Molecular Similarity &
Molecular Descriptors
for Drug Design
N. Sukumar
Center for Biotechnology & Interdisciplinary Studies
(x.4235; nagams@rpi.edu)
January 26, 2006
Structure-Activity Relationships
MOLECULAR
DESCRIPTOR
REPRESENTATION
Re atis
co tic
gn al
iti or
on P
M atte
et rn
ho
ds
Co
Ch mp
em uta
ist tio
ry n a
l
St
MOLECULAR
STRUCTURE
CHEMICAL/
BIOLOGICAL
ACTIVITY
Quantitative Structure Activity Relationship (QSAR) &
Quantitative Structure Property Relationship (QSPR)
The role of data mining in chemistry is to evaluate "hidden"
information in a set of chemical data.
A typical application is the retrieval of structures with defined
biological activity (for drug development) from a database.
Finding the adequate descriptor for the representation of
chemical structures is one of the basic problems in chemical data
mining.
Molecules are normally represented as 2-D formulas or 3-D
molecular models.
While the 3-D coordinates of atoms in a molecule are sufficient
to describe the spatial arrangement of atoms, they lack two
features:
they are not independent on the size of a molecule;
they do not describe additional properties.
http://www.terena.nl/conferences/archive/tnc2000/proceedings/10B/10b5.html
Molecular Similarity
Similarity" can
have quite different
meanings in
chemical
approaches.
Molecular
Similarity does not
just mean similarity
of structural
features.
Similarity in a
chemical context
must include
additional
properties.
It was six men of Indostan
To learning much inclined,
Who went to see the Elephant
(Though all of them were blind),
That each by observation
Might satisfy his mind
The First approached the Elephant,
And happening to fall
Against his broad and sturdy side,
At once began to bawl:
God bless me! but the Elephant
Is very like a wall!
The Second, feeling of the tusk,
Cried, Ho! what have we here
So very round and smooth and sharp?
To me tis mighty clear
This wonder of an Elephant
Is very like a spear!
The Third approached the animal,
And happening to take
The squirming trunk within his hands,
Thus boldly up and spake:
I see, quoth he, the Elephant
Is very like a snake!
The Fourth reached out an eager hand,
And felt about the knee.
What most this wondrous beast is like
Is mighty plain, quoth he;
Tis clear enough the Elephant
Is very like a tree!
The Fifth, who chanced to touch the ear,
Said: Een the blindest man
Can tell what this resembles most;
Deny the fact who can
This marvel of an Elephant
Is very like a fan!
The Sixth no sooner had begun
About the beast to grope,
Than, seizing on the swinging tail
That fell within his scope,
I see, quoth he, the Elephant
Is very like a rope!
And so these men of Indostan
Disputed loud and long,
Each in his own opinion
Exceeding stiff and strong,
Though each was partly in the right,
And all were in the wrong!
- John Godfrey Saxe (1816-1887)
An example of Classification:
Macrocycles musky odor or not?
(C. Davidson and B. Lavine)
musk
non-musk
139 compounds:
103 musks
36 non-musks.
264 molecular descriptors.
Nitroaromatic Musk Candidates
(C. Davidson and B. Lavine)
musk
non-musk
GA/PCA Results with TAE descriptors
(C. Davidson and B. Lavine) 7 selected features
Nitroaromatics and Macrocycles
Results with PEST Descriptors
(C. Davidson and B. Lavine)
3D PC Plot Dim(30)
3
11111111
1111
11
1
1
1
1
1
1
111
1
11
1111
11
1 Macro Non-Musk
2 Macro Musk
11
11 11
1
11
1111
1111 1
111 1
111
111
1111
11111111 1
1
11111
1 Nitro Non-Musk
2 Nitro Musk
PC2
1
1111 11 1
11
-1
22
222
2
2
2
222222
2
22
2
2222
2
2
22
2
2
2
2
2
2
2
2
2222
22
222
22
-2
-3
-6
-4
-2
0
PC1
22
2 2 222
2 22 2
2222
222
222
2
222
22 2 222222
2
2 2 2 222222222
22
2 22 2222222
2 2
2
2
2 2
4
DGNAVGN, DGNH7, DGNW6, DGNW19, DGNW22, DGNB05, DGNB14,
DGNB22, DGNB33, DKNAVGN, DKNH3, DKNW4, DKNW6, DKNB00,
DKNB24, DRNH4, DRNW3, DRNW5, DRNW15, DRNW28, GW16, GW21,
GW28, KW11, KW27, FUKW21, PIPB14, PIPB30, BNPW27, BNPB44
ADMET Property Prediction:
Challenges in Medicinal Chemistry
Multipleparameter
optimization
of lead
structures
Other parameters: patent position, chemical synthesis
The greatest hurdle : ADMET properties.
