To Tie or Not to Tie? That Is the Question

In this review, we provide an overview of entangled proteins. Around 6% of protein structures deposited in the PBD are entangled, forming knots, slipknots, lassos and links. We present theoretical methods and tools that enabled discovering and classifying such structures. We discuss the advantages and disadvantages of the non-trivial topology in proteins, based on available data about folding, stability, biological properties and evolutionary conservation. We also formulate intriguing and challenging questions on the border of biophysics, bioinformatics, biology and mathematics, which arise from the discovery of an entanglement in proteins. Finally, we discuss possible applications of entangled proteins in medicine and nanotechnology, such as the chance to design super stable proteins, whose stability could be controlled by chemical potential.

[1]  Marek Cieplak,et al.  Stabilizing effect of knots on proteins , 2008, Proceedings of the National Academy of Sciences.

[2]  R. Farías,et al.  Microcin 25, a novel antimicrobial peptide produced by Escherichia coli , 1992, Journal of bacteriology.

[3]  José N Onuchic,et al.  Knotting pathways in proteins. , 2013, Biochemical Society transactions.

[4]  Enzo Orlandini,et al.  Probing the Entanglement and Locating Knots in Ring Polymers : A Comparative Study of Different Arc Closure Schemes(Statistical Physics and Topology of Polymers with Ramifications to Structure and Function of DNA and Proteins) , 2011, 1103.0475.

[5]  Pawel Dabrowski-Tumanski,et al.  Complex lasso: new entangled motifs in proteins , 2016, Scientific Reports.

[6]  Eric J. Rawdon,et al.  LinkProt: a database collecting information about biological links , 2016, Nucleic Acids Res..

[7]  S. Rebuffat,et al.  Thermolysin-linearized microcin J25 retains the structured core of the native macrocyclic peptide and displays antimicrobial activity. , 2002, European journal of biochemistry.

[8]  Shang-Te Danny Hsu,et al.  The effect of Parkinson's-disease-associated mutations on the deubiquitinating enzyme UCH-L1. , 2011, Journal of molecular biology.

[9]  Marek Cieplak,et al.  Cotranslational folding of deeply knotted proteins , 2015, Journal of physics. Condensed matter : an Institute of Physics journal.

[10]  Nadrian C. Seeman,et al.  Design and synthesis of a knot from single-stranded DNA , 1991 .

[11]  William R. Taylor,et al.  A deeply knotted protein structure and how it might fold , 2000, Nature.

[12]  Hiroki Abe,et al.  Mean-Square Radius of Gyration and Scattering Function of Semiflexible Ring Polymers of the Trefoil Knot , 2016, Polymers.

[13]  M. Marahiel,et al.  Insights into the biosynthesis and stability of the lasso peptide capistruin. , 2009, Chemistry & biology.

[14]  E. Wang,et al.  The tRNA recognition mechanism of the minimalist SPOUT methyltransferase, TrmL , 2013, Nucleic acids research.

[15]  Vivek Narsimhan,et al.  Dynamics of DNA Knots during Chain Relaxation , 2017 .

[16]  Shang-Te Danny Hsu,et al.  Unraveling the folding mechanism of the smallest knotted protein, MJ0366. , 2015, The journal of physical chemistry. B.

[17]  Anna L. Mallam,et al.  How does a knotted protein fold? , 2009, The FEBS journal.

[18]  Cees Dekker,et al.  Direct observation of DNA knots using a solid-state nanopore. , 2016, Nature nanotechnology.

[19]  A. Ikai,et al.  The importance of being knotted: effects of the C‐terminal knot structure on enzymatic and mechanical properties of bovine carbonic anhydrase II 1 , 2002, FEBS letters.

[20]  Shigeyuki Yokoyama,et al.  Methyl transfer by substrate signaling from a knotted protein fold , 2016, Nature Structural &Molecular Biology.

[21]  Pawel Dabrowski-Tumanski,et al.  LassoProt: server to analyze biopolymers with lassos , 2016, Nucleic Acids Res..

[22]  M. Cieplak,et al.  Topological transformations in proteins: effects of heating and proximity of an interface , 2017, Scientific Reports.

[23]  Shigeyuki Yokoyama,et al.  An enzyme with a deep trefoil knot for the active-site architecture. , 2002, Acta crystallographica. Section D, Biological crystallography.

[24]  Peter Virnau,et al.  Protein knot server: detection of knots in protein structures , 2007, Nucleic Acids Res..

[25]  Neil P King,et al.  Protein stabilization in a highly knotted protein polymer. , 2011, Protein engineering, design & selection : PEDS.

