Folding may be described conceptually in terms of trajectories over a landscape of free energies corresponding to different molecular configurations. In practice, energy landscapes can be difficult to measure. Single-molecule force spectroscopy (SMFS), whereby structural changes are monitored in molecules subjected to controlled forces, has emerged as a powerful tool for probing energy landscapes. We summarize methods for reconstructing landscapes from force spectroscopy measurements under both equilibrium and nonequilibrium conditions. Other complementary, but technically less demanding, methods provide a model-dependent characterization of key features of the landscape. Once reconstructed, energy landscapes can be used to study critical folding parameters, such as the characteristic transition times required for structural changes and the effective diffusion coefficient setting the timescale for motions over the landscape. We also discuss issues that complicate measurement and interpretation, including the possibility of multiple states or pathways and the effects of projecting multiple dimensions onto a single coordinate.

[Erratum, Closure]

An erratum has been published for this article:
Reconstructing Folding Energy Landscapes by Single-Molecule Force Spectroscopy

Article metrics loading...

Loading full text...

Full text loading...


Literature Cited

  1. Alemany A, Mossa A, Junier I, Ritort F. 1.  2012. Experimental free-energy measurements of kinetic molecular states using fluctuation theorems. Nat. Phys. 8:688–94 [Google Scholar]
  2. Anfinsen CB. 2.  1973. Principles that govern the folding of protein chains. Science 181:223–30 [Google Scholar]
  3. Ansari A, Jones CM, Henry ER, Hofrichter J, Eaton WA. 3.  1992. The role of solvent viscosity in the dynamics of protein conformational changes. Science 256:1796–98 [Google Scholar]
  4. Anthony PC, Perez CF, Garcia-Garcia C, Block SM. 4.  2012. Folding energy landscape of the thiamine pyrophosphate riboswitch aptamer. Proc. Natl. Acad. Sci. USA 109:1485–89 [Google Scholar]
  5. Ball FG, Rice JA. 5.  1992. Stochastic models for ion channels: introduction and bibliography. Math. Biosci. 112:189–206 [Google Scholar]
  6. Bell GI. 6.  1978. Models for the specific adhesion of cells to cells. Science 200:618–27 [Google Scholar]
  7. Berkovich R, Garcia-Manyes S, Klafter J, Urbakh M, Fernández JM. 7.  2010. Hopping around an entropic barrier created by force. Biochem. Biophys. Res. Commun. 403:133–37 [Google Scholar]
  8. Berkovich R, Garcia-Manyes S, Urbakh M, Klafter J, Fernández JM. 8.  2010. Collapse dynamics of single proteins extended by force. Biophys. J. 98:2692–701 [Google Scholar]
  9. Berkovich R, Hermans RI, Popa I, Stirnemann G, Garcia-Manyes S. 9.  et al. 2012. Rate limit of protein elastic response is tether dependent. Proc. Natl. Acad. Sci. USA 109:14416–21 [Google Scholar]
  10. Best RB. 10.  2012. Atomistic molecular simulations of protein folding. Curr. Opin. Struct. Biol. 22:152–61 [Google Scholar]
  11. Best RB, Fowler SB, Herrera JLT, Steward A, Paci E, Clarke J. 11.  2003. Mechanical unfolding of a titin Ig domain: structure of transition state revealed by combining atomic force microscopy, protein engineering and molecular dynamics simulations. J. Mol. Biol. 330:867–77 [Google Scholar]
