1932

Abstract

Molecular recognition by proteins is fundamental to the molecular basis of biology. Dissection of the thermodynamic landscape governing protein–ligand interactions has proven difficult because determination of various entropic contributions is quite challenging. Nuclear magnetic resonance relaxation measurements, theory, and simulations suggest that conformational entropy can be accessed through a dynamical proxy. Here, we review the relationship between measures of fast side-chain motion and the underlying conformational entropy. The dynamical proxy reveals that the contribution of conformational entropy can range from highly favorable to highly unfavorable and demonstrates the potential of this key thermodynamic variable to modulate protein–ligand interactions. The dynamical so-called entropy meter also refines the role of solvent entropy and directly determines the loss in rotational–translational entropy that occurs upon formation of high-affinity complexes. The ability to quantify the roles of entropy through an entropy meter based on measurable dynamical properties promises to highlight its role in protein function.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-biophys-060414-034042
2018-05-20
2024-05-18
Loading full text...

Full text loading...

/deliver/fulltext/biophys/47/1/annurev-biophys-060414-034042.html?itemId=/content/journals/10.1146/annurev-biophys-060414-034042&mimeType=html&fmt=ahah

Literature Cited

  1. 1.  Abragam A 1961. Principles of Nuclear Magnetism. Oxford, UK: Clarendon Press
    [Google Scholar]
  2. 2.  Akke M, Brüschweiler R, Palmer AG 1993. NMR order parameters and free energy: an analytical approach and its application to cooperative Ca2+ binding by calbindin-D9k. J. Am. Chem. Soc. 1159832–33Used specific potential energy functions to relate motion measurable by NMR relaxation and thermodynamic quantities.
  3. 3.  Baldwin RL 1986. Temperature dependence of the hydrophobic interaction in protein folding. PNAS 838069–72
  4. 4.  Ben-Naim A, Marcus Y 1984. Solvation thermodynamics of nonionic solutes. J. Chem. Phys. 812016–27
  5. 5.  Bowman GR 2015. Accurately modeling nanosecond protein dynamics requires at least microseconds of simulation. J. Comp. Chem. 37558–66
  6. 6.  Carlsson J, Aqvist J 2005. Absolute and relative entropies from computer simulation with applications to ligand binding. J. Phys. Chem. B 1096448–56
  7. 7.  Caro JA, Kasinath V, Harpole KW, Lim J, Granja J et al. 2017. Entropy in molecular recognition by proteins. PNAS 1146563–68Showed the general applicability of the entropy meter to protein–ligand associations.
  8. 8.  Cavanagh J, Fairbrother WJ, Palmer AGI, Rance M, Skelton NJ 2006. Protein NMR Spectroscopy: Principles and Practice Burlington, MA: Elsevier
  9. 9.  Chandler D 2005. Interfaces and the driving force of hydrophobic assembly. Nature 437640–47
  10. 10.  Clore GM, Szabo A, Bax A, Kay LE, Driscoll PC, Gronenborn AM 1990. Deviations from the simple two-parameter model-free approach to the interpretation of nitrogen-15 nuclear magnetic relaxation of proteins. J. Am. Chem. Soc. 1124989–91
  11. 11.  Cooper A, Dryden DTF 1984. Allostery without conformational change: a plausible model. Eur. Biophys. J. 11103–9
  12. 12.  Dellwo MJ, Wand AJ 1989. Model-independent and model-dependent analysis of the global and internal dynamics of cyclosporine A. J. Am. Chem. Soc. 1114571–78
  13. 13.  DeLorbe JE, Clements JH, Teresk MG, Benfield AP, Plake HR et al. 2009. Thermodynamic and structural effects of conformational constraints in protein–ligand interactions. Entropic paradoxy associated with ligand preorganization. J. Am. Chem. Soc. 13116758–70
  14. 14.  Dill KA 1990. Dominant forces in protein folding. Biochemistry 297133–55
  15. 15.  DuBay KH, Bowman GR, Geissler PL 2015. Fluctuations within folded proteins: implications for thermodynamic and allosteric regulation. Acc. Chem. Res. 481098–105
  16. 16.  Farrow NA, Muhandiram R, Singer AU, Pascal SM, Kay CM et al. 1994. Backbone dynamics of a free and a phosphopeptide-complexed Src homology 2 domain studied by 15N NMR relaxation. Biochemistry 335984–6003
  17. 17.  Ferrage F, Pelupessy P, Cowburn D, Bodenhausen G 2006. Protein backbone dynamics through 13C′–13Cα cross-relaxation in NMR spectroscopy. J. Am. Chem. Soc. 12811072–78
  18. 18.  Finkelstein AV, Janin J 1989. The price of lost freedom: entropy of bimolecular complex formation. Protein Eng. 31–3
    [Google Scholar]
  19. 19.  Frederick KK, Marlow MS, Valentine KG, Wand AJ 2007. Conformational entropy in molecular recognition by proteins. Nature 448325–29The first clear indication that conformational entropy could contribute significantly to protein–ligand associations.