[26]  D. Eisenberg.  Proteins. Structures and molecular properties, T.E. Creighton. W. H. Freeman and Company, New York (1984), 515, $36.95 , 1985 .

[27]  Jonathan T. Siebert,et al.  Entropic Interactions between Two Knots on a Semiflexible Polymer , 2017, Polymers.

[28]  Janusz M. Bujnicki,et al.  Structural and evolutionary bioinformatics of the SPOUT superfamily of methyltransferases , 2007, BMC Bioinformatics.

[29]  Piotr Sułkowski,et al.  Dodging the crisis of folding proteins with knots , 2009, Proceedings of the National Academy of Sciences.

[30]  Marek Cieplak,et al.  Unfolding knots by proteasome-like systems: simulations of the behaviour of folded and neurotoxic proteins. , 2016, Molecular bioSystems.

[31]  S. Nechaev,et al.  Mutations of Bacterial RNA Polymerase Leading to Resistance to Microcin J25* , 2002, The Journal of Biological Chemistry.

[32]  Hui Lu,et al.  Mechanically untying a protein slipknot: multiple pathways revealed by force spectroscopy and steered molecular dynamics simulations. , 2012, Journal of the American Chemical Society.

[33]  S. Hsu,et al.  Backbone 1H, 13C and 15N assignments of YibK and avariant containing a unique cysteine residue at C-terminus in 8 M urea-denatured states [corrected]. , 2014, Biomolecular NMR assignments.

[34]  Youngchang Kim,et al.  The active site of the SET domain is constructed on a knot , 2002, Nature Structural Biology.

[35]  Pawel Dabrowski-Tumanski,et al.  PyLasso: a PyMOL plugin to identify lassos , 2017, Bioinform..

[36]  Eric J. Rawdon,et al.  KnotProt: a database of proteins with knots and slipknots , 2014, Nucleic Acids Res..

[37]  Joanna I. Sulkowska,et al.  Mechanical stretching of proteins—a theoretical survey of the Protein Data Bank , 2007 .

[38]  Joanna I. Sulkowska,et al.  Knotting a Protein in Explicit Solvent , 2014 .

[39]  Stefan Wallin,et al.  The folding mechanics of a knotted protein. , 2006, Journal of molecular biology.

[40]  Marek Cieplak,et al.  Tightening of knots in proteins. , 2008, Physical review letters.

[41]  H. Bayley,et al.  Protein co-translocational unfolding depends on the direction of pulling , 2014, Nature Communications.

[42]  J. Douglas,et al.  Properties of knotted ring polymers. I. Equilibrium dimensions. , 2010, The Journal of chemical physics.

[43]  J Günter Grossmann,et al.  Knotted fusion proteins reveal unexpected possibilities in protein folding. , 2008, Molecular cell.

[44]  Huan-Xiang Zhou,et al.  Loops, linkages, rings, catenanes, cages, and crowders: entropy-based strategies for stabilizing proteins. , 2004, Accounts of chemical research.

[45]  Miguel A. Soler,et al.  Effects of knot type in the folding of topologically complex lattice proteins. , 2014, The Journal of chemical physics.

[46]  Joanna I. Sulkowska,et al.  Pierced Lasso Bundles Are a New Class of Knot-like Motifs , 2014, PLoS Comput. Biol..

[47]  J. Kern,et al.  Total Curvature and Total Torsion of Knotted Polymers , 2007 .

[48]  Marc L. Mansfield,et al.  Fit to be tied , 1997, Nature Structural Biology.

[49]  Antonio Suma,et al.  Pore Translocation of Knotted Polymer Chains: How Friction Depends on Knot Complexity. , 2015, ACS macro letters.

[50]  Jennifer L. Knight,et al.  Antibacterial peptide microcin J25 inhibits transcription by binding within and obstructing the RNA polymerase secondary channel. , 2004, Molecular cell.

[51]  Susanne Hertz,et al.  Statistical Mechanics Of Chain Molecules , 2016 .

[52]  Georg Auburger,et al.  The ubiquitin pathway in Parkinson's disease , 1998, Nature.

[53]  Lukasz Goldschmidt,et al.  Structure and folding of a designed knotted protein , 2010, Proceedings of the National Academy of Sciences.

[54]  Rui D M Travasso,et al.  The folding of knotted proteins: insights from lattice simulations , 2010, Physical biology.

[55]  S. Luti,et al.  Cerato-platanin shows expansin-like activity on cellulosic materials , 2013, Applied Microbiology and Biotechnology.

[56]  Shang-Te Danny Hsu,et al.  The Knotted Protein UCH-L1 Exhibits Partially Unfolded Forms under Native Conditions that Share Common Structural Features with Its Kinetic Folding Intermediates. , 2016, Journal of molecular biology.

