J. CHEM. SOC. FARADAY TRANS., 1994, 90(14), 2047-2056 Mechanistic Aspects of Biological Redox Reactions involving NADH Part 5.-AMl Transition-state Studies for the Pyruvate-L-Lactate interconversion in L-Lactate Dehydrogenase Shoba Ranganathan and Jill E. Gready" Department of Biochemistry, University of Sydney, NSW 2006,Australia The catalytic mechanism for the interconversion of pyruvate to L-lactate by the enzyme L-lactate dehydrogenase (LDH), in the presence of the cofactor nicotinamide adenine dinucleotide (NAD), has been studied using semi- empirical AM1 quantum mechanical calculations. We have characterized the structure of the LDH transition state (TS), in isolation and in the presence of key active-site groups, using a supermolecule model. An initial investi- gation with isolated substrate and cofactor analogues resulted in TS structures for hydride-ion transfer from the cofactor analogue, planar trans-I-methyldihydronicotinamide to eight conformers of the substrate analogue, protonated pyruvic acid.Fragments of essential active-site residues were then introduced in stages. With trun- cated Arg-171 and His-195 residues, the TS for hydride transfer from the cofactor analogue to the substrate pyruvate resembled the active-site configuration in the X-ray crystallographic structure of the abortive LDH-NADH-oxamate ternary complex. The substrate species is carbonyl-protonated and thus the rate-limiting chemi- cal step is hydride transfer. These results contrast with earlier work indicating that carbonyl-protonated pyruvate is unstable in the free state (K.E. Norris, G. B. Bacskay and J. E. Gready, J. Comput. Chem., 1993, 14, 699). Introduction of the Val-138 fragment gave closer agreement with experiment for the orientation of the cofactor analogue's carboxamide side chain in the TS and for the reversibility criteria for the reaction. For each TS located, stable reactant and product complexes have been isolated by following the reaction coordinate, and the optimized structures, energies and charge distributions of the TS, stable reactant and product complexes and the isolated reactants and products are reported. There is significant charge transfer in the TS, with a charge of ca. +0.4 on the nicotinamide species. The catalytic conversion of pyruvate to L-lactate in L-lactate dehydrogenase (LDH), in the presence of the cofactor nicotin- amide adenine dinucleotide (NAD), involves the transfer of both a proton and a hydride ion:' CH,(CO)CO,-+ NADH + H+ e CH,CH(OH)CO,-+ NAD+ The overall reaction kinetics have been the subject of exhaus- tive experimental investigation^'-^ while site-directed muta- genesis and protein engineering ~tudies~-~ have identified the key residues in the active site and their roles.In the enzy- matic reaction, the proton donor has been identified as His-195 (residue numbering as defined by Eventoff et d7),by pH titration and chemical modification work while the hydride ion migrates from the reduced form of the cofactor, NADH.' From the X-ray crystallographic structure of the ternary LDH-NADH-oxamate complex [Protein Data Bank (PDB) entry 1LDM8], several key residues have been identi- fied in the active site, with roles ascribed to binding and reac- tion involving the active complexes and/or the transition state (TS).While Arg-171 (substrate binding) and His-195 (substrate binding and proton donor) are essential, other resi- dues having a possible direct bearing on the reaction mecha- nism and their suggested roles are: Arg-109 (part of a flexible loop) in the activation of His-195 and stabilization of the TS, Asp-168 in the pK, modulation of His-195, and Val-138 in the orientation of the cofactor's carboxamide side chain. A view of the active site, showing the enzyme-bound substrate, the nicotinamide ring of the cofactor and key binding and catalytic residues and the peptide backbone atoms of the mobile loop, is presented in Fig.1. The enzymatic reaction involves the formation of a chiral centre on the active carbon of the substrate and is stereospecific both for the transfer of the pro-R-hydrogen of NADH and for the formation of only one stereoisomer of lactate, i.e. L-lactate. The accepted mechanism involves a concerted proton and hydride transfer' taking place in a hydrophobic and highly charged active site from which solvent has been excluded by the closure of a flexible loop, triggered by cofactor and sub- strate binding. The transition state has been suggested to be more pyruvate-like than lactate-like.g The enzyme itself is proposed to have evolved to bind preferentially the higher- energy pair, pyruvate and NADH, over the lactate-NAD+ pair,'*6 in accordance with the theory of matched internal states," which postulates that the kinetically significant tran- sition state will lie between internal intermediates of approx- imately equal Gibbs energy.Also, the orientation of the carboxamide side chain of the nicotinamide may have a direct bearing on cofactor activation. In the enzyme-bound cofactor, this side chain adopts trans geometry although the cis form is more stable in the free cofactor." It has been proposed that out-of-plane orientations of the side chain could facilitate the catalytic reaction.', Whether the stereo- chemical directionality and control is provided by a non-planar distortion of the nicotinamide ring in the transition state' is another interesting question.Recent theoretical studies on LDH include an AM1 study on the substrate model formaldehyde," a PM3 potential-energy surface calculation'6 and computation of electrostatic interaction energies.' However, several questions noted above still need to be addressed; in particular, the enzyme reaction mechanism at a molecular level, the nature of the transition-state species, the relative energies of the stable intermediates, the molecular components of the charge dis- tribution for the species involved in the transition state and the role of key active-site residues. In the AM1 study of the LDH reaction by Wilkie and Wil- liams,' the substrate pyruvate was substituted by formalde- hyde, the cofactor by dihydropyridine and the proton donor His-195 residue by protonated imidazole.Since LDH is spe- cific for the reduction of 2-0x0 acids, containing the group Val-138 Fig. 1 LDH active site, based on the PDB structure of the LDH- NADH-oxamate ternary complex (1LDM) : (a)stereo representation and (b) two-dimensional view, with key residues and distances (in A) labelled. Dashed lines represent hydrogen bonds. -CO-CO2 -, this choice for the substrate is not a good rep- resentation of the substrate pyruvate, particularly given indi- cations from our earlier work of the unusual properties of protonated pyruvate.' '*I9 The cofactor analogue used, dihy- dropyridine, is unsubstituted and cannot account for the sug- gested activation and orientation effects (cisltrans and in-plane/ out-of-plane) of the carboxamide side chain.Andres et ~1.'