1. Molecular Similarity & Molecular Descriptors for Drug Design
N. Sukumar
Center for Biotechnology & Interdisciplinary Studies
Rensselaer Polytechnic Institute

2. The Informatics Process: Sifting Sand
WISDOM
UNDERSTANDING
KNOWLEDGE
Ram Samudrala in Death Valley: It was taken when I was playing with the sand, without me being aware of it, by my friend Jan when we were exploring Southern California after the second meeting on the Critical Assessment of Protein Structure Prediction.
INFORMATION
DATA

3. Traditional Hypothesis Driven Research Paradigm
Experiment
Data
Result
Design
Data analysis

4. Cheminformatics/Bioinformatics : A Statement of the Problem
Assay Screening or Gene Data (the more data the better)
Experiment
Data
No Prior Hypothesis

5. Structure-Activity Relationships
MOLECULAR
STRUCTURE
CHEMICAL/
BIOLOGICAL
ACTIVITY
DESCRIPTOR
REPRESENTATION
Statistical or Pattern Recognition Methods X
Computational
Chemistry

6. 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.

7. 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.

8. 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: “E’en 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 ( )
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!”

9. An example of Classification: Macrocycles – musky odor or not. (C
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.

10. Nitroaromatic Musk Candidates (C. Davidson and B. Lavine)
non-musk

11. GA/PCA Results with TAE descriptors
(C. Davidson and B. Lavine) 7 selected features

12. Results with PEST Descriptors
Nitroaromatics and Macrocycles
Results with PEST Descriptors
(C. Davidson and B. Lavine)
1 Macro Non-Musk
2 Macro Musk
1 Nitro Non-Musk
2 Nitro Musk
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

13. ADMET Property Prediction: Challenges in Medicinal Chemistry
Multiple-parameter optimization of lead structures
Other parameters: patent position, chemical synthesis
The greatest hurdle : ADMET properties.

14. Intestinal Epithelial Cells Endothelium of Capillarics
Different barriers
Drugs
Mucus Gel Layer
A series of separate barriers (epithelial layer is the most dominant barrier)
Intestinal Epithelial Cells
Lamina Propria
Endothelium of Capillarics
Be absorbed

15. 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 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.

16. Traditional Drug Discovery Scheme
Potency
Absorption
Distribution
Metabolism
Excretion
Toxicity
Lead
Drug

17. In silico prediction of ADME properties
Lead
Absorption
Potency
Distribution
Drug
Excretion
Metabolism
Toxicity

18. Computational ADME-Tox models for drug discovery
Solubility
Absorption
Mutagenicity
Bioavailability
Metabolic stability
Blood-brain barrier permeability
Cardiac toxicity (hERG)
Plasma protein binding

19. 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.
Christopher Lipinski & Andrew Hopkins, NATURE|VOL 432 | 16 DECEMBER 2004, pp

20. Descriptors from Molecular Electronic Properties

21. Molecular Representations

22. 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:

23. 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.

24. MOE Descriptors ® Chemical Computing Group Inc.
Number of aromatic atoms
Number of atoms
Number of heavy atoms
Number of hydrogen atoms
Number of boron atoms
Number of carbon atoms
Number of nitrogen atoms
Number of oxygen atoms
Number of fluorine atoms
Number of phosphorus atoms
Number of sulfur atoms
Number of chlorine atoms
Number of bromine atoms
Number of iodine atoms
Number of rotatable single bonds
Number of aromatic bonds
Number of bonds
Number of double bonds
Number of rotatable bonds
Fraction of rotatable bonds
Number of single bonds
Number of triple bonds
Number of chiral centers
Number of O and N atoms
Number of OH and NH groups
Number of rings
MOE Descriptors ® Chemical Computing Group Inc.
“2-D” Molecular Descriptors can be calculated from the connection table (with no dependence on conformation):
Physical Properties
Subdivided Surface Area Descriptors
Atom Counts and Bond Counts
Connectivity and Shape Indices
Adjacency and Distance Matrix Descriptors
Pharmacophore Feature Descriptors
Partial Charge Descriptors
“3-D” Descriptors depend on molecular coordinates:
Potential Energy Descriptors
Surface Area, Volume and Shape Descriptors
Conformation Dependent Charge Descriptors
Sum of the atomic polarizabilities
Molecular mass density
Total charge of the molecule
Molecular refractivity
Molecular weight.
Log of the octanol/water partition coefficient
Water accessible surface area of all atoms with positive partial charge
Water accessible surface area of all atoms with negative partial charge
Water accessible surface area of all hydrophobic atoms
Water accessible surface area of all polar atoms
Positive charge weighted surface area
Negative charge weighted surface area
Number of hydrogen bond acceptor atoms
Number of acidic atoms
Number of basic atoms
Number of hydrogen bond donor atoms
Number of hydrophobic atoms
Total positive partial charge
Total negative partial charge
Total positive van der Waals surface area
Total negative van der Waals surface area
Fractional positive polar van der Waals surface area
Fractional negative polar van der Waals surface area
Angle bend potential energy
Electrostatic component of the potential energy
Out-of-plane potential energy
Solvation energy
Bond stretch potential energy
Local strain energy
Torsion potential energy
Water accessible surface area
Globularity
Principal moment of inertia
Radius of gyration
van der Waals surface area

25. 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.

