The document discusses the author's work using computational chemistry methods to develop new drugs through structure-based drug design, explores information theoretic properties of confined electronic systems, and proposes a novel 3D quantum mechanics-based structural descriptor called Sr that could be used for molecular similarity comparisons based on approximating the electron density distribution.

1. Drugs and Electrons
David C. Thompson
March 2008

2. Overview
 A little bit about why we make drugs, and
how computational chemistry is used (my
day job)
 A little bit about confined electronic
systems, informational entropy, and
complexity (my evening job)
 A novel 3D QM based structural descriptor
(my afternoon job?)

3. Drugs - why do we make them?
1. Money
2. And I guess you can help people too
3. But mainly for the money

4. Drugs - how do we make them?
 From a computational perspective I will
limit myself to Structure-Based Drug
Design (SBDD)

5. Drugs - how do we make them?
 What are we trying to do?
+ = ?
 In SBDD we use computational chemistry to capture some
part of this incredibly complex interaction by modeling the
protein-ligand binding event
 We typically ‘ignore’:
 Protein flexibility, polarization and other electronic factors,
solvent, entropy . . .

6. And what have I been doing?
 Detailed analysis of the in-house high-throughput virtual
screening protocol
 Accepted in J. Chem. Inf. Mod.
 Fragment-based de novo design
 CONFIRM
 Submitted to J. Comput.-Aided Mol. Design
 A large scale critical assessment of docking programs
 Binding mode prediction
 Enrichment rates in virtual screening
 Method development: Docking pose assessment tool

7. The Hospital that ate my Wife
 Given the tools of our trade:
 I can still work on problems in electronic structure
 Information theoretic properties of strongly
correlated systems
 Prof. Kalidas D. Sen, University of Hyderabad
 Dr. Ali Alavi, University of Cambridge

8. Electrons and how they get along
 PhD in small model quantum systems
 Particles-in-a-box
 Exact solutions
 Archetypal systems for investigating electron
correlation
 Electron correlation arises as a consequence of the
simultaneous interactions of mutually repelling
particles
 It is what makes QM a ‘tricky’ problem both
conceptually, and practically

9. Basic physics of these systems
 Two regions of behaviour
 Small R - kinetic dominance
 Large R - Coulombic dominance
 E ~ A/R2 + B/R + …
 Wigner ‘crystal’ formation at large R

10. Properties of interest
r r
Eigenvalues and
eigenvectors:
E i , "i (x1...x N )
r 2 r r
Density: n (r1 ) = N ! | " | ds1dx 2 ...dx N
Second order rr N(N - 1) 2 r r
density matrix: n 2 (r , r ') = ! |" | ds1ds 2dx 3 ...dx N
2
Physical rr 2 rr r
exchange- n xc (r , r ') = r n 2 (r , r ')# n (r ')
correlation n (r )
hole:
r r 2 r r
First order
density matrix:
$ 1 (x, x') = N ! | " | dx 2 ...dx N
FCI, RHF, UHF, and LDA solutions for both the spherical
(N=2, 3, 4, and 5) and cubic/planar (N=3, and 4) geometries

11. Spherical two electron system

12. Spherical two electron system
 RHF solution is surprisingly simple (S=0)
1 µ max
" (r) =
4#
$ µ =1
Cµ j 0 (% µ 0 r)
 And rapidly convergent for even large R
! max=7)
(µ

13. Spherical two electron system:
RHF and informational entropy
Sr = " $ # (r) ln[ #(r)]dr
S p = " $ % (p) ln[% (p)]dp
ST = Sr + S p
!

14. Spherical two electron system:
Complexity - RHF

15. Spherical two electron system:
Complexity - Hylleraas

16. A novel descriptor?
 Doesn’t Sr look a little familiar?
 Continuous form of a measure used in molecular
similarity:
S = "# pi ln[ pi ]
i
 Could we use Sr as a measure of similarity?
 Moreover, could Sr be a 3D QM-based structural
descriptor?
!
Literature search has shown that this has not been
considered before (I think)

17. 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 sum of fitted s-
Gaussians
"(r) # " Mol (r) = % "$ (r) = % % c$i exp(&'$i (r & R$ ) 2 )
$ $ i
 Turns out that this isn’t as bad as you might think
!

18. Homebrew quantum mechanics
 All of this has been done on my iMac at home
 Molecular integrations performed using the
Becke/Lebedev grids in PyQuante[1]
 Co-opted James into doing MathCad checks for
me. . .
[1] Python Quantum Chemistry - http://pyquante.sourceforge.net/

19. Homebrew quantum mechanics
H1 Rz H2

20. Homebrew quantum mechanics
Molecule Sr
H2O -7.42
H2S 3.94
Benzene -27.09
Cyclohexane (chair) -35.94
Perhaps Sr isn’t that discriminatory?
Plan B - Sr (r) = " #(r)ln[ # (r)]

21. And that might look like. . .

22. Conclusions and outlook
 Hopefully you have a feel for what I have been
working on, and why it might be interesting/useful
 Work with Prof. Sen is being written up
 Extend to planes - see if signature holds for N>2
 At BI incorporate descriptor into a QSAR model
 Is it of any use at all - what about Sp?

23. Acknowledgments
 Wyeth Research
 Prof. Sen and Dr. Alavi
 You all