~have conducted an extensive exploration of the PM3 energy hypersurface calculation for the pyruvate reduction mechanism in LDH, using pyruvate (see Fig. 2) as substrate, 1-methyldihydronicotinamide as the cofactor ana- logue, l-methylguanidinium ion representing the Arg-171 residue and protonated 4-methylimidazole ion as the proton donor, His-195 (illustrated in Fig. 3). This study reports the potential-energy surface for the two processes : proton trans- fer from the protonated imidazole to the carbonyl oxygen of the pyruvate and hydride-ion transfer from nicotinamide to the carbonyl carbon of pyruvate.The TS for the catalytic reaction has been located and the overall process has been interpreted as a stepwise mechanism in which the initial step is proton transfer, followed by hydride-ion migration. Struc- tures corresponding to important points on the energy hyper- surface have been provided. However, in all the structures shown, the carboxamide side chain of the cofactor analogue adopts a novel orientation, pointing towards the guanidinium moiety in contrast to its orientation towards the imidazole J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 d Fig. 2 Structures of substrate species: (a) protonated pyruvate, (b) protonated pyruvic acid, (c) pyruvate and (d) pyruvic acid.r3 is the 06-H bond length in (a). ring in the lLDM structure. Whether reorientation of the carboxamide to reflect the X-ray crystallographic structure would have an impact on the energy hypersurface is uncer- tain and requires study. Also, the molecular charge distribu- tion for the TS structure has not been provided. In the systematic investigation of the LDH enzyme mecha- nism, the structures and energetics of possible substrates and intermediates involved in the catalytic step have been report- ed in our earlier quantum chemical In the present work, we have carried out quantum mechanical cal- culations on the structure of the LDH transition state, in iso- lation and in the presence of key active-site groups, using a supermolecule model.Following an initial computational investigation of isolated substrate and cofactor analogues, the active-site residues have been introduced in stages. At each face b "b)-l-c2 '. N4*l @04 Fig. 3 Structures of (a) trans-1-methyldihydronicotinamide (cofactor analogue), (b) 1-methylguanidinium ion (Arg fragment), (c) Cmethylimidazolium ion (His fragment), (6)acetamide (Val fragment) and (e)acetate ion (Asp fragment). r4 is the N1-H bond length in (c). J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 stage, the possibility of TSs involving both cis and trans con-formers of the carboxamide side chain on the nicotinamide moiety were investigated. The optimized structures, energies and charge distributions of the TS species obtained and the corresponding reactant and product complexes are reported.Computational Models In the enzyme environment, the substrate pyruvate forms an ion pair with Arg-171 which effectively neutralizes its charge. Thus, in addition to pyruvate, the corresponding neutral form, pyruvic acid, was considered as a second model sub- strate. In ref. 18, four possible non-concerted reaction mecha- nisms were set out corresponding to protonation of the carbonyl oxygen of pyruvate and pyruvic acid followed by hydride transfer to the carbonium ion so formed [(i) and (ii)], as well as hydride transfer to the carbonyl carbon of pyruvate and pyruvic acid, followed by protonation of the carbonyl oxygen [(iii) and (iv)]. These postulated mechanisms are now investigated by studying the hydride-transfer reaction from NADH to pyruvate or pyruvic acid or their protonated forms, protonated pyruvate and protonated pyruvic acid.The cofactor NADH has been modelled by the cis and trans con-formers of 1-methyldihydronicotinamide, as in an earlier study on dihydrofolate reductase (DHFR) substrate ana-logues,2l l-methylnicotinamide cation representing the oxi- dized form of the cofactor. At the outset, the hydride transfer from l-methyldihydro- nicotinamide to all the stable of the four substrate species, (a) protonated pyruvate, (b) protonated pyruvic acid, (c) pyruvate and (d) pyruvic acid, has been studied, with the carboxamide side chain in both cis and trans orientations.The chemical structures of the lowest- energy conformers of these substrate species are given in Fig. 2, while that of 1-methyldihydronicotinamideis shown in Fig. 3. The C4 hydrogen labelled H, is transferred to the substrate as a hydride ion. The existence of TS structures for any of these proposed reactions would indicate at least a possibility of such a pathway in the reaction. Different relative orienta- tions of the substrate analogues and the nicotinamide moiety were first sampled in order to locate the lowest-energy TS. Starting from each transition-state structure obtained, con- strained reaction paths22 were followed to locate possible minima, representing the corresponding stable reactant and product complexes. While the gas-phase study of isolated substrate and cofac- tor species permits several favourable relative orientations of the reactants, the active-site residues in the enzyme would impose directional constraints on the approach of the reac- tants.Also, the gas-phase model cannot mimic the true enzyme environment or test for the proposed concerted reac- tion. Therefore, in the second stage, we have introduced frag- ments of two essential residues in their X-ray crystallographic positions:' Arg-171, to bind the carboxylate group of the substrate pyruvate and His-195 as proton donor. The cofac- tor analogue, trans-1-methyldihydronicotinamide,was also initially positioned in its X-ray crystallographic location. With the inclusion of the Arg-171 fragment and protonated His-195 moiety as proton donor, the choice of the substrate species is limited to pyruvate. Arg-171 has been modelled by protonated 1-methylguanidine while His-195 has been rep- resented by protonated 4-methylimidazole, as illustrated in Fig. 3.These fragments have also been used in the theoretical studies of Krechl and co-~orkers.