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Entangled Proteins: Knots, Slipknots, Links, and Lassos

  • Joanna I. SulkowskaEmail author
  • Piotr Sułkowski
Chapter
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 189)

Abstract

In recent years the studies of entangled proteins have grown into the whole new, interdisciplinary and rapidly developing field of research. Here we present various types of entangled proteins studied within this field, which form knots, slipknots, links, and lassos. We discuss their geometric features and indicate what biological and physical role the entanglement plays. We also discuss mathematical tools necessary to analyze such structures and present databases and servers assembling information about entangled proteins: KnotProt, LinkProt, and LassoProt.

Notes

Acknowledgements

This work has been financed from the budget for science in the years 2016-2019 [#0003/ID3/2016/64 MNiSW – Ideas Plus], EMBO [#2057 Installation Grant], and National Science Centre [#2012/07/E/NZ1/01900] to J.I.S. The work of P.S. has been supported by the ERC Starting Grant no. 335739 “Quantum fields and knot homologies” funded by the European Research Council under the European Union’s Seventh Framework Programme.

References

  1. 1.
    C.D. Allen, M.Y. Chen, A.Y. Trick, D.T. Le, A.L. Ferguson, A.J. Link, Thermal unthreading of the lasso peptides astexin-2 and astexin-3. ACS Chem. Biol. (2016)CrossRefGoogle Scholar
  2. 2.
    F.I. Andersson, D.G. Pina, A.L. Mallam, G. Blaser, S.E. Jackson, Untangling the folding mechanism of the 52-knotted protein uch-l3. FEBS J. 276(9), 2625–2635 (2009)CrossRefGoogle Scholar
  3. 3.
    B.T. Andrews, D.T. Capraro, J.I. Sulkowska, J.N. Onuchic, P.A. Jennings, Hysteresis as a marker for complex, overlapping landscapes in proteins. J. Phys. Chem. Lett. 4(1), 180–188 (2012)CrossRefGoogle Scholar
  4. 4.
    S.A. Beccara, T. Škrbić, R. Covino, C. Micheletti, P. Faccioli, Folding pathways of a knotted protein with a realistic atomistic force field. PLoS Comput. Biol. 9(3), e1003002 (2013)Google Scholar
  5. 5.
    D. Bölinger, J.I. Sułkowska, H.-P. Hsu, L.A. Mirny, M. Kardar, J.N. Onuchic, P. Virnau, A Stevedore’s protein knot. PLoS Comput. Biol. 6(4), e1000731–e1000731 (2010)MathSciNetCrossRefGoogle Scholar
  6. 6.
    T. Bornschlögl, D.M. Anstrom, E. Mey, J. Dzubiella, M. Rief, K.T. Forest, Tightening the knot in phytochrome by single-molecule atomic force microscopy. Biophys. J. 96(4), 1508–1514 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    T. Christian, R. Sakaguchi, A.P. Perlinska, G. Lahoud, T. Ito, E.A. Taylor, S. Yokoyama, J.I. Sulkowska, Y-M. Hou, Methyl transfer by substrate signaling from a knotted protein fold. Nat. Struct. Mol. Biol. (2016)Google Scholar
  8. 8.
    M. Chwastyk, M. Cieplak, Cotranslational folding of deeply knotted proteins. J. Phys. Condens. Matter 27(35), 354105 (2015)CrossRefGoogle Scholar
  9. 9.
    D.J. Craik, N.L. Daly, T. Bond, C. Waine, Plant cyclotides: a unique family of cyclic and knotted proteins that defines the cyclic cystine knot structural motif. J. Mol. Biol. 294(5), 1327–1336 (1999)CrossRefGoogle Scholar
  10. 10.
    D.J. Craik, M. Čemažar, C.K.L. Wang, N.L. Daly, The cyclotide family of circular miniproteins: nature’s combinatorial peptide template. Pept. Sci. 84(3), 250–266 (2006)CrossRefGoogle Scholar
  11. 11.
    P. Dabrowski-Tumanski, J.I. Sulkowska, Topological knots and links in proteins. Proc. Natl. Acad. Sci. 114(13), 3415–3420 (2017)CrossRefGoogle Scholar
  12. 12.
