Computational Optimization and Applications

, Volume 45, Issue 2, pp 377–413 | Cite as

An improved hybrid global optimization method for protein tertiary structure prediction

Article

Abstract

First principles approaches to the protein structure prediction problem must search through an enormous conformational space to identify low-energy, near-native structures. In this paper, we describe the formulation of the tertiary structure prediction problem as a nonlinear constrained minimization problem, where the goal is to minimize the energy of a protein conformation subject to constraints on torsion angles and interatomic distances. The core of the proposed algorithm is a hybrid global optimization method that combines the benefits of the αBB deterministic global optimization approach with conformational space annealing. These global optimization techniques employ a local minimization strategy that combines torsion angle dynamics and rotamer optimization to identify and improve the selection of initial conformations and then applies a sequential quadratic programming approach to further minimize the energy of the protein conformations subject to constraints. The proposed algorithm demonstrates the ability to identify both lower energy protein structures, as well as larger ensembles of low-energy conformations.

Keywords

Protein tertiary structure prediction Hybrid global optimization algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

10589_2009_9277_MOESM1_ESM.pdf (99 kb)
Below is the link to the electronic supplementary material (PDF 99,2 kB).

References

  1. 1.
    Levinthal, C.: How to fold graciously. In: Debrunner, P., Tsibris, J.C.M., Münck, E. (eds.) Mossbauer Spectroscopy in Biological Systems, pp. 22–24. University of Illinois Press, Urbana (1969) Google Scholar
  2. 2.
    Anfinsen, C.B.: Principles that govern the folding of protein chains. Science 181(4096), 223–230 (1973) Google Scholar
  3. 3.
    Altschul, S.F., Gish, W., Miller, W., Myers, E.W., Lipman, D.J.: Basic local alignment search tool. J. Mol. Biol. 215, 403–410 (1990) Google Scholar
  4. 4.
    Altschul, S.F., Madden, T.L., Schaffer, A.A., Zhang, J., Zhang, Z., Miller, W., Lipman, D.J.: Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res. 25, 3389–3402 (1997) Google Scholar
  5. 5.
    Karplus, K., Barret, Ch., Hughey, R.: Hidden Markov models for detecting remote protein homologies. Bioinformatics 14(10), 846–856 (1998) Google Scholar
  6. 6.
    Rychlewski, L., Jaroszewski, L., Li, W., Godzik, A.: Comparison of sequence profiles. strategies for structural predictions using sequence information. Proteome Sci. 9, 232–241 (2000) Google Scholar
  7. 7.
    Narayana, S.V., Argos, P.: Residue contacts in protein structures and implications for protein folding. Int. J. Pept. Protein Res. 24, 25–39 (1984) Google Scholar
  8. 8.
    Bowie, J.U., Lüthy, R., Eisenberg, D.: A method to identify protein sequences that fold into a known three-dimensional structure. Science 253, 164–170 (1991) Google Scholar
  9. 9.
    Godzik, A., Kolinski, A., Skolnick, J.: Topology fingerprint approach to the inverse folding problem. J. Mol. Biol. 227, 227–238 (1992) Google Scholar
  10. 10.
    Chothia, C.: One thousand families for the molecular biologist. Nature 357, 543–544 (1992) Google Scholar
  11. 11.
    Grant, A., Lee, D., Orengo, C.: Progress towards mapping the universe of protein folds. Genome Biol. 5, 107 (2004) Google Scholar
  12. 12.
    Jones, D.T.: GenTHREADER: An efficient and reliable protein fold recognition method for genomic sequences. J. Mol. Biol. 287, 797–815 (1999) Google Scholar
  13. 13.
    Skolnick, J., Zhang, Y., Arakaki, A.K., Kolinski, A., Boniecki, M., Szilágyi, A., Kihara, D.: TOUCHSTONE: A unified approach to protein structure prediction. Proteins Struct. Funct. Bioinf. 53, 469–479 (2003) Google Scholar
