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

fast

less fast

slow

pka~29in water


MR

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

S R


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

E

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

bonds

r

nk

k

rrk

2

2

2

)(

)(

)(

0

0

δφ

θθ

φ

θ

∑∑

−++

atoms mn

mn

mn

mn

atoms r

B

r

A

r

qq

nm

nm

612,

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

Frontier:Link atomLSCFGHO...

qm: charmmambermullikenresp

++ΦΦ− ∑ ∑mi mj jm

mj

im

m

rqZ

rq

, ,

∑

−+

atoms mj

mj

mj

mj

rB

rA

612

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

Btot

Btot

/)(exp

/)(exp))(()(

0

0

δρ

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


rHC

rNH

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


S R

PMF: Selection of a Rc

rCHrHN

Rc = rHC – rNH

S R

rHC

rNH


PMF: two bond distances Rc

Rc = rCH – rHN

R S

rCHrHN

Rc = rHC – rCH

rHC

rCH


PMF: two bond distances Rc

Rc = rHC – rNH+ rCH – rHN=R4

rHC

rCH

rNH

rHN


PMF: four bond distances Rc


rHC

rHN

PMF: some failures on R4

)'()( KrrfKrrfRc CHHNRNHHCS +−++−=

rHC

rCH

rNH

rHN

))·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

TS


∑ ∑= =

+ΦΦ−ΦΦ=Imi Imj jm

mj

im

melI r

qZrq

HE, ,

/ˆ/

reactIITSIII EEEEE )()( 11 −− −−−=∆

PMF: mechanism. Electrostatic energy perturbation analysis

Cα

rjI

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

+

or+

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

Pν

µνµ

2

semiempirical

∑∈

−=A

AA PSZqµ

µ)(




Bond Orders

substrate + Lys166 substrate + His297



not correlatedvalues

Bond Orders



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




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

http://cjs-online.com/mayhew/gallery_clipart/9810_chum_guard/hurrah.GIF

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

Technology

Transcript of Talk Jan05