    P. Dabrowski-Tumanski, A.I. Jarmolinska, J.I. Sulkowska, Prediction of the optimal set of contacts to fold the smallest knotted protein. J. Phys. Condens. Matter 27(35), 354109 (2015)CrossRefGoogle Scholar
  13. 13.
    P. Dabrowski-Tumanski, W. Niemyska, P. Pasznik, J.I. Sulkowska, Lassoprot: server to analyze biopolymers with lassos. Nucleic Acids Res. 44(W1), W383–W389, 2016CrossRefGoogle Scholar
  14. 14.
    P. Dabrowski-Tumanski, A. Stasiak, J.I. Sulkowska, In search of functional advantages of knots in proteins. PloS one, 11(11), e0165986 (2016)CrossRefGoogle Scholar
  15. 15.
    P. Dabrowski-Tumanski, A.I. Jarmolinska, W. Niemyska, E.J. Rawdon, K.C. Millett, J.I. Sulkowska, Linkprot: a database collecting information about biological links. Nucleic Acids Res. 45(D1), D243 (2017)CrossRefGoogle Scholar
  16. 16.
    N.L. Daly, D.J. Craik. Bioactive cystine knot proteins. Curr. Opin. Chem. Biol. 15(3), 362–368 (2011)CrossRefGoogle Scholar
  17. 17.
    L.-O. Essen, J. Mailliet, J. Hughes, The structure of a complete phytochrome sensory module in the Pr ground state. Proc. Natl. Acad. Sci. 105(38), 14709–14714 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    B. Ewing, K.C. Millett, Computational algorithms and the complexity of link polynomials. Prog. Knot Theory Relat. Top. 56, 51–68 (1997)MathSciNetzbMATHGoogle Scholar
  19. 19.
    P.F.N. Faísca, Knotted proteins: a tangled tale of structural biology. Comput. Struct. Biotechnol. J. 13, 459–468 (2015)CrossRefGoogle Scholar
  20. 20.
    P.F.N. Faísca, R.D.M. Travasso, T. Charters, A. Nunes, M. Cieplak, The folding of knotted proteins: insights from lattice simulations. Phys. Biol. 7(1), 016009 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    P. Freyd, D. Yetter, J. Hoste, W.B.R. Lickorish, K. Millett, A. Ocneanu, A new polynomial invariant of knots and links. Bull. Am. Math. Soc. 12(2), 239–246 (1985)MathSciNetCrossRefGoogle Scholar
  22. 22.
    E. Haglund, J.I. Sułkowska, Z. He, G-S. Feng, P.A. Jennings, J.N. Onuchic, The unique cysteine knot regulates the pleotropic hormone leptin. PloS one 7(9), e45654 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    E. Haglund, J.I. Sulkowska, J.K. Noel, H. Lammert, J.N. Onuchic, P.A. Jennings, Pierced lasso bundles are a new class of knot-like motifs. PLoS Comput. Biol. 10(6), e1003613 (2014)ADSCrossRefGoogle Scholar
  24. 24.
    E. Haglund, A. Pilko, R. Wollman, P.A. Jennings, J.N. Onuchic, Pierced lasso topology controls function in leptin. J. Phys. Chem. B 121(4), 706–718 (2017)CrossRefGoogle Scholar
  25. 25.
    C. He, G.Z. Genchev, H. Lu, H. Li, Mechanically untying a protein slipknot: multiple pathways revealed by force spectroscopy and steered molecular dynamics simulations. J. Am. Chem. Soc. 134(25), 10428–10435 (2012)CrossRefGoogle Scholar
  26. 26.
    C. He, G. Lamour, A. Xiao, J. Gsponer, H. Li, Mechanically tightening a protein slipknot into a trefoil knot. J. Am. Chem. Soc. 136(34), 11946–11955 (2014)CrossRefGoogle Scholar
  27. 27.
    Y.M. Hou, R. Matsubara, R. Takase, I. Masuda, J.I. Sulkowska. TrmD: a methyl transferase for tRNA methylation with m1G37. The Enzymes (2017)CrossRefGoogle Scholar
  28. 28.
    S.E. Jackson, A. Suma, C. Micheletti, How to fold intricately: using theory and experiments to unravel the properties of knotted proteins. Curr. Opin. Struct. Biol. 42, 6–14 (2017)Google Scholar
  29. 29.
    M. Jamroz, W. Niemyska, E.J. Rawdon, A. Stasiak, K.C. Millett, P. Sułkowski, J.I. Sulkowska, Knotprot: a database of proteins with knots and slipknots. Nucleic Acids Res. 43(D1), D306–D314 (2015)CrossRefGoogle Scholar
