Markov State and Diffusive Stochastic Models in Electron Spin Resonance

  • Deniz SezerEmail author
  • Benoît Roux
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 797)


Electron spin resonance (ESR) spectra of biological macromolecules reflect a wide range of dynamical molecular motions. However, because an electron spin is strongly coupled to its environment, the quantal degrees of freedom must be propagated for hundreds of nanoseconds to calculate spectra with a reasonable resolution of detail. Furthermore, a large number of independent “samples” are necessary for a reliable estimate of the ESR spectrum. For this reason, a direct calculation from molecular dynamics (MD) simulations is inefficient and wasteful route. As a practical alternative, we present a methodology in which stochastic are first constructed from MD simulations and then used to calculate ESR spectra. Discrete Markov state models (MSMs) offer a natural representation of the jump-like isomerization dynamics of a spin label attached to a protein through a flexible linker. A pedagogical introduction to the second half of the formalism—accounting for the coupling between the molecular and the spin dynamics—is also provided. The chapter concludes with a successful application of the methodology to multi-frequency ESR spectroscopy of spin-labeled T4 Lysozyme.


Electron Spin Resonance Spin Label Transverse Magnetization Free Induction Decay Rotational Diffusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abragam A (1961) The principles of nuclear magnetism. Oxford University Press, New York Google Scholar
  2. 2.
    Anderson PW (1954) A mathematical model for the narrowing of spectral lines by exchange or motion. J Phys Soc Jpn 9(3):316–339 CrossRefGoogle Scholar
  3. 3.
    Barnes JP, Liang Z, Mchaourab HS, Freed JH, Hubbell WL (1999) A multifrequency electron spin resonance study of T4 Lysozyme dynamics. Biophys J 76(23):298–3306 Google Scholar
  4. 4.
    Beier C, Steinhoff HJ (2006) A structure-based simulation approach for electron paramagnetic resonance spectra using molecular and stochastic dynamics simulations. Biophys J 91:2647–2664 PubMedCrossRefGoogle Scholar
  5. 5.
    Bennati M, Prisner TF (2005) New developments in high field electron paramagnetic resonance with applications in structural biology. Rep Prog Phys 68(2) Google Scholar
  6. 6.
    Borbat PP, Costa-Filho AJ, Earle KA, Moscicki JK, Freed JH (2001) Electron spin resonance in studies of membranes and proteins. Science 291:266–269 PubMedCrossRefGoogle Scholar
  7. 7.
    Budil DE, Lee S, Saxena S, Freed JH (1996) Nonlinear-least-squares analysis of slow-motion EPR spectra in one and two dimensions using a modified Levenberg-Marquardt algorithm. J Magn Reson, Ser A 120:155–189 CrossRefGoogle Scholar
  8. 8.
    Budil DE, Sale KL, Khairy KA, Fajer PG (2006) Calculating slow-motional electron paramagnetic resonance spectra from molecular dynamics using a diffusion operator approach. J Phys Chem A 110:3703–3713 PubMedCrossRefGoogle Scholar
  9. 9.
    Cekan P, Sigurdsson ST (2009) Identification of single-base mismatches in duplex DNA by EPR spectroscopy. J Am Chem Soc 131(50):18,054–18,056 CrossRefGoogle Scholar
  10. 10.
    Columbus L, Hubbell WL (2002) A new spin on protein dynamics. Trends Biochem Sci 27:288–295 PubMedCrossRefGoogle Scholar
  11. 11.
    Columbus L, Kalai T, Jeko J, Hideg K, Hubbell WL (2001) Molecular motion of spin labeled side chains in α-helices: analysis by variation of side chain structure. Biochemistry 40:3828–3846 PubMedCrossRefGoogle Scholar
  12. 12.
    DeSensi SC, Rangel D, Lybrand TP, Hustedt EJ (2008) The calculation of nitroxide cw-EPR spectra from Brownian dynamic trajectories and molecular dynamics simulations. Biophys J 94(10):3798–3809 PubMedCrossRefGoogle Scholar
  13. 13.
    Earle KA, Dzikovski B, Hofbauer W, Moscicki JK, Freed JH (2005) High-frequency ESR an ACERT. Magn Reson Chem 43:S256–S266 PubMedCrossRefGoogle Scholar
  14. 14.
    Eviatar H, van Faassen E, Levine Y, Hoult D (1994) Time-domain simulation of ESR spectra of nitroxide spin probes. Chem Phys 181:369–376 CrossRefGoogle Scholar
  15. 15.
    Eviatar H, van der Heide U, Levine YK (1995) Computer simulations of the electron spin resonance spectra of steroid and fatty acid nitroxide probes in bilayer systems. J Chem Phys 102:3135–3145 CrossRefGoogle Scholar
  16. 16.