  12. Best RB, Hummer G. 12.  2010. Coordinate-dependent diffusion in protein folding. Proc. Natl. Acad. Sci. USA 107:1088–93 [Google Scholar]
  13. Best RB, Paci E, Hummer G, Dudko OK. 13.  2008. Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules. J. Phys. Chem. B 112:5968–76 [Google Scholar]
  14. Blanco M, Walter NG. 14.  2010. Analysis of complex single-molecule FRET time trajectories. Methods Enzymol. 472:153–78 [Google Scholar]
  15. Borgia A, Wensley BG, Soranno A, Nettels D, Borgia MB. 15.  et al. 2012. Localizing internal friction along the reaction coordinate of protein folding by combining ensemble and single-molecule fluorescence spectroscopy. Nat. Commun. 3:1195 [Google Scholar]
  16. Brockwell DJ, Paci E, Zinober RC, Beddard GS, Olmsted PD. 16.  et al. 2003. Pulling geometry defines the mechanical resistance of a β-sheet protein. Nat. Struct. Biol. 10:731–37 [Google Scholar]
  17. Brujić J, Hermans RI, Walther KA, Fernández JM. 17.  2006. Single-molecule force spectroscopy reveals signatures of glassy dynamics in the energy landscape of ubiquitin. Nat. Phys. 2:282–86 [Google Scholar]
  18. Buchner J, Kiefhaber T. 18.  2005. Protein Folding Handbook Weinheim: Wiley-VCH [Google Scholar]
  19. Bustamante C, Liphardt J, Ritort F. 19.  2005. The nonequilibrium thermodynamics of small systems. Phys. Today 58:43–48 [Google Scholar]
  20. Carrion-Vazquez M, Oberhauser AF, Fowler SB, Marszalek PE, Broedel SE. 20.  et al. 1999. Mechanical and chemical unfolding of a single protein: a comparison. Proc. Natl. Acad. Sci. USA 96:3694–99 [Google Scholar]
  21. Carter BC, Vershinin M, Gross SP. 21.  2008. A comparison of step-detection methods: How well can you do?. Biophys. J. 94:306–19 [Google Scholar]
  22. Chang J-C, de Messieres M, La Porta A. 22.  2013. Effect of handle length and microsphere size on transition kinetics in single-molecule experiments. Phys. Rev. E 87:012721 [Google Scholar]
  23. Chaudhury S, Makarov DE. 23.  2010. A harmonic transition state approximation for the duration of reactive events in complex molecular rearrangements. J. Chem. Phys. 133:034118 [Google Scholar]
  24. Chen G, Wen JD, Tinoco I Jr. 24.  2007. Single-molecule mechanical unfolding and folding of a pseudoknot in human telomerase RNA. RNA 13:2175–88 [Google Scholar]
  25. Chen Y, Parrini C, Taddei N, Lapidus LJ. 25.  2009. Conformational properties of unfolded HypF-N. J. Phys. Chem. B 113:16209–13 [Google Scholar]
  26. Chodera JD, Pande VS. 26.  2011. Splitting probabilities as a test of reaction coordinate choice in single-molecule experiments. Phys. Rev. Lett. 107:098102 [Google Scholar]
  27. Chung HS, Louis JM, Eaton WA. 27.  2009. Experimental determination of upper bound for transition path times in protein folding from single-molecule photon-by-photon trajectories. Proc. Natl. Acad. Sci. USA 106:11837–44 [Google Scholar]
  28. Chung HS, McHale K, Louis JM, Eaton WA. 28.  2012. Single-molecule fluorescence experiments determine protein folding transition path times. Science 335:981–84 [Google Scholar]
  29. Comstock MJ, Ha T, Chemla YR. 29.  2011. Ultrahigh-resolution optical trap with single-fluorophore sensitivity. Nat. Methods 8:335–40 [Google Scholar]
