Transition State Modeling for Catalysis - American Chemical Society

Chapter 31

Modelling of Transition States in Condensed Phase Reactivity Studies Neil A. Burton, Martin J. Harrison, Ian H. Hillier, Nicholas R. Jones, Duangkamol Tantanak, and Mark A. Vincent

Downloaded by NORTH CAROLINA STATE UNIV on September 30, 2012 | http://pubs.acs.org Publication Date: April 8, 1999 | doi: 10.1021/bk-1999-0721.ch031

Department of Chemistry, University of Manchester, Manchester M13 9PL, United Kingdom

In this Chapter we describe the calculation of transition states for condensed phase reactions involving catalysis by an enzyme and by a titanosilicate. Transition structures for hydride transfer between NADPH and FAD in the enzyme glutathione reductase have been determined using a QM/MM potential, for two forms of the enzyme, e. coli and human. Both the transition state structures and energies, and the associated kinetic isotope effects are found to differ for the two enzymes. A cluster has been used to model the transition state for alkene epoxidation by hydrogen peroxide, catalysed by titanosilicates, predicting attack of the oxygen atom of the titanium(IV)-hydroperoxide intermediate that is closer to the metal centre.

The majority of chemical processes and all biochemical ones occur in the condensed, rather than the gas phase. Methods for modelling the potential energy surfaces associated with gas phase reactions are well established and widely available in quantum chemistry packages. Here, for small and medium size systems results of a "chemical" accuracy may be obtained using widely available distributed computational resources. There is now increasing effort to achieve this degree of realism for condensed phase systems, particularly to understand reactivity and catalysis and hence to aid molecular design across a range of important chemical areas. It is to solve these problems that the traditional methods of both computational chemistry and solid state physics are now being focused. In the latter area, periodic calculations based upon a plane wave pseudopotential (PWP) approach, incorporating the work of Car and Parrinello to permit dynamical simulations to be performed, have been used to study solid state structure and

© 1999 American Chemical Society

In Transition State Modeling for Catalysis; Truhlar, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.

401


402 reactivity. Such methods become extremely computationally demanding for large unit cells, and indeed may be inappropriate for systems lacking natural periodicity. However, as long as sufficiently large unit cells are employed, this approach may even be effectively used to study the electronic structure of isolated molecules. The extension of traditional gas phase electronic structure calculations to model the condensed phase is based upon an embedding or hybrid approach. For most systems to be modelled, there is usually a chemical centre, where electronic effects, ranging from electron polarisation to bond breaking and forming occurs. These electronic effects are modulated by an environment, which itself takes no direct part in the chemical process, but of course, can respond both structurally and electronically to the primary process being modelled. In the area of biochemistry, understanding the relationship between enzyme structure and its catalytic effect has been aided by the use of such hybrid calculations (1-4). Here the active site of the enzyme, including the substrate and important catalytic residues are treated quantum mechanically, whilst the remainder of the enzyme is modelled at a lower level, employing one of the force fields commonly used in macromolecular modelling. The Hybrid Model In the traditional hybrid model the system is divided into two regions, one described at an appropriate level of quantum mechanics (QM) and the other using a molecular mechanical (MM) force field. The effective Hamiltonian for the system is written as the sum of the Hamiltonians for the QM and MM regions and the interaction between them; H

eff = HQM +

H

M M + HQM/ MM

0)

the corresponding total energy (E ) can be similarly written as tot

E

tot

=

EQM + E M M + EQM/ MM-

(2)

The interaction term is given by A HQM/MM - ~ X i,s

+

*

s

X m,s

+

m

s

X p 12 m,s . ms

B

(3)

n6 ^ ms.

where m and s label the QM and MM atoms respectively, and i is the index of the electrons of the QM system. The first term of the right hand side of equation (3) accounts for the effect of the formal charges of the MMfragment(q ) on the Q M part and may readily be incorporated into standard QM codes. The final two terms are the remaining Coulombic and Lennard-Jones interaction terms between the Q M s



