as appropriate toimprove predicted side-chain conformations in a largedatasets of high-resolution protein structures. The newforce-field was demonstrated20 to provide significantimprovements in side-chain prediction as the fit to quan-tum chemical data in experimentally relevant regions ofphase space was improved.

The continuum solvation model has been parameter-ized extensively by Levy and co-workers to provideaccurate predictions for a wide range of small moleculesolvation free energies.38 This parameterization includesthe use of a new non-polar term, which reproduces non-polar solvation free energies more accurately formolecules of different shapes (e.g. cyclic and branchedalkanes) as well as providing first-shell corrections tothe generalized Born electrostatics. Finally, as in the caseof the force-field, we have reparametrized key terms inorder to improve conformational side-chain predictionas compared to experimental data. A particular focushas been the ability to predict the formation of surfacesalt-bridges, which are sensitive to the continuumsolvation parameters for ionizable side-chains. Theunmodified surface-generalized Born model over-predicts the formation of surface salt-bridges by a sub-stantial margin; reparametrization of the effectivescreened pair interaction term for these structures leadsto much more accurate results.

We employ specialized sampling algorithms for bothloop and side-chain prediction.21,22 These algorithmsinclude the use of highly detailed rotamer state librariesfor side-chain conformational searching,23 hierarchicalscreening methods based on steric overlap and approxi-mate electrostatics to rapidly eliminate obviously incor-rect conformations, and a multiscale minimizationalgorithm that is one to two orders of magnitudemore efficient than conventional approaches based, for


example, on conjugate gradient and uniform evaluationof the energy at every minimization step.

The method has been calibrated extensively in itsability to predict loop geometries, for loops of lengths5–12 residues.22 Average RMSDs of the predicted struc-tures are in the range of ,0.5–2.0 A depending uponlength, a considerable improvement as compared toalternative methods in the literature. In many cases,highly accurate predictions (less than 1 A RMSD) areobtained, even for long loops such as that consideredhere, and serious failures of the method are very rare, aslong as the preparation of the structure, including anyions or ligands, is carried out appropriately. In the pre-sent work, modeling of the DHAP and GAP ligands isincorporated into the loop prediction calculation for thecomplex, using the QM/MM methodology to generatepartial charges.

Acknowledgements

The authors thank Dr Sharon Rozovsky for help-ful advice in the preparation of the models. Thiswork was supported, in part, by a grant from theNIH to R.A.F. (GM40526 and GM 52018) and toA.M. (GM66388). M.P.J. acknowledges supportfrom NSF grant 0302445.

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Edited by J. Thornton

(Received 30 June 2003; received in revised form 10 November 2003; accepted 12 November 2003)


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