Recent theoretical and computational advances for modeling protein-ligand binding affinities

Advances in Protein Chemistry and Structural Biology

Volumn 85, Issue , 2011, Pages 27-80

  Gallicchio, Emilio ^a   Levy, Ronald M ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80052805301     PISSN: 18761623     EISSN: None     Source Type: Book Series    
DOI: 10.1016/B978-0-12-386485-7.00002-8     Document Type: Article

References (121)

1. N.A. Baker Improving implicit solvent simulations: a poisson-centric view Curr. Opin. Struct. Biol. 15 2005 137 143
2. C.M. Barbieri, M. Kaul, and D.S. Pilch Use of 2-aminopurine as a fluorescent tool for characterizing antibiotic recognition of the bacterial rRNA A-site Tetrahedron 63 17 2007 3567 3574 (Pubitemid 46428352)
3. D. Bashford, and D.A. Case Generalized born models of macromolecular solvation effects Annu. Rev. Phys. Chem. 51 2000 129 152
4. T.L. Beck, M.E. Paulaitis, and L.R. Pratt The Potential Distribution Theorem and Models of Molecular Solutions 2006 Cambridge University Press New York
5. C.H. Bennett Efficient estimation of free energy differences from Monte Carlo data J. Comput. Phys. 22 2 1976 245 268
6. S. Boresch, F. Tettinger, M. Leitgeb, and M. Karplus Absolute binding free energies: a quantitative approach for their calculation J. Phys. Chem. B 107 35 2003 9535 9551
7. S.E. Boyce, D.L. Mobley, G.J. Rocklin, A.P. Graves, K.A. Dill, and B.K. Shoichet Predicting ligand binding affinity with alchemical free energy methods in a polar model binding site J. Mol. Biol. 394 4 2009 747 763
8. N. Brooijmans, and I.D. Kuntz Molecular recognition and docking algorithm Annu. Rev. Biophys. Biomol. Struct. 32 2003 335 373
9. S.P. Brown, and S.W. Muchmore High-throughput calculation of protein-ligand binding affinities: modification and adaptation of the MM-PBSA protocol to enterprise grid computing J. Chem. Inf. Model. 46 3 2006 999 1005 (Pubitemid 43999143)
10. S.P. Brown, and S.W. Muchmore Rapid estimation of relative protein-ligand binding affinities using a high-throughput version of MM-PBSA J. Chem. Inf. Model. 47 4 2007 1493 1503 (Pubitemid 47210052)
11. G. Bussi, F.L. Gervasio, A. Laio, and M. Parrinello Free-energy landscape for β hairpin folding from combined parallel tempering and metadynamics J. Am. Chem. Soc. 128 41 2006 13435 13441 (Pubitemid 44583028)
12. C.-E. Chang, and M.K. Gilson Tork: conformational analysis method for molecules and complexes J. Comput. Chem. 24 16 2003 1987 1998
13. C.-E. Chang, and M.K. Gilson Free energy, entropy, and induced fit in host-guest recognition: calculations with the second-generation mining minima algorithm J. Am. Chem. Soc. 126 40 2004 13156 13164 (Pubitemid 39372346)
14. C.-E. Chang, M.J. Potter, and M.K. Gilson Calculation of molecular configuration integrals J. Phys. Chem. B 107 4 2003 1048 1055
15. C.-E. Chang, W. Chen, and M.K. Gilson Evaluating the accuracy of the quasiharmonic approximation J. Chem. Theory Comput. 1 5 2005 1017 1028
16. C.-e.A. Chang, W. Chen, and M.K. Gilson Ligand configurational entropy and protein binding Proc. Natl. Acad. Sci. USA 104 5 2007 1534 1539 (Pubitemid 46214625)
17. I.-J. Chen, and N. Foloppe Drug-like bioactive structures and conformational coverage with the LigPrep/ConfGen suite: comparison to programs MOE and catalyst J. Chem. Inf. Model. 50 5 2010 822 839
18. J. Chen, C.L. Brooks III, and J. Khandogin Recent advances in implicit solvent based methods for biomolecular simulations Curr. Opin. Struct. Biol. 18 2008 140 148
