Talk Jan05

Reaction Mechanism of Mandelate Racemase in a

QM/MM model: reaction path and catalysis

Xavier Prat-ResinaJanuary 28th, 2005 AD

Lluch’sgroup

Atmospheric Reactions / Enzymatic Reactions / Quantum dynamics

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: mechanismPMF: Rc

Potentials of Mean Force: mechanism and catalysis

less fast

pka~29in water

MR: the reaction

t1/2 =100 000 years

Substrate

MR:structure

concertedmechanism

2 stepwisemechanisms

Elements stabilizingthe anionic intermediate

MR: Active site and reactivity

reactant (S)-mandelateproduct (R)-mandelateS R

Lys166

His297

Glu317

Lys164

MR: Adiabatic mapping concerted mechanism

product (R)-mandelatereactant (S)-mandelate

Lys166

His297

Glu317

Lys164

Glu247

MR: Adiabatic mapping stepwise mechanisms

product (R)-mandelatereactant (S)-mandelateS R

Lys166

His297

Glu317

Lys164

Glu247

MR: Adiabatic mapping mechanisms

If core is not big there will be

coupling between the two zones

2nd order direct location. Permits the

relaxation of the environment

Iterative core/environment

The environment is never relaxed

2nd order direct location

Hessian for a core

There is no transition vector yet. Convergence

problems?

Direct location without Hessian

manipulation

CPR, NEB...chain methods

Not always so intuitive. Hysteresis

TS may not exist

Easy to perform Adiabatic mapping

A H Br

Hessian

frozen

Hessian

minimize

Optimization of TS:possible options

environment minimizationL-BFGS until |genv|<crit

looking for TS in coreRFO until |gcor|<crit

is environment minimized?NO

YESTransition state foundTransition state found

with |gwith |gTOTTOT|<|<critcrit

Initial geometry with a core and an environment

Suggestions:An adequate core sizemust be selected.

When minimizing, the QM wavefunction can be kept frozen (1SCF)

TS search: algorithm

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 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

Adiabaticmapping

TS search

Energetic and structural differences exist

TS search: comparison refined TS with adiabatic mapping

Structure: PDB

Potential Energy Surface: QM/MM

Free energy calculation: umbrella sampling

Molecular Dynamics: SBMD

PMF: computational details

ΦΦ= /ˆ/ elHE

∑∑

dihedrals

angles

∑∑

atoms mn

atoms r

semiemp: AM1,PM3semiemp-SRPEVB, HF, DFT...

Frontier:Link atomLSCFGHO...

qm: charmmambermullikenresp

++ΦΦ− ∑ ∑mi mj jm

atoms mj

QM QM/MM MM

A,B:charmmamberoptimized

charmmambergromosopls

+ Cutoff at 13 Å

Are non-bonded interactions univoquely reproduced in QM/MM?

X: mandelate63 atoms PM3-GHO / 8208 CHARMMStudy of the concerted mechanism

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

[ ] )()()()( 2 tftqmqtqmFtqm iiiiref

iiiiiii +−−Ω−= β

[ ][ ]∫

∫−

−−=

drTKrV

drTKrVRcrRcRc

/)(exp

/)(exp))(()(

Vtot = VQM/MM + k(Rc-Rc0)2 + Px(Rc)

Molecular Dynamics

Statistical treatment(WHAM)

CRRTRW cc +−= )(ln)( ρPMF=f(Rc)!!!

Scanning Rc inincrements of 0.2 Å windows

Every window: 15ps eq / 50ps sampling

Data from TSsearch

1.2001.5092.7361.004Rts

1.1171.6072.6121.055Ir

1.0132.0932.2581.011TS

0.9952.8451.5701.151Is

1.7721.1652.8681.004R

0.9962.8651.5221.194Sts

0.9952.9271.1581.804S

rHNrCHrHCrNH

4.61-0.3502.5432.4711.703-0.6071.864R

16.75-0.3122.0571.4231.227-0.3091.732Rts

16.46-0.3061.8281.1171.005-0.4901.607Ir

19.47-0.0580.9920.1670.165-1.0801.247TS

13.790.398-0.201-1.431-1.275-1.8500.419Is

13.810.412-0.220-1.541-1.343-1.869-0.328Sts

0.00.421-0.043-2.578-1.769-1.932-0.646S

∆EImproper Θ

rNC-rCNrHC-rNH

+rHN-rCH

rHC-rCHrHN-rCHrHC-rNHRc

PMF: Selection of a Rc

rCHrHN

Rc = rHC – rNH

PMF: two bond distances Rc

Rc = rCH – rHN

rCHrHN

Rc = rHC – rCH

PMF: two bond distances Rc

Rc = rHC – rNH+ rCH – rHN=R4

PMF: four bond distances Rc

PMF: some failures on R4

)'()( KrrfKrrfRc CHHNRNHHCS +−++−=

))·tanh(1(21

)( 44 RpcRfS −+=

))·tanh(1(21

)( 44 RpcRfR ++=

structure Sat CHHN rrK −=structure Rat ' NHHC rrK −=

PMF: switching functions with R4

PMF: mechanism. Distance analysis

Significative stabilization of TS with respect to reactants

∑ ∑= =

+ΦΦ−ΦΦ=Imi Imj jm

melI r

reactIITSIII EEEEE )()( 11 −− −−−=∆

PMF: mechanism. Electrostatic energy perturbation analysis

destabilization

stabilization

Product

reactIIprodIII EEEEE )()( 11 −− −−−=∆

PMF: mechanism. Electrostatic energy perturbation analysis

destabilization

stabilization

PMF: mechanism. Comparison with uncatalized reaction

Usually found in the literature to know the origin of the catalysis

Mandelate Racemase+

substrate

PMF: mechanism. Comparison with uncatalyzed reaction

Mulliken Charge(q) and Bond Order(BO) along the reaction coordinate as descriptors of the chemical reaction

∑∑∈∈

− =BA

BA PSPSBOν

νµµνµ

∑∑∈∈ BA

µνµ

semiempirical

∑∈

AA PSZqµ

Bond Orders

substrate + Lys166 substrate + His297

not correlatedvalues

Bond Orders

The enzyme delocalizesthe charge in the phenylring

The symmetry of the carboxylicgroup is different but notcorrelated to the reaction: Mg role

Bond Orders

Atomic Charges

The enzyme does notsubstract charge fromthe Cα

Atomic Charges

The OH group in the enzymetakes more charge: Mg roleAtomic Charges

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...

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

Conclusions: Methodology

The location of saddle points is a valuable task to designan 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!

too restricted methods:QM(1 valley)/MM

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

...the end

Talk Jan05

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