~~*~~ In the TS structure determination, no a priori assumptions have been made as to the mechanism of the reaction: the reactants and products alone have been defined, so that the nature of the transition state would reveal the underlying mechanism. The reactants comprise 1-methylguanidinium cation, 4-methylimidazolium cation, pyruvate and 1-methyldihydronicotinamide,while the product species are 1-methylguanidinium cation, 4-methyl- imidazole, lactate and the 1-methylnicotinamide cation.The 1-methylguanidinium cation is chemically unchanged by the redox reaction. In order to test any dependence of the carboxamide side- chain orientation on the TS, the next stage was to introduce the fragment, CH3CONH2 , representing Val-138, into the supermolecule model. Acetamide was chosen as a suitable model for this residue, to represent the backbone carbonyl of Val-138 in the X-ray structure' and the neighbouring atoms of the peptide backbone. With the introduction of this frag- ment, the rotation of the carboxamide side chain is restricted in a manner similar to that apparent in the enzyme. Finally, Arg- 109 (represented by the 1-methylguanidinium cation, as in the case of Arg-171) and Asp-168 (modelled by acetate ion) were added to the system, to reproduce the charged functional groups of other key residues in the enzyme active site.The structures of the fragments depicting Val-138 and Asp-168 are shown in Fig. 3. Computational Methods The geometries of all equilibrium and TS structures were optimized at the semi-empirical level of theory. The AM1 methodology of Dewar et was adopted, since it is con- sidered the best general-purpose semi-empirical treatment available and, in particular, it provides a better description of intermolecular interactions than MNDO or MIND0/3.2s The calculations were performed on an IBM RS 6000 work-station using the SYDPAC program,26 which incorporates efficient geometry ~ptimization~~ and transition-state search algorithms based on the algorithm of Dewar et aL2' and the GDIIS method of Csaszar and P~lay.~~ Transition states were initially located using the method of Dewar et d2'and refined by the GDIIS procedure.*' The relaxed potential- energy surface in the vicinity of the TS was then calculated as a two-dimensional grid in terms of two internal coordinates describing the path of the migrating species.Structures corre- sponding to low-energy regions of the grid, on either side of the saddle point, were then minimized to obtain stable inter- mediates, representing reactant and product complexes. Results and Discussion Transition-state Structures Hydride Transfer from 1-Methyldihydronicotinamideto Isolated Neutral and Protonated Substrate Species The nicotinamide ring of the cofactor is represented as planar in the X-ray crystallographic structure for the LDH-NADH- oxamate ternary complex' with the carboxamide side chain in a trans coplanar orientation.Taking account of these observations as well as previous AM1 and ab initio results on geometry optimizations of oxidized and reduced nicotina- mide species," the nicotinamide ring was introduced as a planar species. The carboxamide side chain was constrained to be coplanar with the nicotinamide ring, in either the trans or cis orientation. The coplanarity constraint was relaxed only if no TS structure could be obtained with the fixed car- boxamide orientation.Protonated Pyruuate. A TS search was carried out for the reaction of protonated pyruvate (bearing formal charge 0) and 1-methyldihydronicotinamide,yielding L-lactate and 1-methylnicotinamide cation as products, using AM 1 opti- mized geometries'8*20*21 as starting structures. No transition state was located for this substrate species, with either cis-or trans-1-methyldihydronicotinamide. The unusually long Cl-C2 bond (1.6-1.7 A18) in all protonated pyruvate con- formers is further elongated during the TS search, so that the reactant supermolecule tends towards decarboxylation. This observation is in agreement with the behaviour of the proto- nated pyruvate species during geometry optimization,' resulting in a methylhydroxy carbene-carbon dioxide complex.Thus, hydride transfer from the cofactor analogue to protonated pyruvate is unsuitable for modelling the cata- lytic reaction. Protonated Pyruuic Acid. With protonated pyruvic acid (formal charge +1) as the substrate analogue and trans-l-methyldihydronicotinamide, eight transition states (designated TSla-TSlh, in the order of increasing heat of formation) were located. The products of this reaction are L-lactic acid and the 1-methylnicotinamide ion. These struc- tures have been verified as saddle points, by the existence of a single negative frequency of vibration. The TS structures cor- respond to the eight conformers of carbonyl-protonated pyruvic acid.18 For each TS, stable reactant and product complexes have been isolated, by following the reaction coor- dinate backwards or forwards.The relative orientation of the substrate and cofactor species in the TSs is dependent on intermolecular hydrogen-bonding interactions between the OH groups of the protonated pyruvic acid and the carbonyl oxygen of the carboxamide side chain. Therefore, the orienta- tion of the nicotinamide moiety with respect to the proto- nated pyruvate species shows little correspondence to that of the cofactor and the inhibitor, oxamate, in the ternary complex 1LDM.8 Similar intermolecular hydrogen-bonding patterns involving the carboxamide carbonyl oxygen have been observed in the study of the hydride-transfer reaction between 1-methyldihydronicotinamide and folate and dihy- drofolate analogue substrates of DHFR.21 The structure of the lowest-energy transition state (TSla) is shown in Fig.4. The heats of formation of the free reactant and product species, the TS and the reactant and product complexes and the relevant intermolecular geometric parameters (defined by rl, r2 and 6), for the structures TSla-TSlh are listed in Table 1. No transition states were identified with the cis cofactor analogue, in contrast with the model DHFR reaction21 where both cis and trans cofactor analogues lead to TS struc- tures. Solely in the case of TSlh, the TS could not be located when the trans carboxamide side chain was constrained to the plane of the nicotinamide ring. This side-chain torsion was then relaxed, in order to locate the TS and the corre- sponding reactant and product complexes. For these struc- tures, the torsion of the carboxamide side-chain (4)shows significant deviations from the normal value of 180" (Table l), with the carbonyl group directed towards the si face3' of the cofactor analogue. The existence of TS species establishes this reaction as a possible pathway for the LDH enzymic reaction.The sub- strate species in the TS is carbonyl protonated. On the basis of these results, a fast protonation of the substrate carbonyl group followed by hydride-ion transfer from the cofactor appears tenable as a mechanism for the LDH catalytic reac- tion. Pyruuate and Pyruuic Acid. Pyruvate (formal charge -1) and pyruvic acid were then studied for possible hydride transfer from cis-and trans-1-methyldihydronicotinamide, resulting in the formation of deprotonated L-lactate and de- protonated L-lactic acid, respectively, as products, along with the oxidized form of the cofactor, 1-methylnicotinamide cation.For both of these substrate