  14. 14.
    Skolnick, J., Kihara, D., Zhang, Y.: Development and large scale benchmark testing of the PROSPECTOR_3 threading algorithm. Proteins Struct. Funct. Bioinf. 56, 502–518 (2004) Google Scholar
  15. 15.
    Xu, Y., Xu, D.: Protein threading using PROSPECT: Design and evolution. Proteins Struct. Funct. Bioinf. 40, 343–354 (2000) Google Scholar
  16. 16.
    Xu, J., Li, M., Kim, D., Xu, Y.: RAPTOR: Optimal protein threading by linear programming. J. Bioinf. Comput. Biol. 1, 95–117 (2003) Google Scholar
  17. 17.
    Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T.N., Weissig, H., Shindyalov, I.N., Bourne, P.E.: The protein data bank. Nucleic Acids Res. 28(1), 235–242 (2000) Google Scholar
  18. 18.
    Simons, K.T., Kooperberg, C., Huang, C., Baker, D.: Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions. J. Mol. Biol. 268, 209–225 (1997) Google Scholar
  19. 19.
    Rohl, C.A., Strauss, C.E.M., Chivian, D., Baker, D.: Modeling structurally variable regions in homologous proteins with Rosetta. Proteins Struct. Funct. Bioinf. 55, 656–677 (2004) Google Scholar
  20. 20.
    Zhang, Y., Skolnick, J.: Tertiary structure predictions on a comprehensive benchmark of medium to large size proteins. Biophys. J. 87, 2647–2655 (2004) Google Scholar
  21. 21.
    Zhang, Y., Skolnick, J.: Automated structure prediction of weakly homologous proteins on a genomic scale. Proc. Natl. Acad. Sci. 101, 7594–7599 (2004) Google Scholar
  22. 22.
    Zhang, Y., Skolnick, J.: SPICKER: A clustering approach to identify near-native protein folds. J. Comput. Chem. 25, 865–871 (2004) Google Scholar
  23. 23.
    Wu, S., Skolnick, J., Zhang, Y.: Ab initio modeling of small proteins by iterative TASSER simulations. BMC Biol. 5, 17–26 (2007) Google Scholar
  24. 24.
    Xia, Y., Huang, E.S., Levitt, M., Samudrala, R.: Ab initio construction of protein tertiary structure using a hierarchical approach. J. Mol. Biol. 300, 171–185 (2000) Google Scholar
  25. 25.
    Kussel, E., Shimada, J., Shakhnovich, E.I.: A structure-based method for derivation of all-atom potentials for protein folding. Proc. Natl. Acad. Sci. 999, 5343–5348 (2002) Google Scholar
  26. 26.
    Ozkan, S.B., Wu, G.A., Chodera, J.D., Dill, K.A.: Protein folding by zipping and assembly. Proc. Natl. Acad. Sci. 104, 11987–11992 (2007) Google Scholar
  27. 27.
    Srinivasan, R., Rose, G.D.: LINUS: A hierarchic procedure to predict the fold of a protein. Proteins Struct. Funct. Gen. 22, 81–89 (1995) Google Scholar
  28. 28.
    Srinivasan, R., Rose, G.D.: Ab initio prediction of protein structure using LINUS. Proteins Struct. Funct. Bioinf. 47, 489–495 (2002) Google Scholar
  29. 29.
    Zagrovic, B., Snow, C.D., Shirts, M.R., Pande, V.S.: Simulation of folding of a small alpha-helical protein in atomistic detail using worldwide-distributed computing. J. Mol. Biol. 323, 927–937 (2002) Google Scholar
  30. 30.
    Liwo, A., Arlukowicz, P., Czaplewski, C., Oldziej, S., Pillardy, J., Scheraga, H.A.: A method for optimizing potential-energy functions by hierarchical design of the potential-energy landscape: Application to the UNRES force field. Proc. Natl. Acad. Sci. 99, 1937–1942 (2002) Google Scholar
  31. 31.
    Liwo, A., Oldziez, S., Pincus, M.R., Wawak, R.J., Rackovsky, S., Scheraga, H.A.: A united-residue force field for off-lattice protein-structure simulations. I. Functional forms and parameters of long-range side-chain interaction potentials from protein crystal data. J. Comput. Chem. 18, 849–873 (1997) Google Scholar
  32. 32.
    Liwo, A., Pincus, M.R., Wawak, R.J., Rackovsky, S., Oldziej, S., Scheraga, H.A.: A united-residue force field for off-lattice protein structure simulations. II. Parameterization of short-range interactions and determination of weights of energy terms by z-score optimization. J. Comput. Chem. 18, 874–887 (1997) Google Scholar
