Drugs and Electrons David C. Thompson March 2008
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?)
Drugs - why do we make them?1. Money2. And I guess you can help people too3. But mainly for the money
Drugs - how do we make them? From a computational perspective I will limit myself to Structure-Based Drug Design (SBDD)
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 . . .
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
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
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
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
Properties of interest r rEigenvalues andeigenvectors: E i , "i (x1...x N ) r 2 r rDensity: n (r1 ) = N ! | " | ds1dx 2 ...dx NSecond order rr N(N - 1) 2 r rdensity matrix: n 2 (r , r ) = ! |" | ds1ds 2dx 3 ...dx N 2Physical rr 2 rr rexchange- n xc (r , r ) = r n 2 (r , r )# n (r )correlation n (r )hole: r r 2 r rFirst orderdensity 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
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
Spherical two electron system:RHF and informational entropy Sr = " $ # (r) ln[ #(r)]dr S p = " $ % (p) ln[% (p)]dp ST = Sr + S p !
Spherical two electron system: Complexity - RHF
Spherical two electron system: Complexity - Hylleraas
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)
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!
Homebrew quantum mechanics All of this has been done on my iMac at home Molecular integrations performed using the Becke/Lebedev grids in PyQuante Co-opted James into doing MathCad checks for me. . . Python Quantum Chemistry - http://pyquante.sourceforge.net/
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?
Acknowledgments Wyeth Research Prof. Sen and Dr. Alavi You all