Awarded with Best Presentation prize at the Young Modellers Forum 2010 in London.

1. Ignasi Buch, PhD student
Research Unit on Biomedical Informatics
U N I V E R S I TAT
POM P E U FA B R A
MGMS Young Modellers' Forum
London, December 2010

2. Ignasi Buch, PhD student
Research Unit on Biomedical Informatics
U N I V E R S I TAT
POM P E U FA B R A
MGMS Young Modellers' Forum
London, December 2010

3. Energetics, kinetics and binding pathway
reconstruction for enzyme-inhibitor complex
from high-throughput MD simulations
Ignasi Buch, PhD student
Research Unit on Biomedical Informatics
U N I V E R S I TAT
POM P E U FA B R A
MGMS Young Modellers' Forum
London, December 2010

4. Objective
To provide an extensive computational description of
the complete binding process of Benzamidine to
bovine ß-Trypsin.
kon
E+I EI
kof f

5. Methodology
Execution of hundreds of all-atom molecular
dynamics (MD) simulations of the free ligand binding.
Analysis by a Markov State Model (MSM), that
describes the system as a network of transitions
between conformational substates.
Noé F and Fischer S, Curr Op Struct Biol (2008)
Voelz VA et al. J Am Chem Soc (2010)

6. B
kof f
Ki = A C
kon
Building the Quantitative prediction Qualitative description
Markov State Model of experimental data of binding mechanisms

7. Generating the data
Free ligand binding simulations
35,000 atoms
500 trajectories
50 µs of data
x
z
Beta-Trypsin/Benzamidine (3PTB)
ACEMD software
AMBER99SB ff.
Explicit solvent

8. Generating the data
Evaluating binding - RMSD to crystal structure
50
40
30 % bound*
RMSD [˚]
30
A
20
10
0
0 10 20 30 40 50 60 70 80 90 100
Time [ns]
* ligand RMSD <2 Å from crystal pose

9. Generating the data
Evaluating binding - RMSD to crystal structure
50
40
40 10 50 2060 30
70 40
80 50
90 60
100
RMSD [˚]
30
A
Time [ns]
20
Time [ns]
10
0
0 10 20 30 40 50 60 70 80 90 100
Time [ns]
* ligand RMSD <2 Å from crystal pose

10. Why Markov State Models?
Some considerations
A MSM is a kinetic multi-state model directly
from unbiased MD data.
Provides quantitative and qualitative information
of the system.
Definition of states is independent from how the
simulations are done.

11. Definition of states
Microstates - “Raw data”
x
C7
z

12. Definition of states
Macrostates - Coarse-grain into 2500 states
x
C7
z

13. B
kof f
Ki = A C
kon
Building the Quantitative prediction Qualitative description
Markov State Model of experimental data of binding mechanisms

14. Calculating binding rates and affinity
From the Transition matrix to FES
lagtime τ = 50 ns kcal/mol
20 7 kcal/mol
7
6 T(τ )
6.5
10 (i, j)
T (τ )
4
3.5
5
5.5
6
5
4 Number of transitions i → j in time τ
0 Tij =
x [˚]
A
0.5
3
5
Number of starts in i
5.5
4.
3
τ
−10 2
6
5
4
1
−20 7
0 τ >τ
0 10 20 30 40
z [˚]
A τ
τ T(τ )

15. Calculating binding rates and affinity
From the mean first passage time to binding affinity
kcal/mol kon
20 E+I
7 kcal/mol EI
kof f
7
6
6.5
10
ton = 50 ns
4
3.5
5
1 1
5.5
6
5
0
4
kon = kof f =
x [˚]
A
0.5
3
ton C tof f
5
5.5
4.
3
−10 tof f = 2.16 × 106 ns kof f
2
Ki =
kon
6
5
4
1
−20 7
−1 o
0 10 20 30 40
0 ∆G = −kB T
o
ln(Ki C )
z [˚]
A
C = 0.0047 M
(Ligand concentration)

16. Standard free energy of binding
Comparing with experimental results
∆Gmsm
o
= −9.5 kcal/mol
∆Goexp = −6.3 kcal/mol
Mares-Guia M et al, J Med Chem (1965)
Doudou S et al, J Chem Theory and Comput (2009)