26. Wiener number W, Hosoya index Z and 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.

27. Quantum chemical Electron Density Derived descriptors
The wave function  given by solution of the Schrödinger 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 ( )

28. 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

29. Electron Density Derived Molecular Surface Properties
Electrostatic Potential
Electronic Kinetic Energy Density
Electron Density Gradients •N
Laplacian of the Electron Density
Local Average Ionization Potential
Bare Nuclear Potential (BNP) first term of EP
Fukui function F+(r) = HOMO(r)

30. Reconstruction Method
Transferable Atom Equivalents
Reconstruction Method
RECON
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.

31. 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(r)
Every atom is bounded by an atomic surface of zero flux
Atoms defined in this way satisfy the virial theorem
They have properties that are approximately additive and transferable from one molecule to another.

32. Reconstruction Method
Transferable Atom Equivalents
Reconstruction Method
RECON
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

33. Surface Property Distribution Histogram (TAE) Descriptors
Surface histograms can represent property distributions with 80-85% accuracy when histogram bins are used.
PIP (Local Ionization Potential)
surface property for a member of
the Lombardo blood-brain barrier
dataset.

34. Molecular Surface Properties: Wavelet Coefficient Descriptors (WCD)
Wavelet Decomposition:
Creates a set of coefficients that represent a waveform.
Small coefficients may be omitted to compress data.
Wavelet Surface Property Reconstruction:
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.

35. 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

36. 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

37. 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)

38. PEST Property-Encoded Rays

39. Property-Encoded Surface Translation: Shape/Property Hybrid Distribution: EP
Morphine

40. Property-Encoded Surface Translation: Shape/Property Hybrid Distribution: BNP
Morphine

41. Tessellated Protein Surface
using Delaunay Tessellation for Surface Definition

42. Sliced Surface For 1A42 5Å 6Å 4Å

43. Protein Pest (PPEST) Descriptors using MOE Surface as locus for TAE surface properties

44. Protein “PEST” Descriptors for Hydrophobic Interaction Chromatography
MLP2 surface
1BLF MLP2
1BLF EP
135L MLP2
135L EP
135L (lysozyme)
1BLF (lactoferrin)
MLP2 surface

45. Hierarchical Structure of Proteins
REENVYMAKLAEQAERYEEMVEFMEKVSNSLGSEELTVEERNLLSVAYKNVIGARRASWR
IISSIEQKEESRGNEEHVNSIREYRSKIENELSKICDGILKLLDAKLIPSAASGDSKVFY
LKMKGDYHRYLAEFKTGAERKEAAESTLTAYKAAQDIATTELAPTHPIRLGLALNFSVFY
YEILNSPDRACNLAKQAFDEAIAELDTLGEESYKDSTLIMQLLRDNLTLWTSDMQDDGAD
EIKE
Primary
linear sequence
Secondary
local, repetitive spatial arrangements
Tertiary
3-D structure of native fold
Quaternary
non-covalent oligomerization of subunits (single polypeptides) into protein complexes 

46. 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.

47. Higher order - maps and representative conformations
Sims, Gregory E. et al. (2005) Proc. Natl. Acad. Sci. USA 102,
Copyright ©2005 by the National Academy of Sciences

48. Protein fingerprint — Mihaly Mezei
FP0ij= sign {[r(Oi)-r(Ci)] . [r(Cj)-r(Ci)]}
FP1ij= sign {[r(Ni)-r(Ci)] . [r(Cj)-r(Ci)]}

49. QSAR assumptions
The properties of a chemical are implicit in its molecular structure
Molecular structure can be measured and represented with a set of numbers (descriptors or other numerical representation)
Compounds with similar structure exhibit similar properties; compounds with dissimilar structure exhibit dissimilar properties
— What about effects of the environment?
All other factors should be held constant in assay;
Don’t compare apples to oranges.
— But which set of numbers?
What descriptors to use?
Feature Selection.
— Similar in what way?

50. Machine Learning Methods
“If your experiment needs statistics, you ought to have done a better experiment” - Ernest Rutherford
Statistics?