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Drugs and Electrons David C. Thompson March 2008
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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?)
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Drugs - why do we make them?1. Money2. And I guess you can help people too3. But mainly for the money
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Drugs - how do we make them? From a computational perspective I will limit myself to Structure-Based Drug Design (SBDD)
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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 . . .
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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
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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
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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
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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
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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
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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
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Spherical two electron system:RHF and informational entropy Sr = " $ # (r) ln[ #(r)]dr S p = " $ % (p) ln[% (p)]dp ST = Sr + S p !
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Spherical two electron system: Complexity - RHF
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Spherical two electron system: Complexity - Hylleraas
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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)
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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!
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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/
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Homebrew quantum mechanics Molecule Sr H2O -7.42 H2S 3.94 Benzene -27.09Cyclohexane (chair) -35.94 Perhaps Sr isn’t that discriminatory? Plan B - Sr (r) = " #(r)ln[ # (r)]
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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?
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Acknowledgments Wyeth Research Prof. Sen and Dr. Alavi You all
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