  30. de Messieres M, Brawn-Cinani B, La Porta A. 30.  2011. Measuring the folding landscape of a harmonically constrained biopolymer. Biophys. J. 100:2736–44 [Google Scholar]
  31. de Messieres M, Chang J-C, Brawn-Cinani B, La Porta A. 31.  2012. Single-molecule study of G-quadruplex disruption using dynamic force spectroscopy. Phys. Rev. Lett. 109:058101 [Google Scholar]
  32. Dietz H, Rief M. 32.  2004. Exploring the energy landscape of GFP by single-molecule mechanical experiments. Proc. Natl. Acad. Sci. USA 101:16192–97 [Google Scholar]
  33. Dill KA, Ozkan SB, Shell MS, Weikl TR. 33.  2008. The protein folding problem. Annu. Rev. Biophys. 37:289–316 [Google Scholar]
  34. Du R, Pande VS, Grosberg AY, Tanaka T, Shakhnovich ES. 34.  1998. On the transition coordinate for protein folding. J. Chem. Phys. 108:334–50 [Google Scholar]
  35. Dudko OK, Graham TGW, Best RB. 35.  2011. Locating the barrier for folding of single molecules under an external force. Phys. Rev. Lett. 107:208301 [Google Scholar]
  36. Dudko OK, Hummer G, Szabo A. 36.  2006. Intrinsic rates and activation free energies from single-molecule pulling experiments. Phys. Rev. Lett. 96:108101 [Google Scholar]
  37. Dudko OK, Hummer G, Szabo A. 37.  2008. Theory, analysis, and interpretation of single-molecule force spectroscopy experiments. Proc. Natl. Acad. Sci. USA 105:15755–60 [Google Scholar]
  38. Dyer RB. 38.  2007. Ultrafast and downhill protein folding. Curr. Opin. Struct. Biol. 17:38–47 [Google Scholar]
  39. Elms PJ, Chodera JD, Bustamante C, Marqusee S. 39.  2012. The molten globule state is unusually deformable under mechanical force. Proc. Natl. Acad. Sci. USA 109:3796–801 [Google Scholar]
  40. Evans E, Leung A, Heinrich V, Zhu C. 40.  2004. Mechanical switching and coupling between two dissociation pathways in a P-selectin adhesion bond. Proc. Natl. Acad. Sci. USA 101:11281–86 [Google Scholar]
  41. Evans E, Ritchie K. 41.  1997. Dynamic strength of molecular adhesion bonds. Biophys. J. 72:1541–55 [Google Scholar]
  42. Forns N, de Lorenzo S, Manosas M, Hayashi K, Huguet JM, Ritort F. 42.  2011. Improving signal/noise resolution in single-molecule experiments using molecular constructs with short handles. Biophys. J. 100:1765–74 [Google Scholar]
  43. Gao Y, Zorman S, Gundersen G, Xi Z, Ma L. 43.  et al. 2012. Single reconstituted neuronal SNARE complexes zipper in three distinct stages. Science 337:1340–43 [Google Scholar]
  44. Gebhardt JCM, Bornschloegla T, Rief M. 44.  2010. Full distance-resolved folding energy landscape of one single protein molecule. Proc. Natl. Acad. Sci. USA 107:2013–18 [Google Scholar]
  45. Gore J, Ritort F, Bustamante C. 45.  2003. Bias and error in estimates of equilibrium free-energy differences from nonequilibrium measurements. Proc. Natl. Acad. Sci. USA 100:12564–69 [Google Scholar]
  46. Graham TGW, Best RB. 46.  2011. Force-induced change in protein unfolding mechanism: discrete or continuous switch?. J. Phys. Chem. B 115:1546–61 [Google Scholar]
  47. Greenleaf WJ, Frieda KL, Foster DAN, Woodside MT, Block SM. 47.  2008. Direct observation of hierarchical folding in single riboswitch aptamers. Science 319:630–33 [Google Scholar]
  48. Greenleaf WJ, Woodside MT, Abbondanzieri EA, Block SM. 48.  2005. Passive all-optical force clamp for high-resolution laser trapping. Phys. Rev. Lett. 95:208102 [Google Scholar]
