chemical descriptors and molecular graphs

Chemical descriptors and molecular graphsAlessandra Roncaglioni - IRFMN

Problems and approaches in computational chemistry

[email protected]

OutlineOutline

Descriptors definition

Structure Descriptors Descriptors classification (bi- or tri-

dimensional)

Pros & Cons Overview of common descriptor classes

(mainly 2D)

Applications

Sw resources

Further reading2Problems and approaches in computational chemistry – 21 April 2008 – DEI –

Milano

IntroductionIntroduction

Molecular descriptors are numerical values that characterize properties of molecules

Examples: Physicochemical properties

(empirical) Values from algorithms, such as 2D

fingerprints

Vary in complexity of encoded information and in compute time

3Problems and approaches in computational chemistry – 21 April 2008 – DEI – Milano

Theoretical descriptorsTheoretical descriptors

“A molecular descriptor is the final

result of a logic and mathematical procedure which transforms chemical information encoded within a symbolic representation of a molecule into a useful number or the result of some standardized experiment”


www.moleculardescriptors.eu

Desiderable descriptors Desiderable descriptors characteristicscharacteristics Invariance with respect to labelling and

numbering of the molecule atoms Invariance with respect to the molecule roto-

translation An unambiguous computable definition Values in a suitable numerical range allowing structural interpretation no trivial correlation with other molecular descriptors gradual change in its values with gradual changes in

the molecular structure widely applicable preferably, allowing reversible decoding

(back from the descriptor value to the structure)


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dimensional)


(mainly 2D)

Applications

Sw resources


Milano

From chemical From chemical compounds to compounds to descriptorsdescriptors


CAS RN. 145131-25-5N-(2,6-Bis(1-methylethyl)phenyl)-N'-((1-(1-methyl-1H-indol-3-yl)cyclohexyl)methyl)urea

CC(C)C1=CC=CC(C(C)C)=C1NC(=O)NCC2(CCCCC2)C3=CN(C)C4=C3C=CC=C4

Descriptors classificationDescriptors classification

Depending on the structural dimensionality:

Up to 2D (0D-2D)Up to 2D (0D-2D)

Derived from the atomic composition and connectivity of molecules

3D3D

Encoding for energetic and spatial information

Molecular interaction fields (MIF)Molecular interaction fields (MIF)

Encoding for electrostatic and steric variation


2D Descriptors (I)2D Descriptors (I) Many groups accounting for different

characteristics May requires explicit H (check file format) Fast to be calculated (almost all expert

systems rely on 2D descriptors) More reproducible (do not require 3D

structure)but ... Might be focused on local contribution

neglecting intramolecular interactions Ignore conformational flexibility


N CH3

NHO

NH

CH3

CH3

CH3

CH3

2D Descriptors (II)2D Descriptors (II)

but ...

Ignore stereo configuration

Not invariants to tautomerism


N CH3

NHO

NH

CH3

CH3

CH3

CH3

3D Descriptors (I)3D Descriptors (I) Invaraint to roto-traslational changing

They require conformational search

Followed by QM/MM optimization


Sampling

Minimize

3D Descriptors (II)3D Descriptors (II) More complete and realistic description of

relevant molecular characteristics Can discriminate among isomers and provide

hints to select the most stable tautomer

but ...

Computationally more demanding Involve stochastic steps: non deterministic

result Results depend upon the QM/MM theory used

for the optimization Reference structure: minimum conformation

in vacuum not necessairly being the bioactive one


MIF (I)MIF (I) Requires 3D conformation alligned in

the Euclidean space Relates variation in the field with

variation in the activity (3D-QSAR)


Mol 1

St1 St2 … Stm El1 El2 … Elm

Mol 1 … … … … … … … … … …Mol 2 … … … … … … … … … …… … … … … … … … … … … …… … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … Mol n … … … … … … … … … …

Probes: N3+ sp3 Amine NH3 cation N2+ sp3 Amine NH2 cation N2: sp3 NH2 with lone pair N2= sp2 Amine NH2 cation N2 Neutral flat NH2 eg amide N1+ sp3 Amine NH cation N1: sp3 NH with lone pair N1= sp2 Amine NH cation N1 Neutral flat NH eg amide NH= sp2 NH with lone pair N1# sp NH with one hydrogen N: sp3 N with lone pair N:= sp2 N with lone pair N:# sp N with lone pair N-: Anionic tetrazole N NM3 Trimethyl-ammonium cation O sp2 carbonyl oxygen O:: sp2 Carboxy oxygen atom O- sp2 phenolate oxygen O= O of SO4 or sulfonamide OH Phenol or carboxy OH O1 Alkyl hydroxy OH group OC2 Ether oxygen OES sp3 ester oxygen atom ON Oxygen of nitro group OS O of sulfone / sulfoxide OH2 Water OFU Furan oxygen atom C3 Methyl CH3 group C1= sp2 CH aromatic or vinyl .... ............ .... ............ BOTH The amphipathic Probe DRY The hydrophobic Probe

Steric interaction (van der Waals energy calculated by Lennard-Jones function)

Electrostatic interaction (calculated by coulombian type function)

... ... ...