analogues, no transition- state structures were found. Thus, the possibility of hydride J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 N H U NIC Fig. 4 Transition state (TSla) for hydride (HR)transfer from trans-1-methyldihydronicotinamide(NIC) to substrate protonated pyruvic acid (PPA): (a) stereo representation and (b) two-dimensional view. rI, r2, 8 and 4 are the intermolecular parameters. The dashed line represents the intermolecular hydrogen bond (distance given in A).transfer prior to protonation of the substrate moiety seems unlikely. Hydride Transfer from 1-Methyldihydronicotinamideto Pyruuate in the Presence of Arg-171 and His-195 Fragments With the introduction of the Arg-171 fragment (l-methyl- guanidinium ion), the substrate pyruvate forms an ion pair, bearing no net charge. The overall formal charge on the reac- tants (1-methylguanidinium ion, protonated 4-methyl-imidazole, pyruvate and 1-methyldihydronicotinamide) remains +1, the proton and the charge residing with the 4- methylimidazole species. On the other hand, for the product species, the unit positive charge is on the l-methylnicotin- amide ion, the 4-methylimidazole is neutral, while the proton and the hydride ion are now associated with L-lactate.The starting structure for each reactant and product species was its fully optimized AM 1 geometry. The initial intermolecular arrangement of the reactant and product species was based on the X-ray crystallographic locations of the heavy atoms from the Protein Data Bank entry lLDM,' i.e. the cofactor analogue was trans planar and the cis orientation (4= 00) was generated from this geometry by rotation of the carbo- xamide side chain. However, no planarity constraints were imposed on the nicotinamide ring and all coordinates were optimized during the TS search. In Fig. 5, a stereo view of the TS structure (TS2) obtained is given. The different molecular fragments are held together by electrostatic and hydogen-bonding interactions.A com- parison of TS2 with the corresponding atomic coordinates from the PDB entry lLDM, illustrated in Fig. 1, shows that the relative orientations of the reacting species are remark- ably similar, considering the complete optimization of all atomic positions and the absence of the protein backbone to restrict the movement of the Arg-171 and His-195 fragments J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 AM1 results for the hydride-ion transfer reaction from trans-1-methyldihydronicotinamideto eight conformers of proto- nated pyruvic acid ~~ 4H/ species kcal mol-' rl/A r2/A $/degrees 4/degrees TSla R 57.58 co 1.126 -180.0 RC 27.66 2.885 1.128 121.4 180.0 TS 36.90 1.596 1.235 142.7 180.0 PC -7.22 1.129 8.332 302.4 180.0 P 2.97 1.130 03 -180.0 TSlb R 60.66 00 1.126 -180.0 RC 29.43 3.957 1.128 244.4 180.0 TS 37.90 1.601 1.228 206.3 180.0 PC -8.39 1.129 6.316 129.4 180.0 P 1.58 1.129 03 -180.0 TS lc R 58.18 00 1.126 -180.0 RC 27.89 3.221 1.128 108.8 180.0 TS 38.07 1.61 1 1.229 143.0 180.0 PC -7.97 1.131 4.804 50.2 180.0 P 1.74 1.128 00 -180.0 TSId R 67.84 co 1.126 -180.0 RC 33.99 3.861 1.128 248.1 180.0 TS 42.50 1.635 1.218 207.9 180.0 PC -9.17 1.131 7.914 276.0 180.0 P 5.60 1.130 00 -180.0 TSle R 67.84 co 1.126 -180.0 RC 34.08 3.479 1.128 255.3 180.0 TS 42.50 1.636 1.218 207.9 180.0 PC -11.49 1.132 8.137 71.7 180.0 P 5.60 1.130 co -180.0 TSlf R 67.47 co 1.126 -180.0 RC 32.44 4.117 1.126 100.5 180.0 TS 46.16 1.621 1.230 147.0 180.0 PC -9.21 1.132 8.136 78.8 180.0 P 5.60 1.130 00 -180.0 TSlg R 67.31 co 1.126 -180.0 RC 29.44 3.950 1.127 115.5 180.0 TS 48.10 1.699 1.204 146.7 180.0 PC -12.02 1.131 7.136 284.5 180.0 P 1.74 1.130 co -180.0 TSlh R 67.85 00 1.126 -180.0 RC 34.06 3.156 1.129 123.2 165.5 TS 56.5 1 1.602 1.242 161.6 149.2 PC -6.40 1.131 5.707 300.14 126.8 P 5.60 1.130 co -180.0 For each transition state (TSla-TSlh) obtained, heats of formation (AfH/kcal mol- ') and structural parameters, r1, r2, 6 and 4 (Fig.4) are given, for the free reactant (R) and product (P) species, the tran- sition state (TS) structure and the stable reactant and product com- plexes (RC and PC). Structures TSla-TSlh correspond to protonated pyruvic acid conformers PPA1, PPA9, PPA3, PPA17, PPA11, PPA13, PPA7 and PPA15, respectively, of ref.18. Boltzmann-weighted mean AfH values: R, 57.80; RC, 27.87; TS, 37.17; PC, -11.82 and P, 1.73. and to restrain the cofactor to a catalytically favourable orientation. With the introduction of two residue fragments, the amino group of the carboxamide side chain is hydrogen bonded to N1 of the imidazole moiety. On the other hand, the side chain carbonyl group is not involved in the hydrogen-bonding network, in contrast to its major role in the intermolecular arrangement observed for TS 1. This change in the carbonyl group hydrogen-bonding arrange- ment from TS1 to TS2, produces a molecular complex with similar hydrogen-bonding interactions to that observed in the enzyme ternary complex structure (1LDM).In the crystal structure,* the carbonyl oxygen of the carboxamide side chain of the cofactor appears to be hydrogen bonded to a 205 1 0 €30 ARG ON OH C Fig. 5 Transition state (TS2) for hydride (HR)transfer from trans-l-methyldihydronicotinamide(NIC) to substrate pyruvate (PYR), in the presence of 1-methylguanidinium ion (ARG) and protonated 4-methylimidazole (HIS): (a) stereo representation and (b) two-dimensional view. Dashed lines represent intermolecular hydrogen bonds. Key intermolecular distances (in A) are given. water molecule, while the amino group on the side chain par- ticipates in hydrogen bonding to the enzyme. The TS structure represents the hydride-ion transfer step, from the cofactor analogue to the carbonyl-protonated pyru- vate.By following this reaction coordinate, stable reactant and product complexes were located. Interatomic distances r3 and r4 indicate the position of the transferred proton with respect to 06 of the substrate [Fig. 2(a)] and N1 of the 4- methylimidazolium ion [Fig. 3(c)], respectively. The heats of formation, the intermolecular orientation coordinates, rl, r2, 8 and 4 (defined as for TSl), and the proton-transfer coordi- nates, r3 and r4, for the free reactants and products, TS2 and the reactant and product complexes, are presented in Table 2. In both reactant and product complexes, the substrate species carries the imidazole proton, while its carboxylate group forms an ion pair with the 1-methylguanidinium cation.Attempts to locate a TS corresponding to the proton transfer from the 4-methylimidazolium ion to the substrate pyruvate were unsuccessful, in agreement with the PM3 results.I6 The TS search also failed with the cis-cofactor analogue. The values of rl, r2 and 8 for TS2 are, respectively, 1.422 A, 1.302 A and 173.0", which are similar to the corresponding PM3 results, 1.417 A,1.308 8,and 172.9", of Andres et ~1.'