A Combined QMMM Approach to ProteinLigand Interactions:

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A Combined QM/MM Approach to Protein-Ligand
Interactions Polarization Effects of the HIV-1
Protease on Selected High Affinity Inhibitors
Hensen, C. Hermann, J.C. Nam, K. Ma, S. Gao,
J. Holtje, H.D. J. Med. Chem. 2004, 47,
6673-6680
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OUTLINE
? Give background information on AIDS , the HIV-1
Protease, and effective inhibitors of the
HIV-1 Protease ? Introduce Quantum Mechanical
calculations, Molecular Mechanical force
fields, and combined QM/MM techniques used in
computational chemistry. ? Discuss the goals,
methods and results of the paper written by
Hensen, et al.
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AIDS

• What is it?
• Where does it come from?
• Do a lot of people have it?

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What is it?

• AIDS is an acronym for
• Acquired Immunodeficiency Syndrome
• Acquired Not hereditary need to have contact
  with a disease
• causing agent
• Immunodeficiency Weakening of the immune system
• Syndrome Group of symptoms that characterize a
  disease

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AIDS

• What is it?
• Where does it come from?
• Do a lot of people have it?

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Do a lot of people have it?

• United States in 2004 944,305 (cumulative)1
• 42,514 diagnosis in the US in 20041
• Globally in 2004 39.4 million (cumulative)1
• Through 2004 in the US 529,113 dead1

1. Centers for Disease Control and Prevention.
http//www.cdc.gov/hiv
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What is HIV?
Human immune defense system
Retrovirus
Lentivirus
Enveloped RNA viruses
?TM Transmembrane component ?SU Surface
component ?MA Matrix protein ?CA Capsid
protein ?RT Reverse transcriptase ?IN
Integrase ?PR Protease
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Life-Cycle of the HIV Virus
1 Binding and fusion - CD4, CCR5, and
CXCR4 receptors 2 Reverse transcription
- Single stranded RNA to DS-DNA 3 Integration
- Integrase and provirus (dormant) 4
Transcription - Provirus RNA
Polymerase genome mRNA 5 Assembly
- HIV-1 Protease cuts chains of proteins 6
Budding - Host cells outer envelope
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Real Life Budding
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HIV-1 Protease used in Assembly
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Flap Region
? Created by residues 33-62 and 33-62
? Ile50/50 - Critical for substrate binding
? Controls binding to active site
Flexible gate for approaching ligands
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Active Site
? Aspartyl Protease Family - Asp25/25
(symmetric dyad) - Highly conserved 3
amino acid sequence - Aspartic
Acid/Threonine/Glycine - Complex hydrogen
bonding system known as the Firemans
Grip
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Assembly Mechanism
? Gag and Gal-Pol polypeptide cleaved between
Phenylalanine and Proline or Tyrosine and
Proline
Cleavage Mechanism
Bound Water
Nucleophilic attack on carbonyl
Proton stabilization of oxyanion
N-bond protonated and cleaved
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Inhibition
Interruption of HIV-1 PR activity
No mature HIV virus particles
Ritonavir
Saquinavir
Tipranavir
Indinavir
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Difficulties of Enzyme Inhibition

• Viral mutations and viral resistance
• Inadequate drug absorption
• Unable to cross Blood/Brain Barrier
• Used up by other proteases in the stomach
• Side Effects (Liver toxicity, diabetes)
• Compliance with the active site

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Finding Inhibitors That Work
Computational Chemistry
? Polarization Interaction Energy (very system
oriented) - Effect of enzyme
electric field on inhibitor ? Electrostatic
Energy (rigid representation system is not
polarizable) - Correlated to
binding affinity of active site and inhibitor
Product
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Molecular Mechanics
Bonds
Distorted
Molecules
Atoms
Parameters
Bond Stretching E ? k ( r - r0 )2 /
2 Bond Angle Bending E ? k/ (
? - ?0 )2 / 2 Torsions E ? V1 ( 1 cos
???????V2 ( 1 - cos
2??????V3 ( 1 cos 3????????????? Electrostatics
E ? k / / ?q1 q2 / r2 van der Waals
E ?? k / / / ? 1 / r12 - 1 / r6
E Estr Ebnd Etor Eelec Evdw
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Molecular Mechanics
Combinations of equations and calculated
parameters
Force Fields
Provide calculations of molecular geometry and
conformation
Different Force Fields

