Transition State Modeling for Catalysis - American Chemical Society

Chapter 36

Isotope Effects on the ATCase-Catalyzed Reaction 1

2

1

J. Pawlak , M . H . O'Leary , and P. Paneth 1

Institute of Applied Radiation Chemistry, Technical University of Łódź (Lodz), Żeromskiego 116, 90-924Łódź,Poland Dean's Office, School of Natural Sciences and Mathematics, California State University, Sacramento, CA 95819-6123

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2

QM/MM calculations were performed on the reaction between carbamyl phosphate and aspartate catalyzed by aspartate transcarbamoylase (ATCase). The putative tetrahedral intermediate and transition states for two chemical steps were characterized. Carbon isotope effects were calculated theoretically and compared with the experimental data.

Modern computational chernistry offers a pletora of methods to model chemical and biochemical processes. However, due to the complexity of real systems and limitations in the computing power of presently available computers, cornpromises must be made regarding the applied theory level and/or the size of the model. Thus, one of the mndamental questions that has to be answered in all theoretical studies concerns reliability of the method used. It is not surprising that calculations performed at different levels of theoretical scrutinyfrequentlylead to different properties of the modeled systems, such as geometry, charge distribution, mechanism etc. Deciding which results are correct and which are wrong is not necessarily an easy task. Neither is finding a good criterion upon which to ground such decisions. Theoreticians tend to favor giving the highest theoretical level available at the moment the status of a reference against which results of lower level calculations are tested. Inevitably the reference changes with the development of computational methodologies. Experimentalists rather look for agreement between calculated and experimental properties such as geometries and energies of modeled systems. This approach is however possible only for stable reactants. For short-lived intermediates, intermediates on the enzyme surface (which are not amenable for direct measurements), or transition states, such comparison obviously is not possible.

462

© 1999 American Chemical Society

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


463 In recent years hybrid QM/MM methods emerged, which simultaneously take advantage of the precision of quantum methods and the speed of molecular mechanics, permitting us to tackle reactivity in enzymatic and condense phases processes (1-4). Having experimental background we are inclined to use measurable quantities to verify calculated results. Isotope effects are thought to be extremely sensitive probes of transition state properties and thus should provide a very good test of theoretical calculations. Our previous experience with modeling isotope effects indicated that semiempirical methods alone are not suitable for calculations of isotope effects (5,6). However, we did not obtain much improvement in quantification of isotope effects by either ab initio or DFT methods, especially for the primary kinetic isotope effects (6). At the same time we are biased toward low level calculations which would allow improved analysis of the experimentalfindings,rather than making calculations of isotope effects a quest of its own. Thus, the QM/MM technology seemed to be a very attractive alternative. Herein we report hybrid a quantum mechanical - molecular mechanics (QM/MM) approach to the mechanism of aspartate transcarbamylase (ATCase) reaction. ATCase catalyzes the carbamylation of aspartate by carbamyl phosphate in thefirstcommitted step of pyrimidine biosynthesis in E. coli (7): CH2COO" OPO3 "

I

"^-COOH3N

/

I

+

JL

H-r/k. ^COO"

2

CH2COO"

+

J. O^^NH

2

"

H +

'

HOP

°**~

*

H N

I > v

For our purpose it is an ideal model reaction because: 1. experimental isotope effects have been reported (8) for • different atoms (hydrogen, carbon and nitrogen), • equilibrium and kinetic conditions, • wild type and mutated enzymes, • holoenzyme and the catalytic subunit. Further, 2. numerous x-ray structures of the enzyme are available (9) providing a good starting point for modeling the active site of the enzyme. Computational Details Models. The model of reactants in the active site pocket was built based on the initial coordinates (PDB structure) of aspartate transcarbamylase provided by Professor Evan Kantrowitz. These corresponded to the catalytic trimer "frozen" in the active form through N-(phosphonoacetyl)-L-aspartate (PALA), an analogue of the putative intermediate, bound in the active site. The model of the active site of ATCase included aminoacids and water molecules within a 6 A radius of PALA. From this structure 6