  33. 33.
    Lee, J., Scheraga, H.A., Rackovsky, S.: New optimization method for conformational energy calculations on polypeptides: Conformational space annealing. J. Comput. Chem. 18, 1222–1232 (1997) Google Scholar
  34. 34.
    Lee, J., Pillardy, J., Czaplewski, C., Arnautova, Y., Ripoll, D.R., Liwo, A., Gibson, K.D., Wawak, R.J., Scheraga, H.A.: Efficient parallel algorithms in global optimization of potential energy functions for peptides, proteins and crystals. Comput. Phys. Commun. 128, 399–411 (2000) MATHGoogle Scholar
  35. 35.
    Czaplewski, C., Liwo, A., Pillardy, J., Oldziej, S., Scheraga, H.A.: Improved conformational space annealing method to treat beta-structure with the UNRES force-field and to enhance scalability of parallel implementation. Polymer 45, 677–686 (2004) Google Scholar
  36. 36.
    Nanias, M., Chinchio, M., Oldziej, S., Czaplewski, C., Scheraga, H.A.: Protein structure prediction with the UNRES force-field using replica-exchange Monte Carlo-with-minimization; comparison with MCM, CSA, and CFMC. J. Comput. Chem. 26, 1472–1486 (2005) Google Scholar
  37. 37.
    Klepeis, J.L., Floudas, C.A.: ASTRO-FOLD: A combinatorial and global optimization framework for ab initio prediction of three-dimensional structures of proteins from the amino acid sequence. Biophys. J. 85, 2119–2146 (2003) Google Scholar
  38. 38.
    Klepeis, J.L., Floudas, C.A.: Ab initio prediction of helical segments in polypeptides. J. Comput. Chem. 23(2), 245–266 (2002) Google Scholar
  39. 39.
    Klepeis, J.L., Floudas, C.A.: Prediction of beta-sheet topology and disulfide bridges in polypeptides. J. Comput. Chem. 24, 191–208 (2003) Google Scholar
  40. 40.
    Klepeis, J.L., Floudas, C.A.: Ab initio tertiary structure prediction of proteins. J. Glob. Optim. 25, 113–140 (2003) MATHMathSciNetGoogle Scholar
  41. 41.
    Klepeis, J.L., Pieja, M.T., Floudas, C.A.: A new class of hybrid global optimization algorithms for peptide structure prediction: Integrated hybrids. Comput. Phys. Commun. 151, 121–140 (2003) Google Scholar
  42. 42.
    Klepeis, J.L., Pieja, M.T., Floudas, C.A.: Hybrid global optimization algorithms for protein structure prediction: Alternating hybrids. Biophys. J. 84, 869–882 (2003) Google Scholar
  43. 43.
    Klepeis, J.L., Wei, Y.N., Hecht, M.H., Floudas, C.A.: Ab initio prediction of the three-dimensional structure of a de novo designed protein: A double-blind case study. Proteins Struct. Funct. Bioinf. 58, 560–570 (2005) Google Scholar
  44. 44.
    Dunbrack, R.L.: Sequence comparison and protein structure prediction. Curr. Opin. Struct. Biol. 16, 374–384 (2006) Google Scholar
  45. 45.
    Bujnicki, J.M.: Protein structure prediction by recombination of fragments. Chem. Bio. Chem. 7, 19–27 (2006) Google Scholar
  46. 46.
    Floudas, C.A., Fung, H.K., McAllister, S.R., Mönnigmann, M., Rajgaria, R.: Advances in protein structure prediction and de novo protein design: A review. Chem. Eng. Sci. 61, 966–988 (2006) Google Scholar
  47. 47.
    Floudas, C.A.: Computational methods in protein structure prediction. Biotechnol. Bioeng. 97, 207–213 (2007) Google Scholar
  48. 48.
    Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz, K.M. Jr., Ferguson, D.M., Spellmeyer, D.C., Fox, T., Caldwell, J.W., Kollman, P.A.: A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 117, 5179–5197 (1995) Google Scholar
  49. 49.
    MacKerell, A.D. Jr., Bashford, D., Bellott, M., Dunbrack, R.L. Jr., Evanseck, J.D., Field, M.J., Fischer, S., Gao, J., Guo, H., Ha, S., Joseph-McCarthy, D., Kuchnir, L., Kuczera, K., Lau, F.T.K., Mattos, C., Michnick, S., Ngo, T., Nguyen, D.T., Prodhom, B., Reiher, W.E. III, Roux, B., Schlenkrich, M., Smith, J.C., Stote, R., Straub, J., Watanabe, M., Wiórkiewicz-Kuczera, J., Yin, D., Karplus, M.: All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 102, 3586–3616 (1998) Google Scholar
