The document summarizes a study of the reaction mechanism of mandelate racemase using quantum mechanics/molecular mechanics (QM/MM) modeling. It finds that the enzyme stabilizes the transition state of the reaction relative to reactants through electrostatic interactions with active site residues such as Lys166 and His297. This stabilization lowers the reaction's energy barrier compared to the uncatalyzed reaction in water.

1. Reaction Mechanism of Mandelate Racemase in a QM/MM model: reaction path and catalysis Xavier Prat-Resina January 28th, 2005 AD

3. Lluch’s group Atmospheric Reactions / Enzymatic Reactions / Quantum dynamics

4. Overview Mandelate Racemase: Structure and Reaction Mechanism Optimization of Saddle Points in big systems Potentials of Mean Force: Reaction coordinate Conclusions/General Discussion Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc Potentials of Mean Force: mechanism and catalysis

5. fast less fast slow pka~29 in water MR MR: the reaction t 1/2 =100 000 years Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

6. Substrate MR: structure Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

7. concerted mechanism 2 stepwise mechanisms MR: Active site and reactivity Elements stabilizing the anionic intermediate Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

8. reactant (S)-mandelate product (R)-mandelate Lys166 His297 Glu317 Lys164 MR: Adiabatic mapping concerted mechanism Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

9. product (R)-mandelate reactant (S)-mandelate Lys166 His297 Glu317 Lys164 Glu247 MR: Adiabatic mapping stepwise mechanisms Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

10. product (R)-mandelate reactant (S)-mandelate Lys166 His297 Glu317 Lys164 Glu247 MR: Adiabatic mapping mechanisms Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

12. environment minimization L-BFGS until |g env |< crit looking for TS in core RFO until |g cor |< crit is environment minimized? NO YES Transition state found with |g TOT |< crit Initial geometry with a core and an environment Suggestions : An adequate core size must be selected. When minimizing, the QM wavefunction can be kept frozen (1SCF) TS search: algorithm Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

13. mandelate substrate propargyl-glyc. substrate Energy in kcal/mol. In brackets the value corresponding to the refined structure TS search: comparison refined TS with adiabatic mapping Structure Stepwise I Stepwise II Concerted S 0.00 0.00 0.00 TS1 17.77 (18.24) 17.69 (17.78) TS2 19.52 (19.65) 14.77 (14.46) TS3 20.04 (20.06) 14.55 (14.95) TS4 22.54 (22.56) 20.19 (19.50) TS5 25.15 (25.75) 23.57 (23.83) TS6 27.22 (27.28) 28.14 (28.18) R 6.74 6.74 4.63 Stepwise I Stepwise II Concerted 0.00 0.00 0.00 15.90 (19.66) 11.83 (11.24) 19.88 (19.92) 15.33 (15.32) 22.18 (22.20) 16.96 (16.99) 30.12 (22.20) 28.11 (20.68) 22.05 (21.98) 23.16 (22.60) 19.23 (20.08) 23.89 (24.35) 26.45 (24.59) 3.34 3.34 3.34 Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

14. Adiabatic mapping TS search Energetic and structural differences exist TS search: comparison refined TS with adiabatic mapping Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

15. Structure: PDB Potential Energy Surface : QM/MM Free energy calculation : umbrella sampling Molecular Dynamics : SBMD PMF: computational details Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

16. semiemp: AM1,PM3 semiemp-SRP EVB, HF, DFT... Frontier: Link atom LSCF GHO ... q m : charmm amber mulliken resp A,B: charmm amber optimized charmm amber gromos opls + Cutoff at 13 Å PMF: computational details QM QM/MM MM Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

17. Are non-bonded interactions univoquely reproduced in QM/MM? PMF: computational details Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

18. X: mandelate 63 atoms PM3-GHO / 8208 CHARMM Study of the concerted mechanism PMF: computational details Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

19. Stochastic Boundary MD with a sphere of waters 24 Å 0-20:Newton MD zone 20-24: Langevin MD zone harmonic restraint+friction + stochastic 24-...: fixed zone PMF: computational details Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

20. V tot = V QM/MM + k(Rc-Rc 0 ) 2 + Px(Rc) Molecular Dynamics Statistical treatment (WHAM) PMF=f(Rc)!!! Scanning Rc in increments of 0.2 Å windows Every window: 15ps eq / 50ps sampling PMF: computational details Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

