Computer-Chemie-CentrumUniversität Erlangen-Nürnberg Local properties on molecular surfaces Tim...

Computer-Chemie-Centrum Universität Erlangen-Nürnberg

Local properties on molecular surfacesLocal properties on molecular surfaces

Tim Clark

Computer-Chemie-Centrum

Friedrich-Alexander-Universität

Erlangen-Nürnberg


N

N

N

NHCl

Descriptions of MoleculesDescriptions of Molecules


Intermolecular InteractionsIntermolecular 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?


QM-Based DescriptorsQM-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)


Surface DescriptorsSurface 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...... BUT• Surface-based descriptors are expensive to calculate• ... and difficult to interpret.


How Many Descriptors do we How Many Descriptors do we need for Physical Properties? need for Physical Properties?

(and what are they?)(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?


PC-Eigenvalues: Scree PlotPC-Eigenvalues: Scree Plot

0 2 4 6 8 10 12 14 16 18 20 22 24Principal Component Number

0

2

4

6

Eig

enva

lue

s


Prinvipal ComponentsPrinvipal Components

PC # Main descriptors Interpretation

1 Polarizability, molecular weight, volume, surface area, globularity

Size, shape

2 Maximum MEP, mean positive and negative MEPs, total variance

Complementary electrostatic surface descriptors3 Minimum MEP, mean negative MEP,

balance parameter


Physical property SpacePhysical property Space

PC # Main descriptors Interpretation

4 Total MEP-derived charges on nitrogens, # H-bond donors

Complementary Hydrogen-bonding descriptors5 Total MEP-derived charges on H and

O, minimum MEP, # aromatic rings

6 Dipole moment, dipolar density Dipolar polarity

7-9 Total MEP charges on different types of atom

Chemical diversity


What is Missing?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 ?


Local Ionization EnergyLocal 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.

1,

1,

i ii HOMO

Li

i HOMO

IE



MEP IEL



N

H3C CH3 O O

CH3


Other Local PropertiesOther Local Properties

,

,

i ii LUMO norbs

Li

i LUMO norbs

EA

•Local Electron affinity:

•Local Hardness: 2

L LL

IP EA


Local Electron AffinityLocal Electron Affinity

N


Local Electron AffinityLocal Electron AffinityFukui Function


Local HardnessLocal Hardness


PolarizabiltyPolarizabiltyVariational method (Rinaldi and Rivail 1974)

• Fast (no need for excited states)• Comparable to a population analysis

AA

Amol

jijiN

ij

mol

QN

xxPxxPQ

QN

orbs

2

2

4

||||2

1||

4

pxsf

pxxpf

sxxsf

isp

iipp

iiss

Variational Method (AM1)Variational Method (AM1)

0 10 20 30 40

Experimental Polarizabilty (Angstrom3)

0

10

20

30

40

AM

1 ca

lcu

late

d P

ola

riza

bii

ty (

An

gst

rom

3) Std. dev. = 2.99 Å3

PM3 : 4.44 Å3

MNDO : 1.94 Å3


pxsf

pxxpf

sxxsf

isp

iipp

iiss

Parametrized Method (AM1)Parametrized Method (AM1)Test SetTest Set

Std. dev. = 0.70 Å3

PM3 : 0.74 Å3

MNDO : 0.78 Å30 10 20 30 40

Experimental Polarizabilty (Angstrom3)

0

10

20

30

40

AM

1 ca

lcu

late

d P

ola

riza

bii

ty (

An

gst

rom

3)


G. Schürer, P. Gedeck, M. Gottschalk,T. Clark, Int. J.Quant. Chem., 1999, 75, 17-31.


Atomic and “Orbital-“ Atomic and “Orbital-“ PolarizabilitiesPolarizabilities

didi YYXXQ

AA

Amol NαQα

24

Additivity:

Partitioning:


Askskkkssspppkk

kppssssij

iji ijjiji PPPPffPfPfPX 22

A

spkssk

jAkssk

iA

jA

iA

AAijd

fPPPxPPPx

xxPP

X

iijj 22

1

2

1

2

1

,

2

pxsf

pxxpf

sxxsf

isp

iipp

iiss

One-Center TermsOne-Center Terms


AB

BspAspksskksskkkkkssiji ffPPPPPPPY i

BABjA

jBAB

iA

iB

jA

jB

iABA ,,2

2

1

AB

AspiBk

jBk

Bs

BspjAk

iAk

As

iB

jA

jB

iA

BA

ijd

fxPxPP

fxPxPPxxxxP

YjA

iAA

iB

jBB

,

,2

)(2

)(2)(

2

1

Two-Center TermsTwo-Center Terms

B. Martin, P. Gedeck, T. Clark, Int. J. Quant. Chem., 2000, 77, 473.


The Additive Molecular The Additive Molecular Polarizability (AM1)Polarizability (AM1)