464 aminoacids and 7 water molecules which were not in the immediate vicinity of the substrates were removed. N-terrninal ends of aminoacids were capped by hydrogen atoms to form - N H 2 , and C-terrninal ends were capped by amino groups to form C O N H 2 . PALA was replaced by reagents. The net charge of +1 was assigned to the model of the wild type and 0 for the histidine-134 changed into alanine (H134A) enzymes on the basis of expected protonation states of aminoacids and reactants at physiological pH. Models of reactants in aqueous solution were obtained by placing each of the reactants in a large box water molecules with distribution obtained from the TIP3P model (70) and removing all water molecules outside a 6 A radius around a reactant. Models obtained in this way contained 67 and 69 explicit water molecules for aspartate and carbamyl phosphate, respectively. Hybrid QM/MM calculations. Two methods were used for calculations of reactants in the enzyme active site. In both cases the reactants were treated quantum mechanically while the model of the enzyme pocket was treated at the molecular mechanics level. In thefirstmethod the geometry of reagents was optimized in a rigid structure of the active center. Mixed mode, as implemented in HyperChem (77) was used for geometry optimization. The classical region was included as electrostatic potentials, which perturbed the properties of the quantum mechanical region. The interactions of the charges in the classical region with the quantum mechanical region were treated by including them in the one-electron core Hamiltonian for the quantum region. The quantum atoms were those of the reactants treated at the semiempirical level by the PM3 Hamiltonian (12). The remaining part of the system was treated classically. It included 23 aminoacids, which are either within the active site or are essential for the catalysis and 11 molecules of water. In a single point calculation of the whole system (233 heavy atoms and 257 hydrogens) the charge distribution was calculated semiempirically. These charges were then included in the semiempirical Hamiltonian at the geometrical location of atoms of the aminoacids and neighboring water molecules. Thus the semiempirical calculations of the reacting molecules were performed within the electrostaticfieldof the atoms comprising the active site of the enzyme. In the second method geometry of a part of the active site molecules, treated at the molecular mechanics level, was also optimized. An arbitrary selection was made that atoms comprising the active site residues and hydrogens of water molecules which are contained in a sphere with 3.8 A radius from reactants were allowed to change positions while positions the outer sphere atoms were left constrained at the crystallographic values. The calculations were carry out in turns at the quantum level and at the molecular mechanics level. The quantum calculations proceeded exactly in the same manner as described above for thefirst(„rigid") method, the only difference being that part of the active site atoms changed position between steps. The molecular mechanics calculations were carried out for atoms in the sphere layer described by the 3.8 A sphere minus the inner part - reactants. During this step reactant (or transition state) atoms were defined in terms of molecular mechanics force field but their positions were constrained (as well as positions of atoms in the outer sphere from 3.8



465 to 6 A). The number of atoms whose positions were optimized (approximately 90) changed dynamically between steps. Calculations of geometries in aqueous solution were performed in the same manner as those described above for thefirstmethod but instead of atoms of the active site the water molecules were used in the molecular mechanics part. The optimization of geometries of reactants and intermediates, carried out using the RHF PM3 Hamiltonian and the Polak-Ribiere (conjugate gradient) algorithm for reactants and intermediates, was terminated when the RMS gradient reached 0.01 kca^molA)1. Structures of transition states were obtained using the Eigenvector 1 Following method. In these cases the RMS gradients of about 0.3 kcaltmolA)" were obtained. Force field calculations were subsequently performed to ensure the optimized geometries correspond to either reactants (no imaginaryfrequencies)or transition states (exactly one imaginary frequency). The molecular mechanics optimization of active site atoms was performed using the ESFF force field as implemented in the Discover 95.0/3.0 program (13) and was 1 terminated when the gradient reached 0.1 kca^molA)" . The calculations using the flexible method were carried out until no changes in energies were observed in both molecular mechanics and quantum calculations. These are illustrated in Figure 1. Isotope effects calculations. The forcefieldcalculations were repeated for all isotopic species and the resulting isotopicfrequencies,v, were used in calculations of isotope effects according to the Bigeleisen complete equation (14): «£-sinh(K*/2)

