Local properties on molecular surfaces

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Local properties on molecular surfaces
Local properties on molecular surfaces
Tim Clark Computer-Chemie-Centrum Friedrich-Alexan
der-Universität Erlangen-Nürnberg
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Descriptions of Molecules
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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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QM-Based Descriptors

• Electronic
• Molecular Electrostatic Potential (MEP)
• Polarizability
• Donor/Acceptor Properties
• Multipole Moments
• Molecular surface
• Local properties at a surface
• Isodensity (DFT, Murray and Politzer)
• SES (fast)
• Statistics of the local property as descriptors
• MEP (Murray and Politzer)

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Surface Descriptors

• MEP at the surface has a physical basis.
• We should be able to describe intermolecular
  interactions using only surface properties.
• Scaffold-Hopping is more likely if we use only
  surface-based descriptors.
• Surface integral-models provide an interesting
  alternative to statistical QSPR
• Atom-based simulation methods scale badly
  (because they treat atoms)
  ...... BUT
• Surface-based descriptors are expensive to
  calculate
• ... and difficult to interpret.

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How Many Descriptors do we need for Physical
Properties? (and what are they?)

• Choose 26 descriptors that appear again and again
  in our QSPR-models
• Calculate them for the entire Maybridge database
• Calculate the principal components (factors)
• What is the dimensionality of physical property
  space, what are the descriptors?

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PC-Eigenvalues Scree Plot
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Prinvipal Components
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Physical property Space
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What is Missing?

• 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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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
Fukui Function
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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
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One-Center Terms
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Two-Center Terms
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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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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PC-Eigenvalues (Maybridge)
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Principal Components
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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.
• GB/PSA
• Best, S. A. Merz, K. M., Jr. Reynolds, C. H..
  J. Phys. Chem. B 1997, 101, 10479-10487.

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Free energies of hydration
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Free energies of hydration
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Free energies of solvation n-octanol
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Free energies of solvation chloroform
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Enthalpies of hydration
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Partial solvation
Ligand
Receptor
Water
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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 affinites (G3)
• pKas

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Physical-Property Mapping

• Maybridge used as the chemistry dataset
• Use the top six principal components to train a
  100 ? 100 Kohonen net (unsupervised training)
• 2,105 compounds selected from the World Drug
  Index as real drugs used as the drug dataset

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Physical Property Map
Train Kohonen Net
chemistry
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Physical Property Map Drugs
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Physical Property Map Hormones
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Model Applicabilty, Maps as Models?
Aqueous solubility 550 (ompounds)
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Acknowledgments

• Dr. Bernd Beck Dr. Andrew Chalk
• Dr. Peter Gedeck Dr. Bill King
• Dr. Harry Lanig Dr. Torsten Schindler
• Dr. Cenk Selçuki Dr. Paul Winget
• Matthias Brüstle Bernd Ehresmann
• Matthias Hennemann Anselm Horn
• Bodo Martin Gudrun Schürer
• Kendall Byler Jr-Hung Lin
• Dr. Tim F. Mitchell (Cambridge Combinatorial)
• Prof. Johnny Gasteiger
• Pfizer (Dr. Alexander Alex, Dr. Marcel de Groot)
• Bayer Pharma (Dr. Andreas Göller, Dr. Jörg
  Kenderich)
• 4SC Scientific (Dr. Thomas Herz)
• Alexander-von-Humboldt Foundation
• Hewlett-Packard