  50. 50.
    Momany, F.A., McGuire, R.F., Burgess, A.W., Scheraga, H.A.: Energy parameters in polypeptides. VII. Geometric parameters, partial atomic charges, nonbonded interactions, hydrogen bond interactions, and intrinsic torsional potentials for the naturally occurring amino acids. J. Phys. Chem. 79, 2361–2381 (1975) Google Scholar
  51. 51.
    Némethy, G., Gibson, K.D., Palmer, K.A., Yoon, C.N., Paterlini, G., Zagari, A., Rumsey, S., Scheraga, H.A.: Energy parameters in polypeptides. 10. Improved geometrical parameters and nonbonded interactions for use in the ECEPP/3 algorithm, with application to proline-containing peptides. J. Phys. Chem. 96, 6472–6484 (1992) Google Scholar
  52. 52.
    Arnautova, Y.A., Jagielska, A., Scheraga, H.A.: A new force field (ECEPP-05) for peptides, proteins, and organic molecules. J. Phys. Chem. B 110, 5025–5044 (2006) Google Scholar
  53. 53.
    Ortiz, A.R., Kolinski, A., Skolnick, J.: Fold assembly of small proteins using Monte Carlo simulations driven by restraints derived from multiple sequence alignments. J. Mol. Biol. 277(2), 419–448 (1998) Google Scholar
  54. 54.
    McAllister, S.R., Mickus, B.E., Klepeis, J.L., Floudas, C.A.: A novel approach for alpha-helical topology prediction in globular proteins: Generation of interhelical restraints. Proteins Struct. Funct. Bioinf. 65, 930–952 (2006) Google Scholar
  55. 55.
    Klepeis, J.L., Floudas, C.A.: Analysis and prediction of loop segments in protein structures. Comput. Chem. Eng. 29, 423–436 (2005) Google Scholar
  56. 56.
    Mönnigmann, M., Floudas, C.A.: Protein loop structure prediction with flexible stem geometries. Proteins Struct. Funct. Bioinf. 61, 748–762 (2005) Google Scholar
  57. 57.
    Creighton, T.E.: Proteins: Structures and Molecular Properties, 2nd edn. Freeman, New York (1993) Google Scholar
  58. 58.
    Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming: Theory and Algorithms, 2nd edn. Wiley, New York (1993) MATHGoogle Scholar
  59. 59.
    Fletcher, R.: Practical Methods of Optimization, 2nd edn. Wiley, New York (1987) MATHGoogle Scholar
  60. 60.
    Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic Press, Burlington (1981) MATHGoogle Scholar
  61. 61.
    Gill, P.E., Murray, W., Saunders, M., Wright, M.H.: NPSOL 4.0 User’s Guide. Systems Optimization Laboratory, Department of Operations Research, Standford University, CA (1986) Google Scholar
  62. 62.
    Blumenthal, L.M.: Theory and Applications of Distance Geometry. Cambridge University Press, Cambridge (1953) MATHGoogle Scholar
  63. 63.
    Crippen, G.M.: A novel approach to the calculation of conformation: Distance geometry. J. Comput. Phys. 26, 449–452 (1977) MathSciNetGoogle Scholar
  64. 64.
    Crippen, G.M., Havel, T.F.: Distance Geometry and Molecular Conformation. Wiley, New York (1988) MATHGoogle Scholar
  65. 65.
    Moré, J.J., Wu, Z.: Distance geometry optimization for protein structures. J. Glob. Optim. 15, 219–234 (1999) MATHGoogle Scholar
  66. 66.
    Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Clarendon Press, Oxford (1987) MATHGoogle Scholar
  67. 67.
    Brünger, A.T.: X-PLOR, Version 3.1. A System for X-Ray Crystallography and NMR. Yale University Press, New Haven (1992) Google Scholar
  68. 68.
    Braun, W., Go, N.: Calculation of protein conformations by proton-proton distance constraints. A new efficient algorithm. J. Mol. Biol. 186, 611–626 (1985) Google Scholar
  69. 69.
    Güntert, P., Wüthrich, K.: Improved efficiency of protein structure calculations from NMR data using the program DIANA with redundant dihedral angle constraints. J. Biomol. NMR 1, 446–456 (1991) Google Scholar
  70. 70.
    Jain, A., Vaidehi, N., Rodriguez, G.: A fast recursive algorithm for molecular dynamics simulation. J. Comput. Phys. 106, 258–268 (1993) MATHGoogle Scholar
