Next-generation DFT-based quantum
models for simulations of biocatalysis
Darrin M. York
University of
Minnesota
Minneapolis,
Minnesota USA
http://theory.chem.umn.edu
Outline
• AM1/d-PhoT model for RNA catalysis
• Efficient treatment of long-range
electrostatics in semiempirical
calculations
• Improved charge-dependant response
properties
• Selected applications
…in words
• Study phosphate reactivity comprehensively (using small
models) with high-level quantum models (ab initio and DFT)
• Construct accurate semiempirical quantum models capable of
being used in linear-scaling electronic structure and QM/MM
simulations
• Develop improved (accurate, fast and general) models for
electrostatics, solvation and generalized solvent boundary
potentials.
• Investigate how to improve next-generation semiempirical
quantum models to account for charge-dependent response
properties without significant sacrifice of efficiency.
• Validate methods with respect to known reactions in solution,
then apply them to the important problem of RNA catalysis in
a realistic system consisting of many thousands of particles,
and simulated for many tens of nanoseconds.
Phosphates and phosphoranes
Mechanisms for phosphoryl transfer
O
Dissociative
ROlg
O
P
R
O O
O
ROlg
ANDN
Associative
AN+DN
P
O O
DN
Concerted
Olg
ROlg
P

OnucR
ROlg
O
P
O O
O O
O
O
P
O O
OnucR
RO lg
P
O O

OnucR
OnucR
QCRNA – Online!
Molecule (2000+)
http://theory.chem.umn.edu/QCRNA
Reaction Mechanism (300+)
Giese et al., J. Mol. Graph. Model. 25, 423 (2006).
QCRNA – Online!
http://theory.chem.umn.edu/QCRNA
Potential Energy Surface
Reaction
Tables
Graphical
Interface
Giese et al., J. Mol. Graph. Model. 25, 423 (2006).
Phosphate isomerization (Migration)
movie
Liu et al., J. Phys. Chem. B, .109, 19987 (2005); Chem. Commun., 31, 3909 (2005).
Silva-Lopez et al., Chem. Eur. J., 11, 2081 (2005);
Mayaan et al., J. Biol. Inorg. Chem., 9, 807 (2004).
Range et al., J. Am. Chem. Soc., 126, 1654 (2004).
Parameter Optimization: AM1/d Methods
 (λ )    wiα Yi (λ )  Yi
Mol Prop
2
Semi
i

wi  ( i )
DFT
2

2
  (λ )  γ  (C  λ  b) 0
2
T
Training set included a wide variety of biological phosphates and
phosphoranes, hydrogen bonded complexes, proton affinities and
reaction paths of associative and dissociative mechanisms in different
charge states.
Nam et al., J. Chem. Theory Comput., submitted.
Why use a semiempirical model?
It is important to note that for the ribozyme systems of interest, the
details of the mechanisms remain topics of considerable debate.
Hence the goal is to test multiple mechanisms with a model that is
sufficiently predictive to discern the most probable path.
A consensus has emerged that, in certain ribozymes such as HHR and
HDV, a large scale conformational change either precedes or is
concomitant with the chemical step of the reaction.
This necessitates the use of a quantum model that is able to be used
with extensive conformational sampling (i.e., simulation) while providing
an accurate description, in terms of energy, structure and charge
distribution, along multiple mechanistic paths (i.e., not a single predetermined 1-D reaction coordinate) in order to be predictive.
Modification for AM1/d-PhoT Model
Want a d-orbital method for hypervalent species, but one that also
describes reasonably hydrogen bonding interactions. Combine MNDO/d
framework with a modified core-core term similar to AM1 (and retaining
some AM1 parameters unmodified) to build a semiempirical model for
phosphoryl transfer reactions: AM1/d-PhoT
Core-Core Repulsion

MNDO
E AB
 Z A Z B s A s A sB sB 1  e A RAB  e B RAB
E AB 
MNDO
E AB


Z A Z B 4 A biA ( RAB ciA )2
B biB ( R AB ciB )2

 ai e
 ai e
RAB i 1
MNDO

AM1 and PM3
Modified Core-Core Repulsion
E AB 
MNDO
E AB

4
Z AZ B
A biA ( R AB ciA )2
B biB ( R AB ciB )2

G AGB  ai e
 ai e
RAB
i 1
If GA and GB = 0,
 MNDO Hamiltonian
If GA and GB = 1,
 AM1 and PM3