403 and MM fragments. We utilise the code GAUSSIAN (5) to enable both semiempirical and ab initio QM calculations to be carried out within a variety of hybrid schemes. The Gaussian link structure allows evolving electronic structure methods to be coupled to a range of descriptions of the MM region, thus enabling all the standard facilities within both the QM and MM programs to be efficiently utilised. For example for the macromolecular modelling work we use the code AMBER (6) and associated force fields to carry out the MM calculations. Such a hybrid QM(Gaussian)/MM(Amber) implementation allows the geometry of the Q M fragment to be optimised in the field of the MM portion using the redundant internal coordinate algorithm, and conversely the geometry of the MM portion can be optimised in the field of the QMfragment.Although such optimisations of the two portions are not directly coupled at present, an iterative optimisation procedure does allow for the effective optimisation of the combined Q M / M M system. The characterisation of transition geometries can now be routinely carried out by calculation of the second derivatives of the QM/MM energy. The van der Waals (vdw) contributions to the second derivatives are calculated by finite difference of the vdw gradients whereas the electrostatic terms can be calculated either by finite difference or analytically using standard methods. In the optimisations the position of several atoms may befrozento speed convergence by increasing the relative mass of these atoms in the cartesian to internal coordinate conversions. A similar procedure is followed in the calculation of the vibrational frequencies enabling characterisation of the constrained stationary state. When there are covalent linkages between the QM and MM portions their treatment is somewhat arbitrary. Hydrogen termination is used to satisfy the valence of the QM portion, placed at afixeddistance from the appropriate Q M atom. No interactions between these hydrogen termination atoms and the M M portion is included and to avoid unrealistic interactions, the charges of the M M junction atoms attached to the QM system are set to zero, with the charges on the remaining MM atoms scaled to conserve total charge. Such hybrid methods are also being used to model solid state catalysis. We have shown that catalysis by Bronsted acid sites in zeolites may be modified by the inclusion of the electrostatic field due to the infinite lattice (7). In this paper we exemplify our current work by presenting preliminary predictions of transition states both for a reaction catalysed by an enzyme, and by a zeolite based metal oxide system. Hydride Transfer and Kinetic Isotope Effects in Glutathione Reductase. Redox reactions involving hydride transfer are implicated in a number of important biological reactions, involving enzymes such as dehydrogenases and reductases (8). These reactions have traditionally been studied theoretically using a range of quantum mechanical methods, applied to considerably simplified models of the actual biological system (9-11). Both the degree of realism of the model system and the level of sophistication of the quantum mechanical treatment have progressively advanced, with a recent study involving the use of density functional theory (DFT)



404 methods (10). Such calculations are often directed towards interpretation of the measured kinetic isotope effects (KIE) associated with the hydride transfer. However, to date, an isolated gas phase molecular system has always been used, with no explicit consideration of the role of the enzyme on the energetics, or structure, associated with the hydride transfer. An experimentally much studied system is the flavoenzyme, glutathione reductase (GR), which catalyses the reduction of glutathione disulfide (GSSG) to the biological antioxidant glutathione (GSH) (12). The initial, rate determining step of the reaction, is the transfer of a hydride ion from the coenzyme NADPH (Nicotinamide Adenine Dinucleotide Phosphate) to the permanently bound cofactor FAD (Flavin Adenine Dinucleotide), to produce the reduced enzyme as a stable intermediate (13) +

+

E + NADPH + H -> E H + NADP . 2

The first stage of this process is +

NADPH + FAD -> NADP + FADH" the transition state structure for this reaction being shown in Figure 1. We here describe hybrid QM/MM calculations of the hydride ion transfer in the GR enzyme, this being the first prediction of the transition states and KIEs for this reaction, explicitly including the structure of the enzyme. We have studied both the human and e.coli forms of the enzyme to test suggestions, based upon KIE data (14), that there are differences in the corresponding transition states (8). Structures for these enzymes (15) were obtained from the Brookhaven database (16). These were built with AMBER4.0, solvated with 256 TIP3P (17) water molecules and the structures optimised using the AMBER force field. The QM region was chosen to contain the nicotinamide moiety of NADP and the flavin rings of FAD, in addition to a few extra-ring atoms, as shown in Figure 2. The valencies of the QMfragmentwere satisfied by the addition of hydrogen atoms to the QM link atoms. The potential energy surface for hydride transfer was explored by energy minimisation of structures in which the distance between the FAD nitrogen (Nj) and the transferred hydrogen atom (Ht) was decreased in steps of 0.1 A. We use the AMI QM Hamiltonian (18) and optimise the geometry of both the QM and MM moieties for each such structure. Further refinement of the transition state geometry from this procedure leads to a properly characterised transition state structure having a single imaginary frequency. The primary KIEs were calculated for these structures within the rigid rotor, harmonic oscillator approximation (Bigeleisen equation (19)) with a Wigner tunnelling correction (20). The calculated barrier height and structural parameters of the transition state are shown in Table I.