19. C. Chipot, and A. Pohorille Free Energy Calculations. Theory and Applications in Chemistry and Biology Springer Series in Chemical Physics 2007 Springer Berlin, Heidelberg
20. J.D. Chodera, D.L. Mobley, M.R. Shirts, R.W. Dixon, K. Branson, and V.S. Pande Alchemical free energy methods for drug discovery: progress and challenges Curr. Opin. Struct. Biol. 21 2 2011 150 160
21. L.T. Chong, J.W. Pitera, W.C. Swope, and V.S. Pande Comparison of computational approaches for predicting the effects of missense mutations on p53 function J. Mol. Graph. Model. 27 8 2009 978 982
22. W.D. Cornell, P. Cieplak, C.I. Bayly, I.R. Gould, K.M. Merz, and D.M. Ferguson A second generation force field for the simulation of proteins, nucleic acids, and organic molecules J. Am. Chem. Soc. 117 19 1995 5179 5197
23. J.E. DeLorbe, J.H. Clements, M.G. Teresk, A.P. Benfield, H.R. Plake, and L.E. Millspaugh Thermodynamic and structural effects of conformational constraints in protein-ligand interactions. Entropic paradoxy associated with ligand preorganization J. Am. Chem. Soc. 131 46 2009 16758 16770
24. Y. Deng, and B. Roux Calculation of standard binding free energies: aromatic molecules in the t4 lysozyme l99a mutant J. Chem. Theory Comput. 2 5 2006 1255 1273
25. Y. Deng, and B. Roux Computations of standard binding free energies with molecular dynamics simulations J. Phys. Chem. B 113 8 2009 2234 2246
26. A.E. Eriksson, W.A. Baase, J.A. Wozniak, and B.W. Matthews A cavity-containing mutant of t4 lysozyme is stabilized by buried benzene Nature 355 6358 1992 371 373
27. A.M. Ferrenberg, and R.H. Swendsen Optimized Monte Carlo data analysis Phys. Rev. Lett. 63 1989 1195 1198
28. N. Foloppe, and R. Hubbard Towards predictive ligand design with free-energy based computational methods? Curr. Med. Chem. 13 29 2006 3583 3608 (Pubitemid 44873749)
29. H. Fujitani, Y. Tanida, M. Ito, G. Jayachandran, C.D. Snow, and M.R. Shirts Direct calculation of the binding free energies of FKBP ligands J. Chem. Phys. 123 8 2005 084108
30. E. Gallicchio, M. Andrec, A.K. Felts, and R.M. Levy Temperature weighted histogram analysis method, replica exchange, and transition paths J. Phys. Chem. B 109 2005 6722 6731 (Pubitemid 40538440)
31. E. Gallicchio, K. Paris, and R.M. Levy The agbnp2 implicit solvation model J. Chem. Theory Comput. 5 9 2009 2544 2564
32. E. Gallicchio, M. Lapelosa, and R.M. Levy Binding energy distribution analysis method (BEDAM) for estimation of protein-ligand binding affinities J. Chem. Theory Comput. 6 9 2010 2961 2977
33. E. Gallicchio, and R.M. Levy Advances in all atom sampling methods for modeling protein-ligand binding affinities Curr. Op. Struct. Biol. 21 2011 161 166
34. C. Gao, M.-S. Park, and H.A. Stern Accounting for ligand conformational restriction in calculations of protein-ligand binding affinities Biophys. J. 98 5 2010 901 910
35. X. Ge, and B. Roux Absolute binding free energy calculations of sparsomycin analogs to the bacterial ribosome J. Phys. Chem. B 114 29 2010 9525 9539
36. M.K. Gilson, and H.-X. Zhou Calculation of protein-ligand binding affinities Annu. Rev. Biophys. Biomol. Struct. 36 2007 21 42 (Pubitemid 46998108)
37. M.K. Gilson, J.A. Given, B.L. Bush, and J.A. McCammon The statistical-thermodynamic basis for computation of binding affinities: a critical review Biophys. J. 72 1997 1047 1069 (Pubitemid 27113632)
38. H. Gouda, I.D. Kuntz, D.A. Case, and P.A. Kollman Free energy calculations for theophylline binding to an RNA aptamer: comparison of MM-PBSA and thermodynamic integration methods Biopolymers 68 1 2003 16 34 (Pubitemid 36098305)
