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Journal of Biological Physics

, Volume 44, Issue 2, pp 195–209 | Cite as

Folding a viral peptide in different membrane environments: pathway and sampling analyses

  • Shivangi Nangia
  • Jason G. Pattis
  • Eric R. May
Original Paper

Abstract

Flock House virus (FHV) is a well-characterized model system to study infection mechanisms in non-enveloped viruses. A key stage of the infection cycle is the disruption of the endosomal membrane by a component of the FHV capsid, the membrane active γ peptide. In this study, we perform all-atom molecular dynamics simulations of the 21 N-terminal residues of the γ peptide interacting with membranes of differing compositions. We carry out umbrella sampling calculations to study the folding of the peptide to a helical state in homogenous and heterogeneous membranes consisting of neutral and anionic lipids. From the trajectory data, we evaluate folding energetics and dissect the mechanism of folding in the different membrane environments. We conclude the study by analyzing the extent of configurational sampling by performing time-lagged independent component analysis.

Keywords

Protein folding Flock House virus Molecular dynamics Umbrella sampling Non-enveloped virus Membrane active peptides TICA 

Notes

Acknowledgements

This work has been supported by the National Institutes of Health through grant R35GM119762 to E.R.M. Computational resources have been provided through the University of Connecticut Hornet HPC cluster and NSF XSEDE program (grant number TG-MCB140016). We thank Kevin Boyd for his critical reading and providing constructive suggestions on this manuscript.

Funding

This study was funded by NIH (grant number R35GM119762).

Compliance with ethical standard

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10867_2018_9490_MOESM1_ESM.pdf (1.9 mb)
ESM 1 (DOCX 1.92 mb)