Different barriers
Drugs
Mucus Gel Layer
Intestinal Epithelial Cells
Lamina Propria
Endothelium of Capillarics
Be absorbed
A series of
separate
barriers
(epithelial
layer is the
most dominant
barrier)
Motivation
Introduction of a new drug into the market is often the
culmination of a long and arduous process of laboratory
experimentation, lead compound discovery, animal testing and
pre-clinical and clinical trials.
This process, from hit to lead to marketable drug, is typically
as long as 10-15 years
In silico drug discovery:
find a correlation between molecular structure and biological activity
now any number of compounds, including those not yet synthesized,
can be virtually screened on the computer to select structures with the
desired properties.
Virtual ADME/Toxicological screening can weed out
compounds with adverse side effects, identifying the losers
early on in the game.
The most promising compounds can then be chosen for
laboratory synthesis and pre-clinical testing
conserving resources
cheaper medicines
accelerating the process of drug discovery.
Traditional Drug Discovery Scheme
Absorption
Potency
Lead
Distribution
Drug
Excretion
Toxicity
Metabolism
In silico prediction of ADME
properties
Potency
Lead
Absorption
Distribution
Drug
Excretion
Toxicity
Metabolism
Computational ADME-Tox models
for drug discovery
Solubility
Absorption
Mutagenicity
Bioavailability
Metabolic stability
Blood-brain barrier permeability
Cardiac toxicity (hERG)
Plasma protein binding
The figure depicts a cartoon representation of the relationship between the continuum of
chemical space (light blue) and the discrete areas of chemical space that are occupied
by compounds with specific affinity for biological molecules. Examples of such
molecules are those from major gene families (shown in brown, with specific gene
families colour-coded as proteases (purple), lipophilic GPCRs (blue) and kinases (red)).
The independent intersection of compounds with drug-like properties, that is those in a
region of chemical space defined by the possession of absorption, distribution,
metabolism and excretion properties consistent with orally administered drugs
ADME space is shown in green.
stopher Lipinski & Andrew Hopkins, NATURE|VOL 432 | 16 DECEMBER 2004, pp.855-861
Descriptors from Molecular
Electronic Properties
O
H 3C
N
CH3
N
CH3
Molecular Representations
H 3C
N
CH3
N
CH3
Linear Free Energy Relationships
Originally developed by Hammett, then by Taft
Intended to purely quantify the effect of
substituents and leaving groups on ester hydrolysis
Demonstrated the usefulness of parametric
procedures in describing an empirical property
(equilibrium constant, rate constant) in terms of a
parameter describing molecular structure.
This relationship provides the thermodynamic
basis for most implementations of QSAR by the
relations:
http://www.netsci.org/Science/Compchem/feature08.html
Quantitative Structure-Activity
Relationships (QSAR)
QSAR was a natural extension of the LFER approach, with a
biological activity correlated against a series of parameters that
described the structure of a molecule.
The most well known and most used descriptor in QSAR has
been the LOG (Octanol/Water) partition coefficient (usually
referred to as LOG P or LOG P[o/w]). LOG P has been very
useful in correlating a wide range of activities due to its
excellent modeling of the transport across the blood/brain
barrier.
Unfortunately, many regressions do not work well for LOG P,
usually because other effects are important, such as steric and
electronic effects.
Therefore, many other descriptors have been used in QSAR in
addition to LOG P to incorporate these additional effects.
Number of aromatic atoms
Number of atoms
Number of heavy atoms
Chemical Computing Group
Inc. of hydrogen atoms
Number
Number of boron atoms
2-D Molecular Descriptors canNumber
be calculated
from the
of carbon atoms
Number of nitrogen atoms
connection table (with no dependence
on ofconformation):
Number
oxygen atoms
Sum of the atomic polarizabilities
Physical Properties Molecular mass density
Number of fluorine atoms
TotalDescriptors
charge of the Number
molecule of phosphorus atoms
Subdivided Surface Area
Number of sulfur atoms
Molecular refractivity
Atom Counts and
Bond
Counts
Number
of chlorine
atoms partial charge
Molecular
weight.