  20. 20.  Frederick KK, Sharp KA, Warischalk N, Wand AJ 2008. Re-evaluation of the model-free analysis of fast internal motion in proteins using NMR relaxation. J. Phys. Chem. B 1122095–103
  21. 21.  Gans P, Hamelin O, Sounier R, Ayala I, Durá MA et al. 2010. Stereospecific isotopic labeling of methyl groups for NMR spectroscopic studies of high-molecular-weight proteins. Angew. Chem. Int. Ed. 491958–62
  22. 22.  Gardner KH, Kay LE 1998. The use of 2H, 13C, 15N multidimensional NMR to study the structure and dynamics of proteins. Annu. Rev. Biophys. Biomol. Struct. 27357–406
  23. 23.  Gilson MK, Given JA, Bush BL, McCammon JA 1997. The statistical-thermodynamic basis for computation of binding affinities: a critical review. Biophys. J. 721047–69
  24. 24.  Gilson MK, Zhou H-X 2007. Calculation of protein-ligand binding affinities. Annu. Rev. Biophys. Biomol. Struct. 3621–42
  25. 25.  Glass DC, Krishnan M, Smith JC, Baudry J 2013. Three entropic classes of side chain in a globular protein. J. Phys. Chem. B 1173127–34
  26. 26.  Gomez J, Hilser VJ, Xie D, Freire E 1995. The heat capacity of proteins. Proteins 22404–12
  27. 27.  Goto NK, Gardner KH, Mueller GA, Willis RC, Kay LE 1999. A robust and cost-effective method for the production of Val, Leu, Ile (δ1) methyl-protonated 15N-, 13C-, 2H-labeled proteins. J. Biomol. NMR 13369–74
  28. 28.  Guo J, Zhou H-X 2015. Dynamically driven protein allostery exhibits disparate responses for fast and slow motions. Biophys. J. 1082771–74
  29. 29.  Harpole KW, Sharp KA 2011. Calculation of configurational entropy with a Boltzmann–quasiharmonic model: the origin of high-affinity protein–ligand binding. J. Phys. Chem. B 1159461–72
  30. 30.  Henry ER, Szabo A 1985. Influence of vibrational motion on solid-state line-shapes and NMR relaxation. J. Chem. Phys. 824753–61
  31. 31.  Hermans J, Wang L 1997. Inclusion of loss of translational and rotational freedom in theoretical estimates of free energies of binding. Application to a complex of benzene and mutant T4 lysozyme. J. Am. Chem. Soc. 1192707–14
  32. 32.  Hilser VJ, Garcia-Moreno EB, Oas TG, Kapp G, Whitten ST 2006. A statistical thermodynamic model of the protein ensemble. Chem. Rev. 1061545–58
  33. 33.  Hoffman RA 1970. Line shapes in high-resolution NMR. Adv. Magn. Reson. 488–198
  34. 34.  Igumenova TI, Frederick KK, Wand AJ 2006. Characterization of the fast dynamics of protein amino acid side chains using NMR relaxation in solution. Chem. Rev. 1061672–99
  35. 35.  Ishima R, Louis JM, Torchia DA 2001. Optimized labeling of 13CHD2 methyl isotopomers in perdeuterated proteins: potential advantages for 13C relaxation studies of methyl dynamics of larger proteins. J. Biomol. NMR 21167–71
  36. 36.  Ishima R, Petkova AP, Louis JM, Torchia DA 2001. Comparison of methyl rotation axis order parameters derived from model-free analyses of 2H and 13C longitudinal and transverse relaxation rates measured in the same protein sample. J. Am. Chem. Soc. 1236164–71
  37. 37.  Jacobsen JP, Bildsøe HK, Schaumburg K 1976. Application of density matrix formalism in NMR spectroscopy. II. One-spin-1 case in anisotropic phase. J. Magn. Reson. 23153–64
  38. 38.  Jarymowycz VA, Stone MJ 2006. Fast time scale dynamics of protein backbones: NMR relaxation methods, applications, and functional consequences. Chem. Rev. 1061624–71
  39. 39.  Kahl CR, Means AR 2003. Regulation of cell cycle progression by calcium/calmodulin-dependent pathways. Endocr. Rev. 24719–36
  40. 40.  Kainosho M, Torizawa T, Iwashita Y, Terauchi T, Mei Ono A, Guntert P 2006. Optimal isotope labelling for NMR protein structure determinations. Nature 44052–57
  41. 41.  Karplus M, Ichiye T, Pettitt BM 1987. Configurational entropy of native proteins. Biophys. J. 521083–85
  42. 42.  Kasinath V, Sharp KA, Wand AJ 2013. Microscopic insights into the NMR relaxation-based protein conformational entropy meter. J. Am. Chem. Soc. 13515092–100Simulation and theory was used to refine the original construction of the entropy meter.