~ However, there is considerable difference in the orientation of the cofactor moiety in TS2 compared with that shown in ref. 16. To quantify this difference, the orientation of the nicotin- amide (n) moiety with reference to the substrate pyruvate (p) can be defined by z, the dihedral angle Nl(n)-C4(n)-C2(p)-Cl(p) (numbering as in Fig.1 and 2). In TS2, z has a value of 174.2" compared with the value of 195.3" for the PDB entry, ILDM. The value of z computed 2052 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 AM1 results for the hydride-ion transfer reaction from trans-1-methyldihydronicotinamideto pyruvate, in the presence of (a) Arg-171 and His-195 and (b) Arg-171, His-195 and Val-138 residue fragments, characterized by transition states (a)TS2 and (b) TS3 species Af H/kcal mol -' r1/A 4 eldegrees +/degrees r3/A rJA TS2 R 178.1 1 M 1.126 -180.0 co 0.997 RC 54.43 3.049 1.128 150.4 149.4 1.002 2.455 TS 73.85 1.422 1.302 173.0 148.5 0.985 2.683 PC 37.33 1.126 3.276 101.7 153.5 0.967 4.089 P 173.49 1.124 ca -180.0 0.967 a3 TS3 R 127.43 03 1.126 -180.0 co 0.997 RC -24.68 4.704 1.127 117.3 174.0 1.961 1.021 TS 14.80 1.415 1.303 170.9 201.7 0.983 2.622 PC -29.11 1.123 3.247 111.6 172.2 0.970 4.21 1 P 122.8 1 1.124 ca -180.0 0.967 co The heats of formation (A,H/kcal mol-'), structural parameters for the reaction coordinate, rI, rz, 8 and 4 (Fig.4) and proton-transfer coordinates, r3 (Fig. 2) and rg (Fig. 3), are given for the free reactant (R) and product (P) species, the transition-state (TS) structure and the stable reactant and product complexes (RC and PC). for the PM3 transition state16 from the published Cartesian coordinates is only 79.5", with a nicotinamide ring rotation of 115.8' from its PDB orientation.Also, there is considerable difference in the heat of formation values for TS2 (73.85 kcal mol-') and the corresponding TS (44.73 kcal mol- ') report-ed by Andres et The non-planar deformation of the amino group of the car- boxamide side chain can be attributed partly to the inherent limitation of the AM 1 model in representing n-resonance effects in the amide group. The amino group of the carbox- amide side chain is hydrogen-bonded to N1 of 4-methylimidazole. This favourable interaction is lacking for the cis orientation of the carboxamide group and is probably the reason why a TS structure corresponding to cis-l-methyl- dihydronicotinamide has not been located. The nicotinamide ring retains its planar geometry in the transition state, although the carboxamide side chain is 32" out of plane (4 = 148.5'), with the carbonyl group directed towards the si face of the nicotinamide ring.The transition state obtained for this reaction clearly con- tains the protonated pyruvate species, bound to the gua- nidinium ion by the formation of an ion pair. This observation leads us to two important conclusions. First, iso- lated protonated pyruvate, which exhibited an abnormal Cl-C2 bond elongation and was prone to decarboxyl-ation," is stabilized by the formation of an ion pair with the guanidinium ion. The ion pair formed by protonated pyru- vate and 1-methylguanidinium ion in the TS is stable under AM1 geometry optimization conditions and the Cl-C2 bond length (1.546 A) of the protonated pyruvate species is similar to the value 1.508 A, calculated for the lowest-energy conformer of protonated pyruvic acid.' Similar results were obtained by an independent AM1 study on the pyruvate- protonated 1-methylguanidine ion pair, for which the com- puted Cl-C2 bond length (1.513 A) of the pyruvate species is almost identical to that determined for pyruvic acid (1.514 A).2o Secondly, as the carbonyl oxygen of the pyruvate moiety is protonated in the transition state (the reactant species protonated 4-methylimidazole being deprotonated in the TS), the catalytic mechanism is most probably stepwise, with protonation preceding hydride transfer.Hydride Transfer from 1-Methyldihydronicotinamideto Pyruvate in the Presence of Arg-171, His-195 and Val-138 Fragments The addition of an acetamide moiety (shown in Fig.3), rep- resenting the Val-138 residue, to the reactant and product models described above, introduces a hydrogen-bonding interaction of the backbone carbonyl of Val-138 with the amino group of the trans carboxamide side chain of 1-methyldihydronicotinamide. At the outset, the acetamide moiety occupied the position of the corresponding heavy atoms in the PDB entry 1LDM. The transition-state structure obtained (TS3 in Fig. 6) with fragments of three residues (Arg-171, His-195 and Val-138) is quite similar to TS2. The orientation coordinates, rl, r2 and 8, are almost unchanged: 1.416 A, 1.303 A and 170.9", respec- tively. The orientation of the nicotinamide ring with reference ARG 'R AL Fig.6 Transition state (TS3) for hydride (H,)transfer from trans-l- methylidihydronicotinamide (NIC) to substrate pyruvate (PY R), in the presence of 1 -methylguanidinium ion (ARG), protonated 4-methylimidazole (HIS) and acetamide (VAL): (a)stereo representation and (6) two-dimensional view. Dashed lines represent intermolecular hydrogen bonds. Key intermolecular distances (in A) are given. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 to pyruvate (z = 172.8") remains almost unchanged compared with TS2 (z = 174.2"). The carboxamide side chain is now turned only 19" out of the plane of the nicotinamide ring, but towards the re face3' (4 = 201.7"). Although the carboxamide side chain is not coplanar with the nicotinamide ring, as in the crystal structure for the ternary complex (lLDM), the Val-1 38 fragment mimics reasonably well the carboxamide hydrogen-bonding interaction encountered in the enzyme environment.A comparison of TS3 with the PDB structure (Fig. 1) shows that the acetamide fragment is slightly dis- placed compared with the location of the Val-138 residue. This movement is a consequence of the residue fragments not being tethered to the peptide backbone of the enzyme. The Val-1 38 fragment is able to counteract the hydrogen-bonding interaction of the amide hydrogen atoms with N1 of the imidazole ring found in TS2 and partially rectify the out-of- plane torsion of the carboxamide side chain. The cis orienta-tion of the carboxamide side chain is repulsive towards the carbonyl group of the Val-138 fragment and no TS resulted from this conformer. Table 2 lists the heats of formation, the orientation coordinates (rl, r2, 0 and 4), and the proton- transfer coordinates (r3 and r4) for the isolated reactant and product species, the transition state and the stable reactant and product complexes for the substrate-cofactor system in the presence of three residue fragments.TS3 contains protonated pyruvate as the substrate species, forming an ion pair with the 1-methylguanidinium ion, as in the