Computational Chemistry:From Theory to Practice

6th December 2007David C. Thompson

Overview

An introduction to computational chemistry– Which method, where, and why?

A novel 3D QM-based descriptor (perhaps?)

Computational chemistry for drug design– Fragment-based de novo design

Some background, and sometheory

The Problem

Motivation: Top 20 best-selling drugsin America had sales of ~ $65bn in2005[1]

New drug development costs are inexcess of $800M[2]

Roughly 10K structures are made andtested for every new drug reaching themarket[3]

[1] The Best-Selling drugs in America, IMS health, 2006[2] The Tufts Center for the study of drug development[3] Boston Consulting Group, 2005

The Solution

Solve the Schrödinger equation:

Ψ determines all properties of thesystem

!

H" = E"

Unfortunately…

“The underlying physical laws necessaryfor the mathematical theory of a large part ofphysics and the whole of chemistry are thuscompletely known, and the difficulty is onlythat the application of these laws leads toequations much too complicated to besoluble.” – P. A. M. Dirac (1929)

The Solution - DFT?

The electron density, ρ, can be derived fromΨ

And, it turns out that all properties of a systemcan be derived from ρ– ρ is a function of 3 variables– Ψ is a function of 4N variables

This is great, right?– Sure, but didn’t I tell you? In getting this far, I made a functional which

contains all of the “confusion”, and I don’t rightly know what it looks like. . .

Accuracy vs. SpeedAccuracy

Speed

Ph.D

EEHF EDFTEMM PD1

PD2

EDFT can be improved but we need tounderstand the physics of how“electrons get along”: Ec=E-EHF

101102104105-6

Gas phase water: An example

[4] G. K.-L. Chan and M. Head-Gordon, J. Chem. Phys. 118, 8551 2003

A DFT calculationtakes ~9s

An “Exact”calculation[4] took150h, 250Gb ofmemory, and 800Gbof disk

Gas phase water: An example

Water has 10 electrons

The 1A4Q receptor has~104 valence electrons

A full quantummechanical calculationis just not practical

The Hospital that ate my Wife. . .

Information theoretic properties of a model system:

Doesn’t Sr look a little familiar?

!

Sr = " #(r)$ ln[#(r)]dr

Sp = " %(p)$ ln[%(p)]dp

ST = Sr + Sp

A novel descriptor?

Continuous form of a measure used in molecularsimilarity:

Could we use Sr as a measure of similarity?

Moreover, could Sr be a 3D QM-basedstructural descriptor?– Literature search has shown that this has not been

considered before (I think)[5]

!

S = " pii

# ln[pi]

[5] M. Karelson, “Quantum-chemical descriptors in QSAR”, in Computational MedicinalChemistry for Drug Discovery, P. Bultnick et al, Eds., (New York, Dekker, 2003), pp 641-667

A novel descriptor?

We want to make this useful– But we still have the problem of finding ρ in a

timely fashion Why don’t we approximate ρ?

– We construct a pro-molecular density from a sumof fitted s-Gaussians[6]

Turns out that this isn’t as bad as you mightthink[7]

[6] P. Constans and R. Carbó, J. Chem. Inf. Sci. 35, 1046 1995 [7] J. I. Rodriguez, D. C. Thompson, and P. W. Ayers Unpublished data!

"(r) # "Mol(r) = "$ (r)

$

% = c$ii

% exp(&'$i(r &R$ )2)

$

%

Homebrew quantum mechanics

All of this has been done on my iMac at home

Molecular integrations performed using theBecke/Lebedev grids in PyQuante[8]

Co-opted graduate students into doingMathCad checks for me. . .

[8] Python Quantum Chemistry - http://pyquante.sourceforge.net/

Homebrew quantum mechanics

RzH1 H2

Homebrew quantum mechanics

-35.94Cyclohexane (chair)

-27.09Benzene

3.94H2S

-7.42H2O

SrMolecule

Perhaps Sr isn’t that discriminatory?Plan B -

!

Sr(r) = "#(r)ln[#(r)]

And that might look like. . .

Summary

Introduced a novel, 3D, quantummechanics based structural descriptor– Its utility, if any, will be further examined

Feedback is encouraged

Some background, and somepractice

Project involvement

Detailed analysis of in-house high-throughput virtualscreening protocol− Detailed curation of large data set of protein-ligand

complexes

Late-stage discovery project support− Lead optimization− Lead generation

Fragment-based de novo design

Fragment-based de novo design:The problem at hand

Search space of new molecular entities is essentiallyinfinite– The number of chemically feasible, drug like molecules

~1060-10100

Such a large space cannot be searched exhaustively

De novo design offers a broad exploration ofchemical space– The range of molecules generated is only limited by the

heuristics of the de novo design program

Low ligandefficiency area

High ligandefficiency area

!