References

  1. 1.
    Seelig, J.: Thermodynamics of lipid–peptide interactions. Biochim. Biophys. Acta Biomembr. 1666(1–2), 40–50 (2004).  https://doi.org/10.1016/j.bbamem.2004.08.004
  2. 2.
    Leontiadou, H., Mark, A.E., Marrink, S.J.: Antimicrobial peptides in action. J. Am. Chem. Soc. 128(37), 12156–12161 (2006).  https://doi.org/10.1021/ja062927q
  3. 3.
    Marčelja, S.: Lipid-mediated protein interaction in membranes. Biochim. Biophys. Acta Biomembr. 455(1), 1–7 (1976).  https://doi.org/10.1016/0005-2736(76)90149-8
  4. 4.
    Owicki, J.C., McConnell, H.M.: Theory of protein–lipid and protein–protein interactions in bilayer membranes. Proc. Natl. Acad. Sci. U. S. A 76(10), 4750–4754 (1979).  https://doi.org/10.1073/pnas.76.10.4750
  5. 5.
    Nymeyer, H., Woolf, T.B., Garcia, A.E.: Folding is not required for bilayer insertion: Replica exchange simulations of an α-helical peptide with an explicit lipid bilayer. Proteins. Struct. Funct. Genet. 59(4), 783–790 (2005).  https://doi.org/10.1002/prot.20460
  6. 6.
    Cymer, F., Von, H., White, S.H.: Mechanisms of integral membrane protein insertion and folding. J. Mol. Biol. 427(5), 999–1022 (2015).  https://doi.org/10.1016/j.jmb.2014.09.014
  7. 7.
    Sato, H., Feix, J.B.: Peptide–membrane interactions and mechanisms of membrane destruction by amphipathic α-helical antimicrobial peptides. Biochim. Biophys. Acta Biomembr. 1758(9), 1245–1256 (2006).  https://doi.org/10.1016/j.bbamem.2006.02.021
  8. 8.
    Li, C., Salditt, T.: Structure of magainin and alamethicin in model membranes studied by X-ray reflectivity. Biophys. J 91(9), 3285–3300 (2006).  https://doi.org/10.1529/biophysj.106.090118
  9. 9.
    Schümann, M., Dathe, M., Wieprecht, T., Beyermann, M., Bienert, M.: The tendency of magainin to associate upon binding to phospholipid bilayers. Biochemistry 36(14), 4345–4351 (1997).  https://doi.org/10.1021/bi962304x CrossRefGoogle Scholar
  10. 10.
    Leavitt, S., Freire, E.: Direct measurement of protein binding energetics by isothermal titration calorimetry. Curr. Opin. Struct. Biol. 11(5), 560–566 (2001).  https://doi.org/10.1016/S0959-440X(00)00248-7 CrossRefGoogle Scholar
  11. 11.
    Perrin, B.S., Tian, Y., Fu, R., et al.: High-resolution structures and orientations of antimicrobial peptides piscidin 1 and piscidin 3 in fluid bilayers reveal tilting, kinking, and bilayer immersion. J. Am. Chem. Soc. 136(9), 3491–3504 (2014).  https://doi.org/10.1021/ja411119m CrossRefGoogle Scholar
  12. 12.
    Afonin, S., Grage, S.L., Ieronimo, M., Wadhwani, P., Ulrich, A.S.: Temperature-dependent transmembrane insertion of the amphiphilic peptide PGLa in lipid bilayers observed by solid state 19F NMR spectroscopy. J. Am. Chem. Soc. 130(49), 16512–16514 (2008).  https://doi.org/10.1021/ja803156d CrossRefGoogle Scholar
  13. 13.
    Ladokhin, A.S., White, S.H.: Folding of amphipathic α-helices on membranes: Energetics of helix formation by melittin. J. Mol. Biol. 285(4), 1363–1369 (1999).  https://doi.org/10.1006/jmbi.1998.2346 CrossRefGoogle Scholar
  14. 14.
    Wieprecht, T., Seelig, J.: Isothermal titration calorimetry for studying interactions between peptides and lipid membranes. Curr. Top. Membr. 52, 31–56 (2002)CrossRefGoogle Scholar
  15. 15.
    Bechinger, B., Kim, Y., Chirlian, L.E., et al.: Orientations of amphipathic helical peptides in membrane bilayers determined by solid-state NMR spectroscopy. J. Biomol. Nmr. 1(2), 167–173 (1991).  https://doi.org/10.1007/BF01877228 CrossRefGoogle Scholar
  16. 16.
    Bechinger, B., Gierasch, L.M., Montal, M., Zasloff, M., Opella, S.J.: Orientations of helical peptides in membrane bilayers by solid state NMR spectroscopy. Solid State Nucl. Magn. Reson. 7(3), 185–191 (1996).  https://doi.org/10.1016/0926-2040(95)01224-9 CrossRefGoogle Scholar
  17. 17.
    Beschiaschvili, G., Seelig, J.: Melittin Binding to Mixed Phosphatidylglycerol/Phosphatidylcholine Membranes. Biochemistry 29(1), 52–58 (1990).  https://doi.org/10.1021/bi00453a007 CrossRefGoogle Scholar
