1

Molecular Interactions

Lecture 4 - QSAR

Jonathan Hirsthttp://comp.chem.nottingham.ac.uk/teaching/F14NMI

Freak-onomics

• Genomics

• Proteomics

• Pharmacogenomics

• Metabolomics

2

Economics

• Genomics

• Proteomics

• Pharmacogenomics

• Metabolomics

• Economics

Salvage F (2002) Chem Br May issue.

Coping with a data explosion

The on switch

must be round

here somewhere!

3

Quantitative Structure-Activity

Relationship

Hammett equation

(1940)

log(KX/KH) = ρσX

property

act

ivit

y

OH

O

R

Hansch equation

log(1/C) =

Σ c0j + c1jσ + c2jπ + c3jπ2+

c4jEs

property

act

ivit

y

prop 2

Quantitative Structure-Activity

Relationship

4

Current activity

• Non-parametric

statistics

• Artificial intelligence

• Machine learning

• Neural networks

• Genetic algorithms

Quantitative Structure-Activity

Relationship

• Regression applied to drugs

),,( 321 Kxxxfy =

how good a

drug is it?

properties of

a molecule

Quantitative Structure-Activity

Relationship

5

A typical QSAR dataset has…

• few observations

– measurements of drugs are expensive

– 10s – 100s

• (too) many variables

– properties of molecules generated in silico

– 100s – 1000s

– 10,000s if you get really carried away

– no silver bullet

A good QSAR

5.35.50.10 21 +−= xxactivity

6

A less-good QSAR

∑ = −+=

NH

j net

jebactivity

11

1α

∑+=i

ii xwwnet 0where

Small datasets

Quantitative Structure-Relationships (QSAR)

“Activity” = f(molecular structure)

Real valued: a regression problem

7

Quantifying molecular structure: 2D

Me

[ ]000101010000000011011

Quantifying molecular structure: 3D

8

Comparative Molecular Field Analysis (CoMFA)

• Make 3D models of molecules

• Align them

• Sample molecular field values

• Correlate field values with activity

• Electrostatic f(r,charge)

• Steric f(r,bulk)

A field of dreams

9

• Typical number of observations, n = 30-50

• Typical number of variables, p = 1000

p >> n

Solution: use Partial Least Squares (PLS)

Some chemometric nuts and bolts

• Latent variable technique

• Requires a stopping rule

Use cross-validation

• Resistant to collinearities

• Linear

• Sensitive to noise

But it does seem to work

10

Partial Least Squares in brief

• Like Principal Component Analysis (PCA)

• But takes into account the y-variable

PCA

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12

x1

x2

11

After the PCA magic

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12

t1

t2

One slight problem…

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12

t1

t2this is the

important

direction!

12

The PCA way of doing things

• extract orthogonal components

• maximise the variance in X

• use components in multiple linear regression

The PLS way of doing things

• extract orthogonal components.

• maximise the covariance between X and y

• regression is part of the algorithm

13

PLS is a rotation

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12

t1

t2

PLS is interpretable

K+++= 332211 ttty βββ

K+++= 3322111 xwxwxwt

the original variables

14

Fragment-based QSAR

OH

NH

N

O

OH

O

OH

OH

OH

OH

O

OH

OH

OHNH

N

O

OH

O

OH

OH

OH

OH

O

Fragment-based QSAR

15

NH

N

O

OH

O

OH

OH

OH

OH

O

NH

N

OH

O

Fragment-based QSAR

NH

N

O

OH

O

OH

OH

OH

OH

O

0,1,0,0,0,0,0,0,10,5,2,3,1,0,0,0,2,10…

16

How many fragments?

• Size: 4-7 atoms

• 60-400 molecules per dataset

• 1,000 – 20,000 fragments

• PLS derives a predictive model

• error ~0.7 log units

N

N

O

O

O

OH

OH

OH

OH

O

The equation visualised

17

Conclusions

• QSAR datasets: few observations (10s-100s)

• Many variables (100s-10,000s)

• Interpretability favoured

• PLS can do the job

– but not incremental

– memory limitations have been reached

– hierarchical approaches may be the way forward