VAMPnets for deep learning of molecular kinetics

Abstract

There is an increasing demand for computing the relevant structures, equilibria, and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension reduction, clustering the dimension-reduced data, and estimation of a Markov state model or related model of the interconversion rates between molecular structures. This handcrafted approach demands a substantial amount of modeling expertise, as poor decisions at any step will lead to large modeling errors. Here we employ the variational approach for Markov processes (VAMP) to develop a deep learning framework for molecular kinetics using neural networks, dubbed VAMPnets. A VAMPnet encodes the entire mapping from molecular coordinates to Markov states, thus combining the whole data processing pipeline in a single end-to-end framework. Our method performs equally or better than state-of-the-art Markov modeling methods and provides easily interpretable few-state kinetic models.

Full text

Its licence does not allow us to show the full text. Read it at PubMed Central:

References 84

1. 1.

   Lindorff-Larsen K, Piana S, Dror RO, Shaw DE. How fast-folding proteins fold. Science. 2011;334:517-520.

   Not in our library10.1126/science.1208351

2. 2.

   Plattner N, Doerr S, Fabritiis GD, Noé F. Complete protein-protein association kinetics in atomic detail revealed by molecular dynamics simulations and Markov modelling. Nat. Chem. 2017;9:1005-1011.

   Not in our library10.1038/nchem.2785

3. 3.

   Kohlhoff KJ, et al. Cloud-based simulations on google exacycle reveal ligand modulation of gpcr activation pathways. Nat. Chem. 2014;6:15-21.

   Not in our library10.1038/nchem.1821

4. 4.

   Doerr S, Harvey MJ, Noé F, Fabritiis GD. HTMD: high-throughput molecular dynamics for molecular discovery. J. Chem. Theory Comput. 2016;12:1845-1852.

   Not in our library10.1021/acs.jctc.6b00049

5. 5.

   Ufimtsev IS, Martinez TJ. Graphical processing units for quantum chemistry. Comp. Sci. Eng. 2008;10:26-34.

   Not in our library10.1109/mcse.2008.148

6. 6.

   Marx, D. & Hutter, J. in Modern Methods and Algorithms of Quantum Chemistry ofNIC Series Vol. 1, 301–449 Ab initio molecular dynamics: theory and implementation (ed Grotendorst, J.) (John von Neumann Institute for Computing, Jülich, 2000).

   Not in our library

7. 7.

   Schütte C, Fischer A, Huisinga W, Deuflhard P. A direct approach to conformational dynamics based on hybrid monte carlo. J. Comput. Phys. 1999;151:146-168.

   Not in our library10.1006/jcph.1999.6231

8. 8.

   Prinz JH, et al. Markov models of molecular kinetics: generation and validation. J. Chem. Phys. 2011;134:174105.

   Not in our library10.1063/1.3565032

9. 9.

   Swope WC, Pitera JW, Suits F. Describing protein folding kinetics by molecular dynamics simulations: 1. Theory J. Phys. Chem. B. 2004;108:6571-6581.

   Not in our library10.1021/jp037421y

10. 10.

    Noé F, Horenko I, Schütte C, Smith JC. Hierarchical analysis of conformational dynamics in biomolecules: transition networks of metastable states. J. Chem. Phys. 2007;126:155102.

    Not in our library10.1063/1.2714539

11. 11.

    Chodera JD, et al. Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics. J. Chem. Phys. 2007;126:155101.

    Not in our library10.1063/1.2714538

12. 12.

    Buchete NV, Hummer G. Coarse master equations for peptide folding dynamics. J. Phys. Chem. B. 2008;112:6057-6069.

    Not in our library10.1021/jp0761665

13. 13.

    Scherer MK, et al. PyEMMA 2: a software package for estimation, validation and analysis of Markov models. J. Chem. Theory Comput. 2015;11:5525-5542.

    Not in our library10.1021/acs.jctc.5b00743

14. 14.

    Harrigan MP, et al. Msmbuilder: statistical models for biomolecular dynamics. Biophys. J. 2017;112:10-15.

    Not in our library10.1016/j.bpj.2016.10.042

15. 15.

    Humphrey W, Dalke A, Schulten K. Vmd—visual molecular dynamics. J. Mol. Graph. 1996;14:33-38.

    Not in our library10.1016/0263-7855(96)00018-5

16. 16.

    McGibbon RT, et al. Mdtraj: a modern open library for the analysis of molecular dynamics trajectories. Biophys. J. 2015;109:1528-1532.

    Not in our library10.1016/j.bpj.2015.08.015

17. 17.

    Noé F, Nüske F. A variational approach to modeling slow processes in stochastic dynamical systems. Multiscale Model. Simul. 2013;11:635-655.

    Not in our library10.1137/110858616

18. 18.

    Nüske F, Keller BG, Pérez-Hernández G, Mey ASJS, Noé F. Variational approach to molecular kinetics. J. Chem. Theory Comput. 2014;10:1739-1752.

    Not in our library10.1021/ct4009156

19. 19.

    Perez-Hernandez G, Paul F, Giorgino T, D Fabritiis G, Noé F. Identification of slow molecular order parameters for Markov model construction. J. Chem. Phys. 2013;139:015102.

    Not in our library10.1063/1.4811489

20. 20.

    Schwantes CR, Pande VS. Improvements in Markov state model construction reveal many non-native interactions in the folding of ntl9. J. Chem. Theory Comput. 2013;9:2000-2009.

    Not in our library10.1021/ct300878a

21. 21.

