Tim Clark

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Tim Clark Computer-Chemie-Centrum Friedrich-Alexan
der-Universität Erlangen-Nürnberg
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A Non-Atom-Based Paradigm for Modeling, QSAR and
QSPR
A Non-Atom-Based Paradigm for Modeling, QSAR and
QSPR
Tim Clark Computer-Chemie-Centrum Friedrich-Alexan
der-Universität Erlangen-Nürnberg
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Descriptions of Molecules
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Intermolecular Interactions are Everywhere

• Molecule-molecule
• Boiling point/vapor pressure
• Solubility/free energies of solvation
• Partition coefficients
• Transport properties
• Molecule-Receptor
• Binding free energies
• Scoring functions

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Intermolecular Interactions

• Physical components are well known
• Coulomb
• Donor/acceptor
• Dispersion (and repulsion)
• We are accustomed to atom-atom approaches
• Force fields
• QSAR and QSPR
• Are there alternatives?

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What is Missing from MEP-Based Descriptions?

• Purely electrostatic interactions are described
  well
• Donor/Acceptor, Electronegativity and Hardness
  are described by the atom-specific descriptors
• Sums of potential-derived charges
• Counts of H-bond donors and acceptors
• Number of aromatic rings
• ...... etc.
• Can we design suitable local properties ?

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Electron-Density-Based Descriptors

• Electronic
• Molecular Electrostatic Potential (MEP)
• Polarizability
• Donor/Acceptor Properties
• Electron density ? Molecular surface
• Local (? position dependent) properties
• On a grid (ComFA, GRID etc.)
• On a surface
• Isodensity (DFT, Murray and Politzer)
• SES (fast)
• Statistics of the local property on a surface as
  descriptors
• MEP (Murray and Politzer)

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Local Ionization Energy
Sjoberg, P. Murray, J. S. Brinck, T. Politzer,
P. A., Can. J. Chem. 1990, 68, 1440 Murray, J.
S. Abu-Awwad, F. Politzer, P., THEOCHEM 2000,
501-502, 241 Hussein, W. Walker, C. G.
Peralta-Inga, Z. Murray, J. S., Int. J. Quant.
Chem. 2001, 82, 160 Politzer, P. Murray, J.
S. Concha, M. C., Int. J. Quant. Chem. 2002,
88,19.
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Local Ionization Energy
MEP
IEL
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Local Ionization Energy
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Other Local Properties

• Local Electron affinity
• Local Hardness

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Local Electron Affinity
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Local Electron Affinity
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Local Hardness
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Polarizabilty

• Variational method (Rinaldi and Rivail 1974)
• Fast (no need for excited states)
• Comparable to a population analysis

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Variational Method (AM1)
Std. dev. 2.99 Å3 PM3 4.44 Å3 MNDO 1.94 Å3
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Parametrized Method (AM1)Test Set
G. Schürer, P. Gedeck, M. Gottschalk, T. Clark,
Int. J.Quant. Chem., 1999, 75, 17-31.
Std. dev. 0.70 Å3 PM3 0.74 Å3 MNDO 0.78 Å3
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Atomic and Orbital- Polarizabilities
Partitioning
Additivity
B. Martin, P. Gedeck, T. Clark, Int. J. Quant.
Chem., 2000, 77, 473.
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The Additive Molecular Polarizability (AM1)
Std. dev. 0.59 PM3 0.65 MNDO 0.60
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Atomic Polarizability Tensors p-Bromotoluene
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Benzene dimer
-2.3 kcal mol-1 a MNDO -3.6 kcal mol-1
-1.2 kcal mol-1 a MNDO -1.0 kcal mol-1
a S. Tsuzuki, H.-P. Lüthi, J. Chem. Phys. 114,
2001, 3949.
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C2H4CH4 and C2H6CH4
-0.54 kcal mol-1 a MNDO -0.46 kcal mol-1
-0.73 kcal mol-1 a MNDO -0.50 kcal mol-1
S. Tsuzuki, K. Honda, T. Uchimura, K. Tanabe, J.
Phys. Chem. A, 103, 1999, 8265
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CO-Dimer
Ab initio MNDO
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Dispersion Energies (kcal mol-1)
Ab initio
MNDO
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Local Polarizability
Density due to a singly occupied atomic orbital j
Coulson population of atomic orbital j
Mean polarizability calculated for atomic orbital
j
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Local Polarizability
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Correlations Between Local Properties on
Molecular Surfaces
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How do we Describe Physical Properties?