H

u

iH

-sinhQa/2) (1)

u'z - s i n h ( M ^ / 2 )

where u^hv/kaT, h and k are Planck and Boltzman constants, respectively, and T is absolute temperature. Northrop notation (15) is adopted for the isotope effects, with leading superscript denoting heavy isotope and subscripts identifying individual reactions in a reaction scheme. Isotope effects were calculated using the Isoeff program (16). Our model calculations show that the complete equation is more robust than the primary equation which is based onfrequenciestogether with principal moments of inertia and molecular masses. The latter is more sensitive to errors in moments of inertia andfrequencies.Smallfrequenciescan introduce sizable errors due to rounding of calculated values. We have also tested the influence of considerable residual gradients on thefinalisotope effects since we were unable to converge transition states 1 to the RMS gradients below 0.3 kcal(molA)' . However, we have found that although the absolute values of thefrequencieswere off by nearly 20 cm" no errors in isotope effects were observed. This is because isotope effect calculations are reasonably insensitive to the absolute value of afrequencyand depend mainly on the isotopic difference. B

1


466


Results and Discussion We restrain our discussion to carbon isotope effects although nitrogen isotope effects should prove even more sensitive probe. However, we were unable to achieve convergence using the AMI Hamiltonian (77) the first QM/MM method. The PM3 calculations are known to have problems with nitrogen, especially when this atom is involved in hydrogen bonding(5,7c?,79). These problem are nicely illustrated by the calculations of the overall equilibrium isotope effect of the ATCase reaction. Since these were calculations of the equilibrium isotope effects they involved only optimization of stable molecules; aspartate, carbamyl phosphate, and Ncarbamylaspartate. In Table 1 we compare results from QM-PM3/TIP3P and QMAM1/TIP3P obtained using thefirsthybrid method.

c •5

ca L_ O)

i

CO

2

-500 o E -520-

£10 -540 E a

ESFF

"5 1200-

800-I 400I—>—i—'—i—'—i—«—i—•—i—•—i—•—i—»—r

0

2

4

6

8

10

-

12 14 16

Step Figure 1. Convergence of energies and starting semiempirical gradient during optimization of both quantum and molecular mechanics regions.


467 Table 1. Overall equilibrium isotope effects on ATCase reaction method PM3/TIP3P AM1/TIP3P experimental isotope effect 1.0110 1.0094 N 1.0113 1.0001 0. 9990 ± 0.0002


,5

As can be seen the carbon equilibrium isotope effects obtained using both method are both about 1%. The nitrogen equilibrium isotope effects, on the other hand, are significantly different. The PM3 result indicates large positive isotope effect while the value obtained by the AMI method is practically unity (no isotope effect). The comparison of these results with the experimental value of the overall nitrogen equilibrium isotope effect of 0.999 clearly indicates that the result obtained using the QM-PM3/TIP3P scheme is erroneous. Typically equations describing apparent kinetic isotope effect as a function of commitments and intrinsic isotope effects, i.e. isotope effects on individual steps, are developed assuming no isotopicfractionationupon binding of reactants by the protein. We have showed previously both experimentally and theoretically that heavy-atom binding isotope effects can be substantial (18,20). These isotope effects were thought to be important only for atoms directly involved in binding, e.g., oxygen, hydrogen and nitrogen. Our present results indicate that they may be also important for carbon. The comparison of carbamyl phosphate in aqueous solution and bound in the active site indicates substantial stiffening of the net bonding to carbon, as illustrated by the bond lengths given in Table 2. Table 2. Bond lengths to carbon in carbamyl phosphate environment water enzyme bond rAi rAi C=0 1.244 1.227 C-O(P) 1.322 1.293 C-N 1.418 1.457 As can be seen both the C=0 and C-N bonds are substantially shortened upon going from aqueous solution to the active site pocket. On the contrary, the bond between the carbon of carbamyl phosphate and bridging oxygen is elongated, which may reflect enzyme's ability to prepare the phosphate moiety for the departure. Furthermore, the carbonyl bond is strongly polarized due to a hydrogen bond between the oxygen and a hydrogen of one of the water molecules present in the vicinity, which should result in restraining bending motion of the carbonyl group. These changes manifest themselves in inverse binding carbon isotope effect equal to 0.996 for both wild type and mutated enzyme. Atfirstglance the 0.4 % inverse carbon isotope effect seems not realistic. However, we have observed earlier inverse carbon kinetic isotope effects of the similar magnitude (0.995 - 0.9975) on the PEP carboxylic carbon in the PEPC catalyzed reaction (27). Recently Cook reported inverse carbon isotope effects in some decarboxylases (Cook, P.F. University of Oklahoma, personal communication, 1998).