    Fanucci GE, Cafiso DS (2006) Recent advances and applications of site-directed spin labeling. Curr Opin Struct Biol 16:644–653 PubMedCrossRefGoogle Scholar
  17. 17.
    Fedchenia II, Westlund PO, Cegrell U (1993) Brownian dynamics simulation of restricted molecular diffusion. The symmetric and deformed cone models. Mol Simul 11:373–393 CrossRefGoogle Scholar
  18. 18.
    Fleissner MR, Cascio D, Hubbell WL (2009) Structural origin of weakly ordered nitroxide motion in spin-labeled proteins. Protein Sci 18(5):893–908 PubMedCrossRefGoogle Scholar
  19. 19.
    Freed JH (1976) Theory of slow motional ESR spectra for nitroxides. In: Berliner LJ (ed) Spin labeling: theory and application. Academic Press, New York, pp 53–132 Google Scholar
  20. 20.
    Freed JH (2000) New technologies in electron spin resonance. Annu Rev Phys Chem 51:655–689 PubMedCrossRefGoogle Scholar
  21. 21.
    Guo Z, Cascio D, Hideg K, Kalai T, Hubbell WL (2007) Structural determination of nitroxide motion in spin-labeled proteins: tertiary contact and solvent-inaccessible sites in helix G of T4 Lysozyme. Protein Sci 16:1069–1086 PubMedCrossRefGoogle Scholar
  22. 22.
    Hakansson P, Westlund PO, Lindahl E, Edholm O (2001) A direct simulation of EPR slow-motion spectra of spin labelled phospholipids in liquid crystalline bilayers based on a molecular dynamics simulation of the lipid dynamics. Phys Chem Chem Phys 3:5311–5319 CrossRefGoogle Scholar
  23. 23.
    Halle B (2009) The physical basis of model-free analysis of NMR relaxation data from proteins and complex fluids. J Chem Phys 131(22):224,507–224,522 CrossRefGoogle Scholar
  24. 24.
    Hartigan JA (1975) Clustering algorithms. Wiley, New York Google Scholar
  25. 25.
    Jiao D, Barfield M, Combariza JE, Hruby VJ (1992) Ab initio molecular orbital studies of the rotational barriers and the sulfur-33 and carbon-13 chemical shieldings for dimethyl disulfide. J Am Chem Soc 114(10):3639–3643 CrossRefGoogle Scholar
  26. 26.
    Klare JP, Steinhoff HJ (2009) Spin labeling EPR. Photosynth Res 102(2–3):377–390 PubMedCrossRefGoogle Scholar
  27. 27.
    Krstic I, Endeward B, Margraf D, Marko A, Prisner TF (2012) Structure and dynamics of nucleic acids. Top Curr Chem 321:159–198 PubMedGoogle Scholar
  28. 28.
    Kubo R (1954) Note on the stochastic theory of resonance absorption. J Phys Soc Jpn 9(6):935–944 CrossRefGoogle Scholar
  29. 29.
    Kubo R (1969) A stochastic theory of line shape. Adv Chem Phys 15:101–127 Google Scholar
  30. 30.
    Kuprusevicius E, White G, Oganesyan VS (2011) Prediction of nitroxide spin label EPR spectra from MD trajectories: application to myoglobin. Faraday Discuss 148:283–298 PubMedCrossRefGoogle Scholar
  31. 31.
    Langen R, Oh KJ, Cascio D, Hubbell WL (2000) Crystal structures of spin labeled T4 Lysozyme mutants: implications for the interpretation of EPR spectra in terms of structure. Biochemistry 39:8396–8405 PubMedCrossRefGoogle Scholar
  32. 32.
    Levitt MH (2008) Spin dynamics: basics of nuclear magnetic resonance, 2nd edn. Wiley, Chichester Google Scholar
  33. 33.
    Liang Z, Lou Y, Freed JH, Columbus L, Hubbell WL (2004) A multifrequency electron spin resonance study of T4 Lysozyme dynamics using the slowly relaxing local structure model. J Phys Chem B 108:17,649–17,659 CrossRefGoogle Scholar
  34. 34.
    Maragakis P, Lindorff-Larsen K, Eastwood MP, Dror RO, Klepeis JL, Arkin IT, Jensen MO, Xu H, Trbovic N, Friesner RA, Palmer AG, Shaw DE (2008) Microsecond molecular dynamics simulation shows effect of slow loop dynamics on backbone amide order parameters of proteins. J Phys Chem B 112(19):6155–6158 PubMedCrossRefGoogle Scholar
  35. 35.
    Mchaourab HS, Kalai T, Hideg K, Hubbell WL (1999) Motion of spin-labeled side chains in T4 Lysozyme: effect of side chain structure. Biochemistry 38:2947–2955 PubMedCrossRefGoogle Scholar
  36. 36.
    Mchaourab HS, Lietzow MA, Hideg K, Hubbell WL (1996) Motion of spin-labeled side chains in T4 Lysozyme. Correlation with protein structure and dynamics. Biochemistry 35:7692–7704 PubMedCrossRefGoogle Scholar
  37. 37.