  43. 43.  Kasinath V, Valentine KG, Wand AJ 2013. A 13C labeling strategy reveals a range of aromatic side chain motion in calmodulin. J. Am. Chem. Soc. 1359560–63
  44. 44.  Kay LE, Torchia DA, Bax A 1989. Backbone dynamics of proteins as studied by 15N inverse detected heteronuclear NMR spectroscopy: application to staphylococcal nuclease. Biochemistry 288972–79
  45. 45.  Kerfah R, Plevin MJ, Sounier R, Gans P, Boisbouvier J 2015. Methyl-specific isotopic labeling: a molecular tool box for solution NMR studies of large proteins. Curr. Opin. Struct. Biol. 32113–22Summary of the isotopic labeling important for the NMR-based studies described here.
  46. 46.  Kneller JM, Lu M, Bracken C 2002. An effective method for the discrimination of motional anisotropy and chemical exchange. J. Am. Chem. Soc. 1241852–53
  47. 47.  Kranz JK, Lee EK, Nairn AC, Wand AJ 2002. A direct test of the reductionist approach to structural studies of calmodulin activity: relevance of peptide models of target proteins. J. Biol. Chem. 27716351–54
  48. 48.  Krishnan M, Kurkal-Siebert V, Smith JC 2008. Methyl group dynamics and the onset of anharmonicity in myoglobin. J. Phys. Chem. B 1125522–33
  49. 49.  Krishnan M, Smith JC 2012. Reconstruction of protein side-chain conformational free energy surfaces from NMR-derived methyl axis order parameters. J. Phys. Chem. B 1164124–33
  50. 50.  Leavitt S, Freire E 2001. Direct measurement of protein binding energetics by isothermal titration calorimetry. Curr. Opin. Struct. Biol. 11560–66
  51. 51.  Lee AL, Kinnear SA, Wand AJ 2000. Redistribution and loss of side chain entropy upon formation of a calmodulin–peptide complex. Nat. Struct. Biol. 772–77
  52. 52.  Lee AL, Sharp KA, Kranz JK, Song X-J, Wand AJ 2002. Temperature dependence of the internal dynamics of a calmodulin–peptide complex. Biochemistry 4113814–25
  53. 53.  Lee AL, Urbauer JL, Wand AJ 1997. Improved labeling strategy for 13C relaxation measurements of methyl groups in proteins. J. Biomol. NMR 9437–40
  54. 54.  Lee AL, Wand AJ 2001. Microscopic origins of entropy, heat capacity and the glass transition in proteins. Nature 411501–4
  55. 55.  Lee LK, Rance M, Chazin WJ, Palmer AG 1997. Rotational diffusion anisotropy of proteins from simultaneous analysis of 15N and 13Cα nuclear spin relaxation. J. Biomol. NMR 9287–98
  56. 56.  LeMaster DM, Kushlan DM 1996. Dynamical mapping of E. coli thioredoxin via 13C NMR relaxation analysis. J. Am. Chem. Soc. 1189255–64
  57. 57.  Li DW, Brüschweiler R 2009. A dictionary for protein side-chain entropies from NMR order parameters. J. Am. Chem. Soc. 1317226–27
  58. 58.  Li DW, Brüschweiler R 2009. In silico relationship between configurational entropy and soft degrees of freedom in proteins and peptides. Phys. Rev. Lett. 102118108
  59. 59.  Li DW, Showalter SA, Brüschweiler R 2010. Entropy localization in proteins. J. Phys. Chem. B 11416036–44
  60. 60.  Li Z, Raychaudhuri S, Wand AJ 1996. Insights into the local residual entropy of proteins provided by NMR relaxation. Protein Sci. 52647–50
    [Google Scholar]
  61. 61.  Liao X, Long D, Li D-W, Brüschweiler R, Tugarinov V 2012. Probing side-chain dynamics in proteins by the measurement of nine deuterium relaxation rates per methyl group. J. Phys. Chem. B 116606–20
  62. 62.  Lichtenecker RJ 2014. Synthesis of aromatic 13C/2H-α-ketoacid precursors to be used in selective phenylalanine and tyrosine protein labelling. Organ. Biomol. Chem. 127551–60