405

FAD

Figure 1. Transition state geometry showing atom numbering used in models of the hydride transfer.

Figure 2. The QM FAD and NADPH moieties. The dashed lines indicate the QM-MM junction, (a) Flavin Adenine Dinucleotide (FAD) (isoalloxazine end), (b) Nicotinamide Adenine Dinucleotide (NADPH) (nicotinamide end).


406 Table I. Calculated Barrier Height and Structural Parameters of Transition State N2-C-C-Q Barrier Ni-H (A) Na-C-C-Nj (kcal. mol" ) dihedral (°) dihedral (°) 1.6 1.33 E.coli 26.8 5.8 Human 1.50 3.1 20.3 4.3 No M M 29.5 No Glul84 25.4 1.20 No MM 37.0 3.2 5.6 t

1

8


a

Evaluated for human enzyme stationary structures.

Inspection of all the structures shows marked ring pucker both in the isoalloxazine and the nicotinamide rings, with the transferring atoms N± and moving out of the plane of the ring by approximately 5°. Such structural changes have been noted in ab initio model studies on hydride transfer between two nicotinamiderings(21). In contrast to the previous calculations on model systems (9-11), our calculations are able to identify the important role of the enzyme on transition state structure and energetics. Thus, the human enzyme yields a lower barrier and earlier transition state than the e.coli enzyme (Table I), which is reflected in the smaller KIE calculated for the human enzyme (Table II).

-1

Table II. Imaginary Frequencies (cm ) of Transition States and KIEs (k /k ) KIE H

v(H)

v(D)

D

Semi-classical with correction

8

Human EColi No MM a

1373i 1820i 1699i

1109i 1420i 1332i

2.9 3.1 10

3.7 4.4 4.2 (4.2)

b

Wigner tunnel correction (20).

b Result from ab initio model studies (10) in parenthesis.

Although the measured KIEs (14) for the two enzymes studied here are considerably smaller than the values we calculate (due to the composite nature of the rate constants) a value of 3.99 is found for the spinach enzyme (14) (for which no structure is available). The role of the enzyme in lowering the barrier can be readily studied by removal of the formal atomic charges on selected residues followed by re-evaluation of the energy of the stationary structures. Thus, removal of the charges on the nearby Glutamate 184 residue in the human form, which binds the amide group of



407 the NADP, (no Glu 184, Table I), shows that this residue contributes about 50% of the total barrier lowering effect of this enzyme, as judged by comparison with the calculation in which all MM charges have been removed. Location of the transition state in the total absence of the MM environment, leads to a considerably larger barrier than for either of the enzymes studied, and a correspondingly later transition state (Table I). Although the present calculations use a semi-empirical Hamiltonian, they show that the actual enzyme structure is reflected in both the barrier to the reaction and the KIE, and provide a way forward for more realistic modelling of enzyme catalysed reactions. The Mechanism of Alkene Epoxidation by Hydrogen Peroxide Catalysed by Titanosilicates. There is considerable current interest in transition states of epoxidation of alkenes, particularly in view of the use of such reactions to produce stereoselective products. Epoxidation using a variety of organic reagents such as performic acid, dioxirane and oxaziridine has been modelled using high level ab initio methods, with emphasis on the synchronous or asynchronous nature of the oxygen transfer (22). Alkene epoxidation by hydrogen peroxide can be catalysed by titanium containing zeolites such as TS-1, TS-2 and Ti-MCM-41, which involve framework Ti(IV) species (23). The active species is generally considered to be a hydroperoxide species accommodated in the titanium coordination sphere, and possibly hydrogen bonded to a water or alcohol molecule (Figure 3 a) (24). We have carried out preliminary cluster calculations in order to identify the transition state for this epoxidation reaction. On-going studies are to include solid state effects via an embedded cluster approach. However, the bare cluster calculations are a necessary first step in understanding the catalytic role of the Ti(IV) active site. We have identified a low energy transition state which involves transfer of the oxygen atom (0(1)) that is directly bonded to the titanium atom, rather than the terminal oxygen atom (0(2)) (Figure 3b). The calculated transition state has a number of interesting structural features when compared both to the reactant structure, and to the corresponding transition state involving an organic peroxy species. The reactant structure (Figure 3a) has the peroxy group bound sideways, similar to the arrangement in related metal complexes (25). In the transition state there is a lengthening of the Ti-O(l) length and a more substantial reduction in the Ti-0(2) length, corresponding to the development of Ti-0(2) single bond. This structure suggests an early transition state reminiscent of the synchronous structure found for the epoxidation of ethene by performic acid. Not only are the C-C and C-0 lengths very similar in both transition states, but our calculated barrier (11.9 kcal mol" , at the B3LYP/3-21G* level) is close to the value for the organic peroxidation (14.1 kcal mol' , B3LYP/6-31G*) (22). However, in the latter reaction, there is attack by the terminal oxygen atom of the performic acid, with proton migration to the third oxygen atom of the acid. We have located the corresponding transition state for the titanosilicate catalysed reaction (Figure 3c). Here it is the methanol molecule that assists in the deprotonation of the peroxy 1