    Molgedey L, Schuster HG. Separation of a mixture of independent signals using time delayed correlations. Phys. Rev. Lett. 1994;72:3634-3637.

    Not in our library10.1103/physrevlett.72.3634

22. 22.

    Ziehe Andreas, Müller Klaus-Robert. TDSEP — an efficient algorithm for blind separation using time structure. ICANN 98. 1998;675-680.

    Not in our library

23. 23.

    Harmeling S, Ziehe A, Kawanabe M, Müller KR. Kernel-based nonlinear blind source separation. Neural Comput. 2003;15:1089-1124.

    Not in our library10.1162/089976603765202677

24. 24.

    Mezić I. Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dynam. 2005;41:309-325.

    Not in our library10.1007/s11071-005-2824-x

25. 25.

    Schmid, P. J. & Sesterhenn, J. Dynamic mode decomposition of numerical and experimental data. In 61st Annual Meeting of the APS Division of Fluid Dynamics (American Physical Society, 2008).

    Not in our library

26. 26.

    Tu JH, Rowley CW, Luchtenburg DM, Brunton SL, Kutz JN. On dynamic mode decomposition: theory and applications. J. Comput. Dyn. 2014;1:391-421.

    Not in our library10.3934/jcd.2014.1.391

27. 27.

    Williams MO, Kevrekidis IG, Rowley CW. A data-driven approximation of the koopman operator: extending dynamic mode decomposition. J. Nonlinear Sci. 2015;25:1307-1346.

    Not in our library10.1007/s00332-015-9258-5

28. 28.

    Wu H, et al. Variational koopman models: slow collective variables and molecular kinetics from short off-equilibrium simulations. J. Chem. Phys. 2017;146:154104.

    Not in our library10.1063/1.4979344

29. 29.

    Noé F, Clementi C. Collective variables for the study of long-time kinetics from molecular trajectories: theory and methods. Curr. Opin. Struc. Biol. 2017;43:141-147.

    Not in our library10.1016/j.sbi.2017.02.006

30. 30.

    Klus, S. et al. Data-driven model reduction and transfer operator approximation. Preprint at http://arXiv:1703.10112 (2017).

    Not in our library

31. 31.

    Noé F, Clementi C. Kinetic distance and kinetic maps from molecular dynamics simulation. J. Chem. Theory Comput. 2015;11:5002-5011.

    Not in our library10.1021/acs.jctc.5b00553

32. 32.

    Noé F, Banisch R, Clementi C. Commute maps: separating slowly-mixing molecular configurations for kinetic modeling. J. Chem. Theory Comput. 2016;12:5620-5630.

    Not in our library10.1021/acs.jctc.6b00762

33. 33.

    Bowman, G. R., Pande, V. S. & Noé, F. in Advances in Experimental Medicine and Biology Vol. 797 An introduction to Markov state models and their application to long timescale molecular simulation (Springer, Heidelberg, 2014).

    Not in our library

34. 34.

    Husic BE, Pande VS. Ward clustering improves cross-validated Markov state models of protein folding. J. Chem. Theory Comput. 2017;13:963-967.

    Not in our library10.1021/acs.jctc.6b01238

35. 35.

    Sheong FK, Silva DA, Meng L, Zhao Y, Huang X. Automatic state partitioning for multibody systems (APM): an efficient algorithm for constructing Markov state models to elucidate conformational dynamics of multibody systems. J. Chem. Theory Comput. 2015;11:17-27.

    Not in our library10.1021/ct5007168

36. 36.

    Wu H, Noé F. Gaussian Markov transition models of molecular kinetics. J. Chem. Phys. 2015;142:084104.

    Not in our library10.1063/1.4913214

37. 37.

    Weber M, Fackeldey K, Schütte C. Set-free Markov state model building. J. Chem. Phys. 2017;146:124133.

    Not in our library10.1063/1.4978501

38. 38.

    Bowman GR, Beauchamp KA, Boxer G, Pande VS. Progress and challenges in the automated construction of Markov state models for full protein systems. J. Chem. Phys. 2009;131:124101.

    Not in our library10.1063/1.3216567

39. 39.

    Trendelkamp-Schroer B, Wu H, Paul F, Noé F. Estimation and uncertainty of reversible Markov models. J. Chem. Phys. 2015;143:174101.

    Not in our library10.1063/1.4934536

40. 40.

    Kube S, Weber M. A coarse graining method for the identification of transition rates between molecular conformations. J. Chem. Phys. 2007;126:024103.

    Not in our library10.1063/1.2404953

Cited by papers we hold 12

• Direct generation of protein conformational ensembles via machine learning · 2023
  No notice
• Machine Learning-Guided Protein Engineering · 2023
  No notice
• Tetranucleosome Interactions Drive Chromatin Folding · 2021
  Not checked
• Deep learning the structural determinants of protein biochemical properties by comparing structural ensembles with DiffNets · 2021
  Not checked
• Unsupervised Learning Methods for Molecular Simulation Data · 2021
  No notice
• A Unified Sparse Optimization Framework to Learn Parsimonious Physics-Informed Models From Data · 2020
  Not checked
• Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation · 2020
  No notice
• Quantum chemical accuracy from density functional approximations via machine learning · 2020
  No notice
• Data-driven discovery of coordinates and governing equations · 2019
  No notice
• Past–future information bottleneck for sampling molecular reaction coordinate simultaneously with thermodynamics and kinetics · 2019
  No notice
• Deep learning for universal linear embeddings of nonlinear dynamics · 2018
  No notice
• Towards exact molecular dynamics simulations with machine-learned force fields · 2018
  No notice

Reads

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.