case of TS2. However, the substrate species in the corre- sponding reactant complex is not protonated, in contrast to the reactant complex in TS2. This is reflected in the Lowdin bond orders31 calculated for r3 and r4 of 0.028, 0.785 and 0.841,0.004 for the reactant complexes corresponding to TS3 and TS2, respectively, compared with values of 0.850 for r3 in protonated pyruvic acid '' (lowest-energy conformer) and 0.857 for r4 in the 4-methylimidazolium ion.As for the TS2 calculations, no TS could be isolated for the proton-transfer step. Thus, while the proposed mechanism of substrate pro- tonation, followed by hydride transfer from the cofactor ana- logue, is not perturbed by the introduction of the Val-138 fragment, it appears that the stage of the protonation step may be very sensitive to the details of the active-site environ- ment. Comparison of the values of rl and r2 for the TSs obtained so far (Tables 1 and 2) indicates that in all TS1 structures the migrating hydride ion is closer to the nicotinamide species than to the substrate species, i.e.it is reactant-like. This is also the case for TS2 and TS3, except that the TS is less reactant-like than TS1. 8 values for TS2 and TS3 indicate a roughly linear reaction coordinate, while those for TSla- TSlh are quite variable but non-linear. Hydride Transfer from 1-Methyldihydronicotinamideto Pyruvate in the Presence of Arg-171, His-195 and Val-138 Fragments :Inclusion of Arg- 109 and Asp- 168 Fragments Two other key residues, Arg-109 (implicated in polarizing the carbonyl group of the substrate pyruvate and in stabilization of the transition state'v4) and Asp-168 (forming a charge couple with His-195 and implicated in the stabilization of protonated Hi~-195~),have been modelled by the 1-methylguanidinium ion (as in the case of Arg-171) and acetate ion (Fig.2), respectively. The fragments representing these residues were initially placed in their respective X-ray crystallographic locations. Their inclusion in the super-molecule at the reactant or product level, both individually and together, did not result in any further TS structures. In fact, energy-minimized structures for the reactant and product ensembles could not be obtained. While the Arg-109 fragment repelled the protonated His-195 fragment, the 2053 Asp-168 fragment abstracted the H atom attached to N3 of the 4-methylimidazole ion.The inability to locate a TS struc- ture suggests that, within the limitations of the present model, these residue fragments do not play a major role in the stabil- ization of the transition state. Since the residue fragments are not tethered to a protein backbone, the individual reactant and product species are able freely to adopt orientations which would be impossible in the enzymic environment. This stage represents the limit of our simple supermolecule approach to the highly complex LDH catalytic system. Activation Energies for Reactions represented by TS1,TS2 and TS3 The activation energies (E,) for the hydride-transfer reactions characterized by TS1, TS2 and TS3 have been computed from the heats of formation, given in Tables 1 and 2 and illustrated in Fig.7, and are presented in Table 3. The E, values have been calculated relative to the free reactants and the reactant complex, for the forward reaction, and relative to the free products and the product complex, for the reverse reaction. In the case of TS1, the heats of formation have been averaged over the eight TS structures located (TSla-TSlh) and the Boltzmann-weighted mean values given in Table 1 were used to compute E, . Considering E, (in kcal mol- ') for the free reactants and products [reaction (1) of Table 31, the ,150 , , , 100-50-0--50 ' I I I I I R RC TS PC P species Fig. 7 Heats of formation (Af H/kcal mol- ') for the free reactants (R) and products (P), the reactant and product complexes (RC and PC) and the transition state (TS) for TS1 (---) (mean values from Table l), TS2 (-.-.) and TS3 (-). Substrate species for TSl contain the carboxylic acid group (C0,H) while those for TS2 and TS3 contain the carboxylate function (C02-). Table 3 Activation energies (EJ for the forward and reverse reac- tions characterized by TS1, TS2 and TS3 and the corresponding dif- ference in E, (AE) reaction EJrelative to TS1 TS2 TS3 (1) forward reactants -20.6 -104.3 -112.6 reverse products 35.4 -99.6 -108.0 -56.0" -4.6" -4.6" (2) forward reactant complex 9.3 19.4 39.5 reverse product complex 49.0 36.5 43.9 -39.7b -17.1b -4.4b " AE,. AE2. 2054 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 4 Total net AM1 charges for substrate (SUB), hydride ion (HR),cofactor analogue (NIC), fragments of Arg-171 (ARG), His-195 (HIS) and Val-138 (VAL) species at the transition states (TS)and the corresponding reactant and product complexes (RC and PC) for TS1, TS2 and TS3; partial charges for atoms C8 and 09 of the cofactor analogue and the carbonyl bond dipole (p/D)are also given AM1 charges species SUB HR NIC ARG HIS VAL C8 09 PP TS 1 RC 0.96" -0.04b ---0.42 -0.59 3.02 TS 0.67" -0.01 0.34' ---0.37 -0.46 2.50 PC 0.09d -0.9W ---0.35 -0.33 2.02 TS2 RC 0.01" -0.01 0.98 0.01f -0.38 -0.49 2.59 TS -0.40' 0.00 0.44' 0.96 0.W -0.34 -0.36 2.11 PC -0.94' -0.99' 0.95 0.W -0.37 -0.40 2.30 TS3 RC -0.93h -O.OOb 0.96 0.96' 0.01 0.38 -0.50 2.64 TS -0.40" 0.01 0.43' 0.96 0.W 0.01 0.36 -0.39 2.26 PC -0.95' -0.99' 0.96 -0.01J 0.00 0.37 -0.42 2.40 Molecular species for charge calculation are as follows :" protonated pyruvic acid, 1-methyldihydronicotinamide,'1-methylnicotinamide ion, lactic acid, protonated pyruvate, Cmethylimidazole, lactate, pyruvate, protonated Cmethylimidazole.activation barrier for TS formation from the free reactants decreases in the order TS1 (-20.6) % TS2 (-104.3) > TS3 (-112.6), while the barrier for TS formation from the free products also decreases in the same order, TS1 (35.4) % TS2 (-99.6) >TS3 (-108.0). It is observed that the TS structure is higher in energy than the free-product structure in the case of TS1 alone. The difference in E, for the forward and reverse reactions (AE1), which is, of course, the reaction enthalpy, can serve as a measure of the reversibility of reaction (1).AEl and, consequently, the reversibility of reaction (l),increases in the order: TS1 6TS2 = TS3. The E, values for the reactant and product complexes [reaction (2) of Table 31 indicate an increase in the activation barrier for TS formation from the reactant complex in the order TS1 (9.3) <TS2 (19.4) <TS3 (393, while the corresponding barriers for TS formation from the product complex are higher, TS1 (49.0) > TS2 (36.5)c TS3 (43.9), with no regular trend observed. However, the reversibility of reaction (2), estimated in terms of the reac- tion enthalpy as the difference AE,, between the pertinent E, values, shows an increase: TS1 <TS2 < TS3.For TS3 alone, the two reaction enthalpies AE, and AE2 show small similar absolute values, reflecting energetically similar free reactants and products as well as reactant and product com- plexes. Thus, for the reaction characterized by TS3, the inter- nal states are apparently matched, in accordance with the theory of Albery and Knowles," while a substantial improvement in the reversibility of the reaction has been achieved by the inclusion of important residue fragments in the initial model comprising isolated substrate and cofactor analogues, with increased rates of reaction. Ionic Charge Distribution in the Transition States The charges for the substrate, hydride ion, l-methylnicotin- amide, 1-methylguanidinium cation, 4-methylimidazole and acetamide species at the TS structures TS1, TS2 and TS3 can be estimated as the sum of the component atomic charges. The total AM1 charges for these molecular entities, com- puted from Lowdin population analysis,32 are given in Table 4.The charge distributions for each species in the reactant and product complexes, derived from each TS, have also been provided in Table 4, for comparison.For TS1 (and its reac- tant and product complexes), the mean charges have been computed for the conformers TSla-TSlh. The difference in the sign of the charge on the substrate between TS1 and the other two TSs is a direct consequence of the change in the substrate species itself from protonated pyruvic acid to proto- nated pyruvate (or for the reactant complex corresponding to TS3, pyruvate).The positive charge on the cofactor analogue reflects the significant charge transfer associated with the TS structure, for each model. The migrating hydride ion, however, remains almost uncharged, as was observed by Cummins and Gready" for hydride-transfer reactions between the same cofactor analogue and folate and dihydro- folate substrate analogues of DHFR. A comparison of the species partial charges of each TS with those of the corresponding reactant and product com- plexes clearly shows the positive charge development on the 1-methylnicotinamide species. These values (ca. 0.4) suggest that the TSs are more reactant-like than product-like. Analysis of the atomic charges of the substrate and cofac- tor moieties in the free reactants and products (given in Fig.8) shows that the charges on C2 of the substrate species and on N1 of the nicotinamide species (see Fig. 3 for numbering) undergo considerable change. C3 and C5 of the nicotinamide ring are affected to a smaller extent while the charge on the active carbon C4 is less variant. Considering the charges on C2 (substrate species) and N1, C3 and C5 (nicotinamide species) for TS1, TS2 and TS3, the TSs appear more reactant- like than product-like. In all of the charge distributions shown in Fig. 8, the car- boxamide side chain of the nicotinamide species exhibits a high degree of carbonyl-group polarization, including those for the free reactant and free product species. Experimental and molecular modelling studies by La Reau and Ander- aimed at elucidating possible molecular mechanisms for the high degree of stereospecificity of the reaction, con- cluded that the high stereospecificity could not be accounted for by steric exclusion effects from obligatory binding of the carboxamide side chain of the cofactor in the anti conformer.They suggested instead that the stereospecificity was due to an electrostatic effect of polarization of the carbonyl bond by active-site positively charged groups (His-195, Arg- 109 and Arg-171) and the dipole of the 'x2F helix which leads to a reduction in electron density on C4 and stabilization of the TS. With respect to the C4 charge, the present results do not support this contention as there is no evidence for significant electron depletion on C4 in the TSs.The charges on C8 and 09 of the carbonyl group in the TSs have been compared with those for the respective reactant and product complexes in Table 4. The carbonyl bond dipole moments34 (p)derived from these charges have also been computed and given in Table 4. Considering that p is 1.97 Dt for the l-methyl- nicotinamide ion and 2.26 D for l-methyldihydronicotin-amide, it is apparent that the p values for the reactant and product complexes (excluding the product complexes of the t 1 D (Debye) x 3.33564 x C m. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 -0.41 Q -0.32 0 -0.43 -0.25 -0.21 (b1 0.31 -0.1 4 -0.05 0.01 -0:06 -0.13 -0.46 0 -0.26 (c) 0.01 0.10 -0.36 -0.39 0 0 -0.25 o k 0*010.05\K/0-0.23 -0.24 I 0-17 -0.10 0110 Fig.8 AM1 partial charges for C, N and 0 atoms of the substrate and cofactor moieties in (a) the free reactants (pyruvate and 1- methyldihydronicotinamide), (b)the free products (lactate and 1-methylnicotinamide ion), (c) TS1 (substrate analogue is protonated pyruvic acid here), (d) TS2 and (e)TS3. For TS1, mean charges for the structures TSla-TSlh are given. TS1) exceed those observed for the free reactant and product species as well as those of the TSs. Of the three TS models, TS2 and TS3 have p values which are similar and compara- ble with those calculated for the isolated cofactor species. The p values for the reactant and product complexes of TS2 and TS3 are marginally greater than those for the TSs.The anomalous p values for TS1 are a consequence of the net charges on the polarizing substrate species, as compared with the charges on the substrate species in TS2 and TS3. In summary, while there is no significant increase in carbonyl polarization upon TS formation, it is possible that enhanced carbonyl polarization of the reactant and product complexes may be involved in activation of the cofactor and may thus influence the stereospecificity of the enzyme reaction. Conclusions The present study has provided an insight into the catalytic mechanism of the LDH enzyme reaction. Different plausible reaction mechanisms have been explored, at the semi-empirical AM1 level, in a systematic manner, starting with isolated substrate analogues and gradually introducing molecular species indicative of the function of key active-site residues.The results of these computations can be sum-marized as follows : (1) In all of the transition states obtained, the substrate species is protonated. This finding lends support to the pro- posal that the enzyme reaction is a two-step process, with proton transfer to the substrate preceding hydride-ion trans- fer from the cofactor. The fact that the transition states located were for hydride-ion transfer indicates that the overall kinetics of the reaction would be controlled by the hydride-transfer process. This conclusion is in agreement with Wilkie and Williams' hypothesis that proton transfer and hydride transfer are kinetically coupled but dynamically uncoupled.' (2) All the transition