  18. 18.
    Chen, C.H., Wiedman, G., Khan, A., Ulmschneider, M.B.: Absorption and folding of melittin onto lipid bilayer membranes via unbiased atomic detail microsecond molecular dynamics simulation. Biochim. Biophys. Acta Biomembr. 1838(9), 2243–2249 (2014).  https://doi.org/10.1016/j.bbamem.2014.04.012
  19. 19.
    Von, D., Knecht, V.: Antimicrobial selectivity based on zwitterionic lipids and underlying balance of interactions. Biochim. Biophys. Acta Biomembr. 1818(9), 2192–2201 (2012).  https://doi.org/10.1016/j.bbamem.2012.05.012 CrossRefGoogle Scholar
  20. 20.
    Irudayam, S.J., Berkowitz, M.L.: Binding and reorientation of melittin in a POPC bilayer: Computer simulations. Biochim. Biophys. Acta Biomembr. 1818(12), 2975–2981 (2012).  https://doi.org/10.1016/j.bbamem.2012.07.026 CrossRefGoogle Scholar
  21. 21.
    Koehler, L., Ulmschneider, M.B., Gray, J.J.: Computational modeling of membrane proteins. Proteins Struct. Funct. Bioinforma. 83(1), 1–24 (2015).  https://doi.org/10.1002/prot.24703 CrossRefGoogle Scholar
  22. 22.
    Ash, W.L., Zlomislic, M.R., Oloo, E.O., Tieleman, D.P.: Computer simulations of membrane proteins. Biochim. Biophys. Acta Biomembr. 1666(1-2), 158–189 (2004).  https://doi.org/10.1016/j.bbamem.2004.04.012 CrossRefGoogle Scholar
  23. 23.
    Andersson, M., Ulmschneider, J.P., Ulmschneider, M.B., White, S.H.: Conformational states of melittin at a bilayer interface. Biophys. J 104(6), L12–L14 (2013).  https://doi.org/10.1016/j.bpj.2013.02.006 CrossRefGoogle Scholar
  24. 24.
    Bereau, T., Bennett, W.F.D., Pfaendtner, J., Deserno, M., Karttunen, M.: Folding and insertion thermodynamics of the transmembrane WALP peptide. J. Chem. Phys. 143, 24 (2015).  https://doi.org/10.1063/1.4935487 CrossRefGoogle Scholar
  25. 25.
    Im, W., Brooks III, C.L.: Interfacial folding and membrane insertion of designed peptides studied by molecular dynamics simulations. Proc. Natl. Acad. Sci. 102(19), 6771–6776 (2005).  https://doi.org/10.1073/pnas.0408135102 ADSCrossRefGoogle Scholar
  26. 26.
    Tieleman, D.P., Berendsen, H.J.C., Sansom, M.S.P.: Surface binding of alamethicin stabilizes its helical structure: Molecular dynamics simulations. Biophys. J 76(6), 3186–3191 (1999).  https://doi.org/10.1016/S0006-3495(99)77470-9 CrossRefGoogle Scholar
  27. 27.
    Lin, D., Grossfield, A.: Thermodynamics of antimicrobial lipopeptide binding to membranes: Origins of affinity and selectivity. Biophys. J 107(8), 1862–1872 (2014).  https://doi.org/10.1016/j.bpj.2014.08.026 CrossRefGoogle Scholar
  28. 28.
    Lindahl, E., Sansom, M.S.: Membrane proteins: molecular dynamics simulations. Curr. Opin. Struct. Biol. 18(4), 425–431 (2008).  https://doi.org/10.1016/j.sbi.2008.02.003 CrossRefGoogle Scholar
  29. 29.
    Ward, M.D., Nangia, S., May, E.R.: Evaluation of the hybrid resolution PACE model for the study of folding, insertion, and pore formation of membrane associated peptides. J. Comput. Chem. 38(16), 1462–1471 (2017).  https://doi.org/10.1002/jcc.24694 CrossRefGoogle Scholar
  30. 30.
    Shai, Y.: Mode of action of membrane active antimicrobial peptides. Biopolym. - Pept. Sci. Sect. 66(4), 236–248 (2002).  https://doi.org/10.1002/bip.10260 CrossRefGoogle Scholar
  31. 31.
    Shai, Y.: Mechanism of the binding, insertion and destabilization of phospholipid bilayer membranes by α-helical antimicrobial and cell non-selective membrane-lytic peptides. Biochim. Biophys. Acta Biomembr. 1462(1–2), 55–70 (1999).  https://doi.org/10.1016/S0005-2736(99)00200-X CrossRefGoogle Scholar
  32. 32.
    Yuan, T., Zhang, X., Hu, Z., Wang, F., Lei, M.: Molecular dynamics studies of the antimicrobial peptides piscidin 1 and its mutants with a DOPC lipid bilayer. Biopolymers 97(12), 998–1009 (2012).  https://doi.org/10.1002/bip.22116 CrossRefGoogle Scholar
  33. 33.
