Combined Quantummechanics Molecularmechanics

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Combined Quantum-mechanics / Molecular-mechanics
Computational Chemistry 5510 Spring 2006 Hai Lin
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Can We Simulate Enzyme Reactions?

• Proteins Catalyze Biochemical Reactions
• Highly Efficient
• Highly Specific
• Highly Important

• How do enzymes work?
• Which reaction mechanism is involved?
• What is the role of the protein environment?

Molecular Modeling and Dynamics at the Atomic
Level (Classical and/or Quantum)
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Limitations of Molecular Mechanics (MM)
The bond-breaking and bond-forming cannot be
described.
Energy
MM Description Based on the Bonding Pattern of
Product
MM Description Based on the Bonding Pattern of
Reactant
A
A
B
C
B
C
Reactant
Product
Correct description
Progress of Reaction
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Limitations of Quantum Mechanics (QM)
Application of quantum mechanics is limited by
the high computational costs.
Accuracy
Accurate Quantum Mechanical Methods
?
Number of Atoms
1000
10,000
10
100
Atom and Small Molecules
Large Compounds and Nano-clusters
Proteins, DNA, RNA
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Quantum Mechanics vs. Molecular Mechanics
Quantum Mechanics
Molecular Mechanics
? Correctly Describes the Bond- breaking and
Bond-forming
? Does Not Properly Describe the Bond-breaking
and Bond-forming
? Application Limited to Hundreds of Atoms
? Can Treat More Than 10,000 Atoms
A marriage ?
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Combined Quantum-Mechanics/Molecular-Mechanics
(QM/MM)

• Partition the entire system into two regions an
  active site and an interacting environment.

Active Site

• Describe the small active center by QM and
  surrounding protein and solvent by MM.

Protein-Solvent Environment

• Advantages
• Combines an accurate quantum-mechanical
  description with the low computational cost of
  classical mechanics.
• Provides a realistic description for the active
  site in the presence of protein-solvent
  environment.
• Permits detailed analysis of the role of the
  environment.

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Interactions between QM and MM Regions

• Three kinds of interactions
• Bonded (stretch, bend, and torsion) interactions
• Van der Waals interactions
• Electrostatic interactions
• Three embedding schemes for electrostatic
  interactions

Active Site
Protein-Solvent Environment

• Mechanical embedding
• QMMM electrostatic interactions calculated at
  the MM level
• Electric embedding
• QM calculations done with a background charge
  distribution (MM point charges)
• Polarized embedding
• QM and MM regions polarize each other until
  self-consistent.

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Cutting a Covalent Bond
MM QM
Example CF3-CH2OH

• Link-atom scheme
• Saturate the dangling bond at the QM/MM boundary
  by a (parameterized) H atom
• Simple and straightforward
• Local-orbital scheme
• Describe the dangling bonds by a set of local
  sp3-hybrid orbitals
• Theoretically more fundamental, but complicated
  and elaborate to implement
• Redistributed-charge scheme
• Simplify the local hybrid-orbitals by a set of
  point charges
• A classical analog to the local-orbital scheme,
  while simple and straightforward

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Example Highlight P450cam Monooxygenases

• Iron-hemo-proteins Involved in the Metabolism of
  Very Diverse Compounds

• Biohydroxylation of non-activated C-H bonds

• The Elusive Oxidant Compound I (Cpd I)

• Experiments conclude that Cpd I is present in the
  catalytic cycle of P450 but eludes detection due
  to its high reactivity.

For example, Ortiz de Montellano, P. R. Ed.
Cytochrome P450 Structure, Mechanisms and
Biochemistry, 2nd ed. Plenum Press New York,
1995 Vol. 2.
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P450cam by QM/MM Calculations

• Partition the entire system into two regions the
  active site (QM) and the protein-solvent
  subsystem (MM).

• Compare for different protein conformations in
  the molecular dynamics (MD) trajectory.

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A Porphyrin-dominated Radical or a
Sulfur-centered Radical?
Characterization of the Electronic Structure of
the P450 Compound I
(A) Porphyrin-domindated Radical
(B) Sulfur-centered Radical
Model Compounds Similar Enzymes (Chloro
Peroxidase)2
(A)
QM Isolated Model for Active Site3
(B)
QM/MM4
(A)
1 See for example Sono, M. et al. Chem. Rev.
1996, 96, 2841. 2 Antony, J. et al. J. Phys.
Chem. A 1997, 101, 2692. 3 Filatov, M. et. al.
J. Chem. Soc., Perkin. Trans. 1999, 2, 399. 4
Schöneboom, J. C. et al. J. Am. Chem. Soc. 2004,
126, 4017.
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A Porphyrin-dominated Radical or a
Sulfur-centered Radical?

• Stabilized by Polarization due to Protein-Solvent
  Environment

Resonance

• Stabilized by Hydrogen-bonding Network

(A) Preferred in the Protein Pocket
(B) Preferred by Isolated Model
1 Schöneboom, J. C. Lin, H., Reuter, N. Thiel,
W., Cohen, S., Ogliaro, F., Shaik, S. J. Am.
Chem. Soc. 2004, 126, 4017.
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Summary

• Combined Quantum Mechanics and Molecular Mechanics

• Combines an accurate quantum-mechanical
  description with the low computational cost of
  classical mechanics.
• Provides a realistic description for the active
  site in the presence of the protein-solvent
  environment.
• Permits detailed analysis of the role of the
  environment.

• Interactions between QM and MM Regions
• Bonded, VDW, Electrostatic interactions
• Link-atom, Local-orbital, Redistributed-charge
  boundary treatments

• A Demonstration
• The Radical Nature of the Elusive Oxidant
  P450cam Compound I
• (The protein-solvent environment does make a
  difference!)

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Your Homework

• Read the Slides and Textbook

2.10

• Questions
• What kind of interactions (bonded, VDW,
  electrostatic) between QM and MM regions is the
  most important?
• What is the ONIOM method? (Textbook page 51)

• Futher Reading
• If you are interested in learning more about
  QM/MM, the review listed below is good for a
  beginner
• H. Lin, D. G. Truhlar, QM/MM What have we
  learned, where are we, and where do we go from
  here?Theoretical Chemistry Accounts, in press.
  (The keynote presentation in the 10th Electronic
  Computational Chemistry Conference.)