  63. 63.  Lichtenecker RJ, Coudevylle N, Konrat R, Schmid W 2013. Selective isotope labelling of leucine residues by using α-ketoacid precursor compounds. ChemBioChem 14818–21
  64. 64.  Lichtenecker RJ, Weinhaupl K, Reuther L, Schorghuber J, Schmid W, Konrat R 2013. Independent valine and leucine isotope labeling in Escherichia coli protein overexpression systems. J. Biomol. NMR 57205–9
  65. 65.  Lichtenecker RJ, Weinhaupl K, Schmid W, Konrat R 2013. α-Ketoacids as precursors for phenylalanine and tyrosine labelling in cell-based protein overexpression. J. Biomol. NMR 57327–31
  66. 66.  Lipari G, Szabo A 1982. Model-free approach to the interpretation of nuclear magnetic-resonance relaxation in macromolecules. 1. Theory and range of validity. J. Am. Chem. Soc. 1044546–59The model-free formalism provides the fundamental basis for interpretation of NMR relaxation phenomena in terms of molecular motion.
  67. 67.  Lipari G, Szabo A 1982. Model-free approach to the interpretation of nuclear magnetic-resonance relaxation in macromolecules. 2. Analysis of experimental results. J. Am. Chem. Soc. 1044559–70
  68. 68.  Liu W, Zheng Y, Cistola DP, Yang DW 2003. Measurement of methyl 13C-1H cross-correlation in uniformly 13C-, 15N-, labeled proteins. J. Biomol. NMR 27351–64
  69. 69.  Luo H, Sharp K 2002. On the calculation of absolute macromolecular binding free energies. PNAS 9910399–404
  70. 70.  Macura S, Ernst RR 1980. Elucidation of cross relaxation in liquids by two-dimensional NMR spectroscopy. Mol. Phys. 4195–117
  71. 71.  Makhatadze GI, Privalov PL 1993. Contributions of hydration to protein-folding thermodynamics. 1. The enthalpy of hydration. J. Mol. Biol. 232639–59
  72. 72.  Mandel AM, Akke M, Palmer AG 1995. Backbone dynamics of Escherichia coli ribonuclease H1: correlations with structure and function in an active enzyme. J. Mol. Biol. 246144–63
  73. 73.  Marcus Y 1994. A simple empirical model describing the thermodynamics of hydration of ions of widely varying charges, sizes, and shapes. Biophys. Chem. 51111–27
  74. 74.  Marlow MS, Dogan J, Frederick KK, Valentine KG, Wand AJ 2010. The role of conformational entropy in molecular recognition by calmodulin. Nat. Chem. Biol. 6352–58
  75. 75.  Mas G, Crublet E, Hamelin O, Gans P, Boisbouvier J 2013. Specific labeling and assignment strategies of valine methyl groups for NMR studies of high molecular weight proteins. J. Biomol. NMR 57251–62
  76. 76.  McIntosh LP, Dahlquist FW 1990. Biosynthetic incorporation of 15N and 13C for assignment and interpretation of nuclear magnetic resonance spectra of proteins. Q. Rev. Biophys. 231–38
  77. 77.  Millet O, Muhandiram DR, Skrynnikov NR, Kay LE 2002. Deuterium spin probes of side-chain dynamics in proteins. 1. Measurement of five relaxation rates per deuteron in 13C-labeled and fractionally 2H-enriched proteins in solution. J. Am. Chem. Soc. 1246439–48
  78. 78.  Monneau YR, Ishida Y, Rossi P, Saio T, Tzeng S-R et al. 2016. Exploiting E. coli auxotrophs for leucine, valine, and threonine specific methyl labeling of large proteins for NMR applications. J. Biomol. NMR 6599–108
  79. 79.  Motlagh HN, Wrabl JO, Li J, Hilser VJ 2014. The ensemble nature of allostery. Nature 508331–39
  80. 80.  Muhandiram DR, Yamazaki T, Sykes BD, Kay LE 1995. Measurement of 2H T1 and T relaxation-times in uniformly 13C-labeled and fractionally 2H-labeled proteins in solution. J. Am. Chem. Soc. 11711536–44Pioneering development of methods for deuterium relaxation in proteins.