Hydrogen bonding energy

Solvation energy


MIF (II)MIF (II)

Green = steric +; Yellow = steric -; Red = charge -; Blue = charge +

Countur map

MIF (III)MIF (III) More biologically plausible (receptor

interactions) Identifies areas responsible for the

variation of the activitybut … Very sensitive to conformation

selection and to the chosen alignment Proper selection of force fields

Large number of grid point cotribution

QSAR modelling complexity 15Problems and approaches in computational chemistry – 21 April 2008 – DEI –

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OutlineOutline



dimensional)


(mainly 2D)

Applications

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Milano

Types of descriptorsTypes of descriptors Constitutional descriptors Topological descriptors

(topological indexes, connectivity indexes, information contents)

Atom centred fragments Functional groups Fingerprints Electrostatic descriptors(*)

(charge descriptors) Geometric descriptors* Physico-chemical

properties


Quantum- chemical descriptors*

Thermodynamic descriptors(*)

Pharmacophores WHIM & GETAWAY* BCUT (or Burden

eigenvalues) Autocorrelation

descriptors EVA descriptors*

* 3D descriptors

Constitutional Constitutional descriptorsdescriptors The most simple and commonly used

descriptors Reflecting the molecular composition

of a compound without any information about its molecular geometry

Examples Molecular weight Count of atoms and bonds Count of rings


Molecular graphMolecular graph A molecular graph or chemical graph is a

representation of the structural formula of a chemical compound in terms of graph theory.

It’s a very convenient and natural way of representing the relationships between objects: objects are represented by vertexes and the relationship between them by edges.


.

. . .

. . . .. Vertex

Edge

http://en.wikipedia.org/wiki/Structural_formula

http://en.wikipedia.org/wiki/Chemical_compound

http://en.wikipedia.org/wiki/Graph_theory

Topological descriptorsTopological descriptors Calculated from the 2D graph of the

molecule on the basis of connection tables or closely-related formats e.g. the distance matrix

an N x N table showing the distance (in bonds) between each pair of atoms

Obtained by operations on the distance matrices and whose values are independent of vertex numbering or labelling (graph invariants)

Characterize structures according to size, degree of branching, and overall shape, symmetry and cycling


Connection tableConnection table

9

OH

CH2

CHNH2

OHO 13

4

5

6

8

11

12

13


1 O 1 2 12 C 0 1 1 3 2 4

13 O 0 2 24 C 1 2 1 5 1 6

15 N 2 4 16 C 2 4 1 7 17 C 0 6 1 8 2

12 18 C 1 7 2 9 19 C 1 8 1 10 210 C 0 9 2 11 1

13 111 C 1 10 1 12 212 C 1 11 2 7 113 O 1 10 1

Distance matrixDistance matrix

9

OH

CH2

CHNH2

OHO 13

4

5

6

8

11

12

13


1 2 3 4 5 6 7 8 9 10 11 12 13

1 O 1 2 2 3 3 4 5 6 7 6 5 8

2 1 C 1 1 2 2 3 4 5 6 5 4 7

3 2 1 O 2 3 3 4 5 6 7 6 5 8

4 2 1 2 C 1 1 2 3 4 5 4 3 6

5 3 2 3 1 N 2 3 4 5 6 5 4 7

6 3 2 3 1 2 C 1 2 3 4 3 2 5

7 4 3 4 2 3 1 C 1 2 3 2 1 4

8 5 4 5 3 4 2 1 C 1 2 3 2 3

9 6 5 6 4 5 3 2 1 C 1 2 3 2

10 7 6 7 5 6 4 3 2 1 C 1 2 1

11 6 5 6 4 5 3 2 3 2 1 C 1 2

12 5 4 5 3 4 2 1 2 3 2 1 C 3

13 8 7 8 6 7 5 4 3 2 1 2 3 O

Wiener indexWiener index

Counts the number of bonds between pairs of atoms and sums the distances between all pairs

Add up all the off-diagonal elements and divide by 2 (because matrix is symmetrical)


W = 268W = 268

Molecular connectivity Molecular connectivity indexesindexes A whole series of indexes, developed

by Kier & Hall in the late ‘70s, following earlier work by Randić

Identify all possible subgraphs of different sizes in the molecule

Size of subgraph determines the order of the index 0 bond subgraph gives a zero order index 1-bond subgraph gives a 1st order index 2-bond subgraph gives a 2nd order index 3-bond subgraph gives a 3rd order index ...


