QSAR Qualitative Structure-Activity

Relationships Can one predict activity (or properties in

QSPR) simply on the basis of knowledge of the structure of the molecule?

In other, words, if one systematically changes a component, will it have a systematic effect on the activity?

Choice of Model Can approach in two directions:

Simple to complex model Complex to simple model

Simplest Model Linear relationship between x and y Y = mx + b

Minimize error by least squares: (Yi – Y’i)2 = [Yi – (mXi + b)]2

Y’i is predicted value

Least Squares

Correlation coefficient

-1 < r < 1

Another test

Is the line better than the mean?

y = 0.0676x - 0.3882

R2 = 0.0045

-15

-15 -10 -5 0 5 10 15

y = 2.9562x - 0.2597

R2 = 0.8686

-60

-30

0

30

60

-10 -5 0 5 10 15

A circle 2 lines

y = 2.8515x - 31.647

R2 = 0.9179

0

25

50

75

100

10 20 30 40 50

y = 0.0008x + 275.11

R2 = 0.978

0

250

500

750

1000

0 200000 400000 600000 800000

One bad point Wrong model

Multiple Regression Y = f (X1, X2…Xn) Problems:

Choice of model – linear, polynomial, etc.

Visualization Interpretation Computationally demanding

Variable reduction Principal Component Analysis

Principal Component PC1 = a1,1x1 + a1,2x2 + … + a1,nxn

PC2 = a2,1x1 + a2,2x2 + … + a2,nxn

Keep only those components that possess largest variation

PC are orthogonal to each other

Exploring QSAR Pickup the NONLIN program

http://www.trinity.edu/sbachrac/drugdesign2007/

Unzip and install it on your computer

Read the Read.Me and Nonlin.doc documentation

Look at the HeatForm.NLR file with any word processor

Running NONLIN Start an MSDOS window Change to directory where the

code is Cd /d d:\nonlin

Execute the program with data file Nonlin heatForm > output

assignment Propose a QSAR scheme to predict

the Hf of the alkanes

Early Examples Hammett (1930s-1940s)

COOH COO + H K0

COOH COO + H KpX X

COOH COO + H Km

X X

para = log10

meta = log10

Kp

Km

K0

K0

Hammett (cont.) Now suppose have a related series

reflect sensitivity to substituent reflect sensitivity to different system

CH2COOH CH2COO + H K'x

log10K'xK'0

X X

=

Hammett (cont.) Linear Free Energy Relationship

G = -2.303RTlog10KSoG – G0 = -2.303RTandG’ – G’0 = -2.303RTThereforeG’ – G’0 = (G – G0)

Free-Wilson Analysis Log 1/C = ai +

where C=predicted activity, ai= contribution per group, and

=activity of reference

Free-Wilson example

Log 1/C = -0.30 [m-F] + 0.21 [m-Cl] + 0.43 [m-Br] + 0.58 [m-I] + 0.45 [m-Me] + 0.34 [p-F] + 0.77 [p-Cl]+ 1.02 [p-Br] + 1.43 [p-I] + 1.26 [p-Me] + 7.82

NBr

X

Y HClactivity of analogs

Problems include at least two substituent position necessary and only predict new combinations of the substituents used in the analysis.

Hansch Analysis

Log 1/C = a + b + c

where x) = log PRX – log PRH

and log P is the water/octanol partition

This is also a linear free energy relation

Molecular Descriptors Simple rules for describing some aspect of a molecule

Structure Property

2D descriptors only use the atoms and connection information of the molecule

Internal 3D descriptors use 3D coordinate information about each molecule; however, they are invariant to rotations and translations of the conformation

External 3D descriptors also use 3D coordinate information but also require an absolute frame of reference (e.g., molecules docked into the same receptor).

Descriptor examples Physical Properties

MW log P (ocanol/water partition) bp, mp Dipole moment solubility

Descriptor examples Structural descriptors

2D Atom/Bond counts

Number non-H atoms Number of rotatable bonds

Number of each functional group 2C chains, 3C chains, 4C chains, 5C chains, etc. Rings and their size

3D Number of accessible conformations Surface area

Topological Descriptors Weiner Path Index

12

3

4

5

6

7

0 1 2 3 4 2 31 0 1 2 3 1 22 1 0 1 2 2 13 2 1 0 1 3 21 2 3 4 0 4 32 1 2 3 4 0 33 2 1 2 3 3 0

