A talk to Paul W. Ayers' group at McMaster University in Hamilton, ON

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