Water
accessible
surface
area
of all atoms
with positive
Number
of bromine
atoms partial charge
Log
of the
octanol/water
partition
Water
accessible
surface
area
of all
atoms
with negative
Connectivity and
Shape
Indices
Number
of iodine atoms
coefficient
Water accessible
surface area
of all hydrophobic
atoms
Adjacency andWater
Distance
Matrix
Descriptors
Number
of rotatable
accessible
surface
area
of all polar
atoms single bonds
Number
weighted surface
areaofofaromatic
Number
hydrogenbonds
bond acceptor atoms
PharmacophorePositive
Featurecharge
Descriptors
Number
of
bonds
Negative charge weighted surface
areacharge
Number
of acidic atoms
partial
Partial Charge Descriptors Total positive
Number
of
double
bonds
Number
of
basic atoms
Total negative
partial
charge
Number
ofofrotatable
bonds
Number
hydrogen
bond
donor atoms
positive
van
der
Waals
surface
area
3-D Descriptors dependTotal
on Angle
molecular
coordinates:
Fraction
of
rotatable
bonds
bend potential
energy atoms
Number
ofWaals
hydrophobic
Total negative
van
der
surface area
Numbercomponent
of single bonds
Electrostatic
of the potential energy
Potential Energy DescriptorsFractional
positive polar
van bonds
der Waals surface area
Number
of
triple
Out-of-plane potential
energy
Water
accessible
surface
Fractional
negative
polar
van
der Waals
surface
areaarea
Surface Area, Volume and Shape
Descriptors
Number
of
chiral
centers
Solvation energy Globularity
Number
of O and
N atoms
stretch potential
energy
Conformation Dependent ChargeBond
Descriptors
Principal
moment of inertia
Number
of
OH
and
NH
groups
Local strain energy Radius of gyration
Number
of rings
Torsion
potential
energy
van der Waals surface area
MOE Descriptors
Some Topological Descriptors
Wiener number W is the total distance between all carbon
atoms (sum of the distances between each pair of carbon
atoms in the molecule, in terms of carbon-carbon bonds).
The smaller this number, the larger is the compactness of
the molecule.
Method of calculation: Multiply the number of carbon
atoms on one side of any bond by those on the other side;
W is the sum of these two values for all bonds.
W can also be obtained by simply adding all the elements
of the graph distance matrix above the main diagonal.
Hosoya topological index Z is obtained by counting the k
disjoint edges in a graph (for k = 0, 1, 2, 3, ...).
Z counts all sets of non-adjacent bonds in a structure.
Wiener number W, Hosoya index Z
and connectivity index
Connectivity index
(Milan Randic, A.T. Balaban)
= (RiRj)-1/2
is constructed from the row
sums Ri and Rj of the
adjacency matrix using the
algorithm (RiRj)-1/2 for the
contribution of each bond (i,j)
is a bond additive quantity
where terminal CC bonds are
given greater weight than
inner CC bonds.
Quantum chemical
Electron Density Derived
descriptors
The wave function given by solution of the Schrdinger
equation H = E contains all information about the molecule.
All science is either physics or stamp collecting
Ernest Rutherford (Nobel Prize in Chemistry, 1908)
BUT:
(r1, r2, r3, ) is a function of the coordinates of
all the electrons (and nuclei) in the molecule!
The fundamental laws necessary for the mathematical
treatment of a large part of physics and the whole of chemistry
are thus completely known, and the difficulty lies only in the
fact that application of these laws leads to equations that are
too complex to be solved. Paul Dirac (1902 - 1984)
Hohenberg-Kohn theorem
(Density Functional Theory)
The electron density (r)
(r) = *(r1, r2, r3, )(r1, r2, r3, )dr2dr3
contains all information about the ground state. (r) is a
function of only (x,y,z)
BUT:
the electron density (r) is an not a very
sensitive descriptor of chemistry ( near-sightedness of
the electron density)
Disadvantage: Difficult to use (r) directly as descriptor
Advantage:
Can use to simplify descriptor computations:
TAE-RECON method
Electron Density Derived
Molecular Surface Properties
Electrostatic Potential
Electronic Kinetic Energy Density
EP ( r ) =
r R
(r' )dr '
r r'
K ( r ) = ( * + *)
2
G (r ) = * .
Electron Density Gradients
Laplacian of the Electron Density
L(r) = (r) = K (r) G(r)
Local Average Ionization Potential
PIP ( r ) =
Bare Nuclear Potential (BNP)
first term of EP
Fukui function
F+(r) = HOMO(r)
i( r)
(r )
Reconstruction Method
Algorithm for rapid reconstruction of molecular charge densities and
molecular electronic properties
Based on topological quantum theory of Atoms In Molecules
Employs a library of atomic charge density fragments corresponding to
structurally distinct atom types
Associated with each atomic charge density fragment in the library is a
data file which contains atomic charge density-based descriptors encoding
electronic and structural information relevant to the chemistry of
intermolecular interactions.
http://www.drugmining.com/
Topological Theory of
Atoms in Molecules
Definition of an Atom in a Molecule:
An atom is the union of an attractor and its basin
Each atom contains one (and only one) nucleus, which is
the attractor of its electron density distribution (r)
Every atom is bounded by an atomic surface of zero flux
. n = 0
Atoms defined in this way satisfy the virial theorem
They have properties that are approximately additive and
transferable from one molecule to another.