[57]  Szymon Niewieczerzal,et al.  Knotting and unknotting proteins in the chaperonin cage: Effects of the excluded volume , 2017, PloS one.

[58]  P. Dawson,et al.  Design and Synthesis of a Protein Catenane This work was supported by The Skaggs Institute for Chemical Biology, The Sloan Foundation, and NIH-GM570132 (PED). We thank Dr. Songpong Deechongkit for assistance with the analytical ultracentrifuge and CD measurements. , 2001, Angewandte Chemie.

[59]  S. Hsu,et al.  Backbone NMR assignments of a topologically knotted protein in urea-denatured state , 2014, Biomolecular NMR assignments.

[60]  Keith Alexander,et al.  Proteins analysed as virtual knots , 2016, Scientific Reports.

[61]  Eric J. Rawdon,et al.  Subknots in ideal knots, random knots, and knotted proteins , 2015, Scientific reports.

[62]  J. Kern,et al.  Scaling Behavior and Equilibrium Lengths of Knotted Polymers , 2008 .

[63]  José N Onuchic,et al.  Jamming proteins with slipknots and their free energy landscape. , 2009, Physical review letters.

[64]  Peter Virnau,et al.  Structures and folding pathways of topologically knotted proteins , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[65]  Douglas B. Kell,et al.  Comparative Genomic Assessment of Novel Broad-Spectrum Targets for Antibacterial Drugs , 2004, Comparative and functional genomics.

[66]  Antonio Suma,et al.  How to fold intricately: using theory and experiments to unravel the properties of knotted proteins. , 2016, Current opinion in structural biology.

[67]  Pawel Dabrowski-Tumanski,et al.  In Search of Functional Advantages of Knots in Proteins , 2016, PloS one.

[68]  William R. Taylor,et al.  Protein knots and fold complexity: Some new twists , 2007, Comput. Biol. Chem..

[69]  William R. Taylor,et al.  Protein knots: A tangled problem , 2003, Nature.

[70]  S. Jackson,et al.  Molecular knots in biology and chemistry , 2015, Journal of physics. Condensed matter : an Institute of Physics journal.

[71]  Shang-Te Danny Hsu,et al.  Folding analysis of the most complex Stevedore’s protein knot , 2016, Scientific Reports.

[72]  Sophie E Jackson,et al.  Knot formation in newly translated proteins is spontaneous and accelerated by chaperonins. , 2012, Nature chemical biology.

[73]  Piotr Szymczak,et al.  Tight knots in proteins: can they block the mitochondrial pores? , 2013, Biochemical Society transactions.

[74]  G. Vogel.  Meet WHO’s dirty dozen: The 12 bacteria for which new drugs are most urgently needed , 2017 .

[75]  Ellinor Haglund,et al.  Engineering covalent loops in proteins can serve as an on/off switch to regulate threaded topologies , 2015, Journal of physics. Condensed matter : an Institute of Physics journal.

[76]  Chung-Cheng Liu,et al.  Type II DNA topoisomerases: Enzymes that can unknot a topologically knotted DNA molecule via a reversible double-strand break , 1980, Cell.

[77]  Michele Caraglio,et al.  Physical Links: defining and detecting inter-chain entanglement , 2017, Scientific Reports.

[78]  J. I. Sulkowska,et al.  Prediction of the optimal set of contacts to fold the smallest knotted protein , 2015, Journal of physics. Condensed matter : an Institute of Physics journal.

[79]  Andreas Martin,et al.  Knots can impair protein degradation by ATP-dependent proteases , 2017, Proceedings of the National Academy of Sciences.

[80]  P. Virnau,et al.  Sequence determines degree of knottedness in a coarse-grained protein model. , 2015, Physical review letters.

[81]  Sophie E Jackson,et al.  Untangling the folding mechanism of the 52‐knotted protein UCH‐L3 , 2009, The FEBS journal.

[82]  A. Stasiak,et al.  Generation of supercoils in nicked and gapped DNA drives DNA unknotting and postreplicative decatenation , 2015, Nucleic acids research.

[83]  Matthias Rief,et al.  Knotting and unknotting of a protein in single molecule experiments , 2016, Proceedings of the National Academy of Sciences.

[84]  Julien Dorier,et al.  Studies of global and local entanglements of individual protein chains using the concept of knotoids , 2017, Scientific Reports.

[85]  Joanna I. Sulkowska,et al.  Jamming Proteins with Slipknots and Their Free Energy Landscape , 2010 .

[86]  S. Hsu.  Protein knotting through concatenation significantly reduces folding stability , 2016, Scientific Reports.