RandiRandić indexć index Calculated from a the H-depleted

molecular graph where each vertex is weighted by the vertex degree, i.e. the number of connected non-hydrogen atoms

Example:


1

1

33

2

1

1

valence at vertexes

3

3 9

3

6 2

edge terms as reciprocal of

squared root of bond values

bond values as products of

vertex valence

.577

.577 .333

.577.408

.707

Randić index = sum of edge terms = 3.179

Kier & Hall indexesKier & Hall indexes Chi indexes introduces valence values to

encode sigma, pi, and lone pair electrons

δi and δj (i ≠ j) = values of the atomic connectivity

Atomic connectivity δi is calculated by:

Zi = tot nr electrons in the i-th atom

Zi υ = nr of valence electrons

Hi = nr H attached to the i-th atom


Kier Shape IndexesKier Shape Indexes Characterize aspects of molecular shape

Compare the molecule with the “extreme shapes” possible for that number of atoms

Based on the number of atoms (N) and the number of bonds (P) in the graph: 1 = N (N-1)2 / P2

2 = (N-1) (N-2)2 / P2

3 = (N-1) (N-3)2 / P2 (if N is odd) 3 = (N-3) (N-2)2 / P2 (if N is even)

alpha-modified kappa indexes can be generated taking into account the sizes of atoms, relative to C sp3 atom

A molecular flexibility index is derived from these

= 1 2

/ N


Information content Information content indexesindexes Defined on the basis of the Shannon

information theory

ni = nr of atoms in the i-th class

n = tot nr of atoms in the molecule Classes are determined by the coordination

sphere taken into account, leading to indexes of different order k.

Other information content indices:


SIC - structural ICCIC - complementary ICBIC - bonding ICq = nr of edges

Considerations about Considerations about topological descriptorstopological descriptors Frequently used, easily

calculated It is often difficult to disclose the

chemical meaning of highest order indexes

Topological indexes effectively encode the same information as fingerprint fragments in a less obvious way but can be processed numerically


Atom centred fragments Atom centred fragments & functional groups& functional groups Number of specific atom types in

a molecule calculated by knowing the molecular composition and atom connectivities

Number of specific functional groups in a molecule, calculated by knowing the molecular composition and atom connectivities


O

OR

OH

O

R N

O

R

R

2D Fingerprints2D Fingerprints Two types:

One based on a fragment dictionary Each bit position corresponds to a specific

substructure fragment Fragments that occur infrequently may be

more useful Another based on hashed methods

Not dependent on a pre-defined dictionary Any fragment can be encoded

Originally designed for substructure searching, not for molecular descriptors


000101000101000100000000011010100110101000000101000000001000

000101000101000100000000011010100110101000000001000000001000

Fragment dictionariesFragment dictionaries


PharmacophoresPharmacophores Used in drug design Based on atoms or substructures thought

to be relevant for receptor binding: specification of the spatial arrangement of a small number of atoms or functional groups

Typically include H bond donors and acceptors, charged centers, aromatic ring centers and hydrophobic centers

With the model in hand, search databases for molecules that fit this spatial environment

Might be 3D33Problems and approaches in computational chemistry – 21 April 2008 – DEI –

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Creating a Creating a PharmacophorePharmacophore

O

O

OH

O

O

OH


Physico-chemical Physico-chemical PropertiesProperties Will hear about them during QSPR lesson The key descriptor widespread in QSAR is

hydrophobicity LogP – the logarithm of the partition

coefficient between n-octanol and water LogD – correct LogP on the basis of the

dissociated fraction of the compound Experimentally assessed with shaker

flask or reversed phase HPLC It is often useful to be able to calculate a

physico-chemical property for a compound from its structure


LogP calculationLogP calculation Many methods have been proposed for

calculating a good estimate for LogP Fragment-based methods (ClogP) pioneered by Corwin Hansch and Al Leo

(Pomona College) identify large fragments, whose contribution

to logP value is known from their occurrence in other compounds with measured logP

large “training set” of compounds with accurately-measured logP (the “Starlist”)

works very well if test compound has the right fragments

problems arise if test compound contains fragments that are “missing” from the training set


LogP calculationLogP calculation Atom-based methods (AlogP, XlogP,

SlogP) pioneered by Gordon Crippen (Univ. Michigan) based on identifying a series of “atom types” in

the molecule essentially, small atom-centred fragments usually 60-200 such fragments are involved

each atom-type is assigned a numerical value logP is obtained by adding values for the atom

types present in the test molecule atom-type values are obtained by regression

analysis, based on a set of compounds with measured logP

sometimes some extra correction factors are used too


Summary


Rognan D., British Journal of Pharmacology (2007) 152, 38–52

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dimensional)