Std. dev. = 0.59

PM3 : 0.65

MNDO : 0.60

0 10 20 30 40 50

Experimental PolarizabillityC

0

10

20

30

40

50

Cal

cula

ted

Po

lari

zab

ilit

y C


Atomic Polarizability Tensors:Atomic Polarizability Tensors:pp-Bromotoluene-Bromotoluene


Local PolarizabilityLocal Polarizability

1

1

1

1

NAOs

j j jj

L NAOs

j jj

q

q

1j Density due to a singly occupied atomic orbital j

jq Coulson population of atomic orbital j

j Mean polarizability calculated for atomic orbital j


Local PolarizabilityLocal Polarizability

F

Br

Cl


Correlations Between Local Properties Correlations Between Local Properties on Molecular Surfaceson Molecular Surfaces

MEP IEL EAL L L

MEP 1

IEL 0.15 1

EAL -.12 0.18 1

L 0.21 0.81 -.44 1

L 0.29 0.19 0.51 -.14 1


5 10 15 20 25 30 35

PC-number

0

2

4

6

8

PC

-Eig

enva

lue

10

30

50

70

90

Cu

mla

tive

% v

aria

nce

Eigenvalues% Variance

PC-Eigenvalues (Maybridge)PC-Eigenvalues (Maybridge)


Principal ComponentsPrincipal Components

Nr. Descriptors % Variance

1 Electrostatic descriptors, local donor/acceptor descriptors. 23.2

2 Local electron affinity descriptors, local polarizability descriptors

15.9

3 Molecular weight, volume, area, globularity 13.7

(23% before)

4 MEP-derived descriptors 8.2

5 Acceptor properties 7.5

6 Polarizability 4.8


Boiling Points (N = 5453):Boiling Points (N = 5453):Leave 10% out Cross-validation “old“ and “new“ descriptorsLeave 10% out Cross-validation “old“ and “new“ descriptors

-100 0 100 200 300 400 500

Experimental Boiling Point (°c)

-100

0

100

200

300

400

500

Cal

cula

ted

Boi

ling

Poi

nt (

°c)

-100 0 100 200 300 400 500

Experimental Boiling Point (°c)

-100

0

100

200

300

400

500

Cal

cula

ted

Boi

ling

Poi

nt (

°c)

18 Descriptors(18:10:1 = 239 weights)MSE = 0.02MUE = 17.3RMSD = 24.9

10 Descriptors(10:9:1 = 128 weights)MSE = 0.3MUE = 14.6RMSD = 21.0


Surface-integral modelsSurface-integral models

1

, , , ,ntri

i i i i i iL L L L

i

P f V IE EA A

•P = target property

•Ai = area of triangle i

•ntri = number of triangles


Surface-integral modelsSurface-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.


Free energies of hydrationFree energies of hydration

0 -20 -40 -60 -80 -100

Experimental Gsolv(H2O) (kcal mol-1)

0

-20

-40

-60

-80

-100C

alcu

late

d

Gso

lv(H

2O)

(kca

l mo

l-1)

MSE = 0.00

MUE = 1.18

RMSD = 1.69


Free energies of hydrationFree energies of hydration

0

Experimental Gsolv(H2O) (kcal mol-1)

0

Cal

cula

ted

G

solv

(H2O

) (k

cal m

ol-1

)

MSE = 0.00

MUE = 0.79

RMSD = 1.08


Free energies of solvation: Free energies of solvation: nn-octanol-octanol

-10 -6 -2 2

Experimental Gsolv(C8H18) (kcal mol-1)

-10

-6

-2

2C

alcu

late

d

Gso

lv(C

8H18

) (k

cal m

ol-1

)MSE = 0.00

MUE = 0.76

RMSD = 1.00


Free energies of solvation: Free energies of solvation: chloroformchloroform

-14 -12 -10 -8 -6 -4 -2 0 2

Experimental Gsolv(CHCl3) (kcal mol-1)

-14

-12

-10

-8

-6

-4

-2

0

2

Cal

cula

ted

G

solv

(CH

Cl 3)

(kc

al m

ol-1

)MSE = 0.00

MUE = 0.48

RMSD = 0.74


Enthalpies of hydrationEnthalpies of hydration

-100 -80 -60 -40 -20 0

Experimental Hsolv(H2O) (kcal mol-1)

-100

-80

-60

-40

-20

0

Cal

cula

ted

H

solv

(H2O

) (k

cal m

ol-1

)

MSE = 0.00

MUE = 1.74

RMSD = 2.10


Partial solvationPartial solvation

Ligand

Water

Receptor


Sources of dataSources 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


Physical-Property MappingPhysical-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


Physical Property MapPhysical Property Map

“chemistry“

TrainKohonen

Net

“Drugs“

“Drugs“


Physical Property Map: DrugsPhysical Property Map: Drugs


Physical Property Map: HormonesPhysical Property Map: Hormones


Model Applicabilty, Maps as Model Applicabilty, Maps as

Models?Models?

Aqueous solubility

550 (ompounds)


AcknowledgmentsAcknowledgments• 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

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