    Rahmanpour, A., Ghahremanpour, M.M., Mehrnejad, F., Moghaddam, M.E.: Interaction of Piscidin-1 with zwitterionic versus anionic membranes: A comparative molecular dynamics study. J. Biomol. Struct. Dyn. 31(12), 1393–1403 (2013).  https://doi.org/10.1080/07391102.2012.737295 CrossRefGoogle Scholar
  34. 34.
    Tieleman, D.P., Sansom, M.S.P., Berendsen, H.J.C.: Alamethicin helices in a bilayer and in solution: Molecular dynamics simulations. Biophys. J 76(1 I), 40–49 (1999)CrossRefGoogle Scholar
  35. 35.
    Perrin, B.S., Pastor, R.W.: Simulations of membrane-disrupting peptides I: alamethicin pore stability and spontaneous insertion. Biophys. J 111(6), 1248–1257 (2016).  https://doi.org/10.1016/j.bpj.2016.08.014 CrossRefGoogle Scholar
  36. 36.
    Perrin, B.S., Fu, R., Cotten, M.L., Pastor, R.W.: Simulations of membrane-disrupting peptides II: AMP piscidin 1 favors surface defects over pores. Biophys. J 111(6), 1258–1266 (2016).  https://doi.org/10.1016/j.bpj.2016.08.015 CrossRefGoogle Scholar
  37. 37.
    Nangia, S., May, E.R.: Influence of membrane composition on the binding and folding of a membrane lytic peptide from the non-enveloped flock house virus. Biochim. Biochim. Biophys. Acta Biomembr. 1859(7), 1190–1199 (2017).  https://doi.org/10.1016/j.bbamem.2017.04.002
  38. 38.
    Bong, D.T., Steinem, C., Janshoff, A., Johnson, J.E., Ghadiri, M.R.: A highly membrane-active peptide in flock house virus: Implications for the mechanism of nodavirus infection. Chem. Biol. 6(7), 473–481 (1999).  https://doi.org/10.1016/S1074-5521(99)80065-9 CrossRefGoogle Scholar
  39. 39.
    Sugita, Y., Okamoto, Y.: Replica-exchange molecular dynamics method for protein folding. Chem. Phys. Lett. 314(1–2), 141–151 (1999)ADSCrossRefGoogle Scholar
  40. 40.
    Gallicchio, E., Levy, R.M., Parashar, M.: Asynchronous replica exchange for molecular simulations. J. Comput. Chem. 29(5), 788–794 (2008).  https://doi.org/10.1002/jcc.20839 CrossRefGoogle Scholar
  41. 41.
    Periole, X., Mark, A.E.: Convergence and sampling efficiency in replica exchange simulations of peptide folding in explicit solvent. J. Chem. Phys. 126, 1 (2007).  https://doi.org/10.1063/1.2404954 CrossRefGoogle Scholar
  42. 42.
    Lee, K.H., Chen, J.: Multiscale enhanced sampling of intrinsically disordered protein conformations. J. Comput. Chem. 37(6), 550–557 (2016).  https://doi.org/10.1002/jcc.23957 CrossRefGoogle Scholar
  43. 43.
    Faradjian, A.K., Elber, R.: Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 120(23), 10880–10889 (2004).  https://doi.org/10.1063/1.1738640 ADSCrossRefGoogle Scholar
  44. 44.
    Allen, R.J., Warren, P.B., Ten, W.: Sampling rare switching events in biochemical networks. Phys. Rev. Lett. 94, 1 (2005).  https://doi.org/10.1103/PhysRevLett.94.018104 CrossRefGoogle Scholar
  45. 45.
    Dellago, C., Bolhuis, P.G., Csajka, F.S., Chandler, D.: Transition path sampling and the calculation of rate constants. J. Chem. Phys. 108(5), 1964 (1998).  https://doi.org/10.1063/1.475562 ADSCrossRefGoogle Scholar
  46. 46.
    Grubmller, H.: Predicting slow structural transitions in macromolecular systems: conformational flooding. Phys. Rev. E 52(3), 2893–2906 (1995).  https://doi.org/10.1103/PhysRevE.52.2893 ADSCrossRefGoogle Scholar
  47. 47.
    Laio A, Gervasio FL. Metadynamics: A method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science. Rep. Prog. Phys. 2008;71(12).  https://doi.org/10.1088/0034-4885/71/12/126601.
  48. 48.
    Torrie, G.M., Valleau, J.P.: Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J. Comput. Phys. 23(2), 187–199 (1977).  https://doi.org/10.1016/0021-9991(77)90121-8 ADSCrossRefGoogle Scholar
  49. 49.
    Young, W.S., Brooks III, C.L.: A microscopic view of helix propagation: N and C-terminal helix growth in alanine helices. J. Mol. Biol. 259(3), 560–572 (1996).  https://doi.org/10.1006/jmbi.1996.0339 CrossRefGoogle Scholar
  50. 50.
    Bursulaya, B.D., Brooks III, C.L.: Folding free energy surface of a three-stranded β-sheet protein. J. Am. Chem. Soc. 121(43), 9947–9951 (1999).  https://doi.org/10.1021/ja991764l CrossRefGoogle Scholar