39. A.P. Graves, R. Brenk, and B.K. Shoichet Decoys for docking J. Med. Chem. 48 11 2005 3714 3728 (Pubitemid 40776847)
40. R.D. Groot The association constant of a flexible molecule and a single atom: theory and simulation J. Chem. Phys. 97 5 1992 3537 3549
41. O. Guvench, and A.D. Mackerell Computational evaluation of protein-small molecule binding Curr. Opin. Struct. Biol. 19 1 2009 56 61
42. M.S. Head, J.A. Given, and M.K. Gilson Mining minima: direct computation of conformational free energy J. Phys. Chem. A 101 8 1997 1609 1618 (Pubitemid 127619859)
43. D.A. Holt, J.I. Luengo, D.S. Yamashita, H.J. Oh, A.L. Konialian, and H.K. Yen Design, synthesis, and kinetic evaluation of high-affinity FKBP ligands and the X-ray crystal structures of their complexes with FKBP 12 J. Am. Chem. Soc. 115 22 1993 9925 9938
44. J. Hritz, and C. Oostenbrink Hamiltonian replica exchange molecular dynamics using soft-core interactions J. Chem. Phys. 128 14 2008 144121
45. G. Jayachandran, M.R. Shirts, S. Park, and V.S. Pande Parallelized-over-parts computation of absolute binding free energy with docking and molecular dynamics J. Chem. Phys. 125 8 2006 084901
46. W. Jiang, and B. Roux Free energy perturbation Hamiltonian replica-exchange molecular dynamics (FEP/H-REMD) for absolute ligand binding free energy calculations J. Chem. Theory Comput. 6 2010 2559 2565
47. W. Jiang, M. Hodoscek, and B. Roux Computation of absolute hydration and binding free energy with free energy perturbation distributed replica-exchange molecular dynamics J. Chem. Theory Comput. 5 10 2009 2583 2588
48. D. Jiao, P.A. Golubkov, T.A. Darden, and P. Ren Calculation of protein-ligand binding free energy by using a polarizable potential Proc. Natl. Acad. Sci. USA 105 17 2008 6290 6295 (Pubitemid 351758339)
49. D. Jiao, J. Zhang, R.E. Duke, G. Li, M.J. Schnieders, and P. Ren Trypsin-ligand binding free energies from explicit and implicit solvent simulations with polarizable potential J. Comput. Chem. 30 11 2009 1701 1711
50. W.L. Jorgensen Interactions between amides in solution and the thermodynamics of weak binding J. Am. Chem. Soc. 111 10 1989 3770 3771
51. W.L. Jorgensen The many roles of computation in drug discovery Science 303 5665 2004 1813 1818 (Pubitemid 38374866)
52. W.L. Jorgensen Efficient drug lead discovery and optimization Acc. Chem. Res. 42 6 2009 724 733
53. W.L. Jorgensen, and L.L. Thomas Perspective on free-energy perturbation calculations for chemical equilibria J. Chem. Theory Comput. 4 6 2008 869 876
54. W.L. Jorgensen, J.K. Buckner, S. Boudon, and J. Tirado-Rives Efficient computation of absolute free energies of binding by computer simulations. Application to the methane dimer in water J. Chem. Phys. 6 1988 3742
55. W.L. Jorgensen, D.S. Maxwell, and J. Tirado-Rives Development and testing of the opls all-atom force field on conformational energetics and properties of organic liquids J. Am. Chem. Soc. 118 1996 11225 11236 (Pubitemid 26399746)
56. I.V. Khavrutskii, and A. Wallqvist Computing relative free energies of solvation using single reference thermodynamic integration augmented with Hamiltonian replica exchange J. Chem. Theory Comput. 6 11 2010 3427 3441
57. J.L. Knight, and C.L. Brooks Lambda-dynamics free energy simulation methods J. Comput. Chem. 30 11 2009 1692 1700
58. P.A. Kollman, I. Massova, C. Reyes, B. Kuhn, S. Huo, and L. Chong Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models Acc. Chem. Res. 33 12 2000 889 897 (Pubitemid 32056774)
59. I. Kolossvary Evaluation of the molecular configuration integral in all degrees of freedom for the direct calculation of conformational free energies: prediction of the anomeric free energy of monosaccharides J. Phys. Chem. A 101 51 1997 9900 9905 (Pubitemid 127617239)