  81. 81.  Ollerenshaw JE, Tugarinov V, Skrynnikov NR, Kay LE 2005. Comparison of 13CH3, 13CH2D, and 13CHD2 methyl labeling strategies in proteins. J. Biomol. NMR 3325–41
  82. 82.  Ottiger M, Bax A 1998. Determination of relative N−HN, N−C′, Cα−C′, and Cα−Hα effective bond lengths in a protein by NMR in a dilute liquid crystalline phase. J. Am. Chem. Soc. 12012334–41
  83. 83.  Pawley NH, Wang C, Koide S, Nicholson LK 2001. An improved method for distinguishing between anisotropic tumbling and chemical exchange in analysis of 15N relaxation parameters. J. Biomol. NMR 20149–65
  84. 84.  Pelupessy P, Ravindranathan S, Bodenhausen G 2003. Correlated motions of successive amide N-H bonds in proteins. J. Biomol. NMR 25265–80
  85. 85.  Privalov PL, Makhatadze GI 1992. Contribution of hydration and noncovalent interactions to the heat-capacity effect on protein unfolding. J. Mol. Biol. 224715–23
  86. 86.  Privalov PL, Makhatadze GI 1993. Contribution of hydration to protein folding thermodynamics. II. The entropy and Gibbs energy of hydration. J. Mol. Biol. 232660–79
  87. 87.  Rajeshwar R, Smith JC, Krishnan M 2014. Hidden regularity and universal classification of fast side chain motions in proteins. J. Am. Chem. Soc. 1368590–605
  88. 88.  Rosenzweig R, Kay LE 2014. Bringing dynamic molecular machines into focus by methyl-TROSY NMR. Annu. Rev. Biochem. 83291–315
  89. 89.  Ross PD, Subramanian S 1981. Thermodynamics of protein association reactions: forces contributing to stability. Biochemistry 203096–102
  90. 90.  Rule GS, Hitchens TK 2006. Fundamentals of Protein NMR Spectrosopy Dordrecht, Neth: Springer
  91. 91.  Saito H, Ando I, Ramamoorthy A 2010. Chemical shift tensor—the heart of NMR: insights into biological aspects of proteins. Prog. NMR Spectrosc. 57181–228
  92. 92.  Schroghuber J, Sara T, Bisaccia M, Schmid W, Konrat R, Lichtenecker RJ 2015. Novel approaches in selective tryptophan isotope labeling by using Escherichia coli overexpression media. ChemBioChem 16746–51
  93. 93.  Sharp KA, Kasinath V, Wand AJ 2014. Banding of NMR-derived methyl order parameters: implications for protein dynamics. Proteins 822106–17
  94. 94.  Sharp KA, Nicholls A, Fine RF, Honig B 1991. Reconciling the magnitude of the microscopic and macroscopic hydrophobic effects. Science 252106–9
  95. 95.  Sharp KA, O'Brien E, Kasinath V, Wand AJ 2015. On the relationship between NMR-derived amide order parameters and protein backbone entropy changes. Proteins 83922–30
  96. 96.  Spolar RS, Livingstone JR, Record MT Jr. 1992. Use of liquid hydrocarbon and amide transfer data to estimate contributions to thermodynamic functions of protein folding from the removal of nonpolar and polar surface from water. Biochemistry 313947–55
  97. 97.  Steinberg IZ, Scheraga HA 1963. Entropy changes accompanying association reactions of proteins. J. Biol. Chem. 238172–81
  98. 98.  Sturtevant JM 1977. Heat-capacity and entropy changes in processes involving proteins. PNAS 742236–40
  99. 99.  Sun H, Godoy-Ruiz R, Tugarinov V 2012. Estimating side-chain order in methyl-protonated, perdeuterated proteins via multiple-quantum relaxation violated coherence transfer NMR spectroscopy. J. Biomol. NMR 52233–43
  100. 100.  Sun H, Kay LE, Tugarinov V 2011. An optimized relaxation-based coherence transfer NMR experiment for the measurement of side-chain order in methyl-protonated, highly deuterated proteins. J. Phys. Chem. B 11514878–84