  51. 51.
    Mahdavi, S., Kuyucak, S.: Why the Drosophila shaker K+ channel is not a good model for ligand binding to voltage-gated Kv1 channels. Biochemistry 52(9), 1631–1640 (2013).  https://doi.org/10.1021/bi301257p CrossRefGoogle Scholar
  52. 52.
    Vijayaraj, R., Van, D., Bultinck, P., Subramanian, V.: Molecular dynamics and umbrella sampling study of stabilizing factors in cyclic peptide-based nanotubes. J. Phys. Chem. B 116(33), 9922–9933 (2012).  https://doi.org/10.1021/jp303418a CrossRefGoogle Scholar
  53. 53.
    Yesudhas, D., Anwar, M.A., Panneerselvam, S., Kim, H.-K., Choi, S.: Evaluation of Sox2 binding affinities for distinct DNA patterns using steered molecular dynamics simulation. FEBS Open Bio 7(11), 1750–1767 (2017).  https://doi.org/10.1002/2211-5463.12316 CrossRefGoogle Scholar
  54. 54.
    Vermaas, J.V., Tajkhorshid, E.: Differential membrane binding mechanics of synaptotagmin isoforms observed in atomic detail. Biochemistry 56(1), 281–293 (2017).  https://doi.org/10.1021/acs.biochem.6b00468 CrossRefGoogle Scholar
  55. 55.
    Mascarenhas, N.M., Kästner, J.: How maltose influences structural changes to bind to maltose-binding protein: results from umbrella sampling simulation. Proteins Struct. Funct. Bioinforma. 81(2), 185–198 (2013).  https://doi.org/10.1002/prot.24174 CrossRefGoogle Scholar
  56. 56.
    Patrascu, M.B., Malek-Adamian, E., Damha, M.J., Moitessier, N.: Accurately modeling the conformational preferences of nucleosides. J. Am. Chem. Soc. 139(39), 13620–13623 (2017).  https://doi.org/10.1021/jacs.7b07436 CrossRefGoogle Scholar
  57. 57.
    Schaefer, M., Bartels, C., Karplus, M.: Solution conformations and thermodynamics of structured peptides: molecular dynamics simulation with an implicit solvation model. J. Mol. Biol. 284(3), 835–848 (1998).  https://doi.org/10.1006/jmbi.1998.2172 CrossRefGoogle Scholar
  58. 58.
    Banerjee, M., Johnson, J.E.: Activation, exposure and penetration of virally encoded, membrane-active polypeptides during non-enveloped virus entry. Curr. Protein Pept. Sci. 9(1), 16–27 (2008).  https://doi.org/10.2174/138920308783565732
  59. 59.
    Kumar, C., Dey, D., Ghosh, S., Banerjee, M.: Breach: Host membrane penetration and entry by nonenveloped viruses. Cell Press Rev. (Trends In Microbiology).  https://doi.org/10.1016/j.tim.2017.09.010
  60. 60.
    Lewis, J.R., Cafiso, D.S.: Correlation between the free energy of a channel-forming voltage-gated peptide and the spontaneous curvature of bilayer lipids. Biochemistry 38(18), 5932–5938 (1999).  https://doi.org/10.1021/bi9828167 CrossRefGoogle Scholar
  61. 61.
    Bulet, P., Hetru, C., Dimarcq, J.-L., Hoffmann, D.: Antimicrobial peptides in insects; structure and function. Dev. Comp. Immunol. 23(4-5), 329–344 (1999).  https://doi.org/10.1016/S0145-305X(99)00015-4 CrossRefGoogle Scholar
  62. 62.
    Banerjee, M., Khayat, R., Walukiewicz, H.E., Odegard, A.L., Schneemann, A., Johnson, J.E.: Dissecting the functional domains of a nonenveloped virus membrane penetration peptide. J. Virol. 83(13), 6929–6933 (2009).  https://doi.org/10.1128/JVI.02299-08 CrossRefGoogle Scholar
  63. 63.
    Bajaj, S., Dey, D., Bhukar, R., Kumar, M., Banerjee, M.: Non-enveloped virus entry: structural determinants and mechanism of functioning of a viral lytic peptide. J. Mol. Biol. 428(17), 3540–3556 (2016).  https://doi.org/10.1016/j.jmb.2016.06.006 CrossRefGoogle Scholar
  64. 64.
    Abraham, M.J., Murtola, T., Schulz, R., et al.: Gromacs: High-performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 1-2, 19–25 (2015).  https://doi.org/10.1016/j.softx.2015.06.001 ADSCrossRefGoogle Scholar
  65. 65.
    Best, R.B., Zhu, X., Shim, J., et al.: Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone φ, ψ and side-chain χ 1 and χ 2 Dihedral Angles. J. Chem. Theory Comput. 8(9), 3257–3273 (2012).  https://doi.org/10.1021/ct300400x
  66. 66.