  30. 30.
    A.I. Jarmolinska, A.P. Perlinska, R. Runkel, B. Trefz, P. Virnau, J.I. Sulkowska, Proteins? knotty problems (2017) (under review)Google Scholar
  31. 31.
    N.P. King, A.W. Jacobitz, M.R. Sawaya, L. Goldschmidt, T.O. Yeates, Structure and folding of a designed knotted protein. Proc. Natl. Acad. Sci. 107(48), 20732–20737 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    N.P. King, E.O. Yeates, T.O. Yeates, Identification of rare slipknots in proteins and their implications for stability and folding. J. Mol. Biol. 373(1), 153–166 (2007)CrossRefGoogle Scholar
  33. 33.
    G. Kolesov, P. Virnau, M. Kardar, L.A. Mirny, Protein knot server: detection of knots in protein structures. Nucleic Acids Res. 35, W425–8 (2007)CrossRefGoogle Scholar
  34. 34.
    K. Koniaris, M. Muthukumar, Self-entanglement in ring polymers. J. Chem. Phys. 95(4), 2873–2881 (1991)ADSCrossRefGoogle Scholar
  35. 35.
    Y.-L. Lai, S.-C. Yen, Y. Sung-Huan, J.-K. Hwang, pknot: the protein knot web server. Nucleic Acids Res. 35(2), W420–W424 (2007)CrossRefGoogle Scholar
  36. 36.
    Y.-T.C. Lee, C-Y. Chang, S.-Y. Chen, Y.-R. Pan, M.-R. Ho, S.T.D. Hsu, Entropic stabilization of a deubiquitinase provides conformational plasticity and slow unfolding kinetics beneficial for functioning on the proteasome. Sci. Rep. 7, 45174 (2017)ADSCrossRefGoogle Scholar
  37. 37.
    W. Li, T. Terakawa, W. Wang, S. Takada, Energy landscape and multiroute folding of topologically complex proteins adenylate kinase and 2ouf-knot. Proc. Natl. Acad. Sci. 109(44), 17789–17794 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    S.-C. Lou, S. Wetzel, H. Zhang, E.W. Crone, Y.-T. Lee, S.E. Jackson, S.-T.D. Hsu, The knotted protein UCh-L1 exhibits partially unfolded forms under native conditions that share common structural features with its kinetic folding intermediates. J. Mol. Biol. 428(11), 2507–2520 (2016)CrossRefGoogle Scholar
  39. 39.
    R.C. Lua, Pyknot, a pymol tool for the discovery and analysis of knots in proteins. Bioinformatics 28(15), 2069–2071 (2012)CrossRefGoogle Scholar
  40. 40.
    A.L. Mallam, S.E. Jackson, Knot formation in newly translated proteins is spontaneous and accelerated by chaperonins. Nat. Chem. Biol. 8(2), 147–153 (2012)CrossRefGoogle Scholar
  41. 41.
    A.L. Mallam, J.M. Rogers, S.E. Jackson, Experimental detection of knotted conformations in denatured proteins. Proc. Natl. Acad. Sci. 107(18), 8189–8194 (2010)ADSCrossRefGoogle Scholar
  42. 42.
    M.L. Mansfield, Are there knots in proteins? Nat. Struct. Mol. Biol. 1(4), 213–214 (1994)CrossRefGoogle Scholar
  43. 43.
    K.C. Millett, E.J. Rawdon, A. Stasiak, J.I. Sułkowska, Identifying knots in proteins. Biochem. Soc. Trans. 41(2), 533–537 (2013)CrossRefGoogle Scholar
  44. 44.
    S. Najafi, R. Potestio, Folding of small knotted proteins: insights from a mean field coarse-grained model. J. Chem. Phys. 143(24):12B606_1 (2015)Google Scholar
  45. 45.
    W. Niemyska, P. Dabrowski-Tumanski, M. Kadlof, E. Haglund, P. Sułkowski, J.I. Sulkowska, Complex lasso: new entangled motifs in proteins. Sci. Rep. 6, 36895 (2016)Google Scholar
  46. 46.
    W. Niemyska, A.M. Gierut, P. Sulkowski, P. Dabrowski-Tumanski, J.I. Sulkowska, Pylasso a pymol plugin to identify lassos (2017) (under review)Google Scholar
  47. 47.
    S. Niewieczerzal, J.I. Sulkowska, Knotting and unknotting proteins in the chaperonin cage: effects of the excluded volume. PloS one 12(5), e0176744 (2017)CrossRefGoogle Scholar
  48. 48.
