Next-generation DFT-based quantum models for simulations of biocatalysis

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Next-generation DFT-based quantum models for
simulations of biocatalysis

• Darrin M. York
• University of Minnesota
• Minneapolis, Minnesota USA

http//theory.chem.umn.edu
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Outline

• AM1/d-PhoT model for RNA catalysis
• Efficient treatment of long-range electrostatics
  in semiempirical calculations
• Improved charge-dependant response properties
• Selected applications

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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.

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Phosphates and phosphoranes
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Mechanisms for phosphoryl transfer
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QCRNA Online! http//theory.chem.umn.edu/QCRNA
Molecule (2000)
Reaction Mechanism (300)
Giese et al., J. Mol. Graph. Model. 25, 423
(2006).
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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).
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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).
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Parameter Optimization AM1/d Methods
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.
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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 pre-determined 1-D
reaction coordinate) in order to be predictive.
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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
AM1 and PM3
Modified Core-Core Repulsion
If GA and GB 1, ? AM1 and PM3
If GA and GB 0, ? MNDO Hamiltonian
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AM1/d-PhoT Model for Phosphoryl Transfer
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AM1/d-PhoT Model for Phosphoryl Transfer
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AM1/d-PhoT Model for Phosphoryl Transfer
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AM1/d-PhoT Model for Phosphoryl Transfer
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AM1/d-PhoT Model for Phosphoryl Transfer
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Reaction Energies and Barrier Heights
Error Neutral Rxn Neutral Rxn Neutral Rxn Monoanionic Rxn Monoanionic Rxn Monoanionic Rxn Dianionic Rxn Dianionic Rxn Dianionic Rxn Dissociative Rxn Dissociative Rxn Dissociative Rxn
Error AM1/d AM1 PM3 AM1/d AM1 PM3 AM1/d AM1 PM3 AM1/d AM1 PM3
Reaction Energy Reaction Energy Reaction Energy
No. Rxn 5 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 Activation Energy Activation Energy
No. TS 13 11 4 3
MSE 0.76 3.48 -18.76 -2.91 -0.36 -12.74 -3.33 -22.58 -31.77 3.35 10.08 -10.38
MUE 3.61 6.62 18.76 3.57 12.23 16.23 3.33 22.58 31.77 6.60 10.08 10.38
Relative Intermediate Energy Relative Intermediate Energy Relative Intermediate Energy Relative Intermediate Energy Relative Intermediate Energy 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/6-311G(3df,2
p) adiabatic energies
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Linear Free Energy Relations
Transphosphorylation of a cyclic phosphate with
enhanced leaving groups. Slope of plot is the
Brønsted correlation parameter ßlg often used to
characterize phosphoryl transfer reactions. The
logk values were calculated from DFT and are
contained in QCRNA.
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Gas Phase Proton Affinity I
Molecule Ref. Error Error Error Error Error
Molecule Ref. 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/6-311G(3df,2p)//B3LYP/6-31G(d,p)
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Gas Phase Proton Affinity II Phosphorane
Compounds
Molecule Ref. Error Error Error Error Error
Molecule Ref. 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/6-311G(3df,2p)//B3LYP/6-31G(d,p)
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Example QM/MM of Di-anionic Reactions in Water
Rxn Gas Gas Gas Aquo Aquo
Rxn AM1/d DFT AM1/d AM1/d Expt
DMP TS1 82.2 88.3 32.1 32.1 32
TS2 78.7 87.5 31.5 31.5
Prod -13.1 -7.8 -3.1 -3.1
EP TS 84.2 86.7 24.2 24.2 2124
Prod 30.2 35.9 -5.6 -5.6
TMP TS 86.0 89.0 28.8 28.8 32
Prod 25.6 29.3 -0.5 -0.5
Rxn Gas Gas Gas Aquo Aquo
Rxn AM1/d DFT AM1/d AM1/d Expt
DMP TS1 82.2 88.3 32.1 32.1 32
TS2 78.7 87.5 31.5 31.5
Prod -13.1 -7.8 -3.1 -3.1
EP TS 84.2 86.7 24.2 24.2 2124
Prod 30.2 35.9 -5.6 -5.6
TMP TS 86.0 89.0 28.8 28.8 32
Prod 25.6 29.3 -0.5 -0.5
DFT B3LYP/6-311G(3df,2p)
Dejaegere and Karplus, JACS 1993 Cox and Ramsay,
Chem. Rev. 1964
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Problems

• Dispersion interactions
• Relative conformational energies sugar puckering
  and pseudorotation transition states
• Proper treatment of polarizability and multiple
  charge states

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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).
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• 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

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DFT-based model
Giese et al., J. Chem. Phys. 123, 164108 (2005).
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A Variational Electrostatic Projection (VEP)
Method for QM/MM Calculations
Goal Model large-scale electrostatic effects of
solvent-shielded macromolecular environment - and
its linear response in hybrid QM/MM
calculations for a fraction of computational cost
of explicit simulation Method Greens 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).
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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)
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Linear-scaling QM/MM-Ewald Method
Nam et al., J. Chem. Theory Comput., 1, 2 (2005).
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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

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General acid/base mechanism
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Tai-Sung Lee et al., submitted. Mg2 ion is
observed to coordinate the O2 of G8 increasing
its 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).
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Early TS
Late TS
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Other Projects

• Parameters for RNA reactive intermediates
• DNA bending
• Polarization-exchange coupling
• Linear-scaling electronic structure

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Acknowledgements

• George Giambasu
• Dr. Tim Giese
• Yun Liu
• Dr. Evelyn Mayaan
• Adam Moser
• Dr. Kwangho Nam
• Dr. Kevin Range

• Prof Bill Scott
• Prof. Qiang Cui
• Dhd Marcus Elstner
• Prof. Jiali Gao
• Prof. Walter Thiel

• Dr. Olalla Nieto Faza
• Dr. Francesca Guerra
• Dr. Carlos Silva Lopez
• Prof. Xabier Lopez
• Dr. Anguang Hu

• Funding/Resources
• University of Minnesota
• NIH
• ACS-PRF
• Army High-Performance Computing Research Center
• Minnesota Supercomputing Institute