  49. Greenleaf WJ, Woodside MT, Block SM. 49.  2007. High-resolution, single-molecule measurements of biomolecular motion. Annu. Rev. Biophys. Biomol. Struct. 36:171–90 [Google Scholar]
  50. Guo B, Guilford WH. 50.  2006. Mechanics of actomyosin bonds in different nucleotide states are tuned to muscle contraction. Proc. Natl. Acad. Sci. USA 103:9844–49 [Google Scholar]
  51. Gupta AN, Vincent A, Neupane K, Yu H, Wang F, Woodside MT. 51.  2011. Experimental validation of free-energy-landscape reconstruction from non-equilibrium single-molecule force spectroscopy measurements. Nat. Phys. 7:631–34 [Google Scholar]
  52. Hagen SJ. 52.  2010. Solvent viscosity and friction in protein folding dynamics. Curr. Protein Pept. Sci. 11:385–95 [Google Scholar]
  53. Hagen SJ, Hofrichter J, Szabo A, Eaton WA. 53.  1996. Diffusion-limited contact formation in unfolded cytochrome c: estimating the maximum rate of protein folding. Proc. Natl. Acad. Sci. USA 93:11615–17 [Google Scholar]
  54. Hagen SJ, Qiu LL, Pabit SA. 54.  2005. Diffusional limits to the speed of protein folding: fact or friction?. J. Phys. Condens. Matter 17:S1503 [Google Scholar]
  55. Hänggi P, Talkner P, Borkovec M. 55.  1990. Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62:251–341 [Google Scholar]
  56. Harris NC, Song Y, Kiang C-H. 56.  2007. Experimental free energy surface reconstruction from single-molecule force spectroscopy using Jarzynski's equality. Phys. Rev. Lett. 99:068101 [Google Scholar]
  57. Hinczewski M, Gebhardt JCM, Rief M, Thirumalai D. 57.  2013. From mechanical folding trajectories to intrinsic energy landscapes of biopolymers. Proc. Natl. Acad. Sci. USA 110:4500–5 [Google Scholar]
  58. Hoffmann A, Woodside MT. 58.  2011. Signal-pair correlation analysis of single-molecule trajectories. Angew. Chem. Int. Ed. 50:12643–46 [Google Scholar]
  59. Hohng S, Zhou R, Nahas MK, Yu J, Schulten K. 59.  et al. 2007. Fluorescence-force spectroscopy maps two-dimensional reaction landscape of the Holliday junction. Science 318:279–83 [Google Scholar]
  60. Hugel T, Holland NB, Cattani A, Moroder L, Seitz M, Gaub HE. 60.  2002. Single-molecule optomechanical cycle. Science 296:1103–6 [Google Scholar]
  61. Hugel T, Michaelis J, Hetherington CL, Jardine PJ, Grimes S. 61.  et al. 2007. Experimental test of connector rotation during DNA packaging into bacteriophage ϕ29 capsids. PLoS Biol. 5:e59 [Google Scholar]
  62. Huguet JM, Bizarro CV, Forns N, Smith SB, Bustamante C, Ritort F. 62.  2010. Single-molecule derivation of salt dependent base-pair free energies in DNA. Proc. Natl. Acad. Sci. USA 107:15431–36 [Google Scholar]
  63. Hummer G. 63.  2004. From transition paths to transition states and rate coefficients. J. Chem. Phys. 120:516–23 [Google Scholar]
  64. Hummer G, Szabo A. 64.  2001. Free energy reconstruction from nonequilibrium single-molecule pulling experiments. Proc. Natl. Acad. Sci. USA 98:3658–61 [Google Scholar]
  65. Hummer G, Szabo A. 65.  2010. Free energy profiles from single-molecule pulling experiments. Proc. Natl. Acad. Sci. USA 107:21441–46 [Google Scholar]
  66. Hyeon C, Morrison G, Pincus DL, Thirumalai D. 66.  2009. Refolding dynamics of stretched biopolymers upon force quench. Proc. Natl. Acad. Sci. USA 106:20288–93 [Google Scholar]