60. S. Kumar, D. Bouzida, R.H. Swendsen, P.A. Kollman, and J.M. Rosenberg The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method J. Comput. Chem. 13 1992 1011 1021
61. M. Lapelosa, E. Gallicchio, G.F. Arnold, E. Arnold, and R.M. Levy In silico vaccine design based on molecular simulations of rhinovirus chimeras presenting hiv-1 gp41 epitopes J. Mol. Biol. 385 2 2009 675 691
62. M. Lapelosa, G.F. Arnold, E. Gallicchio, E. Arnold, and R.M. Levy Antigenic characteristics of rhinovirus chimeras designed in silico for enhanced presentation of HIV-1 gp41 epitopes J. Mol. Biol. 397 3 2010 752 766
63. T. Lazaridis, and M. Karplus Effective energy function for protein in solution Proteins 35 1999 133 152 (Pubitemid 29165128)
64. M.S. Lee, and M.A. Olson Calculation of absolute protein-ligand binding affinity using path and endpoint approaches Biophys. J. 90 3 2006 864 877
65. R.M. Levy, and E. Gallicchio Computer simulations with explicit solvent: recent progress in the thermodynamic decomposition of free energies and in modeling electrostatic effects Annu. Rev. Phys. Chem. 49 1998 531 567 (Pubitemid 128436899)
66. R.M. Levy, M. Karplus, J. Kushick, and D. Perahia Evaluation of the configurational entropy for proteins: application to molecular dynamics simulations of an α-helix Macromolecules 17 1984 1370 1374
67. P. Liu, B. Kim, R.A. Friesner, and B.J. Berne Replica exchange with solute tempering: a method for sampling biological systems in explicit solvent Proc. Natl. Acad. Sci. USA 102 2005 13749 13754 (Pubitemid 41377651)
68. P. Liu, X. Huang, R. Zhou, and B.J. Berne Hydrophobic aided replica exchange: an efficient algorithm for protein folding in explicit solvent J. Phys. Chem. B 110 38 2006 19018 19022 (Pubitemid 44547290)
69. N. Lu, and D.A. Kofke Accuracy of free-energy perturbation calculations in molecular simulation. I. Modeling J. Chem. Phys. 114 17 2001 7303 7311 (Pubitemid 32508741)
70. N. Lu, J.K. Singh, and D.A. Kofke Appropriate methods to combine forward and reverse free-energy perturbation averages J. Chem. Phys. 118 7 2003 2977 2984
71. H. Luo, and K. Sharp On the calculation of absolute macromolecular binding free energies Proc. Natl. Acad. Sci. USA 99 16 2002 10399 10404
72. A.D. MacKerell, D. Bashford, M. Bellott, R.L. Dunbrack, J.D. Evanseck, and M.J. Field All-atom empirical potential for molecular modeling and dynamics studies of proteins J. Phys. Chem. B 102 18 1998 3586 3616 (Pubitemid 128576688)
73. C. McInnes Virtual screening strategies in drug discovery Curr. Opin. Chem. Biol. 11 5 2007 494 502 (Pubitemid 47589008)
74. Y. Meng, and A.E. Roitberg Constant ph replica exchange molecular dynamics in biomolecules using a discrete protonation model J. Chem. Theory Comput. 6 4 2010 1401 1412
75. J. Michel, and J.W. Essex Prediction of protein-ligand binding affinity by free energy simulations: assumptions, pitfalls and expectations J. Comput. Aided Mol. Des. 24 8 2010 639 658
76. M. Mihailescu, and M.K. Gilson On the theory of noncovalent binding Biophys. J. 87 1 2004 23 36 (Pubitemid 38880061)
77. A. Mitsutake, Y. Mori, and Y. Okamoto Multi-dimensional multicanonical algorithm, simulated tempering, replica-exchange method, and all that Phys. Procedia 4 2010 89 105
78. S. Miyamoto, and P.A. Kollman Absolute and relative binding free energy calculations of the interaction of biotin and its analogs with streptavidin using molecular dynamics/free energy perturbation approaches Proteins 16 3 1993 226 245 (Pubitemid 23183300)