LE = "#G

N$ "

RT ln(IC50)

N

Ligand Efficiency

R. Carr et al., Drug Discov. Today, 10, 987 2005

Project requirements

Exploit potential gaps in literature

If possible use in-house chemical equity

Modular design

Efficient deployment strategy

De novo design: Link or Grow?

LINK

GROW

G. Schneider et al., Nature Reviews Drug Discovery, 4, 649 2005

CONFIRM

Bridge library db

O O-

OH

O O-

OH

d

N

N

NH

O

O O-

OH

+…

d

A pre-prepared bridge library issearched using the atom type of theconnection points, and the distanced as a search query

Bridges that match the search queryare attached to the fragments

Complete molecules are preparedfor docking – enumeration oftautomers, isomers, and ionizationstates

Prepared molecules are dockedinto the target binding site

Bridge Libraries Application of filters

− Molecular Weight• <200 MW

− No. of rotatable bonds• ≤3• ≤4

Conformationalexpansion with OMEGA– 4 bridge libraries

• Lib3 → Lib3E• Lib4 → Lib4E

Lib3

Bridge library derived fromcorporate database

Lib4

Lib3E Lib4E

OMEGA Expansion

≤ 3 rot. bonds ≤ 4 rot. bonds

CONFIRM: Novelty

Bridges come from molecules within the WyethCORP database:– Bridges obtained “…from a given ring scaffold by removing

all of the atoms, except acyclic linker atoms, between pairsof ring systems, and the anchor atoms on the ring system.”[9]

Similar to CAVEAT[10], however:– We do not use orientation of bonds, but location of atoms

(vector vs. scalar)– CAVEAT searches 3D databases looking for suitable

molecular frameworks to satisfy the vector pairs• We already have well defined positions of small molecule

binders

[9] R. Nilakantan et al., J. Chem. Inf. Mod. 46(3), 1069-1077 2006

[10] G. Lauri, and P. A. Bartlett, J. Comp.-Aided. Mol. Design 8(1), 51-66 1994

CONFIRM: Test Sets

Taken from the curated data set of protein-ligandcomplexes– High crystallographic resolution ≤ 2.2Å– Two well resolved fragment moieties connected via a bridge– Both fragments interact with spatially disparate regions of

the protein

0.43

0.43

0.29

0.95

XPSP

0.301.381FCZ

0.402.201YDR

0.271.901A4Q

1.191.801SRJ

RMSD/ÅResolution/ÅPDB Ascension

Code

1SRJ X-ray Structure (green carbons) CONFIRM XP Pose (orange carbons)

3.7Å

-O O

N

N

OH

Fragment 1

Bridge

Fragment 2

CONFIRM: 1SRJ example

1A4Q X-ray Structure (green carbons) CONFIRM XP Pose (orange carbons)

O

O-O

NH2

HN OO

N

Fragment 1 Fragment 2

Bridge

5.9Å

154370Lib4E

84274Lib4

No. withFragment 1 and2 RMSD < 2Å

No. ofUnique

HitsLibrary

CONFIRM: 1A4Q example

CONFIRM: 1MTU exampleImportant for binding – we wish to keep this fragment

Search bridge library for suggestions for bridging atoms

Use ROCS to search for alternative groups to go here

CONFIRM: 1MTU example

Search Lib4E with distance query of 5Å– 2852 bridges

Search Lead-like database using ROCS and thisquery:

Use Combo score, only keep top 100

Use CONFIRM to enumerate, prepare, and dock

X O

N

HN

CONFIRM: 1MTU example

CONFIRM: 1MTU example

CONFIRM: 1MTU example

Summary Following comprehensive literature search, multiple

algorithms for linking/growing fragments developed Final linking approach, dubbed ‘CONFIRM’, uses in-

house chemical equity Modular design, allowed for rapid:

− Implementation− Testing− Analysis and modification

Publication completed, submitted to . . . Currently exploring use on drug discovery projects

Acknowledgments

Computational Chemistry Group at WyethResearch Cambridge

Dr. Christine Humblet Prof. K. D. Sen Prof. P. W. Ayers

– J. S. M. Anderson– J. I. Rodriguez