• Old Descriptors
• 66 descriptors that appear again and again in our
  earlier QSPR-models
• Includes atom counts etc.
• New Descriptors
• 34 descriptors derived from the four local
  properties
• No 2D-based descriptors

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How do we Describe Physical Properties?

• Calculate descriptors for the entire Maybridge
  database
• Calculate the principal components (factors)
• What is the dimensionality of physical property
  space?

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PC-Eigenvalues (New)
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Variance Explained
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Variance Explained
Size, shape
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Boiling Points (N 5453)Leave 10 out
Cross-validation old and new descriptors
18 Descriptors (18101 239 weights) MSE
0.02 MUE 17.3 RMSD 24.9
10 Descriptors (1091 128 weights) MSE
0.3 MUE 14.6 RMSD 21.0
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Surface-integral models

• P target property
• Ai area of triangle i
• ntri number of triangles

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Surface-integral models

• MolFESD
• Pixner, P. Heiden, W. Merx, H. Möller, A.
  Moeckel, G. Brickmann, J. J. Chem. Inf. Comput.
  Sci. 1994, 34, 1309-1319.
• Jäger, T. Schmidt, F. Schilling, B. Brickmann,
  J. J. Comput.-Aided Mol. Des. 2000, 14, 631-646
• Jäger, R. Kast, S. M. Brickmann,. J. Chem. Inf.
  Comput. Sci. 2003, 43, 237-247.

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Partial solvation
Ligand
Receptor
Water
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Free energies of hydration

• N 413
• MUE 1.39 kcal mol-1
• RMSD 1.82 kcal mol-1
• r2 0.99
• q2 0.95

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Free energies of hydration

• N 386
• MUE 1.33 kcal mol-1
• RMSD 1.71 kcal mol-1
• r2 0.70

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Enthalpies of hydration

• N 95
• MUE 1.74 kcal mol-1
• RMSD 2.10 kcal mol-1
• r2 0.99
• q2 0.97

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Local Solvation Free Energy (H2O)
Salmeterol ?Gsolv(H2O) -5.0 kcal mol-1
?Gsolv(n-Octanol) -24.9 kcal
mol-1 ?Gsolv(CHCl3) -25.6 kcal mol-1
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Local Solvation Free Energy (H2O)
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Free Energies of Solvation n-Octanol

• N 179
• MUE 0.82 kcal mol-1
• RMSD 1.09 kcal mol-1
• r2 0.79
• q2 0.73c

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Free Energies of Solvation CHCl3

• N 87
• MUE 0.60 kcal mol-1
• RMSD 0.82 kcal mol-1
• r2 0.82
• q2 0.50

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Local Solvation Free Energy
n-Octanol
Chloroform
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logP as DGsolv Difference

• N 105
• MUE 2.2 kcal mol-1
• r2 0.667
• Slope 2.29

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Sources of data

• The available data are limited in
• Number
• Quality
• Use alternative sources
• e.g. for solvation free energies
• Gas phase proton affinities (G3)
• pKas (Equilibrium constants are always better
  than energies)

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Outlook

• Modelling using molecular surface properties is
  possible
• We need much higher quality data for models of
  the necessary quality
• the models are better than the data
• Local solvation energies are the key to docking,
  pKa calculation, scoring functions,
  amphiphilicity etc.
• biology happens in dirty water
• We can now use definitive gas-phase ab initio
  data to derive accurate parameterization data.
• Local solvation energies point to binding
  features

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Acknowledgments

• Erlangen
• Bernd Ehresmann (local properties, SIMs)
• Jr-Hung Lin (surfaces, multipole electrostatics)
• Anselm Horn (multipole electrostatics)
• Dr. Peter Gedeck (polarizability)
• Dr. Gudrun Schürer (polarizability)
• Bodo Martin (polarizabilities, dispersion)
• Pfizer, Sandwich
• Dr. Alexander Alex
• Dr. Marcel de Groot