  67. Hyeon C, Morrison G, Thirumalai D. 67.  2008. Force-dependent hopping rates of RNA hairpins can be estimated from accurate measurement of the folding landscapes. Proc. Natl. Acad. Sci. USA 105:9604–9 [Google Scholar]
  68. Hyeon C, Thirumalai D. 68.  2003. Can energy landscape roughness of proteins and RNA be measured by using mechanical unfolding experiments?. Proc. Natl. Acad. Sci. USA 100:10249–53 [Google Scholar]
  69. Hyeon C, Thirumalai D. 69.  2008. Multiple probes are required to explore and control the rugged energy landscape of RNA hairpins. J. Am. Chem. Soc. 130:1538–39 [Google Scholar]
  70. Jagannathan B, Elms PJ, Bustamante C, Marqusee S. 70.  2012. Direct observation of a force-induced switch in the anisotropic mechanical unfolding pathway of a protein. Proc. Natl. Acad. Sci. USA 109:17820–25 [Google Scholar]
  71. Janovjak H, Knaus H, Muller DJ. 71.  2007. Transmembrane helices have rough energy surfaces. J. Am. Chem. Soc. 129:246–47 [Google Scholar]
  72. Jansson PA. 72.  1997. Deconvolution of Images and Spectra San Diego: Academic, 2nd ed.. [Google Scholar]
  73. Jarzynski C. 73.  1997. Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78:2690–93 [Google Scholar]
  74. Klimov DK, Thirumalai D. 74.  2000. Native topology determines force-induced unfolding pathways in globular proteins. Proc. Natl. Acad. Sci. USA 97:7254–59 [Google Scholar]
  75. Kramers HA. 75.  1940. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7:284–304 [Google Scholar]
  76. Lang MJ, Fordyce PM, Engh AM, Neuman KC, Block SM. 76.  2004. Simultaneous, coincident optical trapping and single-molecule fluorescence. Nat. Methods 1:133–39 [Google Scholar]
  77. Lannon H, Haghpanah JS, Montclare JK, Vanden-Eijnden E, Brujić J. 77.  2013. Force-clamp experiments reveal the free-energy profile and diffusion coefficient of the collapse of protein molecules. Phys. Rev. Lett. 110:128301 http://link.aps.org/abstract/PRL/v110/e128301 [Google Scholar]
  78. Li H, Wang H-C, Cao Y, Sharma D, Wang M. 78.  2008. Configurational entropy modulates the mechanical stability of protein GB1. J. Mol. Biol. 379:871–80 [Google Scholar]
  79. Li PTX, Bustamante C, Tinoco I Jr. 79.  2007. Real-time control of the energy landscape by force directs the folding of RNA molecules. Proc. Natl. Acad. Sci. USA 104:7039–44 [Google Scholar]
  80. Lin J-C, Hyeon C, Thirumalai D. 80.  2012. RNA under tension: folding landscapes, kinetic partitioning mechanism, and molecular tensegrity. J. Phys. Chem. Lett. 3:3616–25 [Google Scholar]
  81. Liphardt J, Onoa B, Smith SB, Tinoco I Jr, Bustamante C. 81.  2001. Reversible unfolding of single RNA molecules by mechanical force. Science 292:733–37 [Google Scholar]
  82. Manosas M, Collin D, Ritort F. 82.  2006. Force-dependent fragility in RNA hairpins. Phys. Rev. Lett. 96:218301 [Google Scholar]
  83. Marshall BT, Long M, Piper JW, Yago T, McEver RP, Zhu C. 83.  2003. Direct observation of catch bonds involving cell-adhesion molecules. Nature 423:190–93 [Google Scholar]
  84. Morrison G, Hyeon C, Hinczewski M, Thirumalai D. 84.  2011. Compaction and tensile forces determine the accuracy of folding landscape parameters from single molecule pulling experiments. Phys. Rev. Lett. 106:138102 [Google Scholar]
