Rho GTPases pp 57-70 | Cite as

Applying Perturbation Expectation-Maximization to Protein Trajectories of Rho GTPases

Part of the Methods in Molecular Biology book series (MIMB, volume 1821)


Single-particle tracking (SPT) enables the ability to noninvasively probe the diffusive motions of individual proteins inside living cells at sub-diffraction-limit resolution. The stochastic motions of diffusing Rho GTPases encode information concerning its interactions with binding partners and with its local environment. By identifying Rho GTPases’ diffusive states, insight can thus be gained into the spatiotemporal in vivo biochemistry inside live cells at a single-molecule resolution. Here we present perturbation expectation-maximization (pEM), a computational method which simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors: (1) the number of diffusive states, (2) the properties of each such diffusive state, and (3) the probabilities of each trajectory to a respective diffusive state. We provide a step-by-step guide to pEM and discuss considerations for its practical applications, including pEM’s capabilities and limitations.

Key words

Diffusion Diffusive states Perturbation expectation-maximization pEM Rho GTPase Single-particle tracking 



This work was supported by National Science Foundation Grant No. PHY1305509, and by the Raymond and Beverly Sackler Institute for Physical and Engineering Biology.


  1. 1.
    Manley S, Gillette JM, Patterson GH, Shroff H, Hess HF, Betzig E, Lippincott-Schwartz J (2008) High-density mapping of single-molecule trajectories with photoactivated localization microscopy. Nat Methods 5:155–157CrossRefPubMedGoogle Scholar
  2. 2.
    Patterson G, Davidson M, Manley S, Lippincott-Schwartz J (2010) Superresolution imaging using single-molecule localization. Annu Rev Phys Chem 61:345–367CrossRefPubMedPubMedCentralGoogle Scholar
  3. 3.
    Mortensen KI, Churchman LS, Spudich JA, Flyvbjerg H (2010) Optimized localization analysis for single-molecule tracking and super-resolution microscopy. Nat Methods 7:377–381CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Savin T, Doyle PS (2005) Static and dynamic errors in particle tracking microrheology. Biophys J 88:623–638CrossRefPubMedGoogle Scholar
  5. 5.
    Koo PK, Mochrie SG (2016) Systems-level approach to uncovering diffusive states and their transitions from single-particle trajectories. Phys Rev E 94:052412CrossRefPubMedGoogle Scholar
  6. 6.
    Berglund AJ (2010) Statistics of camera-based single-particle tracking. Phys Rev E Stat Nonlinear Soft Matter Phys 82:011917CrossRefGoogle Scholar
  7. 7.
    Koo PK, Weitzman M, Sabanaygam CR, van Golen KL, Mochrie SG (2015) Extracting diffusive states of Rho GTPase in live cells: towards in vivo biochemistry. PLoS Comput Biol 11:e1004297CrossRefPubMedPubMedCentralGoogle Scholar
  8. 8.
    Koo PK and Mochrie SG (2015) Perturbation Expectation-Maximization MATLAB Code.
  9. 9.
    Chenouard N, Smal I, de Chaumont F, Maska M, Sbalzarini IF, Gong Y, Cardinale J, Carthel C, Coraluppi S, Winter M, Cohen AR, Godinez WJ, Rohr K, Kalaidzidis Y, Liang L, Duncan J, Shen H, Xu Y, Magnusson KE, Jalden J, Blau HM, Paul-Gilloteaux P, Roudot P, Kervrann C, Waharte F, Tinevez JY, Shorte SL, Willemse J, Celler K, van Wezel GP, Dan HW, Tsai YS, Ortiz de Solorzano C, Olivo-Marin JC, Meijering E (2014) Objective comparison of particle tracking methods. Nat Methods 11:281–289CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Jaqaman K, Loerke D, Mettlen M, Kuwata H, Grinstein S, Schmid SL, Danuser G (2008) Robust single-particle tracking in live-cell time-lapse sequences. Nat Methods 5:695–702CrossRefPubMedPubMedCentralGoogle Scholar
  11. 11.
    Blair D and Dufresne E (2008) The MATLAB particle tracking code repository.
  12. 12.
    Vestergaard CL, Blainey PC, Flyvbjerg H (2014) Optimal estimation of diffusion coefficients from single-particle trajectories. Phys Rev E Stat Nonlinear Soft Matter Phys 89:022726CrossRefGoogle Scholar
  13. 13.
    Bishop CM (2006) Pattern recognition and machine learning. Springer, New YorkGoogle Scholar
  14. 14.
    Koo PK and Mochrie SG (2016) mleBIC MATLAB Code.
  15. 15.
    Koo PK and Mochrie SG (2016) pEMv2 MATLAB Code.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Molecular and Cellular Biology, Howard Hughes Medical InstituteHarvard UniversityCambridgeUSA
  2. 2.Departments of Physics and Applied PhysicsYale UniversityNew HavenUSA

Personalised recommendations