[87]  Matthias Rief,et al.  Tightening the knot in phytochrome by single-molecule atomic force microscopy. , 2008, Biophysical journal.

[88]  Shoji Takada,et al.  Energy landscape and multiroute folding of topologically complex proteins adenylate kinase and 2ouf-knot , 2012, Proceedings of the National Academy of Sciences.

[89]  Joanna I. Sulkowska,et al.  A Stevedore's Protein Knot , 2010, PLoS Comput. Biol..

[90]  Joanna I Sułkowska,et al.  Knot localization in proteins. , 2013, Biochemical Society transactions.

[91]  Javier Arsuaga,et al.  DNA knots reveal a chiral organization of DNA in phage capsids. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[92]  Matthew T. Weirauch,et al.  Rapid knot detection and application to protein structure prediction , 2006, ISMB.

[93]  Eric J. Rawdon,et al.  Conservation of complex knotting and slipknotting patterns in proteins , 2012, Proceedings of the National Academy of Sciences.

[94]  Joachim Dzubiella,et al.  Sequence-specific size, structure, and stability of tight protein knots. , 2008, Biophysical journal.

[95]  C. Micheletti,et al.  Non-monotonic knotting probability and knot length of semiflexible rings: the competing roles of entropy and bending energy. , 2017, Soft matter.

[96]  Peng Wang,et al.  Single-molecule detection reveals knot sliding in TrmD denaturation. , 2013, Chemistry.

[97]  José N Onuchic,et al.  Hysteresis as a Marker for Complex, Overlapping Landscapes in Proteins. , 2013, The journal of physical chemistry letters.

[98]  Chih-Chieh Chen,et al.  pKNOT v.2: the protein KNOT web server , 2012, Nucleic Acids Res..

[99]  Joanna I. Sulkowska,et al.  Mechanical Strength of 17 134 Model Proteins and Cysteine Slipknots , 2009, PLoS Comput. Biol..

[100]  J. Douglas,et al.  Properties of knotted ring polymers. II. Transport properties. , 2010, The Journal of chemical physics.

[101]  Shang-Te Danny Hsu,et al.  Entropic stabilization of a deubiquitinase provides conformational plasticity and slow unfolding kinetics beneficial for functioning on the proteasome , 2017, Scientific Reports.

[102]  Pietro Faccioli,et al.  Folding Pathways of a Knotted Protein with a Realistic Atomistic Force Field , 2013, PLoS Comput. Biol..

[103]  Jenn-Kang Hwang,et al.  pKNOT: the protein KNOT web server , 2007, Nucleic Acids Res..

[104]  Hiroyuki Hori,et al.  Deep knot structure for construction of active site and cofactor binding site of tRNA modification enzyme. , 2004, Structure.

[105]  Patrícia F.N. Faísca,et al.  Knotted proteins: A tangled tale of Structural Biology , 2015, Computational and structural biotechnology journal.

[106]  Eric J. Rawdon,et al.  Knotting fingerprints resolve knot complexity and knotting pathways in ideal knots , 2015, Journal of physics. Condensed matter : an Institute of Physics journal.

[107]  Francesc X Aviles,et al.  Oxidative folding and structural analyses of a Kunitz-related inhibitor and its disulfide intermediates: functional implications. , 2011, Journal of molecular biology.

[108]  Miguel A. Soler,et al.  Steric confinement and enhanced local flexibility assist knotting in simple models of protein folding. , 2016, Physical chemistry chemical physics : PCCP.

[109]  Miguel A. Soler,et al.  Effects of Knots on Protein Folding Properties , 2013, PloS one.

[110]  Tetsuo Deguchi,et al.  Statistical and hydrodynamic properties of topological polymers for various graphs showing enhanced short-range correlation. , 2016, The Journal of chemical physics.

[111]  Pietro Faccioli,et al.  The Role of Non-Native Interactions in the Folding of Knotted Proteins: Insights from Molecular Dynamics Simulations , 2013, Biomolecules.

[112]  Marek Cieplak,et al.  Structural entanglements in protein complexes. , 2017, The Journal of chemical physics.

[113]  Shang-Te Danny Hsu,et al.  Backbone assignments of the 26 kDa neuron-specific ubiquitin carboxyl-terminal hydrolase L1 (UCH-L1) , 2010, Biomolecular NMR assignments.

[114]  A. Stasiak,et al.  How topoisomerase IV can efficiently unknot and decatenate negatively supercoiled DNA molecules without causing their torsional relaxation , 2016, Nucleic acids research.