79. D.L. Mobley, and K.A. Dill Binding of small-molecule ligands to proteins: "what you see" is not always "what you get" Structure 17 4 2009 489 498
80. D.L. Mobley, J.D. Chodera, and K.A. Dill On the use of orientational restraints and symmetry corrections in alchemical free energy calculations J. Chem. Phys. 125 8 2006 084902
81. D.L. Mobley, J.D. Chodera, and K.A. Dill The confine-and-release method: obtaining correct binding free energies in the presence of protein conformational change J. Chem. Theory Comput. 3 4 2007 1231 1235
82. D.L. Mobley, A.P. Graves, J.D. Chodera, A.C. McReynolds, B.K. Shoichet, and K.A. Dill Predicting absolute ligand binding free energies to a simple model site J. Mol. Biol. 371 4 2007 1118 1134 (Pubitemid 47101818)
83. S. Moghaddam, Y. Inoue, and M.K. Gilson Host-guest complexes with protein-ligand-like affinities: computational analysis and design J. Am. Chem. Soc. 131 11 2009 4012 4021
84. A. Morton, W.A. Baase, and B.W. Matthews Energetic origins of specificity of ligand binding in an interior nonpolar cavity of t4 lysozyme Biochemistry 34 27 1995 8564 8575
85. K. Murata, Y. Sugita, and Y. Okamoto Free energy calculations for DNA base stacking by replica-exchange umbrella sampling Chem. Phys. Lett. 385 1-2 2004 1 7
86. C. Neale, T. Rodinger, and R. Poms Equilibrium exchange enhances the convergence rate of umbrella sampling Chem. Phys. Lett. 460 1-3 2008 375 381
87. H. Okumura, E. Gallicchio, and R.M. Levy Conformational populations of ligand-sized molecules by replica exchange molecular dynamics and temperature reweighting J. Comput. Chem. 31 2010 1357 1367
88. C. Oostenbrink, and W.F. van Gunsteren Free energies of ligand binding for structurally diverse compounds Proc. Natl. Acad. Sci. USA 102 19 2005 6750 6754 (Pubitemid 40675387)
89. V.A. Payne, N. Matubayasi, L. Reed Murphy, and R.M. Levy Monte Carlo study of the effect of pressure on hydrophobic association J. Phys. Chem. B 101 1997 2054 2060 (Pubitemid 127609243)
90. E. Perola, and P.S. Charifson Conformational analysis of drug-like molecules bound to proteins: an extensive study of ligand reorganization upon binding J. Med. Chem. 47 10 2004 2499 2510 (Pubitemid 38580088)
91. S. Piana, and A. Laio A bias-exchange approach to protein folding J. Phys. Chem. B 111 17 2007 4553 4559 (Pubitemid 46787652)
92. A. Pohorille, and L.R. Pratt Cavities in molecular liquids and the theory of hydrophobic solubilities J. Am. Chem. Soc. 112 13 1990 5066 5074
93. A. Pohorille, C. Jarzynski, and C. Chipot Good practices in free-energy calculations J. Phys. Chem. B 114 32 2010 10235 10253
94. M.R. Reddy, and M.D. Erion Free Energy Calculations in Rational Drug Design 2001 Springer-Verlag New York
95. M.V. Rekharsky, T. Mori, C. Yang, Y.H. Ko, N. Selvapalam, and H. Kim A synthetic host-guest system achieves avidin-biotin affinity by overcoming enthalpy-entropy compensation Proc. Natl. Acad. Sci. USA 104 52 2007 20737 20742
96. A.E. Roitberg, A. Okur, and C. Simmerling Coupling of replica exchange simulations to a non-Boltzmann structure reservoir J. Phys. Chem. B 111 10 2007 2415 2418 (Pubitemid 46548721)
97. B. Roux, and T. Simonson Implicit solvent models Biophys. Chem. 78 1999 1 20 (Pubitemid 29206654)
98. L.D. Schuler, X. Daura, and W.F. van Gunsteren An improved gromos96 force field for aliphatic hydrocarbons in the condensed phase J. Comput. Chem. 22 11 2001 1205 1218 (Pubitemid 32662797)
99. I.N. Serdyuk, N.R. Zaccai, and G. Zaccai Methods in Molecular Biophysics: Structure, Dynamics, Function 2007 Cambridge University Press Cambridge, New York