  85. Nettels D, Gopich IV, Hoffmann A, Schuler B. 85.  2007. Ultrafast dynamics of protein collapse from single-molecule photon statistics. Proc. Natl. Acad. Sci. USA 104:2655–60 [Google Scholar]
  86. Neuman KC, Nagy A. 86.  2008. Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy. Nat. Methods 5:491–505 [Google Scholar]
  87. Neupane K, Ritchie DB, Yu H, Foster DAN, Wang F, Woodside MT. 87.  2012. Transition path times for nucleic acid folding determined from energy-landscape analysis of single-molecule trajectories. Phys. Rev. Lett. 109:068102 [Google Scholar]
  88. Neupane K, Yu H, Foster DAN, Wang F, Woodside MT. 88.  2011. Single-molecule force spectroscopy of the add adenine riboswitch relates folding to regulatory mechanism. Nucleic Acids Res. 39:7677–87 [Google Scholar]
  89. Nevo R, Brumfeld V, Kapon R, Hinterdorfer P, Reich Z. 89.  2005. Direct measurement of protein energy landscape roughness. EMBO Rep. 6:482–86 [Google Scholar]
  90. Ng SP, Rounsevell RWS, Steward A, Geierhaas CD, Williams PM. 90.  et al. 2005. Mechanical unfolding of TNfn3: the unfolding pathway of a fnIII domain probed by protein engineering, AFM and MD simulation. J. Mol. Biol. 350:776–89 [Google Scholar]
  91. Oberhauser AF, Hansma PK, Carrion-Vazquez M, Fernández JM. 91.  2001. Stepwise unfolding of titin under force-clamp atomic force microscopy. Proc. Natl. Acad. Sci. USA 98:468–72 [Google Scholar]
  92. Oliveberg M, Wolynes PG. 92.  2005. The experimental survey of protein-folding energy landscapes. Q. Rev. Biophys. 38:245–88 [Google Scholar]
  93. Onoa B, Dumont S, Liphardt J, Smith SB, Tinoco I Jr, Bustamante C. 93.  2003. Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme. Science 299:1892–95 [Google Scholar]
  94. Onuchic JN, Wolynes PG. 94.  2004. Theory of protein folding. Curr. Opin. Struct. Biol. 14:70–75 [Google Scholar]
  95. Pereverzev YV, Prezhdo OV, Forero M, Sokurenko EV, Thomas WE. 95.  2005. The two-pathway model for the catch-slip transition in biological adhesion. Biophys. J. 89:1446–54 [Google Scholar]
  96. Pfitzner E, Wachauf C, Kilchherr F, Pelz B, Shih WM. 96.  et al. 2013. Rigid DNA beams for high-resolution single-molecule mechanics. Angew. Chem. Int. Ed. 52:7766–71 [Google Scholar]
  97. Rief M, Gautel M, Oesterhelt F, Fernández JM, Gaub HE. 97.  1997. Reversible unfolding of individual titin immunoglobulin domains by AFM. Science 276:1109–12 [Google Scholar]
  98. Ritchie DB, Foster DAN, Woodside MT. 98.  2012. Programmed −1 frameshifting efficiency correlates with RNA pseudoknot conformational plasticity, not resistance to mechanical unfolding. Proc. Natl. Acad. Sci. USA 109:16167–72 [Google Scholar]
  99. Schlierf M, Li H, Fernández JM. 99.  2004. The unfolding kinetics of ubiquitin captured with single-molecule force-clamp techniques. Proc. Natl. Acad. Sci. USA 101:7299–304 [Google Scholar]
  100. Shaw DE, Maragakis P, Lindorff-Larsen K, Piana S, Dror RO. 100.  et al. 2010. Atomic-level characterization of the structural dynamics of proteins. Science 330:341–46 [Google Scholar]
  101. Stigler J, Ziegler F, Gieseke A, Gebhardt JCM, Rief M. 101.  2011. The complex folding network of single calmodulin molecules. Science 334:512–16 [Google Scholar]
  102. Suzuki Y, Dudko OK. 102.  2010. Single-molecule rupture dynamics on multidimensional landscapes. Phys. Rev. Lett. 104:048101 [Google Scholar]