468 Energetics patterns obtained for wild type and HI 34A mutated enzymes are similar although different in absolute values by about 90 kcal/mol. More useful for comparison is a pathway with reactants bound in the active site superimposed as shown in Figure 2. Only properties of isomeric structures are shown. Calculated heats of formation of the ternary enzyme - reactants complex with the protonated aspartate are much larger, -489.7 and -452.8 kcal/mol for wild type and H134A enzymes, respectively. The energy difference between complexes comprising protonated and deprotonated forms of aspartate are very different for these enzymes; 104.5 kcal/mol for the wild type enzyme and only 49.4 kcal/mol for the HI34A mutated enzyme. The fate of the proton transferred to the protein should be determined in order to correct the absolute values. This big difference between the two protonation states with environment is worth noticing.

TS1

Figure 2. Energetic pathways for wild type (solid line) and HI34A mutated (dashed line) ATCase. Two important differences in the energetic pathways of the wild type enzyme and its H134A mutation should be noted. Firstly, the irreversible step, the dephosphorylation, proceeds with larger activation energy for the mutant while the activation energies of the reverse decomposition of the tetrahedral intermediate back to thefirsttransition state are very close. This means that the commitment for this step (b=k/k8 in the original paper, see scheme below for the description of rate constants) should be smaller for the mutant than for the wild type enzyme. This conclusion is opposite to the one reached based on the assumption of equal intrinsic isotope effects made in the analysis of experimental isotope effects. Secondly, the dephosphorylation step is much more exothermic in the case of mutated enzyme; activation energies of the enzyme-bound products going back to the second transition state are about 36 and 51 kcal/mol for wild type and H134A enzymes, respectively. For the wild type enzyme this activation energy is less than for the reaction of intermediate partitioning back to thefirsttransition state (about 44 kcal/mol). This means that in the case of reaction 9


469


catalyzed by the wild type enzyme the subsequent step - release of productsfromthe enzyme - may also contribute to the commitments.

Figure 3. Optimized structures of the tetrahedral intermediate I. R = -CHC0 "(CH C0 "). For the first two structures the energy differencefromthe third one is given. For the third structure heats of formation in kcal/mol are given. 2

2

2

An important feature of the mechanism which emergedfromour calculations is synchronicity of the C-N bond making between the aspartate and carbamyl phosphate and N—H—O intramolecular proton transfer between nitrogen and phosphate moiety. Both these changes occur within the same transition state (TS1 in Figure 2). We were unsuccessful infindingany alternative stepwise pathway. We have identified a few structures of the putative tetrahedral intermediate. These are schematically presented in Figure 3. In the first structure the transferred proton is still in hydrogen bonding contact with the nitrogen atom In the second the N—H distance changes to 3.3 A causing this hydrogen bond to break. Finally, the newly formed H-0 bond is rotated by 140 degrees awayfromthe nitrogen. For both enzymes the most stable is this third form of intermediate (Figure 3) and therefore this was used in calculations of isotope effects. In order to discuss calculated isotope effects it is necessary to comment on the relationship between calculated stationary points and the reaction scheme used for the analysis of experimental results. Presented below is the scheme which comprises the major steps of the ATCase catalysis:


470 E C P + ASPH+

EHCP ASP ^ *

|* k2

1

7


Kg

- EH I

ECPASPH+ ^

k

9

k

3

M

^[ECPASPHY

*6

^

» E H + ASPCP + H P 0 " 2

4

The first step is binding of the protonated aspartate, followed by the conformational change in the protein, and subsequent deprotonation of the aspartate, with proton being lost to the enzyme. Conversion of reactants to the tetrahedral intermediate is characterized by the forward rate constant labeled k . Dephosphorylation of this intermediate leads in the next step to products. It should be noted that thisfinalstep includes both formation of products in the active site and their releasefromthe enzyme. We have pointed out on the basis of energetic profiles that this step may be different for the wild type and HI 34A mutated forms of the enzyme. Our active site model is based on the crystallographic data of the reactive (R) conformation of the enzyme. Thus no conclusion about the conformational change can be drawnfromour results and the corresponding step (with rate constants k and k*) is transparent for our discussion. Calculated isotope effects are given in Table 3. The first column lists equilibrium carbon isotope effects on binding already discussed above. The next two columns give kinetic carbon isotope effects on goingfromeither protonated ( k 3 - 7 ) or deprotonated ( k ) aspartate to thefirsttransition state. Since neither deprotonation, nor conformational changes are expected to introduce substantial isotopic fractionation these two isotope effects are expected to be close, which is the case for both enzyme forms. The last two isotope effects are connected with forward ( k ) and backward ( kg) decomposition of the intermediate I. It was assumed in the discussion of the experimental results that these isotope effects should be equal (8b). Our results indicate, however, that these effects are considerably different. This is because the reaction coordinate for going from the intermediate to the first transition state is dominated by the proton transfer and not by the C-N bond formation. Thus the calculated isotope effect is small. The isotope effect on the forward reaction, on the other hand, has a considerable isotope effect, corresponding to early transition state of the C-0 bond breaking process. 7

3

1 3

13

7

13

9

13

isotope effect enzyme Wild type H134A

^binding 0.9964 0.9963

%.

,3

7

1.0344 1.0389

k

7

1.0346 1.0407

% 1.0075 1.0099

% 1.0185 1.0155

Comparison of our theoretical values to the experimentally measured is possible for the carbon kinetic isotope effect on the H134A enzyme. Modifications of the equation (5) from the reference (8b) which include isotope effect on binding, and


471 numerical values for commitments (a=c=0, and b=0.62) lead to the following expression: 131 K

_n

app~

v

131 K

^ binding l

n

k

9

/

u

k

%

+

0.62

j ^

^ '


13

Substitution of calculated individual isotope effects leads to k equal to 1.0404 which matches nicely the experimental value of 1.0413 ± 0.0011 for the H134A enzyme. Such comparison is, unfortunately, not possible for the native enzyme since the observed value depends on the concentration of aspartate. Comparison of the two rows in Table 3 supports our earlier conclusion (Pawlak, J.; O'Leary, M.H.; Paneth, P. unpublished data) that the intrinsic isotope effects for mutated enzymes might be quite differentfromisotope effects on the corresponding steps in wild type enzymes. Only initial results from the second method (flexible active site) are available. We have optimized reactants and the first transition state in the active site pocket. Structures of the transition state obtained by means of these two methods are very similar - proton transfer is slightly more advanced in the structure obtained using flexible model of the active site. Structures of the reactants, on the other hand, are substantially different. The role of histidine-134 which emergesfromthese calculations nicelyfitsconclusions based on experimental data; in the enzyme - reactants complex it is in hydrogen bonding contact with one of the oxygens of phosphate moiety confirming its role in binding carbamyl phosphate. In the transition state it is rotated (Figure 4) so that the hydrogen bonding between histidine proton and carbonyl oxygen is established. Thus this residue proves important for catalysis by polarizing the carbonyl bond.