AM1/d-PhoT Model for Phosphoryl Transfer
AM1/d-PhoT Model for Phosphoryl Transfer
AM1/d-PhoT Model for Phosphoryl Transfer
AM1/d-PhoT Model for Phosphoryl Transfer
AM1/d-PhoT Model for Phosphoryl Transfer
Reaction Energies and Barrier Heights
Error*
Neutral Rxn
AM1/d
AM1
PM3
Monoanionic Rxn
AM1/d
AM1
PM3
Dianionic Rxn
AM1/d
AM1
PM3
Dissociative Rxn
AM1/d
AM1
PM3
Reaction Energy
5
No. Rxn
4
2
3
MSE
2.07
-7.32 -10.78
0.84
-2.48
-4.94
-1.44
-9.00
-2.96
5.25 -23.24 -12.35
MUE
2.86
7.39 10.78
1.96
9.79
8.80
2.28
9.00
5.65
5.25 23.24 12.35
Activation Energy
No. TS
13
11
4
MSE
0.76
3.48 -18.76
-2.91
-0.36 -12.74 -3.33 -22.58 -31.77
MUE
3.61
6.62 18.76
3.57 12.23 16.23
3.33 22.58 31.77
3
3.35 10.08 -10.38
6.60 10.08 10.38
Relative Intermediate Energy
No. Int
8
7
MSE
-1.06 -42.29 -26.61 -6.59 -42.34 -34.10
MUE
2.36 42.29 26.61
6.59 42.34 34.10
*Errors are computed against “B3LYP/6-311++G(3df,2p) adiabatic energies”
Linear Free Energy Relations
Transphosphorylation
of a cyclic phosphate
with enhanced leaving
groups.
Slope of plot is the
Brønsted correlation
parameter βlg often
used to characterize
phosphoryl transfer
reactions.
The logk values were
calculated from DFT
and are contained in
QCRNA.
Gas Phase Proton Affinity I
Molecule
Ref.
Error
B3LYP
AM1/d
AM1
PM3
MNDO/d
H3O+
165.0
-1.1
3.8
-2.0
-11.8
5.6
HOH
390.3
0.1
5.4
20.5
11.3
30.6
CH3OH
381.5
-2.2
2.0
2.7
-1.9
1.8
CH3CH2OH
378.2
-2.2
2.9
4.7
-0.4
5.2
C6H5OH
350.1
-2.4
-3.4
-3.1
-6.9
0.0
CH3CO2H
347.2
-0.8
-2.7
6.1
0.9
9.6
P(O)(OH)(OH)(OH)
330.5
-2.4
-3.4
7.6
15.0
-12.2
P(O)(O)(OH)
310.6
-0.1
1.5
20.6
35.1
-3.6
P(O)(O)(OH)(OH)-
458.9
-1.1
-1.9
16.8
24.7
-2.8
P(O)(O)(O)(OH)2-
581.1
-1.7
10.4
33.7
36.4
16.3
P(O)(OH)(OH)(OCH3)
329.3
0.4
0.3
7.2
14.9
-12.0
P(O)(O)(OH)(OCH3)-
454.9
-1.4
0.7
16.5
22.8
-7.6
P(O)(OH)(OCH3)(OCH3)
329.4
0.7
1.8
7.3
12.3
-14.1
P(O)(OH)(OCH2CH2O)
329.5
-0.1
-0.2
7.6
11.8
-17.1
MSE
-1.0
0.9
9.4
8.5
-5.1
MUE
1.1
2.4
9.8
11.0
11.4
Range et al., Phys. Chem. Chem. Phys. 7, 3070 (2005).
B3LYP: B3LYP/6-311++G(3df,2p)//B3LYP/6-31++G(d,p)
Gas Phase Proton Affinity II: Phosphorane Compounds
Molecule
Ref.
Error
B3LYP
AM1/d
AM1
PM3
MNDO/d
P(OH)(OH)(OH)(OH)(OH)
351.0
-0.4
3.0
9.0
8.3
-1.3
P(OH)(OH)(OH)(OH)(OH)
341.0
-1.8
1.8
13.6
9.0
-8.7
P(OH)(OH)(OCH2CH2O)(OH)
351.9
-0.9
1.2
5.9
1.7
-11.8
P(OH)(OH)(OCH2CH2O)(OH)
343.2
-1.1
-2.5
8.0
-0.5
-17.4
P(OH)(OCH2)(OCH2CH2O)(OH)
345.2
-0.7
-3.5
3.6
-2.3
-20.2
P(OH)(OCH2)(OCH2CH2O)(OH)
352.0
-0.8
2.3
5.4
-0.4
-27.0
P(OH)(OH)(OCH2CH2O)(OCH2)
343.5
-1.1
-0.7
6.2
-0.9
-19.5
MSE
-1.0
0.2
7.4
2.1
-15.2
MUE
1.0
2.1
7.4
3.3
15.2
Range et al., Phys. Chem. Chem. Phys. 7, 3070 (2005).
B3LYP: B3LYP/6-311++G(3df,2p)//B3LYP/6-31++G(d,p)
Example: QM/MM of Di-anionic Reactions in Water
35
EP(-)….OH(-)
DMP(-)…OH(-)
TMP(-)...OH(-)
30
25
20
15
10
5
0
-6
Comparison with DFT and Expt.
Gas
Gas
Rxn
Rxn
DMP
EP
TMP
-5
-4
-3
-2
-1
-5
0
1
2
3
4
5
-10
in kcal/mol
q = R(P-Ol) - R(On-P)
Aquo
Aquo
AM1/d
AM1/d
DFT
DFT
AM1/d
AM1/d
Expt
Expt
TS1
82.2
88.3
32.1
~32
TS2
78.7
87.5
31.5
Prod
-13.1
-7.8
-3.1
TS
84.2
86.7
24.2
Prod
30.2
35.9
-5.6
TS
86.0
89.0
28.8
Prod
25.6
29.3
-0.5
21~24
*DFT: B3LYP/6-311++G(3df,2p)
~32
Dejaegere and Karplus, JACS 1993
Cox and Ramsay, Chem. Rev. 1964
6
Problems
• Dispersion interactions
• Relative conformational energies: sugar
puckering and pseudorotation transition
states
• Proper treatment of polarizability and
multiple charge states
The Problem of Charge-dependent Response Properties
with Semiempirical Methods
Atoms are of
course an
extreme case:
but typically
polarizabilities of
neutral
molecules are
typically off by
25%, and
anions by
significantly
more…
Giese et al., J. Chem. Phys., 123, 164108 (2005).
Goal: Improve charge-dependent response
properties of semiempirical methods
without significantly increasing
computational cost.
Possible solutions:
• Reparameterize models
• Increase minimal basis-set representation
• Make basis set exponents charge
dependent
DFT-based model…
E[  ]  F [  ]    (r )v(r )d r
3



