drugs and electrons

Drugs and Electrons

David C. ThompsonMarch 2008

Overview

A little bit about why we make drugs, andhow computational chemistry is used (myday job)

A little bit about confined electronicsystems, informational entropy, andcomplexity (my evening job)

A novel 3D QM based structural descriptor(my afternoon job?)

Drugs - why do we make them?

1. Money 2. And I guess you can help people too3. But mainly for the money

Drugs - how do we make them?

From a computational perspective I willlimit myself to Structure-Based DrugDesign (SBDD)

Drugs - how do we make them? What are we trying to do?

In SBDD we use computational chemistry to capture somepart of this incredibly complex interaction by modeling theprotein-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 electroncorrelation

Electron correlation arises as a consequence of thesimultaneous interactions of mutually repellingparticles 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( )

( )

( )

( )( )

( ) ( )

( ) !

!

!

"=

#=

"=

"=

"

N2

2

1

2xc

N321

2

2

N21

2

1

N1ii

xd...xd||N'x,x

'rn'r,rnrn

2'r,rn

xd...xddsds||2

1)-N(N'r,rn

xd...xdds||Nrn

x...x , E

rrrr

rrrr

rr

rrrr

rrr

rr

$

Density:

Second orderdensity matrix:

Physicalexchange-correlationhole:First orderdensity matrix:

Eigenvalues andeigenvectors:

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

Spherical two electron system

RHF solution is surprisingly simple (S=0)

And rapidly convergent for even large R(µmax=7)!

"(r) =1

4#Cµ j0µ=1

µmax

$ (%µ0r)

Spherical two electron system:RHF and informational entropy

!

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

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

ST = Sr + Sp

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:

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)!

S = " pii

# ln[pi]

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

Turns out that this isn’t as bad as you might think

!

"(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[1]

Co-opted James into doing MathCad checks forme. . .

[1] 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. . .

Conclusions and outlook

Hopefully you have a feel for what I have beenworking 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