Figure 4. Active site model of ATCase with bounded transition state (rendered as sticks and balls). H134 is highlighted. For color, see the color insert.


472 Acknowledgements Financial support from the State Committee for Scientific Research (KBN), Poland (grant 6P04A05810), and the Fogarty-NIH (grant LWL/62-130-11101), as well as computer time allocation grants from the Poznan Supercomputer & Networking Center, Poland and the Interdisciplmary Center for Modeling, Warsaw, Poland are gratefully acknowledged.


Literature Cited 1. 2. 3. 4. 5. 6. 7. 8.

Warshel, A.; Levitt, M. J. Mol. Biol. 1976, 103, 227. Gao, J. Rev. Comput. Chem. 1996, 7, 119. Bakowies, D.; Thiel, W. J. Phys. Chem. B 1996, 100, 10580. Merz, K.; this volume. Gawlita, E.; Szylhabel-Godala, A.; Paneth, P. J. Phys. Org. Chem. 1996, 9, 41. Czyryca, P.; Paneth, P. J. Org. Chem. 1997, 62, 7305 Alewell, N.M. Ann. Rev. Biophys. Biophys. Chem. 1989, 18, 71. (a) Parmentier, L.E.; O'Leary, M.H.; Schachman, H.K.; Cleland, W.W. Biochemistry 1992, 31, 6570. (b) Parmentier, L.E.; Weiss, P.M.; O'Leary, M.H.; Schachman, H.K.; Cleland, W.W. Biochemistry 1992, 31, 6577. (c) Waldrop, G.L.; Turnbull, J.L.; Parmentier, L.E.; O'Leary, M.H.; Cleland, W.W.; Schachman, H.K. Biochemistry 1992, 31, 6585. (d) Waldrop, G.L.; Turnbull, J.L.; Parmentier, L.E.; Lee, S.; O'Leary, M.H.; Cleland, W.W.; Schachman, H.K. Biochemistry 1992, 31, 6592. (e) Parmentier, L.E.; O'Leary, M.H.; Schachman, H.K.; Cleland, W.W. Biochemistry 1992, 31, 6598. 9. (a) Kantrowitz, E.R.; Lipscomb, W.N. Science 1988, 241, 669. (b) Krause, K.L.; Volz, K.W.; Lipscomb, W.N. J. Mol. Biol. 1987, 193, 527. 10. Jorgensen, W.L.; Chandrasekhas, J.; Madura, J.D.; Impey, R.W.; Klein, M.L. J. Chem. Phys. 1983, 79, 926. 11. Hyperchem v. 5.01, HyperCube, Inc. FL. 12. (a) Stewart, J.J.P. J. Comp. Chem. 1989, 10, 209. (b) Stewart, J.J.P. J. Comp. Chem. 1989, 10, 221. 13. InsightII User Guide, October 1995, San Diego: Biosym/MSI 1995. 14. Melander, L. Isotope Effects on Reaction Rates, Ronald Press Co., New York, 1960. 15. Northrop, D.B. Methods.Enzymol.1982, 87, 607. 16. ISOEFF ver. 6ha and ver. 7 (for Windows) available upon requestfromP. Paneth ([email protected]). MOPAC/AMPAC, AMSOL, SIBIQ, GAMESS, GAUSSIAN and HYPERCHEM formats are currently supported. 17. Dewar, M.J.S.; Zoebisch, E.G.; Healy, E.F.; Stewart, J.J.P. J. Am. Chem. Soc.1985, 107, 3902. 18. Gawlita, E.; Anderson, V.E.; Paneth, P. Eur. Biophys. J. 1994, 23, 353. 19. Schröder, S.; Daggett, V.; Kollman, P. J. Am. Chem. Soc. 1991, 113, 8922. 20. Gawlita, E.; Anderson, V.E.; Paneth, P. Biochemistry, 1995, 34, 6050.


Transition State Modeling for Catalysis - American Chemical Society

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