Reconstruction Method
For each atom in the molecule, determine atom types
and assign closest match from atom type library
Combine densities of atomic fragments
Compute predicted molecular properties
http://www.drugmining.com/
Surface Property Distribution
Histogram (TAE) Descriptors
Surface histograms can represent property distributions with
80-85% accuracy when 10-20 histogram bins are used.
PIP (Local Ionization Potential)
surface property for a member of
the Lombardo blood-brain barrier
dataset.
Molecular Surface Properties:
Wavelet Coefficient Descriptors (WCD)
Wavelet Surface Property
Reconstruction:
Wavelet Decomposition:
Creates a set of
coefficients that represent
a waveform.
Small coefficients may be
omitted to compress data.
16 coefficients from S7 and D7
portions of the WCD vector
represent surface property
densities with >95% accuracy.
1024 raw wavelet coefficients capture
PIP distribution on molecular surface.
PEST Shape/Property Hybrid
descriptors
A TAE property-encoded surface
is subjected to internal ray
reflection analysis.
A ray is initialized with a random
location and direction within the
molecular surface and reflected
throughout inside the electron
density isosurface until the
molecular surface is adequately
sampled.
Molecular shape information is
obtained by recording the ray-path
information, including segment
lengths, reflection angles and
property values at each point of
incidence.
Isosurface (portion removed) with 750 segments
PEST Hybrid Shape/Property
Descriptors
Surface properties and shape information are
encoded into alignment-free descriptors
PIP vs Segment Length
Segment length and point-of-incidence value form 2D-histogram
Each bin of 2D-histogram becomes a hybrid descriptor
PEST Property-Encoded Rays
Ray-tracing algorithm
converges quickly
and provides good
coverage of internal
volume of molecules
Morphine electronic
kinetic energy density
Zoomed graphics (l-r)
PEST Property-Encoded Rays
Property-Encoded Surface Translation:
Shape/Property Hybrid Distribution: EP
Morphine
Property-Encoded Surface Translation:
Shape/Property Hybrid Distribution: BNP
Morphine
Tessellated Protein Surface
using Delaunay Tessellation for Surface Definition
Sliced Surface For 1A42
Protein Pest (PPEST) Descriptors using MOE
Surface as locus for TAE surface properties
Protein PEST Descriptors
1BLF (lactoferrin)
135L (lysozyme)
for Hydrophobic Interaction Chromatography
MLP2 surface
MLP2 surface
135L MLP2
135L EP
1BLF MLP2
1BLF EP
Hierarchical Structure of Proteins
1. Primary
REENVYMAKLAEQAERYEEMVEFMEKVSNSLGSEELTVEERNLLSVAYKNVIGARRASWR
IISSIEQKEESRGNEEHVNSIREYRSKIENELSKICDGILKLLDAKLIPSAASGDSKVFY
LKMKGDYHRYLAEFKTGAERKEAAESTLTAYKAAQDIATTELAPTHPIRLGLALNFSVFY
YEILNSPDRACNLAKQAFDEAIAELDTLGEESYKDSTLIMQLLRDNLTLWTSDMQDDGAD
EIKE
linear sequence
2. Secondary
local, repetitive spatial
arrangements
3. Tertiary
3-D structure of native
fold
4. Quaternary
non-covalent
oligomerization of
subunits (single
polypeptides) into protein
complexes
Ramachandran
Map
In a polypeptide the main
chain N-C and C-C bonds
relatively are free to rotate.
These rotations are
represented by the torsion
angles and , respectively.
G. N. Ramachandran used
computer models of small
polypeptides to systematically
vary and with the
objective of finding stable
conformations.
Higher order - maps and representative conformations
Sims, Gregory E. et al. (2005) Proc. Natl. Acad. Sci. USA 102, 618-621
Copyright 2005 by the National Academy of Sciences
Protein fingerprint Mihaly Mezei
FP0ij= sign {[r(Oi)-r(Ci)] . [r(Cj)-r(Ci)]}
FP1ij= sign {[r(Ni)-r(Ci)] . [r(Cj)-r(Ci)]}
QSAR assumptions
The properties of a chemical are implicit in its
molecular structure What about effects of the environment?
All other factors should be held constant in assay;
Dont compare apples to oranges.
Molecular structure can be measured and
represented with a set of numbers
(descriptors or other numerical But which set of numbers?
What descriptors to use?
representation)
Feature Selection.
Compounds with similar structure exhibit
similar properties; compounds with
dissimilar
Similar
in what way?
structure exhibit dissimilar properties
Machine Learning Methods
If your
experiment
needs statistics,
you ought to
have done a
better
experiment
- Ernest Rutherford
Statistics?