  71. 71.
    Güntert, P., Mumenthaler, C., Wüthrich, K.: Torsion angle dynamics for NMR structure calculation with the new program DYANA. J. Mol. Biol. 273, 283–298 (1997) Google Scholar
  72. 72.
    Stein, E.G., Rice, L.M., Brünger, A.T.: Torsion angle dynamics as a new efficient tool for NMR structure calculation. J. Magn. Reson. 124, 154–164 (1997) Google Scholar
  73. 73.
    Güntert, P.: Structure calculation of biological macromolecules from NMR data. Q. Rev. Biophys. 31, 145–237 (1998) Google Scholar
  74. 74.
    Ponder, J.W., Richard, F.M.: Tertiary templates for proteins. use of packing criteria in the enumeration of allowed sequences for different structural classes. J. Mol. Biol. 193, 775–791 (1987) Google Scholar
  75. 75.
    Dunbrack, R.L., Karplus, M.: Backbone-dependent rotamer library for proteins. Application to side-chain prediction. J. Mol. Biol. 230, 543–574 (1993) Google Scholar
  76. 76.
    Lovell, S.C., Word, J.M., Richardson, J.S., Richardson, D.C.: The penultimate rotamer library. Proteins Struct. Funct. Gen. 40, 389–408 (2000) Google Scholar
  77. 77.
    Dunbrack, R.L.: Rotamer libraries in the 21st century. Curr. Opin. Struct. Biol. 12, 431–440 (2002) Google Scholar
  78. 78.
    Desmet, J., De Maeyer, M., Hazes, B., Lasters, I.: The dead-end elimination theorem and its use in protein sidechain positioning. Nature 356, 539–542 (1992) Google Scholar
  79. 79.
    Looger, L.L., Hellinga, H.W.: Generalized dead-end elimination algorithms make large-scale protein side-chain prediction tractable: Implications for protein design and structural genomics. J. Mol. Biol. 307, 429–445 (2001) Google Scholar
  80. 80.
    Leach, A.R., Lemon, A.P.: Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm. Proteins Struct. Funct. Gen. 33, 227–239 (1998) Google Scholar
  81. 81.
    Xie, W., Sahinidis, N.V.: Residue-rotamer-reduction algorithm for the protein side-chain conformation problem. Bioinformatics 22, 188–194 (2006) Google Scholar
  82. 82.
    Eriksson, O., Zhou, Y., Elofsson, A.: Side chain-positioning as an integer programming problem. In: WABI ’01: Proceedings of the First International Workshop on Algorithms in Bioinformatics, pp. 128–141 (2001) Google Scholar
  83. 83.
    Kingsford, C.L., Chazelle, B., Singh, M.: Solving and analyzing side-chain positioning problems using linear and integer programming. Bioinformatics 21, 1028–1036 (2005) Google Scholar
  84. 84.
    Canutescu, A.A., Shelenkov, A.A., Dunbrack, R.L.: A graph-theory algorithm for rapid protein side-chain prediction. Proteome Sci. 12, 2001–2014 (2003) Google Scholar
  85. 85.
    Holm, L., Sander, C.: Fast and simple Monte Carlo algorithm for side-chain optimization in proteins: Application to model building by homology. Proteins Struct. Funct. Gen. 14, 213–223 (1992) Google Scholar
  86. 86.
    Liang, S., Grishin, N.V.: Side-chain modeling with an optimized scoring function. Proteome Sci. 11, 322–331 (2002) Google Scholar
  87. 87.
    Xiang, Z., Honig, B.: Extending the accuracy limits of prediction for side-chain conformations. J. Mol. Biol. 311, 421–430 (2001) Google Scholar
  88. 88.
    Tufféry, P., Etchebest, C., Hazout, S., Lavery, R.: A new approach to the rapid determination of protein side chain conformations. J. Biomol. Struct. Dyn. 8, 1267–1289 (1991) Google Scholar
  89. 89.
    Lee, C.: Predicting protein mutant energetics by self-consistent ensemble optimization. J. Mol. Biol. 236, 918–939 (1994) Google Scholar
  90. 90.
    Desmet, J., Spriet, J., Lasters, I.: Fast and accurate side-chain topology and energy refinement as a new method for protein structure optimization. Proteins Struct. Funct. Gen. 48, 31–43 (2002) Google Scholar
  91. 91.
    Levitt, M., Gerstein, M., Huang, E., Subbiah, S., Tsai, J.: Protein folding: The endgame. Annu. Rev. Biochem. 66, 549–579 (1997) Google Scholar