• SYBYL -OPLS-AA
• -MMFF94 -AMBER
• -CHARMM

Potential Energy Surface
PROBLEM MM only uses electrostatic energy no
polarization energy!
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Molecular Potential Energy Surface
Every point on surface corresponds to a different
conformation - Looking for Global Minimum
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Quantum Mechanics
Nuclei
No Chemical Bonds
Molecules
Electrons
Electron distribution for fixed arrangement of
nuclei
H? E?
Electronic Motion
Wave Function
Calculates energy of atoms as electrons move
PROBLEM
Except for 1-electron systems, Schrodinger
Equation cannot be solved exactly
Energy for the system
E PE KE
Linear combination of atomic orbitals
NP NN NE
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Approximations
Ab initio
Semi-empirical
Begins calculations from scratch no empirical
parameters
Uses predetermined assumptions and calculated
parameters
Considerable computational resources needed for
anything but small systems
Faster calculations
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Hartree-Fock Theory (Ab initio)
e-
e-
e-
e-
e-
? Uses finite number of mathematical functions,
basis sets, to solve Schrodinger Equation ?
Able to do this because electron-electron
interaction is approximated - Interaction
between electron of one orbital interacting
with all other electrons in the molecule
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Semi-Empirical Method
Only valence electrons
Minimal valence representation in basis set
(unlike HF)
Hartree-Fock Theory
Example
A First Row Transition Metal (Al, Mg) 3dx2y2,
3dz2, 3dxy, 3dxz, 3dyz, 4s, 4px, 4py, 4pz
Central Approximation
??u?vd? 0 ?u and ?v not on same atom
Neglect of Diatomic Differential Overlap Atomic
orbitals residing on different atomic
centers do not overlap
Semi-empirical Austin Model 1 (AM1)
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Electron Correlation
More flexible description of electron-electron
interactions and electron motions
Electrons interact directly and are allowed to
avoid one another (correlated movements)

• Models
• Configuration Interaction (CI)
• -Moller-Plesset (MP)

Electron correlation is included in calculations
Focuses on electron density rather then wave
function
Density Functional Theory
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Density Functional Theory
Electron Spin Densities
Electron density of system
E ET EV EJ EXC
EXC(p) EX(p) EC(p)
Electronic energy
Electron-electron repulsion energy
Kinetic energy of motion
Exchange energy from quantum mechanical wave
function
Potential energy of nuclear-electron attraction
and repulsion
Correlation in motion of electrons
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Combined QM/MM
Solvent (water) MM
QM/MM
QM
Solute enzyme, cofactor, substrate
Diagram courtesy of Yao Fan from U. of Minnesota
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Theory Used by Paper
H H0 HQM/MM HMM
Total E of MM subsystem protein, solvent, and
VDW interactions between MM and QM
Interaction between inhibitor and enzyme
Inhibitor
?Eel ?Eperm ?Epol
Polarization energy
Permanent interaction energy (gas phase)
?Epol ?Estab ?Edist
Total electrostatic interaction energy between
inhibitor and enzyme
Stabilization energy
Electronic distortion energy
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Inhibitors Used by the Paper
NELFINAVIR
MOZENAVIR
TIPRANAVIR
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METHODS
Inhibitor
QM Semi-empirical Austin Model-1
Surrounding Protein Amino Acids and Solvent
MM CHARMM

• Interesting to note that the inhibitor is having
  polarization
• effects accounted for while the enzyme is not.

Enzyme-Inhibitor crystal structure was used as a
starting point for each computational model
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RESULTS
Negative in electrostatics refers to
attractiveness
? Electrostatic interactions are more significant
in determining binding interactions for
Nelfinavir and Tipranavir then for Mozenavir
ALSO
?Eel ?Eperm ?Epol
Electronic polarization of the inhibitor plays a
major role in electrostatic energy (32-39 of
?Eel) - In previous studies polarization only
made up 10-30 of ?Eel
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RESULTS
Quantifying amino acid contributions to inhibitor
interactions
Favorable contribution made to inhibitor-enzyme
interaction
Positive result indicates reduction in
interaction energy
Forms hydrogen bonds with hydroxyl groups of
inhibitors
? Asp25 is most significant residue
O-atoms of sulfonamide unit in Tipranavir and the
Asp30 carboxyl group have repulsive interactions.
Asp30 side chain orients differently.
? Asp30 destabilizes interactions with Tipranavir
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RESULTS
Tipranavir 4-hydroxy-dihydropyrone moiety
is very effective in forming hydrogen
bonds as opposed to aliphatic secondary
hydroxyl groups of Nelfinavir and
Mozenavir.
Hydrogen bond interactions of Tipranavir (seen by
orange dotted lines)
MOZENAVIR
NELFINAVIR
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RESULTS
Mulliken Population Analysis
? Hydroxyl H4 atom of Tipranavir exhibits a
large increase in partial positive charge
(AA) ? 4-hydroxy-dihydropyrone moiety is
perfect for charge polarization using a
push-pull mechanism. - Asp25/25 pushes
away electron density - Ile50/50 attracts
electron density toward the carbonyl group.
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RESULTS
Electron Charge Density Mapping
? Wave functions for inhibitors determined in gas
phase and enzyme active site. - Total
electron density is then calculated
Difference gives charge migration due to
polarization.
Blue Depletion of electron density due to
donating a hydrogen bond to the active
site Red Gain in electron density Seen in
three inhibitors where significant
interactions take place with Ile50/50
Trying to further prove push-pull mechanism of
Tipranavir
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CONCLUSIONS

• Polarization is a crucial component to
  electrostatic enzyme-inhibitor interactions
• The 4-hydroxy-dihydropyrone substructure of
  Tipranavir is the most effective structural
  arrangement for enhancing polarization effects.
• Note Tipranavir has recently obtained FDA
• approval while Mozenavir has been
• dropped.

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SPECIAL THANKS
? Dr. Carol Parish ? Dr. Ellis Bell ? Dr.
Michelle Hamm ? The Parish Research Group