Distance Matrix

w = diji j>i

w = 46

Topological Descriptors Randic Index

1

1

3

3

1

2

1

3

3

9

36

2

.577

.577

.577

.333 .707.408

3.179

valenceat vertex

bond valuesas productof above

edge termas reciprocal ofsquare rooot of above bond values

Sum ofedge terms

Predict bp of alkanes

y = 1.5225x + 7.2917

R2 = 0.9547

50

60

70

80

90

100

30 35 40 45 50 55 60 65

Weiner Index

bp

3D Molecular Descriptors Potential energy Solvation energy Water accessible surface area Water accessible surface area of

all atoms with positive (negative) partial charge

Pharmacophore Specification of the spatial

arrangement of a small number of atoms or functional groups

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

Creating a Pharmacophore

O

O

OH

O

O

OH

3D Pharmacophore searching With the pharmacophore in hand,

search databases containing 3-D structure of molecules for molecules that fit

Can rank these “hits” using scoring system described later

Pharmacophore Descriptors Number of acidic atoms Number of basic atoms Number of hydrogen bond donor atoms Number of hydrophobic atoms Sum of VDW surface areas of hydrophobic

atoms

Lipinski’s Rule of 5

potential drug candidates should Have 5 or fewer H-bond donors (expressed

as the sum of OHs and NHs) Have a MW <500 LogP less than 5 Have 10 or less H-bond acceptors

(expressed as the sum of Ns and Os)

Adv. Drug Delivery Rev., 1997, 23, 3

Docking Interact a ligand with a receptor Need to do the following

A) select appropriate ligands B) select appropriate conformation of receptor C) select appropriate conformations of ligands D) combine the ligand and receptor (docking) E) evaluate these combinations and rank order

them

Selection of Ligands Want drug-like molecules

250< MW < 500 Lipinski’s rules

Search through databases Available Chemicals Directory (ACD) World Drug Index NCI Drug database In-house databases

Receptor Conformation Usually Receptor is assumed to be

static Get structure from X-ray or NMR

experiment Protein Data Bank (

http://www.rcsb.org/pdb/) 41385 Structures

Ligand Conformation Rigid or flexible If rigid, optimize the structure then use

it throughout the docking procedure If flexible, can

A) create a set of low energy conformations and then use this set as a collection of rigid structures in docking

B) optimize structure within active site of receptor, i.e. dock and optimize together

Docking Place ligand in appropriate location

for interacting with the receptor Methodological problem:

1) No best method for defining shape 2) No general solution for packing

irregular objects (the knapsack problem)

Docking Algorithmic Components Receptor and Ligand Description (keep in

mind relative errors of structures, etc.) Bind the Ligand to Receptor

(configuration/conformation search) Geometric search (match ligand and

receptor site descriptions) Search for minimum energy - molecular

dynamics (MD) or monte carlo (MC) Evaluation of the dock (Gbind) also

called scoring

Descriptor Matching MethodDOCK program 1) Generate molecular surface for

receptor 2) Generate spheres to fill the active site

(usually 30-50 spheres)

3) Match sphere centers to the ligand atoms (originally just lowest E conformer, now use multiple conformers, but still rigid) – generates 10K orientations per ligand – Shape-driven!

4) Score the interaction

Fragment-Joining MethodFlexX, LUDI Place base fragments into microstates

of the active site (Fragments can be small molecules like benzene, formaldehyde, formamide, naphthol, etc.)

Optimize position of the Base fragment Join fragments with small connecting

chains made of CH2, CO, CONH, etc.

Scoring (evaluation of the dock) Want to quickly evaluate the

strength of the interaction between ligand and receptor Full free energy computation

Expensive Requires excellent force fields

Empirical method Fast and cheap Requires fitting to a broad set of ligand/receptor

complexes

Empirical Scoring Method of Bohm (LUDI, FlexX, etc.)

Gbind = G0 + h-bonds Ghb f(R,) + ion Gion f(R,) + Glipo Alipo + Grot NROT

G0 reduction in binding energy due to loss of rotation and translation of ligandGhb contribution from ideal hydrogen bondGion contribution from ionic interactionsGlipo contribution from lipophilic interactionsGrot contribution from freezing rotations within ligand

These come from empirical fits.

Bohm Method (cont.) f(R,) are penalty functions for non-

ideal interactions – distances too short/long, angles not linear

f (R,) = f1(R)f2()

f1(R) = 1, R<0.2 Å f2() = 1, <30° 1-(R-0.2)/0.4, R<0.6 Å 1-(-30)/50, <80° 0, R>0.6 Å 0, >80°

R is deviation from ideal H...O/N distance of 1.9 Å is deviation from ideal N/O-H…O/N angle of 180°

Bohm Method (cont.) Alipo is the lipophilic contact

surface, evaluated by a coarse grid of boxes

NROT is the number of rotatable bonds – acyclic sp3-sp3, sp3-sp2 and sp2-sp2. No terminal groups or flexibility of rings incorporated.

H.-J. Bohm, J. Comput.-Aided Mol. Des., 1994, 8, 243-256

Scoring alternatives Many variations on Bohm scheme

Buried Polar term, desolvation term, different forms for the lipophilic term, include metal bonding, etc.

Combine scoring functions, i.e. QSAR with scoring functions as variables

Use empirical score to select set of hits, then refine with free energy minimization