[115]  D W Sumners,et al.  Knotting of random ring polymers in confined spaces. , 2006, The Journal of chemical physics.

[116]  Pawel Dabrowski-Tumanski,et al.  Topological knots and links in proteins , 2017, Proceedings of the National Academy of Sciences.

[117]  P. Doyle,et al.  Trapping a Knot into Tight Conformations by Intra-Chain Repulsions , 2017, Polymers.

[118]  Neil P King,et al.  Knotted and topologically complex proteins as models for studying folding and stability. , 2007, Current opinion in chemical biology.

[119]  Peter Virnau,et al.  Intricate Knots in Proteins: Function and Evolution , 2006, PLoS Comput. Biol..

[120]  Neil P King,et al.  Identification of rare slipknots in proteins and their implications for stability and folding. , 2007, Journal of molecular biology.

[121]  A. Stasiak,et al.  Formation of knots in partially replicated DNA molecules. , 1999, Journal of molecular biology.

[122]  A. Goldberg,et al.  The Direction of Protein Entry into the Proteasome Determines the Variety of Peptide Products and Depends on the Force Needed to Unfold Its Two Termini , 2022 .

[123]  P. Dawson,et al.  Design and Synthesis of a Protein Catenane , 2001 .

[124]  M. Cieplak,et al.  Multiple folding pathways of proteins with shallow knots and co-translational folding. , 2015, The Journal of chemical physics.

[125]  Pawel Dabrowski-Tumanski,et al.  The exclusive effects of chaperonin on the behavior of proteins with 52 knot , 2018, PLoS Comput. Biol..

[126]  Michelle D. Wang,et al.  Molecular mechanism of transcription inhibition by peptide antibiotic Microcin J25. , 2004, Molecular cell.

[127]  Piotr Szymczak.  Translocation of knotted proteins through a pore , 2014 .

[128]  Sophie E Jackson,et al.  Characterization of the Folding of a 52-Knotted Protein Using Engineered Single-Tryptophan Variants. , 2016, Biophysical journal.

[129]  P. Dawson,et al.  Thermodynamics of a designed protein catenane. , 2003, Journal of molecular biology.

[130]  Rhonald C. Lua,et al.  Statistics of Knots, Geometry of Conformations, and Evolution of Proteins , 2006, PLoS Comput. Biol..

[131]  Sophie E Jackson,et al.  Experimental detection of knotted conformations in denatured proteins , 2010, Proceedings of the National Academy of Sciences.

[132]  J. Onuchic,et al.  Funnels, pathways, and the energy landscape of protein folding: A synthesis , 1994, Proteins.

[133]  C. Chothia.  One thousand families for the molecular biologist , 1992, Nature.

[134]  NMR assignments of a hypothetical pseudo-knotted protein HP0242 from Helicobacter pylori , 2014, Biomolecular NMR assignments.

[135]  Duilio Cascio,et al.  Discovery of a thermophilic protein complex stabilized by topologically interlinked chains. , 2007, Journal of molecular biology.

[136]  Peter Virnau,et al.  Proteins' Knotty Problems. , 2019, Journal of molecular biology.

[137]  Marc L. Mansfield,et al.  Are there knots in proteins? , 1994, Nature Structural Biology.

[138]  Flavio Seno,et al.  Linking in domain-swapped protein dimers , 2016, Scientific Reports.

[139]  Sophie E Jackson,et al.  Exploring knotting mechanisms in protein folding , 2008, Proceedings of the National Academy of Sciences.

[140]  Roy Wollman,et al.  Pierced Lasso Topology Controls Function in Leptin. , 2017, The journal of physical chemistry. B.

[141]  D. Craik,et al.  Structure of thermolysin cleaved microcin J25: extreme stability of a two-chain antimicrobial peptide devoid of covalent links. , 2004, Biochemistry.

[142]  José N Onuchic,et al.  Slipknotting upon native-like loop formation in a trefoil knot protein , 2010, Proceedings of the National Academy of Sciences.

[143]  Peter G. Wolynes,et al.  The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein , 2010, PLoS Comput. Biol..

[144]  Raffaello Potestio,et al.  Knotted vs. Unknotted Proteins: Evidence of Knot-Promoting Loops , 2010, PLoS Comput. Biol..

[145]  Jeffrey K Noel,et al.  Energy landscape of knotted protein folding , 2012, Proceedings of the National Academy of Sciences.

[146]  Marek Cieplak,et al.  Untying knots in proteins. , 2010, Journal of the American Chemical Society.

[147]  Miguel A. Soler,et al.  How Difficult Is It to Fold a Knotted Protein? In Silico Insights from Surface-Tethered Folding Experiments , 2012, PloS one.