    Klauda, J.B., Venable, R.M., Freites, J.A., et al.: Update of the CHARMM all-atom additive force field for lipids: validation on six lipid types. J. Phys. Chem. B 114(23), 7830–7843 (2010).  https://doi.org/10.1021/jp101759q CrossRefGoogle Scholar
  67. 67.
    Essmann, U., Perera, L., Berkowitz, M.L., Darden, T., Lee, H., Pedersen, L.G.: A smooth particle mesh Ewald method. J. Chem. Phys. 103(19), 8577–8593 (1995)ADSCrossRefGoogle Scholar
  68. 68.
    Humphrey, W., Dalke, A., Schulten, K.: VMD: Visual molecular dynamics. J. Mol. Graph. 14(1), 33–38 (1996).  https://doi.org/10.1016/0263-7855(96)00018-5 CrossRefGoogle Scholar
  69. 69.
    Tribello, G.A., Bonomi, M., Branduardi, D., Camilloni, C., Bussi, G.: PLUMED 2: New feathers for an old bird. Comput. Phys. Commun. 185(2), 604–613 (2014).  https://doi.org/10.1016/j.cpc.2013.09.018 ADSCrossRefGoogle Scholar
  70. 70.
    Bonomi, M., Branduardi, D., Bussi, G., et al.: PLUMED: A portable plugin for free-energy calculations with molecular dynamics. Comput. Phys. Commun. 180(10), 1961–1972 (2009).  https://doi.org/10.1016/j.cpc.2009.05.011 ADSCrossRefGoogle Scholar
  71. 71.
    Pietrucci, F., Laio, A.: A collective variable for the efficient exploration of protein beta-sheet structures: application to SH3 and GB1. J. Chem. Theory Comput. 5(9), 2197–2201 (2009).  https://doi.org/10.1021/ct900202f CrossRefGoogle Scholar
  72. 72.
    Roux, B.: The calculation of the potential of mean force using computer simulations. Comput. Phys. Commun. 91(1-3), 275–282 (1995).  https://doi.org/10.1016/0010-4655(95)00053-I ADSCrossRefGoogle Scholar
  73. 73.
    Grossfield A. Grossfield, Alan, “WHAM: the weighted histogram analysis method”, version.Google Scholar
  74. 74.
    McGibbon, R.T., Beauchamp, K.A., Harrigan, M.P., et al.: MDTraj: A modern open library for the analysis of molecular dynamics trajectories. Biophys. J 109(8), 1528–1532 (2015).  https://doi.org/10.1016/j.bpj.2015.08.015 CrossRefGoogle Scholar
  75. 75.
    Husic BE, McGibbon RT, Sultan MM, Pande VS. Optimized parameter selection reveals trends in Markov state models for protein folding. J. Chem. Phys. 2016;145(19).  https://doi.org/10.1063/1.4967809.
  76. 76.
    Pérez-Hernández G, Paul F, Giorgino T, De Fabritiis G, Noé F. Identification of slow molecular order parameters for Markov model construction. J. Chem. Phys. 2013;139(1).  https://doi.org/10.1063/1.4811489.
  77. 77.
    Schwantes, C.R., Pande, V.S.: Improvements in Markov state model construction reveal many non-native interactions in the folding of NTL9. J. Chem. Theory Comput. 9(4), 2000–2009 (2013).  https://doi.org/10.1021/ct300878a CrossRefGoogle Scholar
  78. 78.
    Wu H, Mey ASJS, Rosta E, Noé F. Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states. J. Chem. Phys. 2014;141(21).  https://doi.org/10.1063/1.4902240.
  79. 79.
    Prinz JH, Wu H, Sarich M, et al. Markov models of molecular kinetics: generation and validation. J. Chem. Phys. 2011;134(17).  https://doi.org/10.1063/1.3565032.
  80. 80.
    Hills, R.D., Brooks III, C.L.: Subdomain competition, cooperativity, and topological frustration in the folding of CheY. J. Mol. Biol. (2008).  https://doi.org/10.1016/j.jmb.2008.07.007
  81. 81.
    Wu H, Paul F, Wehmeyer C, Noé F. Multiensemble Markov models of molecular thermodynamics and kinetics. 2016.  https://doi.org/10.1073/pnas.1525092113.
  82. 82.
    Jo, S., Suh, D., He, Z., Chipot, C., Roux, B.: Leveraging the information from Markov state models to improve the convergence of umbrella sampling simulations. J. Phys. Chem. B 120(33), 8733–8742 (2016).  https://doi.org/10.1021/acs.jpcb.6b05125 CrossRefGoogle Scholar

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© Springer Science+Business Media B.V., part of Springer Nature 2018
corrected publication April/2018

Authors and Affiliations

  1. 1.Department of Molecular and Cell BiologyUniversity of ConnecticutStorrsUSA

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