  103. Taniguchi Y, Brockwell DJ, Kawakami M. 103.  2008. The effect of temperature on mechanical resistance of the native and intermediate states of I27. Biophys. J. 95:5296–305 [Google Scholar]
  104. Thirumalai D, Hyeon C. 104.  2005. RNA and protein folding: common themes and variations. Biochemistry 44:4957–70 [Google Scholar]
  105. Torrie GM, Valleau JP. 105.  1977. Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J. Comput. Phys. 23:187–199 [Google Scholar]
  106. Watkins LP, Yang H. 106.  2005. Detection of intensity change points in time-resolved single-molecule measurements. J. Phys. Chem. B 109:617–28 [Google Scholar]
  107. Wen J-D, Manosas M, Li PTX, Smith SB, Bustamante C. 107.  et al. 2007. Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results. Biophys. J. 92:2996–3009 [Google Scholar]
  108. Williams PM, Fowler SB, Best RB, Toca-Herrera JL, Scott KA. 108.  et al. 2003. Hidden complexity in the mechanical properties of titin. Nature 422:446–49 [Google Scholar]
  109. Woodside MT, Anthony PC, Behnke-Parks WM, Larizadeh K, Herschlag D, Block SM. 109.  2006. Direct measurement of the full, sequence-dependent folding landscape of a nucleic acid. Science 314:1001–1004 [Google Scholar]
  110. Woodside MT, Behnke-Parks WM, Larizadeh K, Travers K, Herschlag D, Block SM. 110.  2006. Nanomechanical measurements of the sequence-dependent folding landscapes of single nucleic acid hairpins. Proc. Natl. Acad. Sci. USA 103:6190–95 [Google Scholar]
  111. Woodside MT, Garcia-Garcia C, Block SM. 111.  2008. Folding and unfolding single RNA molecules under tension. Curr. Opin. Chem. Biol. 12:640–46 [Google Scholar]
  112. Yu H, Gupta AN, Liu X, Neupane K, Brigley AM. 112.  et al. 2012. Energy landscape analysis of native folding of the prion protein yields the diffusion constant, transition path time, and rates. Proc. Natl. Acad. Sci. USA 109:14452–57 [Google Scholar]
  113. Yu H, Liu X, Neupane K, Gupta AN, Brigley AM. 113.  et al. 2012. Direct observation of multiple misfolding pathways in a single prion protein molecule. Proc. Natl. Acad. Sci. USA 109:5283–88 [Google Scholar]
  114. Yu Z, Koirala D, Cui Y, Easterling LF, Zhao Y, Mao H. 114.  2012. Click chemistry assisted single-molecule fingerprinting reveals a 3D biomolecular folding funnel. J. Am. Chem. Soc. 134:12338–41 [Google Scholar]
  115. Yuan H, Orrit M. 115.  2012. Reaction pathways from single-molecule trajectories. ChemPhysChem 13:681–83 [Google Scholar]
  116. Zhang Q, Brujić J, Vanden-Eijnden E. 116.  2011. Reconstructing free energy profiles from nonequilibrium relaxation trajectories. J. Stat. Phys. 144:344–66 [Google Scholar]
  117. Zhang Y, Dudko OK. 117.  2013. A transformation for the mechanical fingerprints of complex biomolecular interactions. Proc. Natl. Acad. Sci. USA 110:16432–37 [ Erratum] [Google Scholar]
  118. Zhurkov SN. 118.  1965. Kinetic concept of the strength of solids. Int. J. Fract. Mech. 1:311–22 [Google Scholar]
  119. Žoldak G, Rief M. 119.  2013. Force as a single molecule probe of multidimensional protein energy landscapes. Curr. Opin. Struct. Biol. 23:48–57 [Google Scholar]
  120. Zwanzig R. 120.  1988. Diffusion in a rough potential. Proc. Natl. Acad. Sci. USA 85:2029–30 [Google Scholar]

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error