    Mchaourab HS, Steed PR, Kazmier K (2011) Toward the fourth dimension of membrane protein structure: insight into dynamics from spin-labeling EPR spectroscopy. Structure 19(11):1549–1561 PubMedCrossRefGoogle Scholar
  38. 38.
    Meirovitch E, Nayeem A, Freed JH (1984) Analysis of protein-lipid interactions based on model simulations of electron spin resonance spectra. J Phys Chem 88:3454–3465 CrossRefGoogle Scholar
  39. 39.
    Norris JR (1997) Markov chains. Cambridge University Press, Cambridge CrossRefGoogle Scholar
  40. 40.
    Polimeno A, Freed JH (1993) A many-body stochastic approach to rotational motions in liquids. Adv Chem Phys 83:89–210 Google Scholar
  41. 41.
    Polimeno A, Freed JH (1995) Slow motional ESR in complex fluids: the slowly relaxing local structure model of solvent cage effects. J Phys Chem 99:10,995–11,006 CrossRefGoogle Scholar
  42. 42.
    Rabiner LR (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE 77:257–286 CrossRefGoogle Scholar
  43. 43.
    Redfield AG (1957) On the theory of relaxation processes. IBM J Res Dev 1:19–31 CrossRefGoogle Scholar
  44. 44.
    Robinson BH, Slutsky LJ, Auteri FP (1992) Direct simulation of continuous wave electron paramagnetic resonance spectra from Brownian dynamics trajectories. J Chem Phys 96:2609–2616 CrossRefGoogle Scholar
  45. 45.
    Roux B (1994) The calculation of the potential of mean force using computer simulations. Comput Phys Commun 91:275–282 CrossRefGoogle Scholar
  46. 46.
    Schneider DJ, Freed JH (1989) Spin relaxation and motional dynamics. Adv Chem Phys 73:387–527 Google Scholar
  47. 47.
    Sezer D, Freed JH, Roux B (2008) Parametrization, molecular dynamics simulation, and calculation of electron spin resonance spectra of a nitroxide spin label on a polyalanine alpha-helix. J Phys Chem B 112(18):5755–5767 PubMedCrossRefGoogle Scholar
  48. 48.
    Sezer D, Freed JH, Roux B (2008) Simulating electron spin resonance spectra of nitroxide spin labels from molecular dynamics and stochastic trajectories. J Chem Phys 128(16):165,106–165,116 CrossRefGoogle Scholar
  49. 49.
    Sezer D, Freed JH, Roux B (2008) Using Markov models to simulate electron spin resonance spectra from molecular dynamics trajectories. J Phys Chem B 112(35):11,014–11,027 CrossRefGoogle Scholar
  50. 50.
    Sezer D, Freed JH, Roux B (2009) Multifrequency electron spin resonance spectra of a spin-labeled protein calculated from molecular dynamics simulations. J Am Chem Soc 131(7):2597–2605 PubMedCrossRefGoogle Scholar
  51. 51.
    Sezer D, Sigurdsson ST (2011) Simulating electron spin resonance spectra of macromolecules labeled with two dipolar-coupled nitroxide spin labels from trajectories. Phys Chem Chem Phys 13(28):12,785–12,797 CrossRefGoogle Scholar
  52. 52.
    Steinhoff HJ, Hubbell W (1996) Calculation of electron paramagnetic resonance spectra from Brownian dynamics trajectories: application to nitroxide side chains in proteins. Biophys J 71:2201–2212 PubMedCrossRefGoogle Scholar
  53. 53.
    Stoica I (2004) Using molecular dynamics to simulate electronic spin resonance spectra of T4 Lysozyme. J Phys Chem B 108(5):1771–1782 CrossRefGoogle Scholar
  54. 54.
    Tombolato F, Ferrarini A, Freed JH (2006) Dynamics of nitroxide side chain in spin-labeled proteins. J Phys Chem B 110:26,248–26,259 CrossRefGoogle Scholar
  55. 55.
    Usova N, Westlund PO, Fedchenia I (1995) Direct simulation of slow-motion electron spin resonance spectra by solving the stochastic Liouville equation in time domain with stochastic dynamics in the form of trajectories. J Chem Phys 103:96–103 CrossRefGoogle Scholar
  56. 56.
    Zhang Z, Fleissner MR, Tipikin DS, Liang Z, Moscicki JK, Earle KA, Hubbell WL, Freed JH (2010) Multifrequency electron spin resonance study of the dynamics of spin labeled T4 Lysozyme. J Phys Chem B 114(16):5503–5521 PubMedCrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Faculty of Engineering and Natural SciencesSabancı UniversityIstanbulTurkey
  2. 2.Department of Biochemistry and Molecular BiologyThe University of ChicagoChicagoUSA

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