100. M.R. Shirts, and J.D. Chodera Statistically optimal analysis of samples from multiple equilibrium states J. Chem. Phys. 129 12 2008 124105
101. M.R. Shirts, D.L. Mobley, and J.D. Chodera Alchemical free energy calculations: ready for prime time? Annu. Rep. Comput. Chem. 3 2007 41 59
102. M.R. Shirts, D.L. Mobley, and S.P. Brown Drug Design - Structure- and Ligand-Based Approaches Chapter Free-Energy Calculations in Structure-Based Drug Design 2010 Cambridge University Press New York pp. 61-86
103. B.K. Shoichet Virtual screening of chemical libraries Nature 432 7019 2004 862 865 (Pubitemid 40037142)
104. T. Steinbrecher, D.L. Mobley, and D.A. Case Nonlinear scaling schemes for Lennard-Jones interactions in free energy calculations J. Chem. Phys. 127 21 2007 214108
105. Y. Sugita, and Y. Okamoto Replica-exchange molecular dynamics method for protein folding Chem. Phys. Lett. 314 1999 141 151 (Pubitemid 129556751)
106. J.M.J. Swanson, R.H. Henchman, and J.A. McCammon Revisiting free energy calculations: a theoretical connection to mm/pbsa and direct calculation of the association free energy Biophys. J. 86 1 Pt. 1 2004 67 74 (Pubitemid 38067436)
107. Z. Tan On a likelihood approach for Monte Carlo integration J. Am. Stat. Assoc. 99 468 2004 1027 1036 (Pubitemid 39665948)
108. B.L. Tembe, and J.A. McCammon Ligand-receptor interactions Comput. Chem. 8 4 1984 281
109. J. Wagoner, and N.A. Baker Assessing implicit models for nonpolar mean solvation forces: the importance of dispersion and volume terms Proc. Natl. Acad. Sci. USA 103 2006 8331 8336 (Pubitemid 43838455)
110. J. Wang, Y. Deng, and B. Roux Absolute binding free energy calculations using molecular dynamics simulations with restraining potentials Biophys. J. 91 8 2006 2798 2814 (Pubitemid 44526470)
111. B.Q. Wei, W.A. Baase, L.H. Weaver, B.W. Matthews, and B.K. Shoichet A model binding site for testing scoring functions in molecular docking J. Mol. Biol. 322 2 2002 339 355
112. B. Widom Some topics in the theory of fluids J. Chem. Phys. 39 11 1963 2808 2812
113. B. Widom Potential-distribution theory and the statistical mechanics of fluids J. Phys. Chem. 86 6 1982 869 872
114. H.-J. Woo, and B. Roux Calculation of absolute protein-ligand binding free energy from computer simulations Proc. Natl. Acad. Sci. USA 102 19 2005 6825 6830 (Pubitemid 40675400)
115. C.J. Woods, J.W. Essex, and M.A. King The development of replica-exchange-based free-energy methods J. Phys. Chem. B 107 49 2003 13703 13710
116. C.J. Woods, J.W. Essex, and M.A. King Enhanced configurational sampling in binding free-energy calculations J. Phys. Chem. B 107 49 2003 13711 13718
117. C.-Y. Yang, H. Sun, J. Chen, Z. Nikolovska-Coleska, and S. Wang Importance of ligand reorganization free energy in protein-ligand binding-affinity prediction J. Am. Chem. Soc. 131 38 2009 13709 13721
118. I.-C. Yeh, M.A. Olson, M.S. Lee, and A. Wallqvist Free-energy profiles of membrane insertion of the m2 transmembrane peptide from influenza a virus Biophys. J. 95 11 2008 5021 5029
119. H.-X. Zhou, and M.K. Gilson Theory of free energy and entropy in non-covalent binding Chem. Rev. 109 9 2009 4092 4107
120. Z. Zhou, A.K. Felts, R.A. Friesner, and R.M. Levy Comparative performance of several flexible docking programs and scoring functions: enrichment studies for a diverse set of pharmaceutically relevant targets J. Chem. Inf. Model. 47 4 2007 1599 1608 (Pubitemid 47210063)
121. R.W. Zwanzig High-temperature equation of state by a perturbation method. I. Nonpolar gases J. Chem. Phys. 22 8 1954 1420 1426