(mainly 2D)

Applications

Sw resources


Milano

Quantitative Structure-Quantitative Structure-Activity RelationshipsActivity Relationships Tomorrow … Lessons 4&5


ChemoinformaticsChemoinformatics Molecular database management Reverse engineering Chemical similarity assessment


Molecular similarityMolecular similarity The descriptors of a molecule can be considered a vector of

attributes (properties). The attributes may be real number (continuous variables) or

they may be binary in nature (binary variables).


(Range 0 to N)

cba

cSAB

N

i

N

i

N

i iBiAiBiA

N

i iBiAAB

XXXX

XXS

1 1 1

22

1

)()(

For continuous variables For binary variables

Tanimoto similarity coefficient

(Range -.333 to +1)

(Range 0 to 1)

N

i

N

i iBiA

N

i iBiAAB

XX

XXS

1 1

22

1

)()(

2

ba

cSAB

2Hodgkin

index(Range –1 to +1) (Range 0 to 1)

N

iiBiAAB XXD

1

2 cbaDAB 2Euclidean distance

(Range 0 to )

X are vectors

a numnber of bits on for A b numnber of bits on for Bc numnber of bits on for A AND B

Drug designDrug design Hightroughput virtual screening


OutlineOutline



dimensional)


(mainly 2D)

Applications

Sw resources


Milano

Software resourcesSoftware resources Db of calculated descriptors

MOLE db http://michem.disat.unimib.it/mole_db/ Commercial sw

CODESSA, Dragon, MDL, TSAR, .... Free sw

Virtual Computational Chemistry Laboratory www.vvclab.org

MODEL - Molecular Descriptor Lab http://jing.cz3.nus.edu.sg/cgi-bin/model/model.cgi

Open source sw/libraries Chemistry Development Kit (CDK)

http://almost.cubic.uni-koeln.de/cdk/cdk_top Linux4Chemistry

http://www.redbrick.dcu.ie/~noel/linux4chemistry/45Problems and approaches in computational chemistry – 21 April 2008 – DEI –

Milano

Further readingFurther reading

Web www.moleculardescriptors.eu

Book “Handbook of Molecular Descriptors”. Roberto Todeschini and

Viviana Consonni, Wiley-VCH, 2000.

Papers Estrada,E., Molina,E. and Perdomo-López,I. (2001). Can 3D

Structural Parameters Be Predicted from 2D (Topological) Molecular Descriptors? J.Chem.Inf.Comput.Sci., 41, 1015-1021.

Katritzky,A.R. and Gordeeva,E.V. (1993). Traditional Topological Indices vs Electronic, Geometrical, and Combined Molecular Descriptors in QSAR/QSPR Research. J.Chem.Inf.Comput.Sci., 33, 835-857.

Randic,M. (1990). The Nature of the Chemical Structure. J.Math.Chem., 4, 157-184.

Tetko,I.V. (2003). The WWW as a Tool to Obtain Molecular Parameters. Mini Reviews in Medicinal Chemistry, 3, 809-820.


http://www.moleculardescriptors.eu/

Concluding remarksConcluding remarks

Depending on the application define the preferred complexity level for chemical description

Avoid to use meaningless numbers: all descriptor types have advantages and limitations but easily interpretable descriptors might be preferred

Examples


Tautomers (I)Tautomers (I)


Tautomers (II)Tautomers (II)


Lipophilicity descriptor variationPredicted values for logBCF model

3D descriptors variability 3D descriptors variability (I)(I)

Intra Lab.

Inter Lab. (AM1)

Inter Lab. (PM3)

AM1

PM3

B3L HF

HF 82.6 79.9 94.0 -

B3L 85.2 81.6 -

PM3

97.8 -

AM1

-

Lab1 Lab2 Lab3

Lab3 98.6 98.6 -

Lab2 99.5 -

Lab1 -

Lab1 Lab2

Lab2 99.8 -

Lab1 -

LUMO energy


3D descriptors variability 3D descriptors variability (II)(II)

Intra Lab.

Inter Lab. (PM3)

AM1

PM3

B3L HF

HF 85.5 80.2 97.6 -

B3L 82.8 77.2 -

PM3

91.2 -

AM1

-

Lab1 Lab2 Lab3

Lab3 58.4 72.2 -

Lab2 67.4 -

Lab1 -

Dipole moment

Lab 3

Lab 1

Lab 2


chemical descriptors and molecular graphs

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