21. Data from TSsearch PMF: Selection of a Rc r HC r NH 1.200 1.509 2.736 1.004 Rts 1.117 1.607 2.612 1.055 Ir 1.013 2.093 2.258 1.011 TS 0.995 2.845 1.570 1.151 Is 1.772 1.165 2.868 1.004 R 0.996 2.865 1.522 1.194 Sts 0.995 2.927 1.158 1.804 S r HN r CH r HC r NH 4.61 -0.350 2.543 2.471 1.703 -0.607 1.864 R 16.75 -0.312 2.057 1.423 1.227 -0.309 1.732 Rts 16.46 -0.306 1.828 1.117 1.005 -0.490 1.607 Ir 19.47 -0.058 0.992 0.167 0.165 -1.080 1.247 TS 13.79 0.398 -0.201 -1.431 -1.275 -1.850 0.419 Is 13.81 0.412 -0.220 -1.541 -1.343 -1.869 -0.328 Sts 0.0 0.421 -0.043 -2.578 -1.769 -1.932 -0.646 S  E Improper  r NC -r CN r HC -r NH +r HN -r CH r HC -r CH r HN -r CH r HC -r NH R c Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc r CH r HN

22. Rc = r HC – r NH r HC r NH PMF: two bond distances Rc S R Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc Rc = r CH – r HN R S r CH r HN

23. Rc = r HC – r CH r HC r CH PMF: two bond distances Rc Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

24. Rc = r HC – r NH + r CH – r HN =R 4 r HC r CH r NH r HN PMF: four bond distances Rc Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

25. r HC r HN PMF: some failures on R 4 Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

26. r HC r CH r NH r HN PMF: switching functions with R 4 Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

27. PMF: mechanism. Distance analysis Significative stabilization of TS with respect to reactants Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

28. TS PMF: mechanism. Electrostatic energy perturbation analysis C  r jI Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc destabilization stabilization

29. Product PMF: mechanism. Electrostatic energy perturbation analysis Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc destabilization stabilization

30. PMF: mechanism. Comparison with uncatalized reaction Usually found in the literature to know the origin of the catalysis Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

31. + or + Mandelate Racemase + substrate PMF: mechanism. Comparison with uncatalyzed reaction Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

32. + + PMF: mechanism. Comparison with uncatalyzed reaction Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

33. Mulliken Charge( q ) and Bond Order( BO ) along the reaction coordinate as descriptors of the chemical reaction semiempirical PMF: mechanism. Comparison with uncatalyzed reaction Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

34. PMF: mechanism. Comparison with uncatalyzed reaction Bond Orders substrate + Lys166 substrate + His297 Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

35. PMF: mechanism. Comparison with uncatalyzed reaction not correlated values Bond Orders Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

36. PMF: mechanism. Comparison with uncatalyzed reaction Bond Orders substrate + Lys166 substrate + His297 The enzyme delocalizes the charge in the phenyl ring Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

37. PMF: mechanism. Comparison with uncatalyzed reaction The symmetry of the carboxylic group is different but not correlated to the reaction: Mg role Bond Orders substrate + Lys166 substrate + His297 Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

38. PMF: mechanism. Comparison with uncatalyzed reaction Bond Orders substrate + Lys166 substrate + His297 The symmetry of the carboxylic group is different but not correlated to the reaction: Mg role Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

39. PMF: mechanism. Comparison with uncatalyzed reaction Atomic Charges substrate + Lys166 substrate + His297 The enzyme does not substract charge from the C  Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

40. PMF: mechanism. Comparison with uncatalyzed reaction Atomic Charges substrate + Lys166 substrate + His297 Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

41. PMF: mechanism. Comparison with uncatalyzed reaction The symmetry of the carboxylic group is different but not correlated to the reaction: Mg role Atomic Charges substrate + Lys166 substrate + His297 Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

42. PMF: mechanism. Comparison with uncatalyzed reaction The symmetry of the carboxylic group is different but not correlated to the reaction: Mg role Atomic Charges substrate + Lys166 substrate + His297 Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

43. PMF: mechanism. Comparison with uncatalyzed reaction The OH group in the enzyme takes more charge: Mg role Atomic Charges substrate + Lys166 substrate + His297 Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

44. PMF: mechanism. Comparison with uncatalyzed reaction Charge and bond order analysis: Some differences can be seen between enzyme and the uncatalyzed reaction But the difference in the energy barrier comes probably from the electrostatic stabilization of the enzyme: Mg, Glu270, Ser139, Asp195, Glu220... Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

45. Conclusions: Mandelate Racemase The concerted mechanism is the most favourable No anionic stable intermediate exists, but a TS MR catalyzes the reaction in both directions(S  R, R  S) at “similar” rate, being chemically symmetric Some residues are important to stabilize unstable structures Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

46. Conclusions: Methodology The location of saddle points is a valuable task to design an appropriate reaction coordinate The difference between the MEP and Free Energy Path: The energy barrier can be very different (this is not the case) The geometry is conceptually different ...But some characteristics of the reaction remain! Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

47. too restricted methods: QM(1 valley)/MM Conclusions: Methodology Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

48. Conclusions: Methodology The reaction coordinate must include all the relevant degrees of freedom. They are localized in few bonds and angles but may not be trivial even in some proton transfer reactions. It should be a compromise: reduced number of dof to avoid coordinates that donot belong to the path, and general enough to account all the possible reactive conformations too restricted methods: Cartesian coordinates Rc Mandelate Racemase Optimization of TS PMF: mechanism PMF: Rc

49. ...the end