  92. 92.
    Baker, D.: Prediction and design of macromolecular structures and interactions. Philos. Trans. R. Soc. B 361, 459–463 (2006) Google Scholar
  93. 93.
    Adjiman, C.S., Androulakis, I.P., Maranas, C.D., Floudas, C.A.: A global optimization method, αBB, for process design. Comput. Chem. Eng. 20, S419–S424 (1996) Google Scholar
  94. 94.
    Adjiman, C.S., Androulakis, I.P., Floudas, C.A.: Global optimization of MINLP problems in process synthesis and design. Comput. Chem. Eng. 21, S445–S450 (1997) Google Scholar
  95. 95.
    Adjiman, C.S., Dallwig, S., Floudas, C.A., Neumaier, A.: A global optimization method for general twice-differentiable NLPs. i. Theoretical advances. Comput. Chem. Eng. 22, 1137–1158 (1998) Google Scholar
  96. 96.
    Adjiman, C.S., Androulakis, I.P., Floudas, C.A.: A global optimization method for general twice-differentiable NLPs. ii. Implementation and computational results. Comput. Chem. Eng. 22, 1159–1179 (1998) Google Scholar
  97. 97.
    Androulakis, I.P., Maranas, C.D., Floudas, C.A.: αBB: A global optimization method for general constrained nonconvex problems. J. Glob. Optim. 7, 337–363 (1995) MATHMathSciNetGoogle Scholar
  98. 98.
    Floudas, C.A.: Deterministic Global Optimization: Theory, Methods and Applications. Nonconvex Optimization and its Applications. Kluwer Academic, Dordrecht (2000) Google Scholar
  99. 99.
    Lee, J., Scheraga, H.A., Rackovsky, S.: Conformational analysis of the 20-residue membrane-bound portion of melittin by conformational space annealing. Biopolymers 46, 103–115 (1998) Google Scholar
  100. 100.
    Lee, J., Scheraga, H.A.: Conformational space annealing by parallel computations: Extensive conformational search of met-enkephalin and the 20-residue membrane-bound portion of melittin. Int. J. Quant. Chem. 75, 255–265 (1999) Google Scholar
  101. 101.
    Ripoll, D., Liwo, A., Scheraga, H.A.: New developments of the electrostatically driven Monte Carlo method: Tests on the membrane-bound portion of melittin. Biopolymers 46, 117–126 (1998) Google Scholar
  102. 102.
    Kirkpatrick, S., Gelatt, C.D. Jr., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983) MathSciNetGoogle Scholar
  103. 103.
    Gronenborn, A.M., Filpula, D.R., Essig, N.Z., Achari, A., Whitlow, M., Wingfield, P.T., Clore, G.M.: A novel, highly stable fold of the immunoglobulin binding domain of streptococcal protein G. Science 253, 657–661 (1991) Google Scholar
  104. 104.
    Gallagher, T., Alexander, P., Bryan, P., Gilliland, G.L.: Two crystal structures of the B1 immunoglobulin-binding domain of streptococcal protein G and comparison with NMR. Biochem. 33, 4721–4729 (1994) Google Scholar
  105. 105.
    Kambach, C., Walke, S., Young, R., Avis, J.M., de la Fortelle, E., Raker, V.A., Lührmann, R., Li, J., Nagai, K.: Crystal structures of two Sm protein complexes and their implications for the assembly of the spliceosomal snRNPs. Cell 96, 375–387 (1999) Google Scholar
  106. 106.
    Deisenhofer, J., Steigemann, W.: Crystallographic refinement of structure of bovine pancreatic trypsin-inhibitor at 1.5 Å resolution. Acta Crystallogr. Sect. B 31, 238–250 (1975) Google Scholar
  107. 107.
    Wlodawer, A., Walter, J., Huber, R., Sjolin, L.: Structure of bovine pancreatic trypsin-inhibitor: Results of joint neutron and x-ray refinement of crystal form II. J. Mol. Biol. 180, 301–329 (1984) Google Scholar
  108. 108.
    Campos-Olivas, R., Hörr, I., Bormann, C., Jung, G., Gronenborn, A.M.: Solution structure, backbone dynamics and chitin binding properties of the anti-fungal protein from Streptomyces tendae TÜ901. J. Mol. Biol. 308, 765–782 (2001) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Scott R. McAllister
    • 1
  • Christodoulos A. Floudas
    • 1
  1. 1.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA

Personalised recommendations