Post on 03-Jul-2015
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
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
MR
MR: the reaction
t1/2 =100 000 years
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
Substrate
MR:structure
concertedmechanism
2 stepwisemechanisms
Elements stabilizingthe anionic intermediate
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
MR: Active site and reactivity
reactant (S)-mandelateproduct (R)-mandelateS R
Lys166
His297
Glu317
Lys164
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
MR: Adiabatic mapping concerted mechanism
product (R)-mandelatereactant (S)-mandelate
Lys166
His297
Glu317
Lys164
Glu247
S R
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
MR: Adiabatic mapping stepwise mechanisms
product (R)-mandelatereactant (S)-mandelateS R
Lys166
His297
Glu317
Lys164
Glu247
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
MR: Adiabatic mapping mechanisms
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
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)
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
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
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
TS search: comparison refined TS with adiabatic mapping
Adiabaticmapping
TS search
Energetic and structural differences exist
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
TS search: comparison refined TS with adiabatic mapping
Structure: PDB
Potential Energy Surface: QM/MM
Free energy calculation: umbrella sampling
Molecular Dynamics: SBMD
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
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
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
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: computational details
Are non-bonded interactions univoquely reproduced in QM/MM?
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: computational details
X: mandelate63 atoms PM3-GHO / 8208 CHARMMStudy of the concerted mechanism
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: computational details
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
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: computational details
[ ][ ]∫
∫−
−−=
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
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
Every window: 15ps eq / 50ps sampling
PMF: computational details
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
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
S R
PMF: Selection of a Rc
rCHrHN
Rc = rHC – rNH
S R
rHC
rNH
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: two bond distances Rc
Rc = rCH – rHN
R S
rCHrHN
Rc = rHC – rCH
rHC
rCH
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: two bond distances Rc
Rc = rHC – rNH+ rCH – rHN=R4
rHC
rCH
rNH
rHN
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: four bond distances Rc
Mandelate Racemase Optimization of TS PMF: mechanismPMF: 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 −=
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: switching functions with R4
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Distance analysis
Significative stabilization of TS with respect to reactants
TS
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
∑ ∑= =
+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
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
reactIIprodIII EEEEE )()( 11 −− −−−=∆
PMF: mechanism. Electrostatic energy perturbation analysis
destabilization
stabilization
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalized reaction
Usually found in the literature to know the origin of the catalysis
+
or+
Mandelate Racemase+
substrate
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
++
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
Mulliken Charge(q) and Bond Order(BO) along the reaction coordinate as descriptors of the chemical reaction
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
∑∑∈∈
− =BA
BA PSPSBOν
νµµνµ
)()(
∑∑∈∈ BA
Pν
µνµ
2
semiempirical
∑∈
−=A
AA PSZqµ
µ)(
PMF: mechanism. Comparison with uncatalyzed reaction
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
Bond Orders
substrate + Lys166 substrate + His297
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
not correlatedvalues
Bond Orders
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
Bond Orders
substrate + Lys166 substrate + His297
The enzyme delocalizesthe charge in the phenylring
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
The symmetry of the carboxylicgroup is different but notcorrelated to the reaction: Mg role
Bond Orders
substrate + Lys166 substrate + His297
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
Bond Orders
substrate + Lys166 substrate + His297
The symmetry of the carboxylicgroup is different but notcorrelated to the reaction: Mg role
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
Atomic Charges
substrate + Lys166 substrate + His297
The enzyme does notsubstract charge fromthe Cα
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
Atomic Charges
substrate + Lys166 substrate + His297
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
The symmetry of the carboxylicgroup is different but notcorrelated to the reaction: Mg role
Atomic Charges
substrate + Lys166 substrate + His297
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
The symmetry of the carboxylicgroup is different but notcorrelated to the reaction: Mg role
Atomic Charges
substrate + Lys166 substrate + His297
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
PMF: mechanism. Comparison with uncatalyzed reaction
The OH group in the enzymetakes more charge: Mg roleAtomic Charges
substrate + Lys166 substrate + His297
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
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...
Conclusions: Mandelate Racemase
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
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
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
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
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
Conclusions: Methodology
Mandelate Racemase Optimization of TS PMF: mechanismPMF: Rc
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
...the end