17. Standard free energy of binding
Comparing with experimental results
1D Potential of Mean Force protocol
15
∆Gmsm = −9.5 kcal/mol
PMF [kcal/mol]
o 10
∆Goexp = −6.3 kcal/mol
5
∆Go us = −9.17 ± 0.68 kcal/mol ∆G0 = µs aggregate kcal/mol
5 -9.17 ± 0.68 sampling.
Ensemble computation
by Umbrella Sampling.
0
0 10 20 30 40
z [˚]
A
Mares-Guia M et al, J Med Chem (1965)
Doudou S et al, J Chem Theory and Comput (2009)

18. Issues with ligand parametrisation
May explain inaccuracy of results
Conformational Variability of Benzamidinium-Based Inhibitors
Li X et al, J Am Chem Soc (2009)

19. B
kof f
Ki = A C
kon
Building the Quantitative prediction Qualitative description
Markov State Model of experimental data of binding mechanisms

20. Definition of metastable states
Coarse-grain into 5 states
x
C7
z

21. Definition of metastable states
Coarse-grain into 5 states
kcal/mol S4 S3
20 7
6 M180
10 S3 -6.0 -3.0
5 kcal/mol kcal/mol
4 S0
x [˚]
0 S4
A
S1 S0 0
kcal/mol
3
−10 S2 S1
2
S2
1
−20
0 -2.5 -1.0
0 10 20 30 40 kcal/mol kcal/mol
z [˚]
A
Free energy values are relative to state S0

22. Characteristic transition modes
Main transitions between metastable states
S3
S0 S0
S1 S1
S2
6 ns 10 ns
S3 S3
S4
S2
20 ns 58 ns
x
z

23. Characteristic transition modes
Rate-limiting step to binding
S3
S4

24. Conclusions
MSMs proven useful in exploiting high-throughput
MD data to study protein-ligand binding.
Binding affinity obtained is consistent with other
methods suggesting inaccurate ligand
parametrisation.
MSMs can provide new insights on the
mechanisms of ligand binding.

25. Acknowledgements
Research team The GPUGRID volunteers
Gianni De Fabritiis (PI)
S. Kashif Sadiq
Toni Giorgino
Ignasi Buch
Funding
Contact details
ignasi.buch@upf.edu
http://multiscalelab.org
Photo by Julien Lagarde

26. High-throughput all-atom MD simulations
ACEMD
NVIDIA GTX480 GPU
30 days
http://multiscalelab.org/acemd
Harvey MJ et al, J Chem Theory and Comput (2009)
Buch I et al, J Chem Inf Model (2010)

27. System setup
30 Å
Beta-Trypsin/Benzamidine
40
PDB 3PTB
0Å
Å
3 AMBER99SB ff.
Explicit solvent TIP3P
35,000 atoms (9 Cl-)
Harmonic restraint box scheme 69x63x80 Å
Flat-bottom potential k=0.1 kcal/mol/Å2 Temp 298K, 1 atm, ts 4fs, PME, NB 9 Å cutoff

28. Lagtime & Implied timescales
2500-state MSM 5-state MSM
250 60
50
Implied timescale [ns]
200
Relaxation time [ns]
40
150
30
100
20
50 10
0 0
0 20 40 60 0 10 20 30 40 50 60
Lagtime [ns] Lagtime [ns]
τ
τi∗ =−
ln λi
τi∗ is implied timescale (relaxation time) for state i at lagtime τ
λi is eigenvalue for state i at lagtime τ

29. Sensitivity analysis for ton and toff

30. 0.4
0.1
<0.1
0.
3
S3 0.4
0.1
0.4
0.
3
.1
0.
<0
1
0.4 0.1
0.1
0.8
<0.1 0.1
S4 S0
S1
<0.1
1
0.1
0.
0.4
0.
1
0.
3 1
0.
S2 <0.1
0.2
x
z Transition probabilities
5-state MSM

31. S4 S3
M180
-6.0 -3.0
kcal/mol kcal/mol
S0
0
kcal/mol
S2 S1
-2.5 -1.0
kcal/mol kcal/mol
Free energy values are relative to state S0