  101. 101.  Tamura A, Privalov PL 1997. The entropy cost of protein association. J. Mol. Biol. 2731048–60
  102. 102.  Teilum K, Brath U, Lundstrom P, Akke M 2006. Biosynthetic 13C labeling of aromatic side chains in proteins for NMR relaxation measurements. J. Am. Chem. Soc. 1282506–7
  103. 103.  Tjandra N, Feller SE, Pastor RW, Bax A 1995. Rotational diffusion anisotropy of human ubiquitin from 15N NMR relaxation. J. Am. Chem. Soc. 11712562–66
  104. 104.  Tugarinov V, Kay LE 2005. Quantitative 13C and 2H NMR relaxation studies of the 723-residue enzyme malate synthase G reveal a dynamic binding interface. Biochemistry 4415970–77
  105. 105.  Tugarinov V, Sprangers R, Kay LE 2007. Probing side-chain dynamics in the proteasome by relaxation violated coherence transfer NMR spectroscopy. J. Am. Chem. Soc. 1291743–50
  106. 106.  Tzeng S-R, Kalodimos CG 2012. Protein activity regulation by conformational entropy. Nature 488236–40
  107. 107.  Vugmeyster L, Pelupessy P, Vugmeister BE, Abergel D, Bodenhausen G 2004. Cross-correlated relaxation in NMR of macromolecules in the presence of fast and slow internal dynamics. C. R. Phys. 5377–86
  108. 108.  Wand AJ 2013. The dark energy of proteins comes to light: conformational entropy and its role in protein function revealed by NMR relaxation. Curr. Opin. Struct. Biol. 2375–81
  109. 109.  Wand AJ, Bieber RJ, Urbauer JL, McEvoy RP, Gan ZH 1995. Carbon relaxation in randomly fractionally 13C-enriched proteins. J. Magn. Reson. Ser. B 108173–75
  110. 110.  Wang L, Berne BJ, Friesner RA 2011. Ligand binding to protein-binding pockets with wet and dry regions. PNAS 1081326–30
  111. 111.  Wang T, Frederick KK, Igumenova TI, Wand AJ, Zuiderweg ERP 2005. Changes in calmodulin main-chain dynamics upon ligand binding revealed by cross-correlated NMR relaxation measurements. J. Am. Chem. Soc. 127828–29
  112. 112.  Welch GR, Somogyi B, Damjanovich S 1982. The role of protein fluctuations in enzyme action: a review. Prog. Biophys. Mol. Biol. 39109–46Discussion of the potential role of entropy in protein function, which is only now directly testable by experiment.
  113. 113.  Wittebort RJ, Szabo A 1978. Theory of NMR relaxation in macromolecules: restricted diffusion and jump models for multiple internal rotations in amino acid side chains. J. Chem. Phys. 691722–36
  114. 114.  Wüthrich K, Wider G, Wagner G, Braun W 1982. Sequential resonance assignments as a basis for determination of spatial protein structures by high-resolution proton nuclear magnetic resonance. J. Mol. Biol. 155311–19
  115. 115.  Yang D, Kay LE 1996. Contributions to conformational entropy arising from bond vector fluctuations measured from NMR-derived order parameters: application to protein folding. J. Mol. Biol. 263369–82
  116. 116.  Zhang X, Sui X, Yang D 2006. Probing methyl dynamics from 13C autocorrelated and cross-correlated relaxation. J. Am. Chem. Soc. 1285073–81
  117. 117.  Zhou H-X, Gilson MK 2009. Theory of free energy and entropy in noncovalent binding. Chem. Rev. 1094092–107Superb review of the theoretical issues of protein–ligand associations.
/content/journals/10.1146/annurev-biophys-060414-034042
Loading
/content/journals/10.1146/annurev-biophys-060414-034042
Loading

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