This is a presentation made at the Chemical Computing Group UGM in 2010. The work describes a collaboration with a talented summer intern, wherein we looked at the challenging problem of non-covalvent protein-ligand interactions

1. Non-covalent protein-ligand i
N l i li d interactions?
i ?
Easy as π
Jonathan Lai David C. Thompson
Ming Hong-Hao Ingo Mügge

2. π hides a wealth of complexity
c
It is the ratio of circumference (c) to diameter (d) c
d =
It is an irrational number d
It is a transcendental number 3. 1415926535 8979323846 26433832
795028841971 6939937510 58209749
445923078164 0628620899 86280348
It occurs in lots of interesting places: 253421170679 8214808651 32823066
470938446095 5058223172 53594081
• Normalization of the normal distribution 284811174502 8410270193 85211055
596446229489 5493038196 44288109
• Distribution of the primes 756659334461 2847564823 37867831
652712019091 4564856692 34603486
104543266482 1339360726 02491412
• Buffon’s needle problem 737245870066 0631558817 48815209
209628292540 9171536436 78925903
• The Bible (I Kings 7:23 and Chronicles 4:2) 600113305305 4882046652 13841469
519415116094 3305727036 57595919
530921861173 8193261179 31051185
480744623799 6274956735 18857527
π is tricky. So are π-π molecular interactions
ππ 248912279381 8301194912 . . .
31 August 2011
2

3. Presentation Overview: The What, Why, and How of it all
What are we trying to do?
Perform a detailed investigation of π- π stacking interactions between heterocyclic ring
systems and aromatic amino acid side-chains
Why are we trying to do it?
Could we preferentially suggest heterocycles for synthesis?
Can we extract any generalities about geometry?
How are we going to do it?
Extract deposited structural information from the PDB
Evaluate interactions using ab initio methodologies
3

4. Why are π-π interactions important?
Prevalent dispersive driven interactions
Structurally d
St t ll and energetically i
ti ll important i t and i t
t t inter- d intra-molecular
l l
interactions[1]
Sandwich T-shaped Parallel Displaced
-1.33 k l/ l[2]
1 33 kcal/mol -2.24 k l/ l[2]
2 24 kcal/mol -2.22 kcal/mol[2]
2 22 k l/ l
[1] A Medicinal Chemist’s Guide to Molecular Interactions, Caterina Bissantz, Bernd Kuhn, Martin Stahl JMC, Article ASAP (2010)
[2] M. O. Sinnokrot, and C. David Sherrill, J. Phys. Chem. A, 110, 10656-10668 (2006) [CCSD(T) / aug-cc-pVDZ (carbon) / cc-pVDZ (hydrogen)]
4

5. Why are π-π interactions important?
Viramune® (nevirapine)
O
Distance: 4.43Å
Tilt Angle: 16.88° C NH2
HO CH
ΔIE E : -1.38 kcal/mol
Est.
H2C
Nevirapine
Tyrosine OH
1VRT.pdb
O
HN
N
N N
11-cyclopropyl-5,11-dihydro-4-methyl
-6H-dipyrido[3,2-b:2',3'-e]
6H dipyrido[3,2 b:2 ,3 e]
[1,4]diazepin-6-one
5

6. Relibase+[3] Search Query
Filtering Criteria: Focused on compounds of these
motifs:
• π-π stacking interactions
ki i i
N N N
N N
• Crystals w/ resolutions: ≤ 2.5Å
N N
N
• Not nucleic acids
• No duplicates by PDB ID Ignored substituents
• Aromatic, planar ligands Excluded compounds of these
motifs:
O O
Geometric Filtering criteria:
Radius: 3.4Å ≤ x ≤ 4.1Å N
Tilt angle: 0 ≤ x ≤ 40°
Ring pucker: |x| ≤ 5° N
O
[3] Relibase+, v2.2 6

7. Heteroatom Count ( # of Ring systems found in data set)
Motif Histidine Phenylalanine Tyrosine Tryptophan
136 114 93 94
45 67 165 82
98 307 212 101
Pyrazine (1 4
P i (1,4 0 11 4 4
diazine), Triazine,
and Others
Radius: 3.4Å ≤ x ≤ 4.1Å
Tilt angle: 0 ≤ x ≤ 40°
Ring pucker: |x| ≤ 5° 7