 E[  ]     (r )d r  N  0
3
Giese et al., J. Chem. Phys. 123, 164108 (2005).
E[  ]  E[  ref ]  E(1ref, 2,) []
     ref
E  ref
(1, 2 ,)
[]  E[  ]  E[  ref ]
 E[  ] 
3
(r )d r
 

 (r )   ref
2

 E[  ] 
1
3
3

r  
rd
d
)
r
(

   (r ) 

2
 (r )(r)   ref
E[  ]  E[  ]  E(1ref, 2) []  
(r )   ck k (r )
k
E(1ref, 2) []  cT  m  12 cT  η  c
 E[  ] 
3
mi   
i (r )d r

 (r )   ref
  2 E[  ] 
3
3

ij    i (r ) 

(
r
)
d
rd
r
j

 (r )(r)   ref

 3
mi   i (r ) v(r )   Dij (rij ) j (r ) d r
j


i (r ) j (r) 3 3
ij  Dij (rij )  
d rd r 
| r  r |
D(rij )  D(rij ; Ci ,Wi )  D(rij ; C j , W j )
2
2



(
q
)
 i ( qi ) 2 |r  R i |
2
i
i
(u  U i )e
i (r)  2 i (qi ) 
  
1/ 3
 3



 i (qi )  



(
q
)
2
 i i

 i (qi )   i (0)  e
3 Bi qi
A Variational Electrostatic Projection
(VEP) Method for QM/MM Calculations
Goal: Model large-scale electrostatic effects of
solvent-shielded macromolecular environment - and
it’s linear response – in hybrid QM/MM calculations
for a fraction of computational cost of explicit
simulation
Method: Green’s function approach that involves
variational projection and reduced dimensional
mapping of surrounding solvent-shielded
macromolecular environment onto the dynamical
reaction zone
Gregersen and York, J. Phys. Chem. B, 109, 536-556 (2005).
Gregersen and York, J. Comput. Chem., 27, 103 (2006).
Multi-scale Quantum Models
External potential
of solute and
solvent
Stochastic
boundary
Reaction Region
QM active site +
MM surrounding
(Newtonian dynamics)
Buffer Region
(Langevin dynamics)
Linear-scaling QM/MM-Ewald
Method
Nam et al., J. Chem. Theory Comput., 1, 2 (2005).
Applications to enzymes and
ribozymes
• Hammerhead ribozyme
Best characterized ribozyme – but complicated: role of
metals, chemical/conformational steps, non-inline
native structure
• Hairpin ribozyme
No metal cofactor, in-line configuration
General acid/base mechanism
Tai-Sung Lee et al., submitted.
Mg2+ ion is observed to
coordinate the O2’ of G8
increasing it’s acidity in the
early TS and then migrate
closer to the leaving group O5’
position of the scissile
phosphate in the late TS.
Simulations help to explain the
long-standing disconnect
between available structures
and biochemical data (in
particular, thio effect studies).
Early TS
Late TS
Other Projects…
• Parameters for RNA reactive intermediates
• DNA bending
• Polarization-exchange coupling
• Linear-scaling electronic structure
Acknowledgements
•
•
•
•
•
•
•
George Giambasu
Dr. Tim Giese
Yun Liu
Dr. Evelyn Mayaan
Adam Moser
Dr. Kwangho Nam
Dr. Kevin Range
•
•
•
•
•
Dr. Olalla Nieto Faza
Dr. Francesca Guerra
Dr. Carlos Silva Lopez
Prof. Xabier Lopez
Dr. Anguang Hu
•
•
•
•
•
Prof Bill Scott
Prof. Qiang Cui
Dhd Marcus Elstner
Prof. Jiali Gao
Prof. Walter Thiel
Funding/Resources:
• University of Minnesota
• NIH
• ACS-PRF
• Army High-Performance Computing Research Center
• Minnesota Supercomputing Institute