1



408

H C 2

134

IK

H C 2

2.15 ^

H

H

H C^2.06 2

OMe

1.80/

ip M e

X2.2.21

\

2.08 ^ j j ' 2.12

Ti, SiO'

SiO''

1 8 4

'••fjf.H

::o(i),

1.36 HoC*

L 9 5

^P(^y

OSi

OSi

OSi

OSi -1

AE=11.9 kcal mol

Me

I

(a)

(b)

1.32/ 4

H

;i.5i

/ H C-.1.85 2

1.38

/1.17 V

^ . ' 9 17

*•

l V-80

SiO'

OSi

OSi

AE=21.0 kcal mol' (c)

Figure 3. (a) Hydroperoxy intermediate, and (b), (c) transition structures for attack of each hydroperoxide oxygen atom on ethene. A E is the calculated barrier. (Silicon atoms are terminated by hydrogen atoms).


409 1

species. However, the barrier (21 kcal mol' ) is considerably higher, and the transition state structure suggests an asynchronous mechanism.


Summary and Concluding Remarks We have shown how electronic structure calculations can be used to gain insight into complicated reactions occurring in the condensed phase. For the enzyme catalysed reaction involving hydride ion transfer, the enzyme has an important role in lowering the barrier to the reaction. In the case of the epoxidation reaction, promoted by the titanosilicate, similarities and differences compared to the reaction with organic reagents have been identified. Here the role of more distant atoms of the catalyst, not yet included in the cluster calculation, remain to be identified. Acknowledgments We thank EPSRC for support of this research. Literature Cited 1. 2. 3. 4.

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410 11. Mestres, J.; Duran, M.; Bertran, J. Bioorg. Chem. 1996, 24, 69. 12. Voet, D.; Voet, J. G. Biochemistry; Wiley: New York (NY), 1990. 13. Blankenhorn, G. Eur. J. Biochem. 1976, 67, 67. 14. Vanoni, M. A.; Wong, K. K.; Ballou, D. P.; Blanchard, J. S. Biochem. 1990, 29, 5790; Sweet, W. L.; Blanchard, J. S. Biochem. 1991, 30, 8702. 15. Karplus, P. A.; Schulz, G. A. J. Mol. Biol. 1987, 195, 701; J. Mol. Biol. 1989, 210, 163; Mittl, P. R. E.; Schulz, G. E. Protein Science 1994, 3, 799. 16. Brookhaven National Laboratories, Associated Universities Inc. (E.C.1.6.4.2 , 1GET and 1GRB). 17. Jorgensen, W. L.; Chandrasekhar, J.; Madura, J.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. 18. Dewar, M. J. S.; Thiel, W. J. Amer. Chem. Soc. 1977, 99, 4499. 19. Bigeleisen, J.; Wolfsberg, M. Adv. Chem. Phys. 1958, 1, 15; Bigeleisen, J. J. Chem. Phys. 1949,17,675. 20. Wigner, E. Z. Phys. Chem. B 1933, 19, 203. 21. Wu, Y. D.; Lai, D. K. W.; Houk, K. N. J. Amer. Chem. Soc. 1995, 117, 4100. 22. Houk, K. N.; Liu, J.; DeMello, N. C.; Condroski, K. R. J. Am. Chem. Soc. 1997, 119, 10147. 23. Murugavel, R.; Roesky, H. W. Angew. Chem. Int. Ed. Engl. 1997, 36, 477. 24. Khouw, C. B.; Dartt, C. B.; Labinger, J. A.; Davis, M. E. J. Catal. 1994, 149, 195. 25. Boche, G.; Möbus, K.; Harms, K.; Marsch, M. J. Am. Chem. Soc. 1996, 118, 2770.


Transition State Modeling for Catalysis - American Chemical Society

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