    J.K. Noel, J.I. Sułkowska, J.N. Onuchic, Slipknotting upon native-like loop formation in a trefoil knot protein. Proc. Natl. Acad. Sci. 107(35), 15403–15408 (2010)ADSCrossRefGoogle Scholar
  49. 49.
    J.K. Noel, J.N. Onuchic, J.I. Sulkowska, Knotting a protein in explicit solvent. J. Phys. Chem. Lett. 4(21), 3570–3573 (2013)CrossRefGoogle Scholar
  50. 50.
    J.H. Przytycki, P. Traczyk, Invariants of links of conway type. Kobe J. Math. 4, 115–139 (1988)Google Scholar
  51. 51.
    M. Rief, H. Grubmüller, Force spectroscopy of single biomolecules. Chem. Phys. Chem. 3(3), 255–261 (2002)CrossRefGoogle Scholar
  52. 52.
    K.J. Rosengren, R.J. Clark, N.L. Daly, U. Göransson, A. Jones, D.J. Craik, Microcin j25 has a threaded sidechain-to-backbone ring structure and not a head-to-tail cyclized backbone. J. Am. Chem. Soc. 125(41), 12464–12474 (2003)CrossRefGoogle Scholar
  53. 53.
    T.C. Sayre, T.M. Lee, N.P. King, T.O. Yeates, Protein stabilization in a highly knotted protein polymer. Protein Eng. Des. Select. 24(8), 627–630 (2011)CrossRefGoogle Scholar
  54. 54.
    E. Shakhnovich, Protein folding: to knot or not to knot? Nat. Mater. 10(2), 84–86 (2011)ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    T. Škrbić, C. Micheletti, P. Faccioli, The role of non-native interactions in the folding of knotted proteins. PLoS Comput. Biol. 8(6), e1002504 (2012)ADSMathSciNetCrossRefGoogle Scholar
  56. 56.
    M.A. Soler, A. Nunes, P.F.N. Faísca, Effects of knot type in the folding of topologically complex lattice proteins. J. Chem. Phys. 141(2), 07B607_1 (2014)Google Scholar
  57. 57.
    M.A. Soler, A. Rey, P.F.N. Faísca, Steric confinement and enhanced local flexibility assist knotting in simple models of protein folding. Phys. Chem. Chem. Phys. 18(38), 26391–26403 (2016)CrossRefGoogle Scholar
  58. 58.
    M. Sotomayor, K. Schulten, Single-molecule experiments in vitro and in silico. Science 316(5828), 1144–1148 (2007)ADSCrossRefGoogle Scholar
  59. 59.
    J.I. Sułkowska, M. Cieplak, Mechanical stretching of proteins—a theoretical survey of the protein data bank. J. Phys. Condens. Matter 19(28), 283201 (2007)ADSGoogle Scholar
  60. 60.
    J.I. Sułkowska, M. Cieplak, Selection of optimal variants of gō-like models of proteins through studies of stretching. Biophys. J. 95(7), 3174–3191 (2008)ADSCrossRefGoogle Scholar
  61. 61.
    J.I. Sułkowska, P. Sułkowski, P. Szymczak, M. Cieplak, Stabilizing effect of knots on proteins. Proc. Natl. Acad. Sci. 105(50), 19714–19719 (2008)ADSCrossRefGoogle Scholar
  62. 62.
    J.I. Sułkowska, P. Sułkowski, P. Szymczak, M. Cieplak, Tightening of knots in proteins. Phys. Rev. Lett. 100(5), 058106 (2008)Google Scholar
  63. 63.
    J.I. Sułkowska, P. Sułkowski, J.N. Onuchic, Jamming proteins with slipknots and their free energy landscape. Phys. Rev. Lett. 103(26), 268103 (2009)Google Scholar
  64. 64.
    J.I. Sułkowska, P. Sułkowski, J. Onuchic, Dodging the crisis of folding proteins with knots. Proc. Natl. Acad. Sci. 106(9), 3119–3124 (2009)ADSMathSciNetCrossRefGoogle Scholar
  65. 65.
    J.I. Sułkowska, P. Sułkowski, P. Szymczak, M. Cieplak, Untying knots in proteins. J. Am. Chem. Soc. 132(40), 13954–13956 (2010)CrossRefGoogle Scholar
  66. 66.
    J.I. Sułkowska, J.K. Noel, J.N. Onuchic, Energy landscape of knotted protein folding. Proc. Natl. Acad. Sci. 109(44), 17783–17788 (2012)ADSCrossRefGoogle Scholar
  67. 67.
    J.I. Sułkowska, E.J. Rawdon, K.C. Millett, J.N. Onuchic, A. Stasiak, Conservation of complex knotting and slipknotting patterns in proteins. Proc. Natl. Acad. Sci. 109(26), E1715–E1723 (2012)ADSCrossRefGoogle Scholar
  68. 68.
