Ignasi Buch, PhD student
Research Unit on Biomedical Informatics

               U N I V E R S I TAT
               POM P ...
Ignasi Buch, PhD student
Research Unit on Biomedical Informatics

               U N I V E R S I TAT
               POM P ...
Energetics, kinetics and binding pathway
reconstruction for enzyme-inhibitor complex
from high-throughput MD simulations

...
Objective
To provide an extensive computational description of
the complete binding process of Benzamidine to
bovine ß-Try...
Methodology
Execution of hundreds of all-atom molecular
dynamics (MD) simulations of the free ligand binding.

Analysis by...
B
                             kof f
                        Ki =                     A             C
                    ...
Generating the data
     Free ligand binding simulations




                                       35,000 atoms
         ...
Generating the data
Evaluating binding - RMSD to crystal structure



           50


           40


                    ...
Generating the data
     Evaluating binding - RMSD to crystal structure



                50


                40


40   ...
Why Markov State Models?
Some considerations




      A MSM is a kinetic multi-state model directly
      from unbiased M...
Definition of states
    Microstates - “Raw data”




x
                               C7

    z
Definition of states
    Macrostates - Coarse-grain into 2500 states




x
                                                ...
B
                             kof f
                        Ki =                     A             C
                    ...
Calculating binding rates and affinity
             From the Transition matrix to FES



                        lagtime τ ...
Calculating binding rates and affinity
             From the mean first passage time to binding affinity



                 ...
Standard free energy of binding
       Comparing with experimental results




  ∆Gmsm
    o
               = −9.5 kcal/mo...
Standard free energy of binding
       Comparing with experimental results



                                            ...
Issues with ligand parametrisation
      May explain inaccuracy of results




Conformational Variability of Benzamidinium...
B
                             kof f
                        Ki =                     A             C
                    ...
Definition of metastable states
    Coarse-grain into 5 states




x
                                     C7

    z
Definition of metastable states
             Coarse-grain into 5 states




                                               ...
Characteristic transition modes
    Main transitions between metastable states

                                          ...
Characteristic transition modes
Rate-limiting step to binding




                                  S3


 S4
Conclusions
  MSMs proven useful in exploiting high-throughput
  MD data to study protein-ligand binding.

  Binding affini...
Acknowledgements

            Research team              The GPUGRID volunteers
            Gianni De Fabritiis (PI)
     ...
High-throughput all-atom MD simulations


          ACEMD


                     NVIDIA GTX480 GPU


                     ...
System setup




                                                          30 Å
                                          ...
Lagtime & Implied timescales


                                2500-state MSM                                             ...
Sensitivity analysis for ton and toff
0.4

                          0.1
                                                        <0.1




                      ...
S4          S3



                  M180




     -6.0        -3.0
 kcal/mol    kcal/mol



                            S0...
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YMF2010

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

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YMF2010

  1. 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. 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. 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. 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. 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. 6. B kof f Ki = A C kon Building the Quantitative prediction Qualitative description Markov State Model of experimental data of binding mechanisms
  7. 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. 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. 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. 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. 11. Definition of states Microstates - “Raw data” x C7 z
  12. 12. Definition of states Macrostates - Coarse-grain into 2500 states x C7 z
  13. 13. B kof f Ki = A C kon Building the Quantitative prediction Qualitative description Markov State Model of experimental data of binding mechanisms
  14. 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. 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. 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. 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. 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. 19. B kof f Ki = A C kon Building the Quantitative prediction Qualitative description Markov State Model of experimental data of binding mechanisms
  20. 20. Definition of metastable states Coarse-grain into 5 states x C7 z
  21. 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. 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. 23. Characteristic transition modes Rate-limiting step to binding S3 S4
  24. 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. 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. 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. 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. 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. 29. Sensitivity analysis for ton and toff
  30. 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. 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

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