Skip to main content

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 797))

Abstract

Markov state models (MSMs) have a long history in the physical sciences, where they are often referred to as discrete-time master equation models. Therefore, there are many well-established ways of working with and analyzing these models given a valid set of states. However, defining a set of states sufficient for modeling complex molecular processes, like protein folding, is quite difficult. The main purpose of this chapter is to provide a practical guide to building MSMs, with an emphasis on partitioning a molecule’s conformational space into a valid set of states. We will start off with a brief discussion of some of the major requirements for a valid state decomposition. Then we will move on to a more detailed discussion of each of the steps commonly used for building MSMs, including an overview of the various options at each stage and their relative merits. Finally, I will introduce a few advanced topics and conclude with some future directions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

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

    Article  PubMed  Google Scholar 

  2. Bowman GR, Huang X, Pande VS (2009) Using generalized ensemble simulations and Markov state models to identify conformational states. Methods 49:97–201

    Article  Google Scholar 

  3. Noé F et al. (2009) Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations. Proc Natl Acad Sci USA 106:19011–19016

    Article  PubMed  Google Scholar 

  4. Beauchamp KA et al. (2011) MSMBuilder2: modeling conformational dynamics on the picosecond to millisecond scale. J Chem Theory Comput 7:3412–3419

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  Google Scholar 

  6. Senne M, Trendelkamp-Schroer B, Mey ASJ, Schütte C, Noé F (2012) EMMA—a software package for Markov model building and analysis. J Chem Theory Comput 8:2223

    Article  CAS  Google Scholar 

  7. Silva DA, Bowman GR, Sosa-Peinado A, Huang X (2011) A role for both conformational selection and induced fit in ligand binding by the LAO protein. PLoS Comput Biol 7:e1002054

    Article  PubMed  CAS  Google Scholar 

  8. Keller B, Daura X, van Gunsteren WF (2010) Comparing geometric and kinetic cluster algorithms for molecular simulation data. J Chem Phys 132:074110

    Article  PubMed  Google Scholar 

  9. Gonzalez T (1985) Clustering to minimize the maximum intercluster distance. Theor Comput Sci 38:293

    Article  Google Scholar 

  10. Dasgupta S, Long PM (2005) Performance guarantees for hierarchical clustering. J Comput Syst Sci 70:555

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

  12. Noe F et al. (2009) Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations. Proc Natl Acad Sci USA 106:19011

    Article  PubMed  CAS  Google Scholar 

  13. Tarjan R (1972) Depth-first search and linear graph algorithms. SIAM J Comput 1:146

    Article  Google Scholar 

  14. Swope WC, Pitera JW, Suits F (2004) Describing protein folding kinetics by molecular dynamics simulations, 1: theory. J Phys Chem B 108:6571

    Article  CAS  Google Scholar 

  15. Bowman GR, Geissler PL (2012) Equilibrium fluctuations of a single folded protein reveal a multitude of potential cryptic allosteric sites. Proc Natl Acad Sci USA 109:11681

    Article  PubMed  CAS  Google Scholar 

  16. Buchete NV, Hummer G (2008) Coarse master equations for peptide folding dynamics. J Phys Chem B 112:6057

    Article  PubMed  CAS  Google Scholar 

  17. Schütte C, Fischer A, Huisinga W, Deuflhard P (1999) A direct approach to conformational dynamics based on hybrid Monte Carlo. J Comput Phys 151:146

    Article  Google Scholar 

  18. Deuflhard P, Huisinga W, Fischer A, Schütte C (2000) Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains. Linear Algebra Appl 315:39

    Article  Google Scholar 

  19. Deuflhard P, Weber M (2005) Robust Perron cluster analysis in conformation dynamics. Linear Algebra Appl 398:161

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

  21. Bowman GR (2012) Improved coarse-graining of Markov state models via explicit consideration of statistical uncertainty. J Chem Phys 137:134111

    Article  PubMed  Google Scholar 

  22. Yao Y et al. (2009) Topological methods for exploring low-density states in biomolecular folding pathways. J Chem Phys 130:144115

    Article  PubMed  Google Scholar 

  23. Singh G, Memoli F, Carlsson G. Mapper: a topological mapping tool for point cloud data. In: Eurographics symposium on point-based graphics

    Google Scholar 

  24. Lin J (1991) Divergence measures based on the Shannon entropy. IEEE Trans Inf Theory 37:145

    Article  Google Scholar 

  25. Huang X, Bowman GR, Bacallado S, Pande VS (2009) Rapid equilibrium sampling initiated from nonequilibrium data. Proc Natl Acad Sci USA 106:19765

    Article  PubMed  CAS  Google Scholar 

  26. Bolhuis PG, Chandler D, Dellago C, Geissler PL (2002) Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu Rev Phys Chem 53:291

    Article  PubMed  CAS  Google Scholar 

  27. Schütte C et al. (2011) Markov state models based on milestoning. J Chem Phys 134:204105

    Article  PubMed  Google Scholar 

  28. Levin AM et al. (2012) Exploiting a natural conformational switch to engineer an interleukin-2 superkine. Nature 484:529

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gregory R. Bowman .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Bowman, G.R. (2014). An Overview and Practical Guide to Building Markov State Models. In: Bowman, G., Pande, V., Noé, F. (eds) An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation. Advances in Experimental Medicine and Biology, vol 797. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7606-7_2

Download citation

Publish with us

Policies and ethics