    J.I. Sułkowska, J.K. Noel, C.A. Ramírez-Sarmiento, E.J. Rawdon, K.C. Millett, J.N. Onuchic, Knotting pathways in proteins. Biochem. Soc. Trans. 41(2), 523–527 (2013)CrossRefGoogle Scholar
  69. 69.
    P. Szymczak, Tight knots in proteins: can they block the mitochondrial pores? Biochem. Soc. Trans. 41(2), 620–624 (2013)CrossRefGoogle Scholar
  70. 70.
    P. Szymczak, Periodic forces trigger knot untying during translocation of knotted proteins. Sci. Rep. 6 (2016)Google Scholar
  71. 71.
    W.R. Taylor, A deeply knotted protein structure and how it might fold. Nature 406(6798), 916–919 (2000)ADSCrossRefGoogle Scholar
  72. 72.
    K.L. Tkaczuk, S. Dunin-Horkawicz, E. Purta, J.M. Bujnicki, Structural and evolutionary bioinformatics of the spout superfamily of methyltransferases. BMC Bioinform. 8(1), 73 (2007)CrossRefGoogle Scholar
  73. 73.
    L. Tubiana, E. Orlandini, C. Micheletti, Probing the entanglement and locating knots in ring polymers: a comparative study of different arc closure schemes. Prog. Theor. Phys. Suppl. 191, 192–204 (2011)ADSCrossRefGoogle Scholar
  74. 74.
    I. Tuszynska, J.M. Bujnicki, Predicting atomic details of the unfolding pathway for yibk, a knotted protein from the spout superfamily. J. Biomol. Struct. Dyn. 27(4), 511–520 (2010)CrossRefGoogle Scholar
  75. 75.
    E. Uehara, T. Deguchi, Statistical and hydrodynamic properties of topological polymers for various graphs showing enhanced short-range correlation. J. Chem. Phys. 145(16), 164905 (2016)ADSCrossRefGoogle Scholar
  76. 76.
    P. Virnau, L.A. Mirny, M. Kardar, Intricate knots in proteins: function and evolution. PLoS Comput. Biol. 2(9), e122 (2006)Google Scholar
  77. 77.
    P. Virnau, A. Mallam, S. Jackson, Structures and folding pathways of topologically knotted proteins. J. Phys. Condens. Matter 23(3), 033101 (2010)ADSCrossRefGoogle Scholar
  78. 78.
    J.R. Wagner, J.S. Brunzelle, K.T. Forest, R.D. Vierstra, A light-sensing knot revealed by the structure of the chromophore-binding domain of phytochrome. Nature 438(7066), 325–331 (2005)ADSCrossRefGoogle Scholar
  79. 79.
    S. Wallin, K.B. Zeldovich, E.I. Shakhnovich, The folding mechanics of a knotted protein. J. Mol. Biol. 368(3), 884–893 (2007)CrossRefGoogle Scholar
  80. 80.
    I. Wang, S.-Y. Chen, S.-T.D. Hsu, Unraveling the folding mechanism of the smallest knotted protein, mj0366. J. Phys. Chem. B 119(12), 4359–4370 (2015)CrossRefGoogle Scholar
  81. 81.
    I. Wang, S.-Y. Chen, S.-T.D. Hsu, Folding analysis of the most complex stevedore’s protein knot. Sci. Rep. 6 (2016)Google Scholar
  82. 82.
    M. Wojciechowski, À. Gómez-Sicilia, M. Carrión-Vázquez, M. Cieplak, Unfolding knots by proteasome-like systems: simulations of the behaviour of folded and neurotoxic proteins. Mol. Biosyst. 12(9), 2700–2712 (2016)CrossRefGoogle Scholar
  83. 83.
    Y. Zhao, S. Niewieczerzal, P. Dabrowski-Tumanski, J.I. Sulkowska, The exclusive effects of chaperonin on the behavior of the 52 knotted proteins (under review)Google Scholar
  84. 84.
    F. Ziegler, N.C. Lim, S.S. Mandal, B. Pelz, W.-P. Ng, M. Schlierf, S.E. Jackson, M. Rief, Knotting and unknotting of a protein in single molecule experiments. Proc. Natl. Acad. Sci. 201600614 (2016)Google Scholar

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Authors and Affiliations

  1. 1.Centre of New Technologies, University of WarsawWarsawPoland
  2. 2.Faculty of PhysicsUniversity of WarsawWarsawPoland
  3. 3.Walter Burke Institute for Theoretical PhysicsCalifornia Institute of TechnologyPasadenaUSA

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