![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](https://image.slidesharecdn.com/ymf2010101210-110113141004-phpapp01/85/YMF2010-8-320.jpg)
![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](https://image.slidesharecdn.com/ymf2010101210-110113141004-phpapp01/85/YMF2010-9-320.jpg)
![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 )](https://image.slidesharecdn.com/ymf2010101210-110113141004-phpapp01/85/YMF2010-14-320.jpg)
![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)](https://image.slidesharecdn.com/ymf2010101210-110113141004-phpapp01/85/YMF2010-15-320.jpg)
![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)](https://image.slidesharecdn.com/ymf2010101210-110113141004-phpapp01/85/YMF2010-17-320.jpg)
![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](https://image.slidesharecdn.com/ymf2010101210-110113141004-phpapp01/85/YMF2010-21-320.jpg)
![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](https://image.slidesharecdn.com/ymf2010101210-110113141004-phpapp01/85/YMF2010-28-320.jpg)
YMF2010
- 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