8. Non-covalently Bound Set (Histidine)
Two distinct clusters
1. “T-shaped”
T shaped
2. “Sandwich/Displaced sandwich”
p
Conformations between clusters are still
accessible (e.g. radius ~ 4.5Å, tilt angle ~ 30 )
(e g 4 5Å 30°)
Can still extract a wealth of information (e g
(e.g.
ligand orientation, minimum contact distance)
Radius: 3.0Å ≤ x ≤ 5.0Å
Tilt angle: 0 ≤ x ≤ 80°
Ring pucker: |x| ≤ 5° 8

9. Non-covalently bound Amino Acid Set
HIS PHE
Radius: 3.0Å ≤ x ≤ 5.0Å
TYR TRP
Tilt angle: 0 ≤ x ≤ 80°
Ring pucker: |x| ≤ 5° 9

10. How did we use MOE?
Custom MOE browser
• Review complexes from PDB
• Automatically prepare Q-CHEM[4] input
— CCSD(T) / aug-cc-pVDZ basis
— Account for BSSE (EAB, EA, and Eb)
• Triage to ensure correct bond orders
• Interface with HPC environment for job
submission
[4] Q-CHEM, v3.2 10

11. What do the results tell us?
A little more than we could possibly understand
Shape: Position with respect to plane of His. (Below) (Above)
Size & Colour: CCSD(T) Energy (kcal/mol) [Small and red is a very attractive interaction] 11

12. Density Functional Theory (DFT) and Dispersion
DFT is formally exact in the ground state, if
the exact form of EXC[ρ] is known
• It is not
DFT migrated from solid-state physics into
the chemistry community to great effect
y y g
D
• Local density approximation works well
for materials, not so well for molecules
• Add non-locality to better approximate
inhomogeneity of molecular density
– Perdew’s ‘Jacob’s Ladder of functionals’
There are a number of well-known issues involving DFT, including its inability to deal
with dispersion[5]
[5] C. David Sherrill, J. Chem. Phys., 132, 110902 (2010) 12

13. Density Functional Theory (DFT) and Dispersion
1
CCSD(T) / kcal/mol
0
-4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5
-1
ωB97X-D[6] / kcal/mol
-2
R
R² = 0.941
-3
D
-4
-5
[6] Jeng-Da Chai and Martin Head-Gordon, Phys. Chem. Chem. Phys. 10, 6615 (2008)
-6
6
13

14. Dig into the data[7]
Above (A) Below (B) Below (C)
Above (45)
Volumetric
clustering
l t i
Below (B)
Below (52)
• Focus on pyrimidine (98 structures) Below (C)
• Use volumetric clustering
Correlation with overall dipole?
[7] boyd, danah. 2010. "Privacy and Publicity in the Context of Big Data." WWW. Raleigh, North Carolina, April 29 14

15. AM1 Dipole Moment versus ωB97X-D for pyrimidine
containing systems
AM1 Dipole Moment
0
1 2 3 4 5 6
-1
-2
ωB97X kcal / mol
-3
X-D
-4
R² = 0.6402
-5
-6
6
Electrostatic component masks dispersive interaction, making our quest for a
canonical geometry somewhat redundant 15

16. Outlook and Future Work
Robust workflow in place to extract π-π interactions and to
run QM calculations within our HPC environment
• π-π iinteractions tend to b di l d sandwiches
i d be displaced d ih
• Potential energy surface is shallow
• Calculating and analyzing interaction potential energy surface
g y g p gy
is challenging
• ωB97X-D appears to be a viable alternative to CCSD(T)
• Substantial electrostatic component to interaction energy
— Correlation of pyrimidine energy with total AM1 dipole
moment
Select suitable, representative, displaced sandwich geometry
and evaluate heterocyclic systems
16

17. Cultural Highlight
Ethnographic examination of
‘financiers’
financiers
— Investment bankers
— Risk managers
— Fund managers
“All models are wrong, but some
models are useful” – G. E. P. Box
useful
“If exactitude is elusive, it i better to be
tit d i l i is b tt t b
approximately right than certifiably
wrong” – B. B. Mandelbrot
The Big Short, Michael Lewis, W. W. Norton (2010)

18. Acknowledgements
Dr. Sandy Farmer
Dr. Miguel Teodoro
Dr. Bryan McKibben
18