states obtained in our study are for the trans orientation of the carboxamide side chain of 1-methyldihydronicotinamide. No transition state has been iso- lated for the corresponding cis conformer.The nicotinamide ring retained its planar conformation in all the TS structures reported. This result differs from that obtained using ab initio methods by Wu and Ho~k~~but needs to be treated with some caution, as semiempirical methods are inadequate for predicting small ring distortions. However, the present results indicate that nicotinamide-ring distortion is not essential for the formation of a viable TS.The question of whether non- planar nicotinamide conformations in the TS could account for the stereospecificity of the LDH reaction12 is thus not addressed in the present study. The trans carboxamide side chain tends to adopt a conformation almost coplanar with the nicotinamide ring in TS3, in which hydrogen bonding of the carboxamide amino group with the Val-138 residue frag- ment has been explicitly introduced. However, without mod- elling the active-site enzyme environment in a more comprehensive manner, the relevance of suggested out-of- plane orientations of the carboxamide side chain in the tran- sition ~tate'~*l~ cannot be assessed. (3) The transition state TS3, containing fragments of key active-site residues, Arg-171, His-195 and Val-138, is judged to be representative of the LDH transition state in that it represents a reaction having 'matched internal states'.'' (4) There is considerable charge transfer accompanying the formation of the transition state, with the nicotinamide moiety carrying a positive charge of ca.0.4. Interestingly, the migrating hydride ion and the active carbon (C4) of the nico- tinamide species remain virtually uncharged. Based on the pattern of atomic charge distribution, the TS can be classified as more reactant-like than product-like. The enhanced polar- ization of the carboxamide carbonyl group observed in the reactant and product complexes may be involved in directing the stereospecificity of the enzyme reaction, but we found no support for the proposal of La Reau and Anderson33 for increased polarization of the carbonyl group in the TS or for electron depletion at C4 of the nicotinamide species in the TS.The present study has located TS structures for simple models of the LDH active site, using semi-empirical AM1 methodology, and the nature of the substrate species in the TS has been characterized. The planar conformation of the 2056 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 nicotinamide ring and the trans orientation of the carbo- xamide side chain have been confirmed, although the slightly out-of-plane orientation of the carboxamide side chain could be due to the limitations of the present models, in represent- ing the complete enzyme environment in the vicinity of the 11 12 13 P.L. Cummins and J. E. Gready, J. Mol. Struct. (Theochem), 1989,183,161. H. Eklund and C-I. Branden, in Pyridine Nucleotide Coenzymes, Part A, ed. D. Dolphin, 0. Avramovic and R. Poulson, Wiley, New York, 1987, p. 55. S. A. Benner, Experimentia, 1982,38,633. active site. The intrinsic nature of the carboxamide carbonyl polarization is evident from the charge distribution. However, possible mechanistic roles of some of the key active-site residues, such as Arg-109 and Asp-168, have not been established. Computations at a higher level of theory (ab initio 3-21G) are under way to test the stability of the results obtained at the semi-empirical AM1 level. Also, a more com- plete investigation incorporating the entire enzyme environ- ment and solvent is being undertaken, using a combined quantum and molecular mechanical approach.14 15 16 17 18 19 F. H. Westheimer, in Pyridine Nucleotide Coenzymes, Part A, ed. D. Dolphin, 0. Avramovic and R. Poulson, Wiley, New York, 1987, p. 255. J. Wilkie and I. H. Williams, J. Am. Chem. SOC., 1992, 114, 5423. J. Andres, V. Moliner, J. Krechl and E. Silla, Bioorg. Chem., 1993,21, 260. J. L. Gelpi, R. M. Jackson and J. J. Holbrook, J. Chem. SOC., Faraday Trans., 1993,89, 2707. K. E. Norris and J. E. Gready, J. Mol. Struct. (Theochem), 1993, 279,99. K. E. Norris, G. B. Bacskay and J. E. Gready, J. Comput. Chem., 1993, 14, 699. The award of an H.B. and F.M. Gritton Research Fellowship 20 K. E. Norris and J. E. Gready, J. Mol. Struct.(Theochem), 1992, 258,109. is gratefully acknowledged by S.R. 21 P. L. Cummins and J. E. Gready, J. Comput. Chem., 1990, 11, 791. References 22 J. J. P. Stewart, L. P. Davis and L. W. Burggraf, J. Comput. Chem., 1987,8,1117. 1 2 3 4 5 6 7 8 A. R. Clarke, T. Atkinson and J. J. Holbrook, Trends Biochem. Sci., 1989,14, 101. C. R. Dunn, H. M. Wilks, D. J. Halsall, T. Atkinson, A. R. Clarke, H. Muirhead and J. J. Holbrook, Philos. Trans. R. SOC. London B, 1989,332, 177. J. J. Holbrook, A. Liljas, S. J. Steindel and M. G. Rossmann, in The Enzymes, ed. P. D. Boyer, Academic Press, New York, 2nd edn., 1975, vol. 11, p. 191. A. R. Clarke, D. B. Wrigley, W. N. Chia, D. A. Barstow, T. Atkinson and J. J. Holbrook, Nature (London), 1986,324,699. K. W. Hart, A. R. Clarke, D. B. Wrigley, W. N. Chia, D. A. Barstow, T. Atkinson and J. J. Holbrook, Biochem. Biophys. Res. Commun., 1987,146,346. A. R. Clarke, H. M. Wilks, D. A. Barstow, T. Atkinson, W. N. Chia and J. J. Holbrook, Biochemistry, 1988,27, 1617. W. Eventoff, M. G. Rossmann, S. S. Taylor, H-J. Torff, H. Meyer, W. Keil and H-H. Kiltz, Proc. Natl. Acad. Sci. USA, 1977,74,2677. J. L. White, M. L. Hackert, M. Buehner, M. J. Adams, G. C. Ford, P. J. J. Lentz, I. E. Smiley, S. J. Steindel and M. G. Rossmann, J. Mol. Biol., 1976, 102, 759. 23 24 25 26 27 28 29 30 31 32 33 34 35 J. Krechl and J. Kuthan, J. Mol. Struct. (Theochem), 1988, 170, 239. M. J. S. Dewar, E. G. Zoebisch, E. F. Healy and J. J. P. Stewart, J. Am. Chem. SOC., 1985,107,3902. J. J. P. Stewart, J. Comput. Aided Mol. Des., 1990,4, 1. P. L. Cummins, SYDPAC, unpublished work. P. L. Cummins and J. E. Gready, J. Comput. Chem., 1989, 10, 939. M. J. S. Dewar, E. F. Healy and J. J. P. Stewart, J. Chem. SOC., Faraday Trans. 2, 1984,80,227. P. Csaszar and P. Pulay, J. Mol. Struct. (Theochem), 1984, 114, 31. D. Voet and J. G. Voet, in Biochemistry, Wiley, New York, 1990, p. 347. L. C. Cusachs and P. Politzer, Chem. Phys. Lett., 1968,1, 529. M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 1984, 105, 180. R. D. La Reau and V. E. Anderson, Biochemistry, 1992,31,4174. U. Burkert and N. L. Allinger, in Molecular Mechanics, Amer-ican Chemical Society, Washington, DC 1982, p. 196. Y-D. Wu and K. N. Houk,J. Am. Chem. SOC., 1991,113,2353. 9 A. R. Clarke, T. Atkinson and J. J. Holbrook, Trends Biochem. Sci., 1989, 14, 145. 10 W. J. Albery and J. R. Knowles, Biochemistry, 1976, 15, 5631. Paper 3/07631H; Received 30th December, 1993